The Music of Stravinsky: Collected Essays 9814968625, 9789814968621

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The Music of Stravinsky

The Music of Stravinsky Collected Essays

Pieter C. van den Toorn

Published by Jenny Stanford Publishing Pte. Ltd. 101 Thomson Road #06-01, United Square Singapore 307591

Email: [email protected] Web: www.jennystanford.com British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

The Music of Stravinsky: Collected Essays Copyright © 2023 by Jenny Stanford Publishing Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN  978-981-4968-62-1 (Hardcover) ISBN  978-1-003-35916-6 (eBook)

To Richard Taruskin, 1945–2022 “public adversary, private pal”

Contents Prefaceix Acknowledgmentsxi Introduction 1. Some Characteristics of Stravinsky’s Diatonic Music

1 17

2. Taruskin’s Angle Reply to van den Toorn (Richard Taruskin) 3. Stravinsky Re-barred

95 113

4. Neoclassicism and Its Definitions Motives Polychords; C-Major Tonalities; Octatonic Sets Continuing Conflicts 5. Will Stravinsky Survive Postmodernism?

159 167 177 183

6. Stravinsky, Les Noces (Svadebka), and the Prohibition against Expressive Timing

221

7. Stravinsky and the Octatonic A Reconsideration (Dmitri Tymoczko) The Sounds of Stravinsky (Pieter C. van den Toorn) Octatonicism Reconsidered Again (Dmitri Tymoczko)

243 243 289 313

9. The Rite of Spring Briefly Revisited: Thoughts on Stravinsky’s Stratifications, the Psychology of Meter, and African Polyrhythm

385

8. Stravinsky, Adorno, and the Art of Displacement Adorno Interpreted Displacement Defined Rebuttals

123

191

337 342 353 367

10. Individual and “Class Generality”: Reflections on the Postwar Years of Babbitt, Schoenberg, and Stravinsky 435 Index497

Preface

Igor Stravinsky seems never to have lacked an appreciative audience. The international celebrity that was his with The Firebird in 1910 was his late in life as well. His neoclassical works of the 1920s, 30s, and 40s, although less popular than the ballet scores composed earlier for the Ballets Russes, attracted a devoted following. Constantly on the move during this period, introducing his music in Europe and the United States, he conducted and performed at the piano. The serial and twelve-tone works of his American years were not popular at all, but in his programs Stravinsky was always careful to cushion the new with the old and the familiar. In 1959, he began co-authoring books of comment and reminiscence with Robert Craft, his associate who, when not assisting him at the podium, began publishing his own studies of the composer. The six books of “conversation” authored by Stravinsky and Craft attracted a wide audience during the 1960s, and for a while the two were very much in the news. Stravinsky’s stature had reached its peak. The authority he had come to wield in the world of music was truly colossal. Yet the issues more immediately at stake in these pages are musical rather than biographical. They concern the composer’s musical language, features of that distinctive voice that managed to assert itself above and beyond the radical changes that accompanied the three stylistic periods, Russian, neoclassical, and serial. In fact, the term style (as in stylistic period), implying inflection at a musical surface of some kind, can hardly stand as a descriptive cover for the changes triggered by the three giant leaps in musical orientation: the folk songs and verses of the Russian period that were followed by the Baroque and Classical models of neoclassicism, and then by an entirely new method of composition, serialism and the twelve-tone system. The foundation of Stravinsky’s music changed dramatically at each stage. And attempts therefore to compile a list of features that distinguish his music as a whole are forced to contend with a good deal of qualification along these lines. Such is the case with the list that follows, the separate entries of which are summarized in the Introduction and then taken up at various points in the chapters that lie ahead:

x

Preface



1. Harmonic and melodic materials derived from the octatonic scale (the “diminished scale”, as it has been known in American jazz circles); 2. Forms of octatonic-diatonic interaction; 3. Superimposition involving the above-noted materials; 4. Polyrhythmic stratification, in which two or more motives or chords, layered, repeat according to varying spans or cycles; 5. “Block” structures, in which two or more self-contained blocks of material are placed in an abrupt juxtaposition with one another; 6. Metrical displacement of repeated motives and chords (such displacement being so entirely characteristic of Stravinsky’s music as to assume the earmarks of a common denominator); 7. A strict performing style, with the beat maintained with a minimum of rubato or nuance; 8. A percussive approach to composition and instrumentation; staccato doublings of the legato lines; a percussive use of the piano and string pizzicato as a means of punctuation. Thus, apropos of item (2) above, the diatonic component in Stravinsky’s Russian-period works is invariably modal, while neoclassical works tend to implicate the major and minor scales of tonality. And while, apropos of item (4), the stratifications in Russian-period works are polyrhythmic in conception, they may not be in neoclassical works such as Oedipus Rex (1927) at rehearsal nos. 167-69 and the Symphony of Psalms (1930) at no. 4 in the first movement. None of the eight features and processes listed above is uniquely Stravinskian, even if they are typical of his music. None appears in all of Stravinsky’s works, and some may not even be found in the majority of them. Crucially, however, they overlap the three orientations; they are present in major works from each of the three periods. And it is in the manner of their interaction that Stravinsky’s mark may be sensed a bit more closely. If the metrical displacement (6) of a repeated motive or chord is to be felt by the listener, then the beat must be maintained evenly (7). And the repetition of a motive or chord displaced metrically might be highlighted in the manner indicated by item (8). And so forth.

Acknowledgments

I am grateful to the staff at the music libraries at the University of California at Santa Barbara and Berkeley for their assistance on numerous occasions. Richard Taruskin and Dmitri Tymoczko kindly granted permission for the re-publishing of their responses to some of the essays. Many of the illustrations were set with great skill by Andre Mount, who in addition helped with some of the digital aspects of the project. Cattarina van den Toorn devoted countless hours to many of the technical challenges, while odds and ends were often attended to by Anna-Marie, Linnea, Hendrik, John Willem, and Pieter. I am grateful to them as well.

Introduction

Stretching across forty or so years, the essays in this volume address the dynamics of Igor Stravinsky’s music from a variety of analytical, critical, and aesthetic angles. Underscored are the features of melody, harmony, rhythm, and form that would remain consistently a part of Stravinsky’s oeuvre regardless of the changes in orientation from the Russian period to the neoclassical and the early serial. The Rite of Spring (1913), Les Noces (1917–23), the Symphony of Psalms (1930), and the Symphony in Three Movements (1945) are discussed in detail, as are many of the circumstances attending the conception of these works. Other concerns include the composer’s “formalist” aesthetics and the strict performing style he pursued as an interpreter and conductor of his music. The essays are arranged in chronological order, according to the year of their publication. They are modestly continuous in this form, in ways that could not have been anticipated at the time of their conception. Chapter 1, “Some Characteristics of Stravinsky’s Diatonic Music”, sets the stage where melody and harmony are concerned, while Chapter 3, “Stravinsky Re-barred”, does so from the standpoint of meter and rhythm. The concluding Chapter 10, “Reflections on the Postwar years of Babbitt, Schoenberg, and Stravinsky”, is newly composed and published here for the first time. Interactions between the three composers are discussed, as is the standoff between Stravinsky and Schoenberg and the relocation of The Music of Stravinsky: Collected Essays Pieter C. van den Toorn Copyright © 2023 Jenny Stanford Publishing Pte. Ltd. ISBN 978-981-4968-62-1 (Hardcover), 978-1-003-35916-6 (eBook) www.jennystanford.com

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Introduction

this celebrated divide, by the early 1940s, to within the confines of Los Angeles, California. Even in the twilight years of their respective careers, Stravinsky and Schoenberg remained at a distance from one another.

1. The Octatonic-Diatonic Approach

Chapter 1, “Some Characteristics of Stravinsky’s Diatonic Music”, turns initially to the ballet score Petrushka (1911) and the modal diatonicism that underlies many of the composer’s Russian-period works. Closely associated with that diatonicism is a vocabulary of triads, (0 2 3 5 7 9) hexachords, and (0 2 3 5) minor tetrachords. The latter (0 2 3 5)s, invariably melodic in conception, are often incomplete or gapped by a minor third, with the four pitches reduced to three in the form of a (0 2 5) or (0 3 5) trichord. Typically openended, repeated, and confined to a perfect fourth, these trichords are apt to assume a folk-like character. Of the many examples that apply in this regard, see the Db-Bb-Eb-Bb ostinato, first in the English horn and then in the timpani, that stretches through several dance movements in Part I in The Rite of Spring. Or see, in the opening pages of Les Noces, the repetition of the (E D B) trichord in the soprano solo. No less crucial to Stravinsky’s perspective is the fact that the triad and the (0 2 3 5) minor tetrachord are shared by the octatonic set. Moving in Stravinsky’s Russian-period works from a diatonic to an octatonic context (or to some form of combination of the two), it is often an (0 2 3 5) tetrachord, complete or incomplete, that serves as the principle connecting link. In octatonic contexts, triads and (0 2 3 5) tetrachords are transposed along the 0-3-6-9 minor-third cycle, an “equal” or symmetrical division of the octave. While the triadic complexes, which include dominant as well as minor sevenths, implicate the 1-2, half step-whole step ordering of the octatonic scale, the (0 2 3 5)s implicate the reverse, the 2-1, whole step-half step ordering. As a matter of convenience in “Some Characteristics”, the triadic conception is labeled “Model A”, the (0 2 3 5) tetrachordal conception, “Model B”. Both Models A and B are featured in Russian-period works, which date from the years of the composer’s apprenticeship in St. Petersburg to about 1920. The neoclassical works, from the early

Introduction

1920s in France to the mid-1950s in Los Angeles, confine themselves in large part to the triadic vocabulary of Model A. Transposed along one of the three minor-third cycles in neoclassical works, the triads interact not with the modal diatonicism of the earlier period, but rather with the major and minor scales of tonality. Such is the nature of Stravinsky’s neoclassicism. Departing with the triads of Model A and certain rhythmic and formal practices, Stravinsky sought an accommodation not only with the external forms of tonality, but also with the stylistic veneer of Baroque and Classical music. Both the scales and the veneer come with impurities and in bits and pieces, which is true of the functional relations of tonality as well. What tends to distinguish Stravinsky’s use of the octatonic scale from that of, say, Nikolai Rimsky-Korsakov or Claude Debussy, is his practice of superimposing the triadic and tetrachordal vocabulary of Models A and B.1 Given the four triads situated along one of the three minor-third cycles or octatonic collections in Model A, superimposition entails the stacking of one of these triads, or parts thereof, on top of another. New dissonant sonorities were created by such means, the tritone-related triads of the celebrated “Petrushka chord” being only one of a great many examples. Often enough, the entities being superimposed are kept separate in register and instrumentation, contributing in this way to the sense of a clash. Typical of Stravinsky as well is his method of stratification,2 where, polyrhythmically, two or more motives or chords repeat according to cycles that vary independently of one another. Passages adhering to such a construction are found in Russian and neoclassical works, even in some of the late serial ones. No less pervasive where

1There are two early examples of this technique of superimposition. Tritone-related triads, (F A C)(B D# F#), may be found superimposed in an extended sketch of Rimsky-Korsakov’s composed shortly before his death in June 1908. The sketch was intended for an opera, Zemlya I nebo or Heaven and Earth, which was never completed. The same superimposed triads may be found in the Prélude symphonique, an instrumental work composed by another of Rimsky-Korsakov’s pupils, Maximilian Steinberg. For further comment, see Richard Taruskin, Stravinsky and the Russian Traditions (Berkeley: University of California Press, 1996), I, 402–08. Or see Richard Taruskin, “Catching Up with Rimsky-Korsakov”, Music Theory Spectrum 33, no. 2 (2011), 176–77; reprinted in Richard Taruskin, Russian Music at Home and Abroad (Berkeley: University of California Press, 2016), 92–93. For still further comment, see Pieter C. van den Toorn, “Catching Up with Taruskin”, Music Theory Spectrum 33, no. 2 (2011), 220–21. 2See Chapter 10.

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Introduction

matters of form are concerned is juxtaposition,3 Stravinsky’s habit of placing two or more “blocks” of heterogeneous content in an abrupt kind of juxtaposition with one another . When repeated, the order and length of the blocks may vary, but the content, instrumentation, and dynamics remain fixed. All four dance movements of Les Noces were composed in this fashion, as was the Symphonies of Wind Instruments (1920), and, perhaps most famously, the first movement of the Symphony of Psalms.

2. Origins of the Octatonic-Diatonic Approach

The groundwork for an octatonic or octatonic-diatonic approach to pitch in Stravinsky’s music was laid even earlier in the past century by Arthur Berger and his study of “Pitch Organization in Stravinsky”.4 Curiously, however, while detailed and highly persuasive in his analysis of a handful of passages from Stravinsky’s music, Berger dismissed Model B’s (0 2 3 5) tetrachords altogether. Whether a closer examination of Stravinsky’s Russian-period works or the music of the composer’s immediate predecessors in St. Petersburg would have led Berger to a different conclusion is a difficult question. Berger’s familiarity at the time with works such as Petrushka, The Rite of Spring, and Les Noces was undoubtedly intimidate. Stravinsky’s source for the octatonic was Rimsky-Korsakov, with whom he studied privately for about three years (1905–08) in St. Petersburg. And Rimsky-Korsakov, in his notebooks and teaching materials, acknowledged both sides of the octatonic coin. He called the triads and seventh chords of Model A “harmonic”, the (0 2 3 5) tetrachords of Model B “melodic”.5 Passages implicating both models may be found in Rimsky-Korsakov’s operas and symphonic poems, including Sadko (1897) and Kaschei the Immortal (1902). In his autobiography, My Musical Life, Rimsky-Korsakov credited 3See, especially, Pieter C. van den Toorn, Stravinsky and “The Rite of Spring” (Berkeley: University of California Press, 1987), 97–114; Gretchen Horlacher, Building Blocks: Repetition and Continuity in the Music of Stravinsky (Oxford: Oxford University Press, 2011); and Pieter C. van den Toorn and John McGinness, Stravinsky and the Russian Period (Cambridge: Cambridge University Press, 2012), 96–107, 225–35. 4Arthur Berger, “Problems of Pitch Organization in Stravinsky”. In Perspectives on Schoenberg and Stravinsky, ed. Benjamin Boretz and Edward T. Cone (New York: Norton, 1972), 123–54. 5See Taruskin, Stravinsky and the Russian Traditions, 272–306.

Introduction

a descending sequence in Franz Liszt’s first symphonic poem, “Ce qu’on entend sur La Mongtagne”, with having stirred him in the direction of the octatonic. Underlying this sequence was “a scale which subsequently played an important role in many of my compositions”.6 An account of the historical background of Stravinsky’s Russian period would have to await the publication in 1996 of the two hefty volumes of Richard Taruskin’s Stravinsky and the Russian Traditions.7 The exquisite detail of these volumes – a “Biography of the Musical Works”, as the author dubbed them – would represent a landmark not only in the study of twentieth-century music, but in American musicology more generally. Working independently from an historical perspective during the 1970s, Taruskin arrived at many of the same conclusions regarding Stravinsky’s musical language. He, too, adopted an octatonic-diatonic approach, doing so along the lines of Models A and B or Rimsky-Korsakov’s harmonic and melodic categories. As we shall see in Chapters 2 and 5, differences of opinion with Taruskin would arise on occasion. But these disputes pale when placed beside the fruitfulness of the cross-fertilization. Lying to the background of the actual presentation and rationalization of Models A and B is Benjamin Boretz’s MetaVariations (1969),8 sections of which began appearing in successive issues of Perspectives of New Music in 1969. It would be difficult to overestimate the assistance rendered by this tract, Boretz’s PhD dissertation at Princeton University. Helpful above all was the lengthy commentary on the nature of musical structure, Boretz’s analysis of Petrushka, first tableau, and the uses to which general musical systems and classes of works were put.

3. Analytical Fallout

The discussion of The Rite of Spring, begun in Chapter 1, is continued in Chapter 9. Given the prevalence of the vocabulary of both Models A and B in The Rite, much attention is focused on the ways in which

6Nikolai Rimsky-Korsakov, My Musical Life, trans. Judah A. Joffee (New York, Tudor, 1935), 78. 7See note 1. 8Benjamin Boretz, Meta-Variations: Studies in the Foundations of Musical Thought (Red Hook: Open Space), 1995.

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Introduction

these two sides of the octatonic coin are linked. Underscored is the typical disposition of the dominant-seventh chord in The Rite, in first inversion and confined to the octave. Bunched together in this fashion, the root, seventh, and fifth of the chord, reading down, are detached as a melodic (0 2 5) trichord. Most conspicuously in the opening of the “Augurs of Spring”, Eb, Db, and Bb of the dominantseventh chord on Eb are detached as a Db-Bb-Eb-Bb ostinato in the English horn. The fixed register renders the transformation all the more apparent to the ear. Many of the dance movements of The Rite are polyrhythmic stratifications, the most extensive of these being the section at rehearsal nos. 64–71 in the “Ritual of the Rival Tribes” and the “Procession of the Sage”. The spans separating the repetition of the A-D-C-D fragment in the horns are highly irregular; the fragment falls off and on the half-note beat as the tactus. In polyrhythmic settings of this kind, alignment changes as each reiterating fragment relates not only to the meter, but also to the other fragments. In Chapter 9, samples of African polyrhythm are enlisted as a means of setting Stravinsky’s methods in relief. Chapter 4, “Neoclassicism and Its Definitions”, turns to Stravinsky’s Symphony in Three Movements (1945), a late neoclassical venture composed in Los Angeles during World War II. Parts of the second movement, Andante, were originally intended to accompany scenes from a screenplay by Franz Werfel, Song of Bernadette. Stravinsky’s participation in this project was aborted, however, although the film was eventually released by 20th Century Fox with the music of another composer, Alfred Newman. (Arriving in Los Angeles in February of 1941, Stravinsky cherished the hope of boosting his income by composing for the cinema.) Those parts of the Andante originally conceived for Werfel’s film are solidly octatonic. In fact, Model A’s triadic vocabulary plays a major interacting role in all three of the Symphony’s movements. In the opening section of the first movement at Rehearsal nos. 0-34, the C-major tonality is defined initially by the dominant G or (G B D) followed by the Neapolitan chord (Db F Ab), with the latter resolving back to the dominant; the pitch Ab is sustained as a suspension. But the G/(Db F Ab) tritone relationship, labeled “Motive A” in the analysis, is also octatonic, the implications of which surface unmistakably in the lengthy sections that lie ahead at rehearsal nos. 7, 13, 22, and 34.

Introduction

Octatonic as well is the “Motive B” stretch that follows the tritone relationship of the opening measures. And introduced by Motive B is the principal unit of vocabulary in the first movement, an octave split internally on either side by a major or minor third – a version of the incomplete triad, in effect. What defines that unit of vocabulary within Model B is the octatonic scale. We should note that Schoenberg’s concept of “developing variation”,9 while appropriate at times to the Symphony of Three Movements, first movement, is hardly so when the bulk of Stravinsky’s music, which includes the most familiar works, is taken into account. Stravinsky was not ordinarily a developing-variation composer, whether along the lines of the Classical style from Haydn to Brahms or Schoenberg’s extended tonal, atonal, or twelve-tone music.10 And the reason for this absence has primarily to do with his rhythmic practices. As we shall see below, Stravinsky often shifted the metrical alignment of motives when they are repeated. In doing so, he sought to maximize the effect of the displacement by retaining all other features of the motive as a kind of foil. Highly characteristic of his music, metrical displacement and the literal nature of the repetition that follows as a consequence are at odds with the Schoenbergian notion of a motive and its developing variation in the music of eighteenth, nineteenth, and twentieth centuries. Stravinsky’s late neoclassical phase, which begins in 1941 with his arrival in Los Angeles, is treated a bit more comprehensively in Chapter 10. In the opening section of the “Basle” Concerto in D (1946), first movement, the D-major tonality interacts not only with Model A’s triads, but also with its interlocking (0 3 4)(3 4 7)(3 6 7) major-minor third units. Modeled with a Tonnetz featuring the (0 3 4 7) tetrachord, the interaction of Model A’s (0 3 7) (0 4 7) triads and (0 3 4)(3 4 7)(3 6 7) major-minor thirds with the major and minor

9See Arnold Schoenberg, Fundamentals of Musical Composition, ed. Gerald Strang and Leonard Stein (London: Faber and Faber, 1967), 8. “Homophonic music can be called the style of developing variation. This means that in the succession of motiveforms produced through variation of the basic motive, there is something that can be compared to development, to growth”. See also Walter Frisch, Brahms and the Principle of Developing Variation (Berkeley: University of California Press, 1983). 10Developing variation, its relevance or non-relevance to Stravinsky’s music, is discussed at greater length in van den Toorn and McGinness, Stravinsky and the Russian Period, 118–19, 194–95, 271–84. See also Chapter 10.

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scales of tonality is typical of late neoclassical works, including the Danses Concertantes (1942), Babel (1944), the Symphony in Three Movements (1945), and Orpheus (1947).

4. Meter and Rhythm

The uses of meter and rhythm in Stravinsky’s music are first addressed in Chapter 3, “Stravinsky Re-barred”. In response to a brief study by Leonard Meyer of the shifting bar lines in the opening March of The Soldier’s Tale (1918), Chapter 3 focuses initially on the repetition of a short, rising figure in this music, B-C#-D. Although the figure is barred throughout the March as an irregular 3/8 measure, its alignment relative to the ostinato, which acts as a kind of meter lying to the background, shifts constantly. In relation to the 2/4 meter implied by the ostinato, B-C#-D enters on and off the quarternote beat as the likely tactus. Similar strategies of displacement in Les Noces and the “Evocation of the Ancestors” in The Rite of Spring are discussed at length. A more comprehensive treatment of the opening of Les Noces may be found in Chapter 6, of the opening of the “Evocation” in turn in sections VII and IX of Chapter 9. At hand are the mechanics of that most predictable of identifying features of Stravinsky’s music, metrical displacement.11 Such displacement, inherently a part of the polyrhythmic structures encountered already, assumes a much larger role when Stravinsky’s music is considered in its entirety. Often enough, when a motive or chord is repeated, its alignment relative to the meter is changed. Typically, Stravinsky repeats not to vary or develop in the manner of the Classical style, but rather to displace metrically. And the psychology runs as follows: Metrical parallelism can play a crucial role in the establishment of a meter in the listener’s mind. When the repetition of a motive or chord is aligned metrically as before (parallelism), not only is the meter confirmed, but expectations are raised that subsequent repeats will be aligned similarly. When these expectations are thwarted by metrical displacement, the listener’s sense of the meter is apt to be threatened or disrupted altogether. 11For

an account of metrical displacement in Stravinsky’s music, one that addresses its psychological as well as the music-technical implications, see, in addition to Chapters 6 and 8 in this volume, van den Toorn and McGinness, Stravinsky and the Russian Period, 13–43.

Introduction

Meter is entrained, it should be stressed, made physically a part of the listener. Displacement is felt physically by the listener. When a motive is displaced metrically in Stravinsky’s music, all other features are likely to be repeated literally. The repetition, which includes the motive’s articulation, lacks elaboration. And there are no transpositions or imitative exchanges. These static, unchanging conditions serve a purpose, for they allow the metrical placement and displacement of a motive to stand in relief. The literal repetition acts as a foil for what does change, namely, metrical alignment and the spans that separate motivic repeats. Moreover, where the performance of this music is concerned, the conventions of expressive timing or rubato must be kept in check. If the metrical displacement of a motive or chord is to have its effect on the listener, then the beat must be maintained strictly in performance.12 And so begins the composer’s lifelong battle with interpretation and nuance, not with the formalist aesthetics, necessarily, but rather with these practical matters of performance. The need for a strictly held beat springs from the rhythmic invention as a necessary condition thereof. These wider implications of metrical displacement are addressed in Chapter 6 by way of Les Noces, and in Chapter 8 by way of The Rite of Spring, Renard, and the Symphonies of Wind Instruments. Especially in Chapter 8, the descriptive comment of Theodor Adorno, among other critics, is brought to the fore. A final word on these matters of performance appears in the concluding sections of Chapter 9.

5. Performance Practice

Of course, to claim that the need for a strict beat in the performance of Stravinsky’s music “springs from the rhythmic invention as a necessary condition thereof” (see above), is to look to the music for an explanation of that need. It is to underscore the specifically musical ends that are served by the application of a steady beat. And the assumption is that listeners sense those ends, just as the 12On

the relationship between metrical displacement and the importance of maintaining a steady beat, see the analysis of a passage from Renard in van den Toorn, “Catching Up with Taruskin”, 217–21. For Taruskin’s reply to this analysis, see Taruskin, Russian Music, 109–14.

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composer, in the act of shifting the metrical alignment of a repeated figure, might take the strict beat for granted. Which is not to imply that these closely allied factors are without complication. In the concluding chapter of Stravinsky’s Poétique musicale, the composer’s insistence on a strict performing style is directed not only at his own music, but at music in general.13 And from what may be gleaned from recordings preserved from the late 1930s and 40s, Stravinsky practiced what he preached. In performances of Mozart’s music, for example, the beat is strictly enforced, although admittedly with results that are curious at times and perhaps not altogether convincing.14 In addition, beginning in the early 1920s, Stravinsky’s application of a strict beat would anticipate more general trends in the twentieth century, the preferences at mid-century for “straight”, unnuanced readings of all manner of repertory. And so the problem is as follows: it can hardly be assumed that the rhythmic-metric play that, in much of Stravinsky’s music, provides the strict beat with a musicspecific purpose is present in this much larger category of music. Occasionally, no doubt, conditions internal to the music can seem to compel the use of a metronomic beat. More generally, however, purposes of this kind are missing, and the strict approach acquires a rationale of its own. Pursued as an end in itself, the approach becomes a fad or a style, which indeed is how it is most often represented. The suppression of expressive rubato and nuance duly acquires a form of aesthetics, one that is Modernist and reflective of the times. Crucially, expressive timing or rubato is associated with the human element. The deviation from the regular or the exact is the medium by which emotion is conveyed. Such are the means by which performers make their mediating presence felt. And they do so by venting their affections, as it were, allowing something of 13Igor Stravinsky, Poétique musicale, sous forme de six lec̜ons, bilingual ed. (Cambridge:

Harvard University Press, 1970), 160–65. Later, Stravinsky softened his stance somewhat, acknowledging the existence of a “Romantic tradition” that stood in opposition to a “Classic tradition”. While the former was dependent “strongly on mood and interpretation”, the latter, which included the performing requirements of his own works, was closely tied to the dance. See Igor Stravinsky and Robert Craft, Conversations with Stravinsky (New York: Doubleday, 1959), 133–35. 14See the discussion of Mozart’s Fugue in C Minor, K. 426, as recorded by Stravinsky and his son Soulima, in Taruskin, Russian Music, 492–97.

Introduction

their aroused state to be communicated. The conveyance of these emotions by means of rubato and nuance comes naturally to the performer. To some extent, the means are spontaneous or reflexive rather than learned. And to cut back severely on the use of rubato is thus also to cut back on that which is “only human”. If Stravinsky could dismiss the use of rubato and nuance as a form of “vanity” or “exhibitionism”,15 then, just as easily, Taruskin could condemn the sharp curtailment in that use as a form of “dehumanization”.16 The strict beat could be sensed as unfeeling, mechanical, and anti-humanist. By submitting themselves selflessly to the notated page (“selfless submission”), to a form of “execution” rather than “interpretation”, as Stravinsky phrased it,17 performers were depriving themselves of their “right to any exercise of subjective judgment”.18 Closely related to the strict beat is Stravinsky’s objectivist aesthetics, according to Taruskin, his authoritarian manner, and the sympathies he seems to have harbored during the 1920s and 30s for right-wing politics and Mussolini’s Italy.19 It should be noted, however, that expressive timing and nuance are not matters solely of emotion or subjectivity. In their separate and opposing ways, both Stravinsky and Taruskin err in this regard. Slight modifications of timing and punctuation, whether notated or coming by way of the performer alone, have served as a means of structure. Intensifying, often by exaggeration, the delays and accelerations already a part of the music (the delay of the note of suspension in tonal music, for example), rallentandos, ritardandos, ritenutos, morendos, and accelerandos have been expressions of structural clarification as well as engagement. In the interests of a phrase and its articulation, for example. the downbeat marking the end of a cadence might be delayed. This might occur minutely and almost imperceptibly as part of a hierarchy of such delays, with the weightiest coinciding with the larger phrases or Poétique musicale, 160–65. Russian Music, 484. 17Stravinsky, Poétique musicale, 160–63. 18Richard Taruskin, “Stravinsky and Us”, in Jonathan Cross, ed., The Cambridge Companion to Stravinsky (Cambridge: Cambridge University Press, 203), 282. 19On the ties between Stravinsky’s strict performing style and his formalist aesthetics, see Taruskin, “Stravinsky and Us”, 282–83. On the composer’s right-wing sympathies during the 1920s and 30s, see Richard Taruskin, Defining Russia Musically (Princeton: Princeton University Press, 1997), 385–88, 450–54. 15Stravinsky, 16Taruskin,

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Introduction

sections.20 In turn, following the slowing-down process at a cadence, the beginning of the next phrase might be accompanied by a slight accelerando. These departures reflect formal divisions, the manner in which a section of music has been parsed by the performer. And it has generally been understood that performers intervene with a purpose of this kind as key. Expressive modifications are not isolated effects (mere caprice or display on the performer’s part), but a means towards a larger end. And artistic performances have generally been weighed in this light, that is, by the extent to which the modifications are “true” to the music, placed at the service of a convincing sense of structure. No less than with the rubato accompanying performances of, say, the Beethoven piano sonatas, the strict style and its drastic reduction in the use of such modification in performances of Stravinsky music is structural in origin. Just as with the slight ritardandos and accelerandos that serve to clarify the boundaries of phrases and larger groupings in Beethoven’s music, the reduction in the use of such devices can help to expose metrical placement and displacement in Stravinsky’s. And it is essential that the musical motivation behind the need for a relatively “straight” reading of Stravinsky’s music be felt by the listener. This will allow a crisp, secco approach in the articulation of his music to be sustained without listeners having to imagine themselves at the mercy of a kind of metrical tyranny, an “ethic of scrupulous submission”, to return to Taruskin’s commentary. The strict beat can be maintained sympathetically rather than mechanically or submissively. 20Among the many studies linking performance nuance to the expression of structure,

see Eric Clarke, “Expression in Performance: Generativity, Perception, and Semiosis”, in John Rink, ed., The Practice of Performance (Oxford: Oxford University Press, 2007): “Phrase boundaries are marked by a decrease in tempo in proportion to the phrase boundary’s structural importance”. Clarke concludes, “a large-scale sectional break will typically be approached with a greater degree of slowing than a small-scale group boundary”. For an alternative theory on the use of expressive effect in performance, see David Huron, Sweet Anticipation: Music and the Psychology of Expectations (Cambridge: MIT Press, 2006), 314–18. In Huron’s view expressive timing and especially delaying tactics have less to do with structure and its conveyance than with the predictable nature of events such cadences and the resolutions of suspensions. “High predictability provides an opportunity to heighten the tension response and thereby increase the pleasure evoked by [the resolution]. In performed music, highly marked ritards may occur just prior to the resolution of a tendency tone—but this resolution may not necessarily coincide with an important structure division” (316).

Introduction

6. Issues of Criticism and Debate Especially with Taruskin, differences of interpretation began to arise in response to the critical and biographical comment in Conversations with Stravinsky (1959),21 authored jointly by the composer and his close advisor Robert Craft. Conversations was followed in short order by five additional volumes, with further comment by the composer succeeded by entries from Craft’s diaries. Key among the bones of contention with Taruskin was the nature and scale of Rimsky-Korsakov’s influence on Russian-period works like The Firebird (1910), Stravinsky’s use of authentic Lithuanian folk songs in The Rite of Spring, the meaning and significance of the composer’s “formalist” aesthetics, and the right-wing, reactionary politics he pursued while in France during the 1930s. These and other topics are spread across Chapter 2, “Taruskin’s Angle”, which is followed by a reply by Taruskin. The discussion is continued in Chapter 5, “Will Stravinsky Survive Postmodernism?” In Taruskin’s Stravinsky and the Russian Traditions, an early piece like The Firebird is viewed almost entirely as a remnant of the composer’s apprenticeship, “a veritable monument to the stillrevered Rimsky”.22 The opposing view, outlined in Chapter 5, takes a close look at the Finale of The Firebird, especially at the Allegro section beginning at rehearsal no. 17. Treated as separate “blocks” of material, the two phrases of a borrowed folk song are repeated independently of their original order and then displaced relative to an implied meter. These techniques of “block” juxtaposition and metrical displacement, typical of Stravinsky, are as conspicuously present in the Finale as they are in the music that followed during the Russian and neoclassical eras. The larger point here, however, is not that one of these views is necessarily correct and the other wrong. The focus, rather, is on the many ways in which the musical context is enlivened when differing approaches of this kind are played off against one another. While some sections of The Firebird readily reflect Stravinsky’s past, others provide a good deal more than just “an inkling of the Stravinsky to come”.23 21See

note 13. Stravinsky and the Russian Traditions, 590. 23Taruskin, Stravinsky and the Russian Traditions, 588. 22Taruskin,

13

14

Introduction

Owing in large part to Taruskin’s remarkable research, we now know a great deal about the choreographic beginnings of The Rite, the composer’s close collaboration with Nikolai Roerich, and the imagined prehistoric rites that were realized as dance movements. In our attempts to interpret The Rite, however, to what extent are the circumstances surrounding its conception privileged? Already in 1914, a year or so after The Rite’s tumultuous premiere in Paris, Stravinsky’s preference for The Rite as music rather than ballet, in the concert hall rather than the theater, became known. A fuller detachment of music and its appreciation from the world at large was undoubtedly the larger context – Music Alone, as this idea is expressed in Peter Kivy’s monograph on the subject.24 Music was to be listened to for its own sake. Indeed, music seems very much to have been “a world unto itself” for Stravinsky. His notorious dictum about the powerlessness of music “to express anything at all”25 was later amended to read “music expresses itself”.26 Meaning and significance were not denied, only attempts to come to terms verbally with the underlying connection of music. Sensed and felt, that connection was given immediately in experience; Stravinsky’s scattered reflections on the matter of music’s deeper meaning point to an aesthetics of the “specifically musical”.27 Music’s expressive qualities were qualities

24Peter Kivy, Music Alone: Philosophical Reflections on the Purely Musical Experience (Ithaca: Cornell University Press, 1990). 25Igor Stravinsky, An Autobiography (New York: W.W. Norton, 1962), 53–54. 26Igor Stravinsky and Robert Craft, Expositions and Developments (New York: Doubleday, 1962), 101. Stravinsky’s “refusal to see subjective confession as music’s raison d’etre” is praised in Milan Kundera, Testaments Betrayed: An Essay in Nine Parts, trans. Linda Asher (New York: Harper Collins, 1994). According to Kundera, that very “refusal” had spawned a quality of its own, one “mercifully” free of a “human subjectivity” that had grown oppressive and “burdensome” (71). On the other hand, Richard Taruskin has argued very differently. Stravinsky paid a “price” for his steadfast recoil from “human subjectivity” and the personal; see Taruskin, “Stravinsky and Us”, 276–81. And see Taruskin, Defining Russia Musically, 360–467. The composer’s formalist detachment of music and its comprehension from the concerns of everyday life led inevitably to lapses in moral judgment, to follow Taruskin, to a reactionary politics during the 1930s that was indifferent to the horrors of this period, and then to an ugly anti-Semitism practiced into the 1940s. For yet another view of these matters, see van den Toorn and McGinness, Stravinsky and the Russian Period, 284–91. And see chapter 5 in this volume. 27See Eduard Hanslick, The Beautiful in Music, trans. Gustav Cohen (New York: Liberal Arts Press, 1957), 47.

Introduction

at all “only in musically expressive form”, only as they are expressed in music.28 Chapter 7, a colloquy, begins with Dmitri Tymoczko’s lengthy challenge to the octatonic-diatonic approach, “Stravinsky and the Octatonic: A Reconsideration”. His challenge is followed by a rebuttal, “The Sounds of Stravinsky”, which is then followed by an additional reply by Tymoczko, “Octatonicism Reconsidered Again”. “The sounds of Stravinsky” is more than just a defense of the octatonicdiatonic approach, however, but a critique of Tymoczko’s analytical application of a large and diverse assortment of scales. Readers can judge for themselves on these matters, consulting the original challenge, the rebuttal, and Tymoczko’s reply to the latter.

28Carl Dahlhaus, “Fragments of a Musical Hermeneutics”, trans. Karen Painter, Current

Musicology 50: 8–10.

15

Chapter 1

Some Characteristics of Stravinsky’s Diatonic Music

Stravinsky’s music has seemed stubbornly to resist binding theoretical legislation. That this may be considered curious is owing to the conviction—voiced by those familiar with the literature— that there is a consistency, an identity, or distinctiveness here that certainly ought to lend itself to such legislation. Curious, too, because the attention accorded this music over the past fifty years has been staggering: the elusive (if at times highly suggestive) imprint of tonally functional relations has been circumvented in appeals to a “basic cell” rationale whereby “coherence” is attributed to the unfolding of some intervallically conceived cohesiveness; “neoClassical” ventures have been juxtaposed with models drafted from Baroque and Classical C-scale literature in an effort to track down the contamination, the departure from traditional (tonal) form, or the “impurities” or “wrong notes” with which Stravinsky has been cited. Roy Travis, apropos the first pages of the Introduction to Le Sacre, has suggested that, by substituting “tonic sonority” for “tonic triad”, Copyright 1975 and 1977, Perspectives of New Music. Used by permission. This article first appeared in two parts in Perspectives of New Music, vol. 14, no. 1 (1975); vol. 15, no. 2 (1977). The Music of Stravinsky: Collected Essays Pieter C. van den Toorn Text Copyright © 1975, 1977 Perspectives of New Music Layout Copyright © 2023 Jenny Stanford Publishing Pte. Ltd. ISBN 978-981-4968-62-1 (Hardcover), 978-1-003-35916-6 (eBook) www.jennystanford.com

18

Some Characteristics of Stravinsky’s Diatonic Music

we might find techniques analogous to those of tonal practice (as interpreted by Heinrich Schenker); and Allen Forte has subjected the whole of Petroushka (with its sizable “chunks” of diatonic material) to a Schenker-type analysis.1 But I think it questionable whether the analytical methods in even the most revealing of these and similar endeavors can be considered all that appropriate with respect to the bulk of Stravinsky’s work (or with respect to any concern for consistency, identity, or distinctiveness), whether, respecting the last of these, the transfer of terms and concepts intimately associated with tonal practice to a music which is at least problematic in this respect does not confuse rather than illuminate, jeopardizing at the same time any binding, “particularizing” understanding this analytic-theoretical reckoning might have afforded the literature for which it was intended. Moreover, apart from the philosophical or psychological understanding to which some have addressed themselves, existing attempts to bind in semi-technical terms have had the most frightful of results, a dialogue so misleading, so full of contradiction as to stupefy, frighten, or otherwise offend the most conscientious of readers. And we might cite the general confusion which permeates the pages of Paul Collaer’s discussion as exemplary in this respect.2 For here, as in other such documents, a bewildering succession of descriptive terms and explanatory notions, invariably left un- or under-defined, deprives the undertaking of all meaning and consequence: Stravinsky’s music, everywhere and at once, is made to represent or encompass every conceivable technique. And the descriptive terms and explanatory notions associated with this literature may now seem symptomatic of confusion rather than of any understanding or coming to terms: “pantonality” and “pandiatonicism” appear, in the presence of “diatonicism”, merely to suggest the absence of tonally functional relations; and “poly-” or “bi-tonality”—horrors of the musical imagination—have widely 1Roy Travis, “Towards a New Concept of Tonality?”, Journal of Music Theory (November, 1959); Allen Forte, Contemporary Tone Structures (New York: Columbia University Press, 1955); or, for an example of the model approach, see Edward Cone’s “The Uses of Convention: Stravinsky and his Models”, Stravinsky, ed. Paul Henry Lang (New York: W. W. Norton, 1963). 2A History of Modern Music, trans. Sally Abeles (Cleveland: World, 1961).

Some Characteristics of Stravinsky’s Diatonic Music

(and mercifully) been dismissed as too fantastic (unreal) or too illogical to warrant serious consideration.3 So we might take heed of these discomforting signs. It may be that this literature, with its multiplicity of “styles”, its diverse and seemingly conflicting orientations (“Russian”, “neo-Classical”, “serial”, the—in Arthur Berger’s words—“congenital” one toward traditional harmony), its (unfortunate?) sandwiched position between the pillars of tonality and twelve-tone ordering procedures (pillars which, admittedly, might not eventually prove as pillar-like as they now seem), is quite incapable of yielding (or succumbing to) a truly useful set of binding theoretical propositions. Moreover, as long as this literature continues to attract the kind of interest and attention it has in the past, the likelihood of such a design seems, ironically, all the more improbable. In our quest for a theoretical framework and an accompanying analytical approach (or approaches) which will satisfy our binding instincts—substantiate our sense of a distinctive presence—and prove effective in dealing with the specificity of individual works or groups of works, we may have to contend not with consistency, identity, or distinctiveness, but with consistencies, identities, and distinctivenesses, several preoccupations which may or may not correspond to the familiar orientation categories or “stylistic trends”, each of these suggesting theoretical formulations with (perhaps slightly) different approaches in analytical method. Which brings us to Arthur Berger’s classic discussion of “Pitch Organization in Stravinsky”4 where “binding theoretical legislation”—a “self-contained theory” as he puts it—is wisely forsaken (or left to some future date) in favor of a method of classification which deals with what appear to be usefully definable consistencies, identities, or distinctivenesses: 1) diatonic writing (music accountable to the diatonic pitch collection) where pitchclass priority may assert itself by means other than tonally functional, so that, in addition to the familiar C-scale or “major scale”, this assertion may implicate alternative interval orderings with respect 3See,

for example, Allen Forte, op. cit., p. 137; or, Benjamin Boretz, “Meta-Variations, Part IV: Analytic Fallout (I)”, Perspectives of New Music, Vol. 11, No. 1, p. 149. 4“Problems of Pitch Organization in Stravinsky”, Perspectives of New Music, Vol. 2, No. l, pp. 11–42.

19

20

Some Characteristics of Stravinsky’s Diatonic Music

to the collection (e.g., E-scale or D-scale), this latter terminology introduced by Berger for purposes of circumventing tonal and modal implications where they are clearly irrelevant; 2) octatonic writing (music accountable to the octatonic pitch collection) based on a kind of “background” (0, 3, 6, 9) symmetrical partitioning of the 1, 2, 1, 2, 1, 2, 1, (2) interval ordering of the scale; 3) octatonic-diatonic interaction which, in Berger’s words, “produces a curious alchemy which brings tonal functionality in its wake”, circumstances demonstrated by his analysis of the Symphony of Psalms, first movement, where octatonic “blocks” are juxtaposed with diatonic “blocks” referable to the E-scale on E, through which G, as a symmetrically-defined octatonic partitioning element, steadily asserts itself to provide, via the “halfcadence” which concludes the first movement, the grounds for “the tonal bias that obviously governed its [the Symphony’s] conception.” And while it is the first of these (“diatonic writing”) which is of concern here, I shall want briefly to discuss implications regarding the latter two classes, “octatonic writing” and “octatonic-diatonic interaction”. For it is the persistence of “octatonic writing” in this literature—or the partitioning that may handily be inferred on its behalf—that seems most to justify the kind of classification Berger indicates. Moreover, the very “characteristics” here to be examined apropos “diatonic writing” can best be understood as they interact with referentially octatonic material. So, following these preliminary remarks on octatonic construction, we can, in Part II, begin to explore the regularities governing this interaction which, in Part III, should provide an adequate foundation for a discussion of Histoire where the octatonic collection figures only slightly.

I

Now surely no one—not even the most rabid of accountability buffs (among whom I include myself)—would want to infer everywhere, or claim that the octatonic collection is active referentially in even the majority of Stravinsky’s works (although, were we to limit these to the lengthiest or “most significant”—the ones we care most about, say, twenty or twenty-five—such a claim would by no means be inconceivable: see Lists 1 and 2, pp. 108ff.). Beyond contention,

Some Characteristics of Stravinsky’s Diatonic Music

however, is the fact that, beginning with The Firebird Introduction (wholly octatonic, excepting a few measures) and extending through works like Petroushka (1911), Le Sacre (1913), Les Noces (1917), Symphonies of Wind Instruments (1920), the Symphony of Psalms (1930), Babel (1944), and the Symphony in Three Movements (1945) where the heaviest concentration is to be found, numerous “blocks”, passages, and sections of material lie scattered throughout this literature where confinement is explicit (of substantial duration, relatively unimpaired by outside “interference”, and with the collection complete or nearly so: List No. 1). And, while slight changes or adjustments may be detected and correlated with the “Russian”, “neo-Classical”, and (early) “serial” categories, Stravinsky appears in general to have been remarkably consistent in his partitioning habits. Berger alludes to the various (0 3 7/0 4 7/0 4 7 10/0 4 7 10 1) triadic and (0 13 4) tetrachordal articulative complexes which, implicating the 1, 2 interval ordering of the scale, are available, in symmetrical formation, at pitch numbers 0, 3, 6, and 9, a partitioning perspective which he credits “for the uniqueness of the relations Stravinsky employed”. But while a preference respecting this perspective seems unmistakable when the literature is viewed as a whole (a preference possibly symptomatic of the lengthy “neo-Classical” period, the (0 3 7/0 4 7) triads of this 1, 2 interval ordering obviously constituting a more lucrative foundation for accommodation in this “neo-Classical” respect than the (0 2 3 5) tetrachords of the reverse 2, 1 ordering), there is sufficient evidence, particularly in material of the “Russian” variety, to suggest the opposite: the (reverse) 2, 1, 2, 1, 2, 1, 2, (1) interval ordering of the scale, implicated, for the most part, by the (0 2 3 5) articulative complex with interval order 2, 1, 2, this (0 2 3 5) articulation available, in symmetrical formation, at pitch numbers 0, 3, 6, and 9 with respect to this (reverse) 2, 1 ordering. So respecting these alternative interval orderings (and the partitioning that may be inferred or referred to them), I have sketched two comprehensive models, Models A and B, the partitioning formats inferrable from (or applicable to) the “blocks”, passages and sections of Lists 1 and 2. And, having proceeded this far, I might briefly entertain certain conditions regarding the structure of the scale and the partitioning outlined in these models.

21

22

Some Characteristics of Stravinsky’s Diatonic Music

List No. 1 2)

The Firebird (1910)

3)

Petroushka (1911)

4)

Le Sacre du Printemps (1913)

5)

The Nightingale (1914)

8)

Les Noces (1917)

7)

Renard (1915)

10) Symphonies of Wind Instruments (1920) 12) Symphony of Psalms (1930) 14) Babel (1944)

Introduction: excepting mm. 10–12, 16–18.

Second tableau: Nos. 48–52. Third tableau: Nos. 77–81. (1911 version.)

Part I: Introduction, Nos. 6 (and near repeats), 8; Danses des adolescentes, Nos. 16–18, 22–24; Jeu du rapt, Nos. 38–40, 40 + 6–43, 44. Part II: Action Rituelle des Ancêtres, Nos. 131–135, 138. Act III: No. 108.

Nos. 9 + 1–11, 20–26, 41 + 1–43, 53–56.

First tableau: Nos. 1 (and near repeats), 11. Second tableau: Nos. 35–40. Third tableau: Nos. 68–72, 82–87.

Nos. 0–6 (and near repeats at Nos. 9, 26, 37 and 39). (1947 version.) First Movement: Nos. 0–2, 3–6, 7–9. Nos. 0, 16–24.

15) Scènes de Ballet (1944)

Nos. 0–2.

17) Concerto in D (1946)

Nos. 0–5.

16) Symphony in Three Movements (1945)

First Movement: Nos. 5–16, 22–38, 88–96. Second Movement: Nos. 125 + 1–130, 131. Third Movement: Nos. 152–154, 156–157 + 1, 161–164, 191–194.

Some Characteristics of Stravinsky’s Diatonic Music

List No. 2 1)

2)

Fireworks (1908)

The Firebird (1910)

Nos. 0–9, 16–21.

3)

Petroushka (1911)

4)

Le Sacre du Printemps (1913)

Second tableau: Nos. 48–52, 59–62. Third tableau: Nos. 77–81. Fourth tableau: No. 125–finish. (1911 version.)

5)

The Nightingale (1914)

7)

Renard (1915)

6) 8)

9)

Three Pieces for String Quartet (1914) Les Noces (1917)

L’Histoire duSoldat (1918)

11) Octet (1923)

12) Symphony of Psalms (1930) 13) Concerto in Eb “Dumbarton Oaks” (1938)

Introduction; Kastchei section: Nos. 9–11.

Part I: excepting Danses des adolescentes at Nos. 28–30, and Rondes printanierès at Nos. 48–57. Part II: Glorification de l’elue, Nos. 104–121; Evocation des ancêtres, Nos. 121–129; Action rituelle des ancêtres, Nos. 129–142. Act III: Nos. 108–112. No. 1.

Nos. 9–11, 20–26, 41–56.

First tableau: excepting Nos. 9, 12–13. Second tableau: Nos. 29, 31–40, 53–62. Third tableau: Nos. 67–72, 78–80, 82–87. Fourth tableau: Nos. 87–106. Music to Scene II. The Devil’s Dance.

Tema con variazioni: Nos. 24–56.

First Movement. Third Movement: Nos. 1–6, 8, 15–20, 29. Third Movement: Nos. 52–58.

23

24

Some Characteristics of Stravinsky’s Diatonic Music

14) Babel (1944)

Nos. 0–8, 16–30.

15) Scènes de Ballet (1944)

Nos. 0–5.

17) Concerto in D (1946)

Nos. 0–5.

16) Symphony in Three Movements (1945)

First Movement: Nos. 0–38, 58–69, 88–97, 105–112. Second Movement: Nos. 112–118, 125–140. Third Movement: Nos. 142–164, 191–195.

18) Orpheus (1947)

Nos. 4–47.

20) Agon (1957)

Prelude: mm. 122–145. Interlude: mm. 254–277 (and near repeat at mm. 387–410). Bransle Simple: mm. 278–309. Bransle Gay: mm. 310–335. Bransle Double: mm. 336–386. Pas-de Deux: mm. 411–462.

19) Canticum Sacrum (1955) Section I: mm. 10–17 (and near repeats). Section II. Section V: mm. 307–312 (and near repeats).

21) Threni (1958)

Mm. 1–7; mm. 35–44 (and near repeats); mm. 204–17.

MODEL A i

ii

iii

F

f♯

A♭

0

1

3

Collection I:

E

Collection III:

F♯

Collection II:

pitch numbers: intervals:

f

g

iv

v

vi

B

c

G

a♭

B♭

A

b♭

C

a

4

6

vii

viii

D

e♭

9

10

b

D♭

d♭

E♭

7

(i)

d

(E)

e

(F♯)

1 2 1 2 1 2 1 (2)

(F)

(1)

Some Characteristics of Stravinsky’s Diatonic Music

MODEL B i

Collection I:

E

Collection III:

F♯

Collection II:

pitch numbers: intervals:

ii

iii

iv

D

c

d

C♯

e

E♭

F

e♭

0

2

3

v

vi

vii

viii

a

G♯

f♯

8

9

11

b

B♭

a♭

d♭

C

b♭

5

B 6

G

A

(i)

f

(E)

g

(F♯)

(F)

(1)

2 1 2 1 2 1 2 (1)

25

26

Some Characteristics of Stravinsky’s Diatonic Music

(1) The octatonic scale may be defined as any collection of eight distinct pitch classes which, when confined to the octave and thus arranged in scale formation, will exhibit the interval ordering of alternating whole and half steps. (2) When holding a particular passage accountable to the collection, the collection may be designed to incorporate essential data regarding pitch and/or construct priority. And with this in mind, it will be useful always to distinguish between the referential collection, the total pitch-class content inferrable from the passage in question, and the referential ordering of intervals the collection will assume on the basis of

Some Characteristics of Stravinsky’s Diatonic Music

the pitch class to which priority is assigned. (The pitch class of priority, pitch number 0, will also determine, in semitonal count, the numbering of the remaining seven pitch classes.) (3) Given the symmetrical nature of such a collection of alternating whole and half steps, it follows that there are but three collections distinct with respect to total pitch-class content; or, to put it another way, the collection is limited to three transpositions.5 Thus, were we to continue transposing beyond the initial transposition from E to F and F♯ in Model A, these further “transpositions”, beginning at pitch number 3, would merely duplicate the initial statements with respect to pitch content and interval ordering. (4) In addition, it follows that such an arrangement of alternating whole and half steps yields but two possible interval orderings, the one with its second scale degree at an interval of a semitone from the first, the other with its second scale degree at an interval of a whole tone: 1, 2, 1, 2, 1, 2, 1, (2) as in Model A; 2, 1, 2, 1, 2, 1, 2(1) as in Model B. And it is at this point that the critical distinction arises. For it is on the basis of these competing interval orderings—or, more readily, on the basis of differences in the partitioning of the collection which are referable to (or may, in turn, be inferred from) these orderings—that Models A and B have been constructed to comprehensively represent two distinct kinds of construction or partitioning that emerge from an examination of the literature. And for those acquainted with some of the passages listed, these models may already be of service in that known passages and relations may be “hooked up” perhaps in a “structural-level” manner similar to that pursued in this inquiry. But for the uninitiated—and perhaps for the “already acquainted” as well—it seems advisable to proceed with these further observations and instructions in mind, all of which pertain to the structure of the scale and the partitioning outlined in Models A and B, and all naturally pertinent in various ways to the analytical endeavors to be undertaken. 5Hence Olivier Messiaen’s classification of the scale among the various “modes of limited transposition”: Technique de mon langage musical (Paris: Leduc, 1944).

27

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Some Characteristics of Stravinsky’s Diatonic Music

So with respect to the symmetrical discipline in the interval orderings of the scale exhibited by Models A and B:6

(1) The alternating whole and half steps divide the octatonic octave into four numerically equal partitions at pitch numbers 0, 3, 6, and 9. Pitch number 6, the fifth scale degree and at the interval of a tritone from 0, is an axis around which the two halves of the octave are symmetrical; and at pitch numbers 3 and 9 there is another axis around which two quarters of the octave (halves of the tritone) are analogously symmetrical. (2) But the interval ordering initiated at 0, 3, 6, and 9 in Model A is 1, 2, while that in Model B is 2, 1. Hence it is this variance in the interval ordering which permits, beyond the more “background” (0, 3, 6, 9) partitioning common to both models, the critical distinction between Models A and B to become readily apparent at the “foreground” surface-articulative level: (0 3 7/0 4 7) triadic partitioning of the scale at 0, 3, 6, and 9 in Model A and (0 2 3 5) tetrachordal partitioning of the scale at 0, 3, 6, and 9 in Model B. In Model A, pitch numbers 0, 3, 6, and 9 are bequeathed not only the interval of 7 (the “supporting fifth”), but are “roots” of (0 3 7/0 4 7) “major” and “minor” triads as well as of (0 4 7 10) “dominant seventh” and (0 4 7 10 1) “dominant minor ninth” chords, the entire succession of pitch classes, with much overlapping, still referable to any given collection. So the assertion of Model A on behalf of any particular passage will naturally reflect a preoccupation with (0 3 7/0 4 7) triadic partitioning. (Traditional terminology is here invoked in a supplementary manner for purposes of identification, there being no intent to implicate tonally functional relations.) On the other hand, pitch numbers 0, 3, 6, and 9 in Model B are bequeathed the interval of 5 and the (0 2 3 5) tetrachord with interval order 2, 1, 2, so that the assertion of Model B on behalf of any particular passage will

6See Berger, op. cit., p. 21. In addition to quoting directly from Berger in these preliminary remarks, I am also paraphrasing liberally, seeing, on the one hand, no reason to alter what has already been presented in a thoroughly efficient manner, but, on the other, an occasional need to revise in accordance with the findings of this inquiry. And it should be noted in this connection that Berger, in contrast to these findings, finds little use for the 2, 1 interval ordering of the scale and (0 2 3 5) tetrachordal partitioning (Model B).

Some Characteristics of Stravinsky’s Diatonic Music

in turn reflect a preoccupation with (0 2 3 5) tetrachordal partitioning at the articulative level.

And, with respect to pitch-class and/or construct priority in Models A and B: ... Within any given octatonic collection ... the first element of any of the partitions of the octave at 0, 3, 6, and 9 has the potentiality of being the pitch class of priority in an identical ordering referable to the same given octatonic collection ... That is to say, not only is each of the partitions a “transposition” of the other, in a sense, but the interval ordering of the total collection defined in relation to the first element of each partition is also identical; hence, each of the four possible orderings is also a different “transposition” of the octatonic scale. (Strictly speaking, this is really “rotation”, since the collection has only three transpositions ...) Therefore, in the interval ordering of the scale there are, loosely speaking, four potential “tone centers” of equal weight and independence ...7

What this means is that, given the symmetrical four-part partitioning and the reproduction in content and interval ordering of the scale when “transposing” from pitch number 0 to 3, 6, and 9 (“rotation”), there exists an identity, or, with respect to tritone partitioning, a numerical equality between the elements of this partitioning, so that in order for one pitch class and/or construct to assert priority over the others it must eliminate this identity, equality, or potential for “equal weight and independence”. And such elimination—the assertion of pitch class and/or construct priority—will occur by means of contextual articulation, tonally functional relations (dominant and subdominant relations) being unavailable to these octatonic partitioning elements, “potential priorities” or “accented tones”: persistence, octave reinforcement, metric accentuation, influence of surrounding material, etc.8 And already it may be possible to envision here a condition peculiar to Stravinsky’s octatonic contexts, one wherein two or more of these symmetrically defined partitioning elements or “potential 7Berger,

ibid. will not mean, however, that in juxtaposition or interpenetration with nonoctatonic material (or even in passages where octatonic reference is unimpaired), tonally functional relations, even if judged parenthetical, will not somehow impose themselves. See Berger’s discussion of the Symphony of Psalms (op. cit., p. 32). 8This

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Some Characteristics of Stravinsky’s Diatonic Music

priorities”, generally with (0 3 7/0 4 7) or (0 2 3 5) articulative “support”, assert themselves to a degree that relations assume a deadlocked character, and particularly in cases where emphasis is placed on the (0, 6) tritone partitioning of the scale, that these relations impose themselves all the more forcefully in the form of an inert, self-contained, tension-clinched complexe sonore within which no selection of pitch-class priority seems legitimate, and, indeed, the search for one somewhat beside the point. Berger, in a brief analysis of the “Petroushka chord” at Nos. 49 and 51 of the score (1911 version), invoked Stravinsky’s use of “polarity” in describing the nature of these contexts, a term which, to Berger, seemed to reflect an awareness on the composer’s part: ... of the special properties of the tritone which make it possible for pitches at 0 and 6 ... by virtue of similitude or equal and thus independent weight, to remain in equilibrium or—to the end that a tone center is asserted by neither—to stand in a certain opposition. This speculation might easily take flight in a direction which would establish, as a necessary condition of “polarity”, the denial of priority to a single pitch class precisely for the purpose of not deflecting from the priority of the whole complexe sonore.9

So given the scale’s inherent ability to foster (symmetrically defined) multiple priorities—and, naturally, the tendency for Stravinsky’s material to reflect this ability—attempts to determine single pitch-class and/or construct priorities in contexts referable to the scale will entail certain hazards. And even when a pitch class or construct does assert priority, it will be the sense of deadlock that is immediately striking and deserving of analytical attention. And so, with the symmetrical nature of the scale in mind, we might feel inclined to attach special significance to (0, 3, 6, 9) “background” partitioning when examining a particular passage, or to consider a recognition of the pitches or constructs which delineate a two, three, or four-part partitioning of the scale with respect to (0, 3, 6, 9) symmetrically-defined partitioning far more critical than any designation as to which of these might ultimately qualify as pitch number 0 (i.e., as the most likely candidate for pitch-class priority

9Berger, p. 25. “Polarity” emerges from Berger’s own translation of a passage from Stravinsky’s Poetique Musicale (Cambridge: Harvard University Press, 1942), p. 26.

Some Characteristics of Stravinsky’s Diatonic Music

status according to the criteria noted above: persistence, octave reinforcement, metric accentuation, etc.). Moreover, respecting Models A and B, it should be noted in this connection that the partitioning elements or “potential priorities” in these displays (e.g., E, G, B♭, D♭ in Collection I) are interchangeable with respect to pitch-class and/or construct priority. While allowing for the assertion of priority, these models are, by definition, comprehensive or panoramic, providing the reader with the full potential of (0 3 7/0 4 7) triadic and (0 2 3 5) tetrachordal partitioning as that potential is reflected in the literature. And they are adaptable with respect to the number of (0, 3, 6, 9) partitioning elements that might actually be stipulated by a particular passage. For Stravinsky’s octatonic settings, while frequently approaching a realization of the potential for “equal weight and independence” among two or more of the (0, 3, 6, 9) partitioning elements—or their (0 3 7/0 4 7) triadic or (0 2 3 5) tetrachordal complexes— seldom encompass all four at the same time, and then seldom on an equal footing: configurations tend to gravitate around two or three of these elements within any significant period of time.10 To take but one example: Nos. 48–52 from Petroushka, and, in particular, the “Petroushka chord” at Nos. 49 and 51. Were we here to accept the interpretation of this “chord” as containing two (0 4 7) triadic sub-complexes (one based on C, the other on F♯), to apportion greater weight to the (0 4 7) triad on C (and hence to the pitchclass C) by virtue of its isolation and reinforcement in succeeding passages (despite, obviously, the potential for “equal weight and independence” yielded by (0, 6) tritone partitioning in an octatonic setting), but to disregard “interference” in the piano figuration at No. 50 and the vertical dyads at No. 49 of which the A♯/C dyad is conspicuous since it refers to relations of significance in the first tableau and might therefore have prompted, with respect to a more “global” perspective, a different kind of “background” partitioning, the following “structural-level” format might apply, stipulating (0, 10Exceptions

may be found in he Sacre at No. 42 (Jeu du rapt), in Renard at No. 24, and in Les Noces at Nos. 35–40, 68–72, and 82–87. But with respect to “equal footing”, a strong case can be made for an E♭ pitch-class priority (or a (0 4 7 10) “dominant seventh” complex on E♭) in Le Sacre as a result of its prominence “in and about”, while in Renard a G pitch-class priority is unmistakable despite the “harmonization” of a melody with all (0 4 7) triads of Collection I (on G, B♭, D♭, and E) present in succession.

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6) tritone partitioning of Collection III in terms of C and F♯, Model A, where pitch numbers 3 and 9 are inoperative as partitioning elements, and, indeed, are absent from the configuration:11

(1) 0

(2) 0, 6

(3) (0 4 7)

(3a) (0 4 7) (6 10 1) (4) (10 1 6) (0 4 7)

(5) 0 1 (3) 4 6 7 (9) 10 (0)

And, apart from the partitioning that may be inferred from the “blocks” and passages of Lists 1 and 2 and comprehensively defined via Models A and B, it should by now be apparent that it is with reference to this partitioning—Stravinsky’s octatonic settings— that the most useful of notions (e.g., “harmonic stasis”, “polarity”, “superimposition”, “juxtaposition”) achieve their sharpest definition. Indeed, while accountability to the collection is consistently ignored (or, more probably, overlooked) by proprietors and propagators alike, these terms are invariably invoked (unknowingly))on behalf of octatonic activity, the “blocks” and passages of Lists 1 and 2 (where relations are just as invariably dubbed “typical” or “characteristic”), prompted by readings, for example, of Le Sacre and Les Noces which abound with such activity. Thus, the notion of “polarity”, following its appearance in Poetique Musicale, appears in Pierre Boulez’s celebrated discussion of rhythmic organization, where it is conceived—anachronistically vis à vis Le Sacre, where octatonic activity not only abounds but is as unsullied by tonal implications as any in the literature—in terms of a subdominant-tonic-dominant relation;12 whence it emerges in Berger’s discussion, interpreted in terms of the (0, 3, 6, 9) symmetrically defined partitioning elements 11And that Stravinsky was conscious of these referential implications seems indicated

by the return of the “Petroushka chord” at No. 77 in the third tableau, where the (0 4 7) triadic “sub-complexes” are articulated at E♭ and A, an articulation which thus neatly completes (0, 3, 6, 9) “background” partitioning of Collection III in terms of C, E♭, F♯, and A, Model A. 12Notes of an Apprenticeship, trans. Herbert Weinstock (New York: Alfred A. Knopf, 1968), p. 74.

Some Characteristics of Stravinsky’s Diatonic Music

of the octatonic collection, elements which assume, apropos “polarity”, a degree of (symmetrically defined) “equal weight and independence” and “stand in a certain opposition”. And “superimposition” and “juxtaposition” bring similar case histories to mind. In the writings of Boulez, superimposition is viewed, contemptuously, as an “irreducible aggregation”, a “coagulation” which creates for the “superimposed” fragments a “false counterpoint”, all of this “eminently static in the sense that it coagulates the space-sound into a series of unvarying stages ... and in the sense that it annuls the entire logic of the development.”13 But this “coagulation” is attributed—anachronistically, again—to “complexities grafted onto the old organization”, these “complexities” constituting a mere “surcharge of an existent [tonal] language”,14 a perspective perhaps not wholly unreliable since the (0 3 7/ 0 4 7) triads and (0 4 7 10) “dominant sevenths” of Model A, as complexes of pitch elements, are not only part of that “existent (tonal) language”, but their (0, 3, 6, 9) symmetrical definition, given proper “voice-leading”, may be considered as having been available at least in succession (although, apropos Le Sacre, implications of this sort are completely irrelevant, there being, in addition, no tonally functional threat à la Symphony of Psalms, first movement, so that any attempt to define these “complexities” along tonal lines—something Boulez eschews beyond the casual equation of “polarity” with the subdominant-tonicdominant relation—would most assuredly “confuse rather than illuminate”), but a perspective which fails to consider the referential basis, the (octatonically conceived) symmetrical nature of the deadlock, “coagulation”, or “superimposition”. For superimposition is only superficially (or partially) viewed as the grafting of articulative fragments which, in typical Stravinskian fashion, remain “fixed” in registral distribution. The notion will seem apt insofar as “a certain opposition”, “contradiction”, or “polarity” is defined with respect to content, a content which, octatonically speaking, would project this “opposition,” “contradiction,” or “polarity” among the fragments being superimposed (possibly (0 3 7/0 4 7) triadic or (0 2 3 5) 13Boulez,

p. 248. p. 74.

1414Boulez,

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tetrachordal) in the (0, 3, 6, 9) partitioning sense indicated.15 And so I trust that Boulez’s lively description of superimposition (forwarded in however condescending a manner) will be interpreted and understood with reference to Models A and B, there being, manifestly, nothing in Stravinsky’s music quite so conducive to the production of “superimpositions” which “coagulate the space-sound” than the (0, 3, 6, 9) symmetrically defined (0 3 7/0 4 7/0 4 7 10) triads and (0 2 3 5) tetrachords of Models A and B (Boulez’s neglect of these referential implications in Le Sacre notwithstanding). Finally, juxtaposition brings us to within range of pending concerns, raising, as it does, the issue of octatonic-diatonic interaction. For List No. 1 is composed of “blocks” and passages of material, these “blocks” and passages subject generally to repeats (or near repeats) in their respective contexts, each of these “blocks” exhibiting an unusual degree of stability, distinctiveness, self-sufficiency, and insulation. Quite so. For, as here defined, symmetrical construction within “blocks” defies internally motivated “development” along traditional tonal lines (the sense of “harmonic progression”, “resolution”, and “cadence” associated with tonality and the C-scale), change, progress, or “development” possible only by abruptly cutting off the deadlock, only by terminating activity and juxtaposing it with something new in the collectional reference 15At

the articulative level, maximum “opposition”, “contradiction”, or “polarity”—and hence maximum content differentiation—is afforded by the (0, 6) tritone-related (0 3 7/0 4 7) triads of Model A—as in the “Petroushka chord”—and by the (0, 6) tritone-related (0 2 3 5) tetrachords of Model B—as at No. 134, Action rituelle des ancêtres, in Le Sacre. And, to avoid possible confusion here, it should be borne in mind that “reconciliation” or subsumption of “contradictory” or “polarized” pitch elements (or articulative fragments) in terms of the symmetrically cohesive octatonic reference collection does not eliminate the respect in which, at another level of determinacy, separate entities in the partitioning of this collection—or, in the case of (0, 3, 6, 9) symmetrical partitioning, “a certain opposition”, “contradiction”, or “polarity” manifested by these entities—are recognized. To follow Benjamin Boretz in this regard, the “levels” of a structural-level conceptualization constitute (re) interpretations of the passage or piece in question in terms of the particular entity or grouping forwarded (expressions of particular kinds and degrees of determinacy), each of these (re) interpretations added to or superimposed on (rather than replacing or superseding) preceding (or succeeding) levels of (re) interpretation, all this constituting “the essential basis of that functional multiplicity exhibitable by musical entities . . .” “Meta-Variations, Part II”, PNM, Vol. 8, No. 2, p. 68. See, also, by the same author, “Musical Syntax (II)”, PNM, Vol. 10, No. 1.

Some Characteristics of Stravinsky’s Diatonic Music

or in the partitioning thereof (through which, however, some relation, possibly “continuously operative”, might be “left hanging” as a connecting link or “thread”). In other words, juxtaposition, like superimposition, is no mere formality, no mere architectural curiosity to be understood solely in terms of meter, dynamics, instrumentation, or register. Juxtaposition is content motivated, prompted by the conditions of balance, “equilibrium”, “polarity”, deadlock or locked confrontation which typify Stravinsky’s octatonic settings,16 the results discernible, in the most conspicuous of cases, in terms of a shifting in the collectional reference (possibly from octatonic to diatonic), each of the juxtaposed “blocks” acquiring, in the process, a collectional identity. And while it is quite true that, as a procedure, juxtaposition transcends its applicability to octatonic construction (having been, like superimposition, perhaps rather deeply rooted in Stravinsky’s inventive processes), octatonic construction seems nevertheless to propel the most incisive formulation. But further. Even with juxtaposition conveniently investing the “blocks” and passages of octatonic (or diatonic) reference with a degree of distinctiveness, self-sufficiency and insulation (conveniently lending itself, in other word, to the selective analysis that underlies Berger’s classification and the octatonic partitioning formats outlined above), analysis, pursued with a vengeance, is seldom a dead end, seldom exceptionally tidy or accommodating. By which I mean that the observer, having digested the passages of explicit reference (List No. 1) by way of all the various testing devices known to musicians (transposing, inverting, altering a given registration or pitch distribution: in short, improvising as a means of “getting into” the material), would have to be exceptionally deliberate were he/she not at some point to apprehend, beyond explicit reference, the still more numerous “blocks” and passages exhibiting forms of octatonic-diatonic inter penetration, passages where the octatonic collection, given some prior familiarity, might 16“Deadlock”

or “locked confrontation” in that there is always this sense of a “pulling and tugging” or of an “opposition” among the participating, superimposed, registrally “fixed” (0, 3, 6, 9) symmetrically defined partitioning elements or articulative fragments (a felt “opposition” in which the variance in rhythmic periods defined by the reiterating articulative fragments naturally plays a role), so that the balance or “equilibrium” is seldom passive or frictionless but surging with an inner, selfcontained tension.

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Some Characteristics of Stravinsky’s Diatonic Music

reasonably be inferred whatever the “interference” from conflicting sets (or systems) of reference (see List No. 2).17 To put it another way: octatonic-diatonic interaction poses the question not only of a juxtaposition of “blocks” referentially octatonic or diatonic, but of an intermingling of these references. And so, apropos the Symphony of Psalms: while we might generally describe the first movement as a piece wherein octatonic “blocks” referable to Collection I (Model A, with a generally (0, 3, 6) “background” partitioning in terms of E, G, and B♭) are juxtaposed with diatonic “blocks” referable to the E-scale on E through which E, or the (0 3 7) triad on E (the “Psalms chord”), is punctuated as the principal connecting link (that which is shared, not to mention the gradual 17Obviously,

the criteria applied in this selection and classification allow for considerable flexibility in the drawing of inference: explicit reference (“of substantial duration, relatively unimpaired by outside ‘interference’, with the collection complete or nearly so”) for List No. 1; partial accountability (cases, generally, of octatonicdiatonic interaction via abrupt “block” juxtaposition or interpenetration) for List No. 2. And this is necessarily so given the extent and variety of the material at hand. Thus, apropos the middle section of the Symphony in Three Movements (1945): Nos. 125 + 1–130 are octatonic (accountable to Collection I, Models A and B partitioning) except for the “interference” of a single pitch, G♭, which is first articulated in the harp as part of a (0 4 7) triad “rooted on” G♭, “first inversion”. Now, in order to acknowledge octatonic hegemony but to account at the same time for the slight here-and-there “interference” of this element and of the (0 4 7) triad it articulates (of which, however, the B♭ and D♭ are accountable to Collection I), it seemed appropriate to include the passage on both lists. On the other hand, a more determined effort to isolate octatonic passages of explicit reference (List No. 1) from those exhibiting “interference”, partiality, or octatonic-diatonic interpenetration (List No. 2) was made on behalf of Le Sacre (1913), Les Noces (1917), and the Symphony of Psalms (1930), all these works heavily endowed with lengthy “chunks” of octatonic concentration. Thus, while the entire Introduction of Le Sacre was included on List No. 2 as a case of partial accountability (or, with respect to the accumulatively climactic Nos. 10–12, a case of obvious octatonic-diatonic interpenetration), only certain rehearsal numbers or “blocks” of this section were included on List No. 1. And so it will often be the case that the “blocks” and passages of List No. 1 (explicit reference) are situated within lengthier contexts where the collection is inferrable on a partial or octatonic-diatonic interpenetration basis (List No. 2). And it follows: 1) that the lists should be regarded as comprising “blocks” and passages with symptoms in the direction of the classification indicated (since, obviously, even the question of explicit reference is here a question of degree), and 2) that the lists should not be regarded as “complete” since it will always be possible to infer further or differently respecting either the classification indicated or perhaps some slightly altered perspective, it being therefore inevitable that certain passages will be found disregarded (or overlooked), and possibly certain others, listed, questionable—at least at this stage—as to their octatonic credentials. The lists are intended as handy guides to octatonic penetration in Stravinsky’s music.

Some Characteristics of Stravinsky’s Diatonic Music

ascendancy of G and its (0 4 7 10) articulation, also shared), there are nevertheless critical points where these references interpenetrate by virtue of the coming together, the simultaneous engagement, of elements not held in common. And all this is scrupulously acknowledged in Berger’s analysis, Berger calling attention to the interpenetrating, non-octatonic (non-Collection I) C at Nos. 3 and 6, the implication being that the dominant-tonic-like resolution concluded by the second movement on behalf of the “half-cadence” on G in the first is anticipated at the outset by a suggestive “feel” in this direction. (Similar “global” conditions govern the Symphony in Three Movements, first movement, where the opening material, wholly octatonic (Collection I: Model A, with a generally (0, 6) “background” partitioning in terms of G and D♭), is “superimposed” over an interpenetrating C-scale on C reference in the trombones at No. 1 and over interpenetrating C-scale passages in the strings at Nos. 4 and 16–20, so that the (tonally incriminating) C-ending to which this Collection I material resigns itself in the final measures—a (0 4 7) triad on C, riddled, to be sure, with a telling peculiarity or “impurity”: a B is positioned so as to preserve the earlier (octatonically inspired) assertions of priority on the part of both G and E (E at No. 29)—may also be said to have been anticipated by an earlier suggestive “feel”.) But octatonic-diatonic interpenetration—the “curious alchemy” as Berger calls it—is not limited to “neo-Classical” material, nor need it “bring tonal functionality in its wake” à la Symphony of Psalms, first movement. For the whole of this literature is saturated with the most varied exhibitions of octatonic-diatonic interpenetration, exhibitions discernible already in Fireworks at Nos. 0–9 and 16–21 and subsequently in Le Sacre, Renard, and Les Noces, exhibitions which, even when later of the “neo-Classical” variety, by no means invariably prompt the tonally incriminating behavior noted by Berger. And this brings us to what I clearly perceive as a series of misinterpretations in Berger’s concluding remarks, misinterpretations which betray a “neo-Classical” bias (quite understandable, of course, this orientation encompassing the bulk of Stravinsky’s output, and the Model A partitioning perspective does predominate), misinterpretations which could have been overlooked (since they do not seriously detract from the import of Berger’s message), but which I prefer to recite since, by directly contradicting findings critical to this inquiry, they very conveniently bring these to the fore:

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... The [0 2 3 5] tetrachord with interval order 2, 1, 2 ... is one that proliferates in manifold folktune-derived motives and melodic fragments throughout Stravinsky’s “Russian” period ... What could be more natural than a merger of two predilections—the other being his well-known one for the tritone—out of which would issue a new scale: D, e, F, g; G♯, a♯, B, c♯, two tritone-related tetrachords thus bringing the D-scale into the orbit of the octatonic scale? The answer to this question is fundamental: if such were the case the octatonic scale would suffer a severe loss of identity. Thus, in terms of the important first degree (or of each “accented” element of the disjunct dyads in the normal representation of the scale), the succession of consecutive scale degrees would yield nothing different from any referential ordering of intervals in the familiar white-note vocabulary until the fifth degree were reached—and even this, in terms of Classical practice, could be a so-called “tendency tone.” It is the new “rhythm,” in the ordering of intervals, that defines the uniqueness of the relations Stravinsky employed, namely, an ordering that gives up its secret, not at the fifth, but at the fourth degree, defining a tetra-chord whose first and fourth elements are related by the interval of 4 semitones.18

For Berger’s conclusions notwithstanding, the “blocks” and passages of Lists 1 and 2—especially those of the “Russian” era, some of these to be examined—provide sufficient evidence for frequent analytical “assertions” of Model B with respect to (0 2 3 5) partitioning and the 2, 1 interval ordering of the scale implicated. Relations in Le Sacre—which I assume are as uniquely Stravinskian as any in the literature—frequently exemplify (0 2 3 5) articulative partitioning by way of the “two tritone-related tetrachords” Berger mentions, these (0, 6)-related (0 2 3 5) (6 8 9 11) tetrachords spanning the interval of 11 (a “major seventh”), a 0–11 “interfragmental” (“between” fragments) vertical interval span which not only accounts for much of the static “vertical chromaticism” in the piece but is very nearly “continuously operative” or “globally” determinate with respect to octatonic activity generally, the elements of this (0, 11) partitioning, 0–11 interval span or relation, asserting from one “block” or section to the next, degrees of priority, degrees of “equal weight and independence”, and standing “in a certain (“fixed” or polarized) opposition”: as just two of the many examples, see No. 64 toward the end of the Jeux des cités rivales 18Berger,

p. 36.

Some Characteristics of Stravinsky’s Diatonic Music

where the “upper” G-F-E-D complete (0 2 3 5) tetrachord stands “in opposition” to the “lower” C♯-A♯-G♯ incomplete (6 8 9 11) tetrachord; or, in Part II, No. 134 in the Action rituelle des ancêtres, where the “upper” C♯-B-A♯-G♯ complete (0 2 3 5) tetrachord stands “in opposition” to the “lower” G-F-E-D complete (6 8 9 11) tetrachord, the (0, 6)-defined (0 2 3 5) (6 8 9 11) partitioning in both these “blocks” referable to Collection I, Model B, and representing, in pitch and interval content, precisely the one to which Berger refers. (The uppermost pitch element and the “upper” of the two (0, 6)-related (0 2 3 5) (6 8 9 11) tetrachords—complete or (0 2 5/0 3 5) incomplete—generally “preside” in Le Sacre, the “lower” (6 8 9 11) tetrachord less persistently pursued and often represented merely by pitch number 11, this predominance being just one of the many reasons why, in case of (0 2 3 5) articulative partitioning, I generally prefer a descending scale representation and pitch numbering, a “reading down” situation to the customary ascending approach. I shall discuss this further in Part II.) Moreover, at Nos. 13–30 in the Danses des adolescentes, the octatonic contribution, conspicuous at Nos. 14–18 and 22–24, is accounted for in terms of the persistent E♭-D♭-B♭ incomplete (0 2 3 5) ostinato which stands “in opposition” to the (0 2 3 5) tetrachord or (0 4 7) triad on C, a (0, 3) “background” partitioning of Collection III in terms of E♭ and C, Model B; and, to the extent that the elements of this contribution gradually give way to an unimpaired diatonic D-scale on E♭ reference at Nos. 28–30 (where the (0 2 3 5) tetrachord in terms of E♭-D♭-C-B♭ serves as the principal connecting link, that which is shared between Collection III and the D-scale on E♭), the transaction is manifestly one wherein “the D-scale is brought into the orbit of the octatonic scale”. (I know of no more accurate description of these Danses proceedings.) And, respecting any “loss of identity” incurred by (0 2 3 5) partitioning and the 2, 1 interval ordering of the scale implicated vis à vis the diatonic pitch collection, we might note that, as the collection stands engaged, the 1, 2 interval ordering, implicated by the various (0 3 7/0 4 7), (0 4 7 10), and (0 13 4) articulative complexes, is far more vulnerable with respect to “tendency tone” behavior, there being numerous instances of octatonic reference in Stravinsky’s “neo-Classical” ventures where the (0 1 3 4) complex is conceived in terms of (0 3 4/3 4 7/3 6 7) “major-minor third” emphasis

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where pitch numbers 3 and 6 of this 1, 2 ordering, regardless of their potential for “equal weight and independence” in the (0, 3, 6, 9) symmetrical partitioning of the collection outlined in Model A, are more conventionally conceived as (or can, in my estimation, best be described as) “tendency tones” or “melodic leading tones” to pitch numbers 4 and 7 of the (0 4 7) triad, this “tendency tone” potential naturally available to each of the (0 4 7) triads at 0, 3, 6, and 9, Model A.19 In other words, I quite often find it advantageous to regard (or hear) cases of “major-minor third” emphasis—or of the (0 3 4/3 4 7/3 6 7) “clash”, perhaps the most persistently pursued of all “impurities”, certainly the most frequently cited—as octatonically inspired, as a species of octatonic-diatonic interpenetration, so that, apropos the C-scale on D reference at Nos. 112—118 in the second movement of the Symphony in Three Movements, pitch numbers 3 and 6, the F and G♯, may serve conventionally as “leading tones” to 4 and 7 of the (0 4 7) triad on D, but also as intruding “impurities” in the G-scale setting where the (0 3 4) “clash” signals the elevation of these pitch classes—and particularly of F—from “dependency tones” to independent pitch elements on a par with their neighbors warranting accountability at the collectional level, an accreditation which the C-scale cannot properly confer. And so I would interpret in terms of an interpenetration between the C-scale on D and Collection II, where 0 = D, noting: 1) that D assumes “overall” priority, and serves, with its (0 4 7) triad, as the principal connecting link (that which is shared), and 2) that a duality is manifested in the functional behavior of pitch numbers 3 and 6, but that, respecting the octatonic (Collection II) contribution, the F and G♯, while asserting independence, do not really act as symmetrically defined partitioning elements of priority with a degree of “equal weight and independence” vis à vis the D in the sense demonstrated in Model A, there being no (0 3 7/0 4 7) articulative “support” at F or G♯ to implement this potential, a circumstance which naturally undermines the “identity” of the contribution, placing Collection II 19Berger’s

interpretation of pitch number 6 as a (possible) Classical “tendency tone” in the 2, 1 interval ordering of the scale (Model B) seems grossly abstract (or completely irrelevant) with respect to (0 2 3 5) tetrachordal partitioning in Stravinsky’s music, there being, to my knowledge, no instances of such partitioning where this pitch number 6, reading “up” or “down”, is not readily identified with the (6 8 9 11) tetrachordal articulative unit, standing thus in a (0, 6) symmetrically defined (“fixed” or polarized) “opposition” to pitch number 0 or the (0 2 3 5) tetrachord.

Some Characteristics of Stravinsky’s Diatonic Music

at a rather severe disadvantage vis à vis its diatonic counterpart, the C-scale on D. And, among countless similar examples, the introductory passage from the “Basel” Concerto in D (1946) seems exemplary in these respects, the total pitch content inferrable at Nos. 0–5, D, F, F♯, A, B, as octatonic (Collection II) as it is diatonic (C-scale on D)—as diatonic, of course, only by virtue of the “leading tone” interpretation of F, pitch number 3. For, here again, the “point” of the passage would seem to rest in the dual nature of E♯/F, pitch number 3—or in the dual nature of the (0 3 4/3 4 7) “major-minor third” complex—the E♯/F occasionally articulated as a “leading tone” to the F♯, pitch number 4 of the (0 4 7) triad on D, and occasionally as an intruding “impurity” by virtue of the (3 4 7) simultaneities and the (0 3 4/3 4 7) figuration, all of this, incidentally, pursued without the slightest trace of tonally functional behavior. And so, in addition to tonal functionality à la Psalms, the (0 3 4/3 4 7/3 6 7) “major-minor third” phenomenon strikes me as just another way in which octatonic partitioning (Model A) and traditional C-scale conventions or inflections interrelate, so that, were we to investigate from a diatonic perspective, we could credit the interpenetrating octatonic collection for systematically “subverting” the C-scale with (0 3 4/3 4 7/3 6 7) “impurity”; or, from an octatonic perspective, acknowledge the manner in which Model A partitioning is modified by a “neo-Classical” concern for C-scale conventions and “tendency tone” inflections. And, of course, the attraction of this perspective is that it allows for a hearing, understanding, or definition of certain “neo-Classical” phenomena in terms of a lifelong preoccupation with octatonic partitioning, a consistency, identity or distinctiveness in pitch organization transcending the considerable changes in “stylistic” orientation from Firebird (1910) to Agon (1957). And by extending accountability to these phenomena, the “literature” perspective afforded allows, at the same time, for a more penetrating account of peculiarity in the exhibition of these phenomena from one piece to the next. But to return to the “Russian” era: the “neo-Classical” (Model A) bias underlying Berger’s conclusions may have been prompted by a commitment to the familiar ascending approach in scale representation and pitch numbering. Thus, at Nos. 35–40 and

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82–87 in Les Noces (explicit reference: List No. 1), Berger infers (0, 6) “background” partitioning in terms of A and E♭; and, given the pitch content (Collection III), this approach naturally yields the 1, 2 interval ordering for the scale at A or E♭: A-B♭-C-D♭-E♭-E-F♯-G-(A). But the problem with this determination (and the pitch numbering it implies) is that it obscures the essential (0 2) reiterations and the (0 2 5) “basic cell” articulated by way of A-G/E♭-D♭ and A-G-E/E♭-D♭-B♭ (reading down, with the uppermost pitch generally “presiding” as the more insistent), these (0 2) and (0 2 5) groupings very nearly “continuously operative” in Les Noces with respect to both diatonic and octatonic activity. And the only means of recording (0, 6) tritone partitioning in terms of A and E♭ and this “global” articulation (at A and E♭) here) would be via a descending formulation which would, far more conveniently than the ascending form, expose the priorities, associative factors, connecting links or “threads” discernible “above” the “blocks” of varied referential implications: A-G-F♯-E-E♭-D♭-C-B♭(A), reading down (or, from E♭, also reading down). So questions regarding the “identity” of the collection or the “uniqueness of the relations Stravinsky employed” are not as clear-cut or as easily defined as Berger would have us believe. But we have, it seems to me, in this roundabout fashion, come to some understanding as to what to expect from an examination of Stravinsky’s diatonic (or octatonic) writing particularly as it relates to the “Russian” category: juxtaposed “blocks”, at times referentially octatonic, at times diatonic, and at times exhibiting an interpenetration between these references. Moreover, juxtaposition itself affords an invaluable clue as to analytical method. For, confronted with the kind of “discontinuity” it imposes—confronted with the “sudden breaks” which, in Edward Cone’s words, “affect every musical dimension”—why burden ourselves with analytictheoretical schemes of “continuity” or “coherence” which, if not entirely inapplicable, cannot be the most advantageous (the most compelling or instructive) since they ignore this most telling and conspicuous feature?20 Why not accept abrupt “block” juxtaposition and the referential implications, and proceed accordingly? These questions (or propositions) underlie the particular analytic-theoretical approach of this inquiry. 20“Stravinsky:

The Progress of a Method”, PNM, Vol. 1, No. 1, p. 18.

Some Characteristics of Stravinsky’s Diatonic Music

II Attention will now be drawn to the diatonic hexachordal segment with a pitch numbering of 0 2 3 5 7 9 (0) reading down (interval order: 2, 1, 2, 2, 2, (3)), and the D-scale with a pitch numbering of 0 2 3 5 7 9 10 (0) also reading down (interval order: 2, 1, 2, 2, 2, 1, (2)).21 And while these references—or the partitioning manifested on their behalf—may occasionally be apprehended in material of the “neo-Classical” persuasion, like (0 2 3 5) partitioning of the octatonic collection and the 2, 1 interval ordering of the scale implicated (Model B), I tend to associate them with the “Russian” period generally, an association which I attribute in part to Stravinsky’s addiction at the time to all manner of (0 2 3 5) folkish fragments (some genuine, most ingeniously pseudo), again, Berger’s conclusions notwithstanding. Indeed, were the “Russian” label to wield a legitimacy transcending the preoccupation with these (0 2 3 5) fragments (and with Russian popular verse), this legitimacy would have to reside, it seems to me, 21Apropos

the (0 2 3 5 7 9) diatonic hexachord, see Benjamin Boretz’s analysis of Petroushka, first tableau, in “Meta-Variations, Part IV: Analytic Fallout (II)”, PNM, Vol. 9, No. 1. Boretz infers the (0 2 3 5 7 9) hexachord in terms of the (E-D-C♯-B-A-G) collection at No. 1, and discusses Petroushka’s diatonicism independent of tonal considerations. But some non-correspondences with the present analysis are noteworthy. While Boretz, as here above, equates abrupt “block” juxtaposition with “pitch-collection change”, he interprets the juxtaposed “blocks” as “time spans”; and his reference to the symmetry that obtains from the pattern or patterns of these “spans” is a facet of abrupt “block” juxtaposition not here taken into account. More significantly, Boretz’s “referential” diatonic hexachord is the (D-E) (A-G) (B♭-C) collection first introduced at No. 2(—2), from which he subsequently at m. 27 derives an “extension” in the form of a “superimposition of two hexachords inversionally related . . . producing the ‘diatonic collection’ as their union”, with respect to which he interprets succeeding “blocks” or “time spans”; however, in the present study, the (0 2 3 5 7 9) hexachord is the “referential” diatonic hexachord, with respect to which succeeding “blocks” are interpreted. Moreover, Boretz does not subscribe to any “local” assertion of pitchclass priority (the “inversionally related” hexachords merely produce the diatonic collection “as their union”), while the present study’s D-scale on G determination at Nos. 3–6 obviously does. Thus, a certain significance is here attached to the (0 2 3 5 7 9) hexachord, the nature of its “incompleteness”, the nature of its affiliation with the D-scale, the pairs of (0 2)’s which encircle it, and (0 7)-defined adjacency or “overlapping”, concerns which relate ultimately to the interaction, intervention, or “intrusion” of referentially octatonic material, a matter alluded to only briefly in Boretz’s discussion. And these special (0 2 3 5 7 9) hexachordal considerations may have been prompted by a Stravinsky-”Russian”-period hearing and understanding, a hearing and understanding of consistency, identity, and distinctiveness for this particular body of works.

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in this to-be-examined partitioning and in the regularities governing octatonic-diatonic interaction, some of this between-reference (or between-”block”) connecting link regularity perhaps already vaguely discernible in the pitch numbering. Moreover, while the integrity of the (0 2 3 5 7 9) hexachord will naturally hinge on the absence (or peripheral behavior) of a 7th pitch element—a closing of the gap, so to speak, with pitch number 10 (reading down) completing the diatonic collection—it harbors a partitioning strategy that will often ensure it a measure of referential cohesiveness even where such an element does insinuate itself. Indeed, a circumstance tending to underscore (0 2 3 5 7 9) integrity is the flexibility often reserved for 7th pitch-class identity, so that, of the two pitch elements that might “close the gap”, the “intrusion” of a pitch number 10 (reading down) would render (0 2 3 5 7 9) surroundings fully diatonic—tending to implicate the D-scale, but with the hexachord’s partitioning formulae often intact—and the “intrusion” of a pitch number 11 (reading down), (0 2 3 5 6 8 9 11) octatonic-(0 2 3 7 9) diatonic, a species of octatonic-diatonic interpenetration. And this flexibility, in turn, allows many (0 2 3 5 7 9) contexts to act as “go-betweens” with respect to (more) fully committed diatonic, octatonic, or octatonicdiatonic frameworks, with the elusive 7th pitch element acting as a kind of pivot. (Only pitch number 7 resists the (0 2 3 5 6 8 9 11) octatonic order, Model B, and only the omission of a pitch number 10, the diatonic collection. And the 7th pitch may intrude pivot-like “elsewhere”, of course, although the (0 2 3 5 7 9) “gap” seems most vulnerable in this respect.) Very well. We begin with a passage where the credentials for (0 2 3 5 7 9) inference seem impeccable: the opening passage or “block” of Petroushka at Nos. 0–2 (–2) and its abbreviation at No. 2 + 3 (see Ex. 1). For here, the omission of a 7th pitch element—indeed, the adverse consequences that accrue from any forced “closing of the gap” with an F or F♯—testify to (0 2 3 5 7 9) integrity in terms of the (E-D-C♯-B-A-G) collection, foreclosing any referral of this “block” to the A-scale on D, or to the “Key of D-minor” (in the sense, perhaps, of an “ascending minor scale” at No. 1, or a “descending minor scale” at No. 2), there being, in addition to this very critical absence of a—in my estimation—truly unthinkable F, no tonally functional transactions. (F as the “missing” 7th pitch element—pitch number 11 with respect to the (0 2 3 5 7 9) numbering at Nos. 0–2 (–2)—does

Some Characteristics of Stravinsky’s Diatonic Music

Example 1

not appear until No. 3; and here the (0 2) and (0 2 3 5) articulation, in terms of C-B♭-A-G, accentuates G rather than D (or A), circumstances which implicate the D-scale on G rather than the A-scale on D, and which thus provide the opening (2 0) and (7 9) reiterations, D-E and A-G, with a new referential framework and consequent pitch numbering.) Indeed, of the two pitch elements that might “close the gap” at Nos. 0–2 (–2) and 2 + 3, F♯ seems by far the more “thinkable”; but try imposing either one, the F or the F♯, into these (E-D-C♯-BA-G) surroundings, and the effect is manifestly ruinous. And so, straight away, we perceive in this critical withholding of a 7th pitch element the “open” quality Stravinsky means to impart with respect to any potential leanings toward a (more) fully accredited diatonic,

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Some Characteristics of Stravinsky’s Diatonic Music

octatonic, or octatonic-diatonic framework, it being left for future “blocks” to implement this potential, to decide the (0 2 3 5 7 9) hexachord’s fate, and very often by way of an “intruding” outside 7th pitch element. Of course, F does appear on the first beats of subsequent (near) repeats of the No. 0 “block”: at Nos. 8 + 4 and 11 + 5 (see Ex. 1), and in the instrumental “fill” accompanying the final (near) repeat at No. 27. And, indeed, it is my understanding that this imposition does alter the referential implications. For not only does F (or the (0 3 7) triad on D) intervene, but the (0 2 3 5) tetrachord in terms of E-D-C♯-B (articulated by the cello at Nos. 1 and 2 + 5) is omitted. Moreover, in these subsequent (near) repeats, the F (or the (0 4 7) triad on D) may clearly be apprehended as a continuation of the material of the No. 8 “block”, material which invariably precedes these No. 0 “block” (near) repeats, and from which a (0 3 7/0 4 7) triadic partitioning of the (D-C-B-A-G-F) collection may be inferred with respect to (0 2 3 5 7 9) hexachord reference. Consequently, respecting these subsequent No. 0 “blocks” (near) repeats, I would interpret referentially in terms of the (D-C-B-A-G-F) collection or the A-scale on D. But before coming to any conclusions regarding (0 2 3 5 7 9) activity in the first tableau (conclusions which would view the (0 2 3 5 7 9) hexachord as a referential “norm” or “home base” from which subsequent “blocks” diverge, often, as we have indicated, by way of a 7th pitch “intrusion”), we might retreat to a somewhat more long-range, “global”, or “continuously operative” perspective. For I have found it useful in this respect to interpret Petroushka as a piece wherein two simultaneities move “back-and-forth” (accordianlike, as so many have observed, a feature by no means limited to Petroushka, but one which may seem unusually conspicuous); and from here to determine that the two simultaneities which move “back-and-forth” very often jointly number six pitch elements, three to each simultaneity. (Thus, respecting this “global” number-ofelements approach, our (0 2 3 5 7 9) hexachord of the first tableau appears as just one of several hexachordal collections or orderings.) And from here to suggest that, either “on top” or “on the bottom” (or both), the simultaneities are often related by the interval of 2. And, respecting successive “block” (pitch-identity) content realizations of these simultaneities, to conclude that of the three (0 2) reiterations

Some Characteristics of Stravinsky’s Diatonic Music

(A-G, D-E, B(j-C) which define the two oscillating simultaneities (A/D/B♭)-(G/E/C), reading down, at Nos. 2, 3 and subsequent (near) repeats of these “blocks”, at least one of these (content-defined) (0 2) dyads survives “globally” (on a more-or-less “continuously operative” basis), especially respecting material of the first, second, and fourth tableaux. Still, apropos the “global” attitude, I prefer to leave inferences regarding (content-defined) dyadic “survival” to the reader, finding it sufficient for our purposes merely to record, from one “block” to the next, the two simultaneities which move “back-and-forth”. Thus, at Nos. 0–2(–2) and 2 + 3, these simultaneities are (A/D)-(G/E), numbering four elements, not six; and, beneath this stipulation, a different kind of partitioning is recorded in recognition of the (2 0) and (7 9) reiterations, D-E and A-G, and the (0 2 3 5) tetrachord, E-D-C♯-B, these articulative groupings jointly yielding the (E-D-C♯-BA-G) hexachordal collection with the pitch numbering of (02 3 5 79). (I prefer, as well, to leave inferences regarding “local” (or sectional) assertions of pitch-class and/or dyad priority to the commentary, reserving for analytical representation the articulative partitioning and the consequent referential implications, this latter constituting the focus of our concern even though “local” definitions of priority are critical to our deliberations and may sometimes be inferred from the assigned scale representations and pitch numberings. Sometimes, because E is scarcely the most likely candidate for pitchclass priority status as pitch number 0 at Nos. 0–2 (–2) and 2 + 3; D is, owing primarily to metric accentuation. However, the two pitch classes which encircle the (0 2 3 5 7 9) hexachord on each side (four in all: the D-E, A-G (2 0) and (7 9) reiterations at Nos. 0–2(–2) and 2 + 3) will soon be found, from one piece to the next, to exercise a uniquely (0 2 3 5 7 9) conceived life of their own respecting pitchclass priority, an exercise often foreclosing rulings as to (single) pitch-class priority even on a purely “local” basis.) Then, at No. 2, the oscillating simultaneities number six elements. And a B♭-C reiteration is here added to the D-E and A-G reiterations (which serve as between-”block” connecting links), this B♭-C unit inserted in place of the C♯-B dyad of the opening E-D-C♯-B (0 2 3 5) tetrachord. And these three (0 2) reiterations, together with the (0 2 3 5) tetrachord now articulated in terms of C-B♭-A-G (with G accentuated rather than D) yield the (E-D-C-B♭-

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A-G) collection, a retrograde inversion of the opening hexachordal ordering, so that the reference collection is altered with respect to total pitch-class content and referential ordering. Then, at No. 3, following an abbreviation of the Nos. 0–2 (–2) opening “block” at No. 2 + 3 (not shown), F, withheld up to this point as the “missing” 7th pitch element—pitch number 11 with respect to the two preceding referential orderings—is introduced in an extension of the C-B♭A-G (0 2 3 5) tetrachordal fragment of the No. 2 “block”. And this imposition completes the diatonic collection, the (0 2) and (0 2 3 5) articulation accentuating G and implicating the D-scale on G with respect to referential ordering. And I would extend this determination as to reference to the following “block” at No. 5 as well, the borrowed folk melody bursting forth here as a final destination, with respect to which the preceding “blocks” assume, retroactively, a preparatorylike character. Still, we might consider the tonal alternative to our interpretation of No. 5 in Ex. 1. For an observer could claim that the G is as readily identified with the (0 4 7) triad on C as it is with the (0 3 7) triad on G, and that this identification suggests a “harmonization” of the borrowed melody “in the key of F-major” (with “added notes”) : VI-IV-V-VI-IV(II)-V. And, indeed, I find myself by no means unsympathetic to such a reading (or hearing): the (A/D/B♭)-(G/E/C) simultaneities reinterpreted at No. 5 in terms of a “half-cadence” or IV(II)-V progression “in F”. The only problem, of course, is that the dominant-tonic resolution (the tonal “imperative”, as Berger calls it), the “tonic” (0 4 7) triad on F which must in some sense underlie such a perspective (be at least conceivable at some point, if not actualized), is not only scrupulously avoided but seems about as inconceivable (as unlikely or as undesirable) in these surroundings as was the “missing” 7th pitch element, the F, in the opening (0 2 3 5 7 9) preparatory “blocks”. And so the tonal reading seems predicated on an entirely “local” (No. 5 “block”) reckoning of affairs. But further. Were we to abstract from the “harmonization” at No. 5 the three (0 3 7/0 4 7) triads which are the foundation of the display, we might discover in the referential implications probable cause of the inconceivable (or undesirable) “tonic” (0 4 7) triad on F: the—in my estimation—predominating (0 3 7) triad on G and the oscillating (0 4 7) triads on B♭ and C “underneath” refer to the (G-F-E-D-C-B♭) collection with respect to (0 2 3 5 7 9) hexachordal

Some Characteristics of Stravinsky’s Diatonic Music

reference, and thus provide the setting with a similar (0 2 3 5 7 9) conceived “harmonic stasis” (the (0 2 3 5 7 9) incapacity for real “harmonic progression” beyond the accordion effect) as was realized in the opening passages or “blocks”. In other words, from within the (completed) diatonic collection at No. 5 where the articulation implicates the D-scale on G, we may infer a “foundational” (0 3 7/0 4 7) triadic articulative partitioning accountable to the (0 2 3 5 7 9) hexachord where G may be identified with the (0 4 7) triad on C, with the (0 3 7) triad on G, or may be inferred as “centric” with respect to the compound simultaneity, in which case the concept of “added notes” need not be invoked. (Notice, too, the (7 3 0/7 4 0) “second inversion” of the triads at No. 5 + 4, a circumstance which naturally reinforces G as the pitch class of priority.) This inferrable (0 3 7/0 4 7) partitioning of the (0 2 3 5 7 9) hexachord at No. 5 is of consequence since it may again be inferred—unimpaired—at No. 8 (and at subsequent (near) repeats of this “block”) in terms of the (D-C-B-A-G-F) collection. Thus, the “breaking-up” passage at No. 7 (see Ex. 3, below) is interpreted in terms of the (A-G-F♯-E-D-C) collection where B♭— not F—serves as the “intruding” outside 7th pitch element as pitch number 11. (I infer C from the (0 4 7) triad on C which directly precedes the “breaking-up” at No. 7, and from the E-D-G grace-note sequence; and, respecting B♭ as the outside 7th pitch element vis à vis the (A-G-F♯-E-D-C) collection, I shall presently discuss the octatonic implications of this pitch number 11 “intrusion” when turning to No. 35 in the Danse Russe.) Then, at No. 8, the oscillating simultaneities, a (0 3 7) triad on D and a (0 4 7) on G (a kind of “harmonization” of the opening flute interval) implicate the (D-C-B-A-G-F) collection; and at No. 11 this oscillation alternates with identical (0 3 7/0 4 7) relations expressed in terms of the (A-G-F♯-E-D-C) collection. And notice, at No. 11, that the overlapping of (0 2 3 5 7 9)’s produces a (0 3/0 4) “major-minor third” play in terms of F/F♯ with a quite different “feel” to it than the “neo-Classical” examples referred to earlier. And I attribute this difference in “feel” to the question of reference generally, noting that the (0 3 4) phenomenon at No. 11 results from this simple (0 7)-defined (0 2 3 5 7 9) overlapping (as it does conspicuously again in Scene I of Histoire), while in the “neoClassical” examples it derives from (or can best be interpreted in terms of) a species of octatonic-diatonic interpenetration, where the

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referential ordering of the diatonic collection is that of the C-scale which interpenetrates with the octatonic scale, 1, 2 interval ordering (Model A), the latter being credited as the source for the “impurity” via its “intruding” pitch numbers 3 and 6. And, naturally, this insight constitutes, to my mind, just one of the many useful distinctions that can be drawn respecting (“locally” defined) identical phenomena (or “habits”) inferrable from material of the “Russian” and “neoClassical” categories, a distinction which relates to the question of reference, or, more readily, to the partitioning formulated on its behalf. More critical to our deliberations, however, is the clue this No. 11 (0 2 3 5 7 9) overlapping affords as to overall (0 2 3 5 7 9) planning in the first tableau. For we may now assemble the four content-distinguishable (0 2 3 5 7 9) collections inferrable from this section, and, owing to their (0 7)-defined or “circle-of-fifths” adjacency, arrange these according to the chain, sequence or “spread” of overlapping (0 2 3 5 7 9)’s suggested by No. 11 (see Ex. 2). And, apropos this compression of (0 2 3 5 7 9) strategy, we can begin to confront in the consequent exemplification (Exx. 2–4b) what I consider to be the three key issues regarding (0 2 3 5 7 9) activity in the “Russian” period generally: 1) the (0 2) (7 9), (0 2 3 5) (7 9 0), and (0 3 7/0 4 7) partitionings inferrable on behalf of the single (0 2 3 5 7 9) collection, Ex. 2a; 2) the “uniquely (0 2 3 5 7 9) conceived” exercise in pitch-class priority, where the pairs of (0 2)’s which encircle the hexachord—each of these pairs defining the point of overlap respecting (0 7) or “circle-of-fifths” adjacency— constitute (or may be constituted as) a series of (0 7)’s or “fifths”, an abstraction which allows additional insight into the question of “harmonic stasis” or the “coming together” (by “superimposition”) of elements formerly interpretable in terms of a subdominant-tonicdominant relation (but available, formerly, only in succession),22 and thus further insight into the seeming irrelevance of (single) pitchclass priority rulings in many (0 2 3 5 7 9) contexts, but an abstraction which does not deny the encircling (0 2) and (7 9) units a certain articulative cohesiveness in many of these contexts, a cohesiveness 22Thus,

Boulez’s interpretation of “polarity” in terms of a subdominant-tonicdominant relation in Le Sacre may not be entirely unwarranted, at least insofar as the brief and scattered passages of unimpaired diatonicism (generally D-scale or (0 2 3 5 7 9) hexachordal) are concerned.

Some Characteristics of Stravinsky’s Diatonic Music

evidenced already by the (2 0) and (7 9) reiterations, D-E and A-G, which enclose the (E-D-C♯-B-A-G) collection at Nos. 0–2(–2), Ex. 2b; 3) the regularities governing octatonic-diatonic interaction or interpenetration with respect to (0 2) or (0 2 3 5) partitioning of the octatonic scale, 2, 1 interval ordering (Model B), and the (0 2 3 5 7 9) hexachord. And while I shall defer momentarily the question of pitch-class priority, Nos. 7 and 35 in the first tableau do afford an opportunity to examine octatonic-diatonic interaction where the above discussed outside 7th pitch element—B♭ as pitch number 11 respecting the (A-G-F♯-E-D-C) collection and ordering inferrable at Nos. 7 and 35—signals, pivot-like in place of pitch number 10, a “leaning” toward octatonic-diatonic interpenetration (the B♭ is not accounted for in terms of diatonic collection), this pitch number 11 “intrusion” therefore constituting a first “regularity” in octatonicdiatonic interaction with the between-reference connecting link discernible in terms of the (0 2 3 5) tetrachord, A-G-F♯-E here.

Example 2

2a

Example 2a

2b

Example 2b

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Example 3

For, respecting these “blocks” at Nos. 7 and 35 and the inferred (0 2 3 5 6 8 9 11) octatonic- (0 2 3 5 7 9) diatonic interpenetration (see Ex. 3), I find it instructive to consider how very close we are here to the illustrious “Petroushka chord” at Nos. 49 and 51 of the second tableau, a compound simultaneity containing (0, 6) tritonerelated (0 4 7)’s on G and F♯ (six elements in all, accountable to Collection III) where the (0 4 7) triad on F♯ is (4 7 0) “first inversion”, preserving the B♭-C reiteration of the first tableau.23 (After all, to follow Stravinsky’s own account, Petroushka was initially conceived with this referentially octatonic, second tableau, material.) For only the D of the (A-G-F♯-E-D-C) collection at Nos. 7 and 35, pitch number 7, resists the interpenetrating octatonic Collection III (however critical this D is to (0 2 3 5 7 9) identity, it constituting, 23How

close we are, indeed, to the “sound” of Le Sacre, where the static “vertical chromaticism” becomes interpretable in terms of an octatonically conceived (0–5, 11) “global” partitioning unit, with an “upper” (0 2 3 5) tetrachord standing “in opposition” to a “lower” pitch number 11. Still, the B♭ and the E-D-C grace-note sequence at No. 7 could be interpreted, alternatively, in terms of a continuation of the (G-F-E-D-C-B♭) hexachord, in terms of a superimposition of the predominating (A-G-F♯-E-D-C) hexachord over this (G-F-E-D-C-B♭) collection, and thus in terms of (0 7)-defined (0 2 3 5 7 9) adjacency “once removed” (see Ex. 2). And, indeed, a similar alternative in hearing and understanding presents itself on behalf of the “low” A♭ in the very opening ostinato pattern of Renard. But while I can—at least partially— subscribe to this alternative, the octatonic implications of pitch number 11—or the A-G-F♯-E-C-B♭ span—are, at No. 7, in my estimation unmistakable, in view not only of the (pending) “Petroushka chord”, but of the exemplification or realization of these implications in Stravinsky’s subsequent “Russian” works.

Some Characteristics of Stravinsky’s Diatonic Music

with the C, one of the pairs of (0 2)’s which enclose the (A-G-F♯-ED-C) collection); and with the referentially octatonic (Collection III) B♭ (A♯ in the “Petroushka chord”), only C♯ is missing. (So we have, then, in this Collection III-(A-G-F♯-E-D-C) interpenetration at Nos. 7 and 35, at least a hint of coming attractions.) And, below, in Ex. 4a, I have merely “summarized” this first—and in my estimation typically “Russian”—”regularity” in moving from a diatonic to an octatonic or octatonic-diatonic context: the referentially octatonic pitch number 11 respecting the interpenetrating (0 2 3 5 7 9) diatonic and (0 2 3 5 6 8 9 11) octatonic orders, “intrudes”, while the between-reference connecting link (that which is shared) is realized in terms of the “upper” (0 2 3 5) tetrachord, A-G-F♯-E here. But note, in Ex. 4a, that the (7 9) or (7 9 0) unit of the (0 2 3 5 7 9) hexachord (or the “lower” (7 9 10 0) tetrachord of the (completed) D-scale) may serve as the connecting link to still another octatonic collection (Collection II here) ; and in this second possibility, pitch number 6 (the E♭ here) often becomes the “intruding” 7th pitch element. (Still, in restructuring the octatonic scale accordingly, this number 6 merely becomes another pitch number 11; and, apart from the interval of 11, what is immediately striking in these referentially octatonic pitch number 11 “intrusions” is the (0 6) tritone relation defined by pitch numbers 5 and 11—with a pitch number 11 “intrusion”—and by pitch numbers 0 and 6—with a pitch number 6 “intrusion”. Furthermore, note in Ex. 4a that a pitch number 6 “intrusion” may implicate Collection III as well as II.) Accordingly, respecting any given (0 2 3 5) (7 9(10)0) partitioning of the (0 2 3 5 7 9) hexachord or D-scale, two of the three contentdistinguishable octatonic collections ((0 2 3 5) partitioning, Model B) may be implicated in octatonic-diatonic interaction. And, were we to reverse this procedure by commencing with an octatonic framework (see Ex. 4b), any given octatonic collection may implicate, via its four content-distinguishable (0 2 3 5)’s, four content-distinguishable (0 2 3 5 7 9)’s or D-scales in interacting proceedings. (I note this “reversal” in anticipation of Le Sacre.)

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Example 4a

Example 4b

Still, the tonally inclined observer could interpret the B♭ at Nos. 7 and 35 as the “flatted sixth degree” respecting the predominating (0 4 7) triad on D (presumably implicating the G-scale on D), an interpretation perhaps particularly apropos at No. 35 where conventional “voice-leading” may be inferred on behalf of B♭. And, again, I find myself not unsympathetic to such a reading. For were we to turn to the Finale of The Firebird (1919 concert suite), we would find that a “harmonization” of the folk melody at No. 17 is similarly accountable to the (0 2 3 5 7 9) hexachord (the (F%-E-D♯C♯-B-A) collection), implicated by a “foundational” alternation of (0 4 7) triads on B and A (see Ex. 5). And, indeed, preceding this “block” at No. 17, a similar flexibility manifests itself with respect to 7th pitch class identity, the “closing of the (F♯-E-D♯-C♯-B-A) gap” with a G♯ or G; and, G, as pitch number 11, does “behave” in a more or less conventional “flatted sixth degree” fashion, a “resolution” to the F♯ of the (0 4 7) triad on B quite unmistakable over the bar line at No. 14. But tonally conceived “voice-leading” of this sort seems irrelevant at No. 7 in Petroushka; the “low” B♭ stands, rather, in an “unresolved”, “fixed”, or polarized “opposition” to the “upper” A-GF♯-E tetrachord or (0 4 7) triad on D, a “deadlocked” situation. And I therefore find it fitting to interpret Nos. 7 and 35 in terms of a (0 2 3 5 6 8 9 11)-(0 2 3 5 7 9) interpenetration, not only because B♭—apropos tonal conventions—“behaves” unconventionally (and cannot, without reference to such conventions, be accounted for in terms of the inferred diatonic collection), but because its “behavior” is suitably accounted for in terms of the symmetrically defined (0 2 3 5)(6 8 9 11) partitioning of Collection III (Model B), a partitioning that anticipates, to some extent, the (more) fully committed (Collection III) octatonic framework of the “Petroushka chord” in the second tableau.*

Some Characteristics of Stravinsky’s Diatonic Music

Example 5

Now in Le Sacre the situation is reversed. Instead of a pervading diatonicism, a pervading “vertical chromaticism” is likely to attract our attention, with respect to which we might view the patches of unimpaired diatonicism as subsidiary and as diverging. Yet, “above” the “blocks” or sections of varying referential implications, the (0 2 3 5) tetrachord—complete or (0 2 5/0 3 5) incomplete—may still be apprehended as the principal articulative between-reference (or between-”block”) connecting link. And, respecting the “global” approach generally, I find: (1) that this static-oriented “vertical chromaticism” is defined with remarkable consistency in terms of a 0–11 “inter-fragmental” interval span, “inter-fragmental” in the sense that, rather than being “melodic” or fragmental, it is habitually “harmonic” in defining the vertical span between pitches of unmistakable priority among principal “superimposed” (or registrally “fixed”) articulative fragments);24 (2) that this 0–11 interval span, or (0, 11) partitioning, is persistently octatonic (or octatonically conceived, “hooking up” to Model B) in the sense that, reading down, it very often contains (or is articulated by means 24Thus,

unlike Petroushka, pitch number 11 respecting the (0 2 3 5) (6 8 9 11) tetrachordal numbering (reading down) is with us, octatonically (Model B), from the very beginning, and inferrable on a more or less “global” or “continuously operative” basis. And my reasons for citing the 0–11 interval span—or (0, 11) partitioning—as “globally” more “basic” or “fundamental” than, say, the (0 6) tritone relation defined by pitch numbers 5 and 11 in the (0–5, 11) format, are owing primarily to the metric accentuation invariably accorded this 0–11 span or (0, 11) partitioning unit, an accentuation which, apart from its persistence, renders the span or unit highly conspicuous from one “block” or section to the next.

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of) an “upper” (0 2 3 5) tetrachordal fragment—again, complete or incomplete—which stands “in a certain (“fixed” or polarized) opposition” to a “lower” pitch number 11, the “lower” of Model B’s (0, 6) tritone-related (0 2 3 5) (6 8 9 11) tetrachords, (6 8 9 11), less frequently in evidence: in the Introduction at No. 6 (and subsequent repeats), see the “upper” B♭-G-F (0 3 5) incomplete (0 2 3 5) tetrachord “in opposition” to the “lower” B; in the Danses des adolescentes at No. 13, the “upper” E♭-D♭-B♭ (0 2 5) incomplete (0 2 3 5) tetrachord “in opposition” to the “lower” E; in the Jeux des cités rivales at No. 64, the “upper” G-F-E-D complete (0 2 3 5) tetrachord “in opposition” to the “lower” G♯; in the Action rituelle des ancêtres at No. 131 (Part II), the “upper” C♯-B-A♯-G♯ complete (0 2 3 5) tetrachord “in opposition” to the “lower” D; and these are only a few of the more conspicuous examples of this “global” (0–5, 11) partitioning; (3) that the diatonic side to octatonic-diatonic interaction is most often accounted for in terms of the D-scale or the (0 2 3 5 7 9) hexachord, where, as indicated by Exx. 3–4b (see Exx. 1–5 and List No. 1 in Part 1), a shared (0 2 3 5) tetrachord serves as the principal articulative between-reference connecting link. So I consider Le Sacre primarily octatonic (inferred singly or with reference to some form of octatonic-diatonic interpenetration: cf. Lists 1 and 2), “globally” approachable with this (0–5, 11) partitioning unit in mind, a partitioning (0 2 3 5)-tetrachordal in conception—articulated by means of Model B’s (0, 6) tritonerelated (0 2 3 5) (6 8 9 11) tetrachords with a generally greater emphasis placed on the “upper” of the two—but which, owing to the frequently articulated (0 2 5) incompleteness of the tetrachords, lends itself to (0 4 7 10) “dominant seventh” articulation as well. And the “dissonance”, “vertical chromaticism”, or “primitivism” associated with Le Sacre thus becomes an octatonically conceived “dissonance”, “vertical chromaticism”, or “primitivism”, qualified at points by diatonic penetration often in the form of the D-scale or the (0 2 3 5 7 9) hexachordal segment. And while the first of the Three Pieces for String Quartet, Renard, Les Noces, and L’Histoire du Soldat continue to exhibit a preoccupation with (0 2 3 5) partitioning and the 2, 1 interval ordering of the scale implicated (Model B), never, in these ensuing works, does this preoccupation manifest itself with such persistence. And so, finally, whatever else Le Sacre may be presumed to represent, it can—in my estimation—unquestionably

Some Characteristics of Stravinsky’s Diatonic Music

be regarded as the most extensive and varied account of Model B partitioning in the literature, perhaps in any literature. MODEL A

Collection I:

Collection II:

Collection III:

pitch numbers: intervals:

i

E F

F♯ 0

ii f

f♯ g

1

iii G

A♭ A 3

iv

v

vi

C

d♭

a♭

B♭

4

6

a

b♭

B

vii

viii

E♭

e

b

D♭

7

9

c

D

d

e♭

10

(i)

(E) (F)

(F♯)

1 2 1 2 1 2 1 (2)

(1)

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Some Characteristics of Stravinsky’s Diatonic Music

MODEL B

Collection I:

Collection II:

Collection III:

pitch numbers: intervals:

i

E F

F♯ 0

ii

d

e♭ e

2

iii

iv

E♭

d♭

C♯ D 3

v

b

B♭

5

6

c

B C

vi

vii

b♭

A

a♭ a

8

G

G♯ 9

viii f

f♯ g

11

(i)

(E) (F)

(F♯)

2 1 2 1 2 1 2 (1)

(1)

Of course, space scarcely permits a detailed “block”-by-”block” explanation of these conclusions. But there are a few passages in Part I which bear on our probing of Stravinsky’s diatonic writing (or

Some Characteristics of Stravinsky’s Diatonic Music

on his octatonic-diatonic writing), passages which will naturally also reflect this octatonically conceived (0–5, 11) “global” determinacy. And in the first of these, the Danses des adolescentes from the No. 13 “block” to Nos. 28–30 (see Ex. 6), I have recognized, first of all, the E♭-D♭-B♭ (0 2 5) incomplete (0 2 3 5) tetrachordal ostinato as the between-reference connecting link; second, the “global”— and octatonically conceived—(0–5, 11) partitioning as “locally” interpreted; and, third, the partitioning inferrable on an entirely “local” or “block” basis. And, naturally, the point here is that the passage very appropriately demonstrates the “reversal” of Le Sacre. For in contrast to the diatonic framework of Petroushka with respect to which, at Nos. 7 and 35, pitch number 11 could be viewed as an occasional referentially octatonic “intrusion”, the Danses des adolescentes is primarily octatonic to begin with (as is the preceding Introduction); and so the unimpaired diatonic D-scale on E♭ reference at Nos. 28–30 is reached via the gradual elimination of an already persistently present pitch number 11—the E here, referable to Collection III—and its substitution, anticipated already at No. 24, by pitch number 10, the F; reached, as well, by the substitution of the remaining (non-D-scale on E♭) octatonic elements, the A and G by A♭ and G♭. And I might briefly review these circumstances with the idea of shedding some additional light on the descending approach in scale representation and pitch numbering as it so very appropriately applies to Stravinsky’s (0 2 3 5)-tetrachordally oriented music, referentially octatonic or diatonic. For the question arises here in the Danses des adolescentes: how do we stand with respect to pitch-class and/or (0 2 3 5) priority? For once (0, 11) partitioning is acknowledged and its pitch numbers are assumed to encompass priority, it should be obvious that, insofar as “local” (“block” and/or sectional) content realization is concerned, should either of these pitch numbers assert priority over the other while conforming to the (0–5, 11) format over a significant period of time, the resultant (0, 3, 6, 9) symmetrically defined partitioning would be different in each case. This “problem” does not really arise in the Introduction, there being insufficient evidence, in my view, for a settlement in favor of either 0 or 11 both with respect to individual “blocks” (the B♭ or B at No. 6, for example) and with respect to the section as a whole. And so pitch number 0 is simply the “upper”

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Some Characteristics of Stravinsky’s Diatonic Music

Example 6

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Some Characteristics of Stravinsky’s Diatonic Music

pitch element in the (0–5, 11) partitioning or 0–11 interval span, the successive “blocks” of the Introduction realizing the potential for “equilibrium”, “opposition”, or “equal weight and independence” with respect to pitch numbers 0 and 11, priority extending no “further” than varying content realizations of the (0, 11) or (0–5, 11) partitioning units—or, with respect to the Introduction as a whole, no “further” than the relation asserted by this partitioning. (The same holds for Le Sacre as a whole, of course: “global” partitioning is assertible in terms of the (0, 11) or (0–5, 11) relation so that, in the “global” part of the analysis, pitch notation will merely represent varying local (“block”, sectional, or inter-sectional) content realizations of this relation.) But at Nos. 13–30 in the Danses, at Nos. 37 and 40 in the triadically oriented Jeu du rapt, and certainly in the first part of the Rondes printanières, there is little doubt that the uppermost pitch, pitch number 0, and, at Nos. 13–30, its (0 2 3 5) tetrachord, acquire a sectional and even inter-sectional advantage, one that should properly be taken into account. And beginning at No. 13, this pitch number 0 is E♭. For already at No. 16—and certainly at Nos. 28–30—its priority is assured, becoming less assertive in the jeu du rapt, but unmistakable again in the first part of the Rondes printanières. But were we now, in the Danses at No. 13, to recognize E♭ as pitch number 0 (and to recognize the extra “weight” of the “upper” E♭-D♭-B♭ incomplete tetrachord), the resultant interval ordering, given the pitch content (Collection III)—and given the customary ascending approach in scale formation and pitch numbering—would be the 1, 2 triadic form of Model A. And for the time being this “triadic ordering” is out of the question. (0 2 3 5) tetrachordal partitioning predominates until the Jeu du rapt, and is only obscured by resorting to Model A’s ascending 1, 2 interval ordering. So if we are to account for (0 2 3 5) tetrachordal partitioning via Model B, Collection III, and the gradual ascendancy of E♭ and the E♭-D♭-B♭ “upper” incomplete tetrachord in the Danses at Nos. 13–30, the only proper means of representation would be a descending 2, 1 scale beginning on E♭ at No. 13. And by descending from E♭, the symmetrically defined partitioning elements would be E♭, C, A, and F♯ (as stipulated by both Models A and B for Collection III)—not E, G, B♭, and D♭ when

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ascending from E—a most appropriate and telling representation by virtue of the following circumstances: (1) the unmistakable assertion of C as a “local” partitioning element in the reference collection (Collection III) by virtue of its consistent exclusion or isolation from the E♭-D♭-B♭ incomplete (0 2 3 5) tetrachordal ostinato at Nos. 12 + 4, 14, 16–18, and 22–28, and by virtue of the C-B♭-A-G tetrachord at Nos. 16–18, where C is obviously the “accented” partitioning element (not G), owing, among other things, to the sustained C’s in the oboes and bassoons; (2) without tetrachordal support (the A and F♯ being relatively inactive at Nos. 13–30), the reduction in intensity (except for the “block” at No. 13 and its successive repeats) of E as a potent “opposition” element to E♭ (the (0, 11) partitioning), or as a potent “opposition” element to the “upper” E♭-D♭-B♭ incomplete tetrachord (the (0–5, 11) partitioning), a weakening which coincides with the gradual assimilation of E into a (0 4 7) triad on C at Nos. 14, 16–18, and 23 (scrupulously (4 7 0) “first inversion”, however, with E metrically accented to sustain, however minimally, the (0, 11) articulation), a “low-key” accompaniment assimilation here, but prophetic in terms of the E♭, C (0 4 7 10) “dominant seventh” partitioning ultimately reached in the Jeu du rapt at No. 37; (3) the mostly (Model A) triadically octatonic Jeu du rapt at Nos. 37 and 39–43 will refer to Collection III (excepting one “block” at 40 + 6), where the symmetrically defined partitioning elements via Model A are, of course, E♭, C, A, and F♯, so that a descending 2, 1 scale beginning at No. 13 would allow the content connection between (0 2 3 5) tetrachordal partitioning in the Danses and (0 4 7 10) triadic partitioning in the Jeu du rapt to be defined with respect to the reference collection (Collection III) and the “accented” partitioning elements. Hence, beginning at No. 13, reconstruction (modeling) should exhibit a descending numbering and 2, 1 scale formation for purposes of identifying an E♭ pitch-class priority and (0 2 3 5) tetrachordal partitioning accountable to Collection III. And, needless to say, those passages or sections indifferent to these temporary Danses and Jeu du rapt expressions of priority (e.g., No. 6 in the Introduction) are not in the least misrepresented when we extend, for purposes of uniformity, this descending (0–5, 11)

Some Characteristics of Stravinsky’s Diatonic Music

“global” determination to the whole of Le Sacre.25 (In other words, the determination may at certain points reflect priority on the part of pitch number 0, but, more often than not, merely a “globally” persistent (0–5, 11) registral distribution or vertical interval span, with respect to which priority extends no “further” than varying “local” content realizations of the relation asserted by this grouping.) Accordingly, in the Jeu du rapt at No. 37 (see Ex. 7), we note, first, the return to Collection III and “local” (0, 3) partitioning in terms of E♭ and C (as inherited from the Danses); and, second, that “block” partitioning alters (or reinterprets) the articulative appearance of the (0–5, 11) “global” unit in terms of a thoroughly (0 4 7 10) “dominant seventh” orientation (Model A). Thus—as anticipated by the No. 13 “block”—the “upper” E♭-D♭-B♭ (0 2 5) incomplete (0 2 3 5) ostinato figure is articulated vertically as part of a (0 4 7 10) “dominant seventh” on E♭; and E’s earlier Danses affiliation with the (0 4 7) triad on C is fully confirmed, the (4 7 0) articulation now (0 4 7 (10)) “root position”. 25Note

that the symmetry which underlies (0 2 3 5) partitioning of the octatonic scale (Model B) and the D-scale extends to the (0 2 3 5) tetrachord itself, making the “switch” from the customary ascending approach to a descending approach in scale representation and pitch numbering (a “reading up” to a “reading down” situation) far less burdensome or problematic than might at first be expected. And while a certain awkwardness may be felt in adhering to a descending formula with Model B’s (0 2 3 5) partitioning and an ascending formula when referring to Model A’s (0 3 7/0 4 7/0 4 7 10) complexes (where the scale may still descend, however), the greater illumination the descending formula affords in exposing (0 2 3 5) partitioning and the essential connecting link relations vis-à-vis octatonic-diatonic interaction in Stravinsky’s “Russian” period material outweights—obviously, in my judgment—any awkwardness incurred by the discrepancy. And note, further, that by resorting to a descending formula with Model B’s (0 2 3 5) partitioning, the “accented” symmetrically defined partitioning elements, pitch numbers 0, 3, 6, and 9, are identical in Models A and B for each of the three content-distinguishable octatonic collections (e.g., the E♭, C, A, and F♯ partitioning elements for Collection III); and this identity—or “link” between Model A and Model B partitioning—is critical not only in the Danses and Jeu du rapt sections of Le Sacre, but in much of Stravinsky’s “Russian” material. And, yes, as Models A and B and the various “summaries” in the exemplification of these pages indicate, I do tend to associate Model B’s (0 2 3 5) partitioning with a more “melodic”, linear, fragmental, or contrapuntal attitude (or framework), and Model A’s (0 7/0 4 7/0 4 7 10) triadic complexes with a more “harmonic” or vertical perspective (at least insofar as the “Russian” period is concerned).

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Some Characteristics of Stravinsky’s Diatonic Music

Example 7

Still, while this (0 4 7 10) re-orientation obscures the (0 2 3 5) tetrachordally oriented “global” (0–5, 11) format, note how carefully

Some Characteristics of Stravinsky’s Diatonic Music

preserved—and thus re-affirmed—is the registral distribution or vertical span of the (0–5, 11) “global” unit at No. 37, how the (4 7 10 0) “first inversion” articulation of the “upper” (0 4 7 10) “dominant seventh” (E♭/D♭/B♭/G at No. 37) preserves, in simultaneity, the “upper” E♭-D♭-B♭ (0 2 5) incomplete (0 2 3 5) tetrachord which still stands “in a certain opposition” to the “lower” pitch number 11, the E.26 And, indeed, we may apprehend in this preservation a certain logic br rationale behind the persistent incompleteness of the “upper” (0 2 3 5) tetrachord. For it is by virtue of its (0 2 5) incompleteness that the (0 2 3 5) tetrachord becomes readily adaptable to both (0 2 3 5) tetrachordal and (0 4 7 10) “dominant seventh” partitioning of the octatonic collection, its pitch numbers, in the process of transformation, merely becoming pitch numbers 0, 10, and 7 (reading up) of a (0 4 7 10) “dominant seventh” complex. And this same point seems apropos respecting Stravinsky’s “Russian” period generally: (0 2 5) incompleteness renders the (0 2 3 5) tetrachord more flexible with respect to articulative partitioning, so that, in adapting itself to both (0 2 3 5) tetrachordal partitioning (Model B) and (0 4 7 10) “dominant seventh” partitioning (Model A), it may not only define the articulative connecting link in octatonic-diatonic interaction, but the connecting link respecting these differing modes of articulative partitioning of the single octatonic collection as well. (It may also explain, somewhat, the preponderance of—or apparent predilection for—the (0 4 7 10) “dominant seventh” complexes of Model A, at least insofar as the “Russian” era is concerned; and when “extended”, conceptually, to include the “lower” (7 9 0) incomplete (7 9 10 0) tetrachord of the (0 2 3 5 7 9) hexachord, (0 2 5) “incompleteness” may indeed be envisioned, even when inferred on a relatively “foreground” articulative level (as the “basic cell” of Les Noces, for example), as reflecting something fundamentally distinctive about “Russian” thought.) Thus, in “moving” from No. 14 26At

Nos. 38 and 40 + 6 (not shown in Ex. 7), the (0, 3)-related (0 4 7 10) complexes on E♭ and C are transposed “down” to within Collection II: (0 4 7 10)’s on B and A♭, implicating a (B-A-G♯-F♯-F-E♭-D-C) octatonic ordering. And the “global” 0–11 interval span in terms of B-C is punctuated in the timpani, horn, and bass clarinet, one of the few instances where this “globally” determinate “inter-fragmental” 0–11 interval span becomes fragmental or linear. Another instance is the opening “block” of the Jeux des cités rivales, where the tuba and timpani again punctuate, fragmentally, the B-C (Collection II) 0–11 interval span.

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Some Characteristics of Stravinsky’s Diatonic Music

in the Danses to Nos. 37 and 39–43 in the Jeu du rapt, this (0 2 3 5) tetrachord in its (0 2 5) incomplete form as E♭-D♭-B♭ is first an ostinato fragment accountable to Collection III; second, a melodic fragment accountable to the D-scale on E♭ at Nos. 28–30; and, third, pitch numbers 0, 10, and 7 (reading up) of a (0 4 7 10) complex again accountable to Collection III at No. 37. And, in Ex. 8, I have sketched another “summary” to encompass this sequence of “events”, this time from the vantage point of the between-reference connecting link itself (the E♭-D♭-B♭ incomplete (0 2 3 5) tetrachord here); and we note in this conceptualization that the (0 2 3 5) tetrachord “passes through” the (0 2 5) or (0 2 5) (11) incomplete—and “globally” determinate—”stage” before it branches off toward the committed (0 4 7 10) framework of the Jeu du rapt.

Example 8

But to return, briefly, to No. 37 (see Ex. 7) : “local” (0, 3) partitioning is extended to (0, 3, 6, 9) partitioning owing to the F♯ punctuated in the timpani and the A-G-F♯-E (0 2 3 5) tetrachord of the interpenetrating (or “superimposed”) (A-G-F♯-E) (D-C-B-A)

Some Characteristics of Stravinsky’s Diatonic Music

D-scale fragment articulated “above” the compound simultaneity containing the (0, 3)-related (0 4 7 10)’s on E♭ and C. (Hence, No. 37 is ultimately interpretable in terms of a Collection III-D-scale on A interpenetration, notwithstanding the predominance of the octatonic contribution.) And, at climactic points such as at No. 42, this (0, 3, 6, 9) extension is articulated by (0 4 7 10)’s at E♭, C, A, and F♯. Furthermore, this climactic (0 4 7 10) articulation of (0, 3, 6, 9) octatonic partitioning is transposed at No. 44 to within Collection II: F-E♭-D-C-B-A-G♯-F♯. And, as might be expected, the “upper” F-E♭-C (0 2 5) incomplete (0 2 3 5) tetrachord inferrable from the “upper” F/E♭/C/A “dominant seventh” complex at No. 44 serves to connect this (0, 3, 6, 9) Collection II partitioning with the No. 37 D-scale fragment which is re-introduced at No. 46 in terms of the (F-E♭-D-C) (B♭-A♭-G-F) D-scale collection. Finally, the (F-E♭-D-C-B-A-G♯-F♯) -Collection II ordering of the Jeu du rapt at Nos. 44 and 47 presides again in the Jeux des cités rivales at Nos. 57 + 2 and 57 + 4 (and at ensuing (near) repeats of these “blocks”) where an “upper” (0 4 7) triad on F stands “in opposition” to a “lower” G♯-F♯ reiteration. And, in the return to (0 2 3 5) tetrachordal partitioning at No. 64 (see Ex. 9), an “upper” (0 2 3 5) complete tetrachord, G-F-E-D, stands not only “in opposition” to a “lower” pitch number 11, the G♯, but “in opposition” to the “lower” of Model B’s (0, 6) tritone-related (0 2 3 5) (6 8 9 11) tetrachords, C-♯A♯-G♯ here, articulated by the trombones and tubas. Still, this Collection I realization of the (0–5, 11) “global” unit at No. 64 is qualified by the interpenetrating (0 2 3 5 7 9) diatonic hexachordal segment. And so, No. 64 becomes interpretable in terms of a (G-F-ED-C♯-B-A♯-G♯) octatonic-(G-F-E-D-C-B♭) diatonic interpenetration, with the “upper” (0 2 3 5) tetrachord, G-F-E-D, serving as the betweenreference connecting link. And, in Ex. 10, I have again “summarized” by inserting this G-F-E-D fragment in the (0 2 3 5) tetrachordal connecting link “slot” of Ex. 8; and the following “summary” resorts to pitch numbering for a ready “literature” access. Still, the (0–5, 11) “global” unit of Le Sacre is retained in the final “summary” of Ex. 11 in recognition of those instances where, in moving from right to left (from a diatonic to an octatonic or octatonic-diatonic context), it is most often pitch numbers 6 and/or 11 which “intrude” to signal the intervention of octatonic relations.

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Example 9

Example 10

Example 11

Some Characteristics of Stravinsky’s Diatonic Music

Thus, respecting all these varied “summaries”, we may note that Ex. 4a demonstrates “the regularities governing octatonic-diatonic interaction” (or interpenetration) in moving from a (0 2 3 5 7 9) or (0 2 3 5 7 9 10 0) diatonic to a (0 2 3 5 6 8 9 11) octatonic context (or octatonic-diatonic context), where any content realization of this transaction will allow, via the two content-distinguishable (0 2 3 5) (7 9 (10) 0) tetrachords of the (0 2 3 5 7 9) hexachord or D-scale, two possibilities for octatonic penetration coming often by way of a pitch number 6 and/or 11 “intrusion”; and that Ex. 4b examines these same “regularities”—the connection remains the same—but in moving from an octatonic to a diatonic context, so that, of the four content-distinguishable (0 2 3 5)’s available to any given octatonic collection, four possible (0 2 3 5 7 9)’s or D-scales may be implicated. And, finally, the point of Exx. 8, 10, and 11 is the exhibition of these “regularities” from the standpoint of the (0 3 5/0 2 5/0 2 3 5) connecting link itself, so that, in moving from left to right or vice versa (from an octatonic to a diatonic passage or vice versa), we need merely “realize” the connecting link in order to “activate” the conceptualization. And so each “summary” demonstrates the same type of linkage in octatonic-diatonic interaction from a slightly different angle; and, when “laid against the data”, they jointly afford, it seems to me, a fair indication as to what Stravinsky’s “Russian” period material is all about.27 And the perspective adopted on behalf of the diatonic framework of Petroushka, first tableau, may again seem tempting with Les Noces. For, here again, a (0 2 3 5 7 9) passage—however uniquely conceived in the form of a Collection II-(F♯-E-D♯-C♯-B-A) interpenetration at Nos. 10, 17, 20, and 67—serves as a mediating “go-between” (or transition) in moving from a diatonic context to a variety of octatonic or octatonic-diatonic settings (see Exx. 13–15); and, in lengthy passages at Nos. 62–65 and 75–82 in the second and third tableaux (see Exx. 17 and 18), the (0 2 3 5 7 9) hexachord—or the partitioning manifested on its behalf— serves as a referential “home base” with respect to which a “closing of the gap”, pivot-like, renders the surroundings fully diatonic with a pitch number 10—but with the hexachord’s partitioning formulae intact (e.g., Nos. 80–82, Ex. 17)—or signals a “leaning” toward octatonic penetration with a pitch number 11 (e.g., Nos. 58 or 62–65, Ex. 18). 27The phrase, “laid against the data”, occurs in Benjamin Boretz’s “Musical Syntax (II)”,

pnm, Vol. 10, No. 1, p. 236.

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Example 12

But already the first page affords a stunning illustration of these maneuvers: the E-D-B fragment, “open” and uncommitted even with respect to (0 2 3 5 7 9) identity owing to its (0 2 5) incompleteness, “becomes” octatonic (Collection I) at No. 1 with the “intrusion” of pitch numbers 6 and 11, the E-D-B unit serving, in this “moving” from a diatonic—or “open”—framework to an octatonic arrangement, as the articulative connecting link (see Ex. 12; and the reader may insert E-D-B into the (0 2 3 5) connecting link “slot” of Ex. 11 for a “summary”). And while pitch number 11, the F, is situated in an “upper” position at No. 1 (and at ensuing (near) repeats of this “block”), and thus articulates the interval of 7 rather than of 5 with pitch number 6, the B♭, I prefer to retain Model B’s descending scale representation and pitch numbering so as not only to correlate pitch number 0 with the “presiding” E—Model A’s ascending formulation could apply equally—but, more significantly (or more determinately), to identify and expose, in the representation and corresponding pitch numbering, E-D-B as the (0 2 5) connecting link in this octatonic-diatonic interaction, as that which is articulatively shared between—or that which is sustained conceptually “above”— the “blocks” of varying referential implications. Still, the experience of Le Sacre prompts us to view the (0 2 5) “basic cell” of Les Noces as an incomplete (0 2 3 5) tetrachord, incomplete in the same (0 2 5) fashion as was the persistent “upper” E♭-D♭-B♭ ostinato of the Danses des adolescentes. For, again, (0 2 5) incompleteness will constitute the associative factor respecting not only octatonic-diatonic interaction, but the differing modes of articulative partitioning represented by Models A and B.

Some Characteristics of Stravinsky’s Diatonic Music

Example 13

Example 14

The transition passage in Exx. 13–15 occurs four times throughout the first and third tableaux. And, in the three occurrences furnished by the exemplification, it serves to unite a “presiding” (F♯-E-D♯C♯-B-A) hexachordal framework with a fully committed octatonic framework at Nos. 11 and 68 (Exx. 13 and 15), and with an octatonicdiatonic framework at No. 21 (Ex. 14). And, in all three examples, it is pitch numbers 7 and 9 —or the “lower” (7 9 0) incomplete (7 9 10 0) tetrachord of the “presiding” (F♯-E-D♯-C♯-B-A) collection, B-A-F♯—which serves as the connecting link to the fully committed (B-A-G♯-F♯) (F-E♭-D-C) Collection II “blocks” at Nos. 11 and 68, and to the Collection II-D-scale on A “block” at No. 21. (The “upper” F♯E-D♯-C♯ (0 2 3 5) tetrachord, as the connecting link, would naturally have implicated Collection III.)

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Example 15

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Still, as the successive analyses of this passage indicate, the transition is only partially accounted for in terms of this “presiding” (0 2 3 5 7 9) hexachord. For while the (F♯-E-D♯-C♯-B-A) collection “presides” on top (or is “central” to the activity especially when, at Nos. 10 and 67, the preceding tenor fragment is included), the entire framework contains (or is articulated by means of) three “superimposed” (0 2 3 5 7 9)’s (see Ex. 16). And each of these “superimposed” (0 2 3 5 7 9)’s is represented vertically (or triadically) by its (0 2)-related (0 4 7) triads, each of these pairs of (0 4 7)’s naturally exhausting the (0 2 3 5 7 9) collection to which it is accountable. Moreover, respecting the linear perspective, Collection III seems favored in any potential octatonic interaction owing to the F♯-E-D♯-C♯ and A-G-F♯-E “upper” (0 2 3 5)’s of the (F♯-E-D♯-C♯-B-A) and (A-G-F♯-E-D-C) hexachordal collections. But Collection I is also implicated in the transition, by the G-F succession—or the G-F-D unit—and the (0 4 7) triad on G of the (D-C-B-A-G-F) hexachord; and, subsequently at No. 18 (not shown), the transition does proceed to a Collection I passage.

Example 16

So the question arises: why Collection II at Nos. 11, 21, and 68? How does it acquire the advantage in this “moving” to an octatonic framework? And the answer, of course, is that it is the triadic articulation of these three superimposed (0 2 3 5 7 9)’s, the succession of six (7 0 4) “second inversion” (0 4 7)’s “rooted on” D, C, B, A, G, and F (note the “upper” D-C-B-A tetrachord of this (0 2 3 5 7 9), accountable to Collection II) which tips the balance in favor of Collection II, to an extent that the transition becomes interpretable in terms of a Collection II-(F♯-E-D♯-C♯-B-A) interpenetration, with the seeds of the succeeding Collection II settings thus firmly imbedded in the transition itself. In other words, three of the six (0 4 7)’s are accountable to Collection II; and the (0 4 7) succession is flanked

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by (0 4 7)’s on D and F, both of these accountable to Collection II. Moreover, that Stravinsky was conscious of this transitional commitment seems evident in the (near) repeat at No. 21: a (0 4 7 10) “dominant seventh” complex on A♭ is outlined in Piano IV to complete the “background” (0, 3, 6, 9) symmetrical partitioning of Collection II in terms of a (0 4 7/0 4 7 10) articulation at B, D, F, and A♭. So in Exx. 13, 14, and 15, I would interpret the transition in terms of a Collection II-(F♯-E-D♯-C♯-B-A) interpenetration, noting that the between-reference connecting link is discernible not only in terms of the B-A-F♯ (7 9 0) incomplete (7 9 10 0) tetrachord, but in terms of the (0 4 7) triad on B. But the octatonic setting at Nos. 68–70 merits further consideration. For while the instrumental contribution at Nos. 68–70 is accountable to Collection II (explicit reference, List No. 1: the G♯F-B-D ostinato of Piano IV articulates the (0, 3, 6, 9) symmetrically defined partitioning elements of Collection II, these elements constituting the “roots” of the (0 4 7 10) complexes introduced by Pianos I and III), the vocal contribution is represented by a succession of (0 2 5)’s at E, C♯, B♭, and G. And while pitch numbers 2 and 5 of these (0 2 5)’s are accountable to Collection II (and are, indeed, metrically accented—especially pitch number 2—in this 2-2-5-5-2-2-5-2-0-22-5 rendition of the (0 2 5) “basic cell”, a rendition introduced in the first tableau at Nos. 9 and 16 within a diatonic framework), pitch number 0, as E, C♯, B♭, and G, lies outside Collection II. In fact, the vocal (0, 3, 6, 9) defined succession of (0 2 5)’s is, in its entirety, accountable to Collection I. And so the Collection II passage at Nos. 68–70 moves very smoothly into a Collection I passage at Nos. 70–72 (not shown), where Piano IV’s G♯-F-B-D ostinato may continue as the shared “diminished seventh” chord of Collections II and I (although the elements of this G♯-F-B-D “diminished seventh” ostinato pattern do not represent, for Collection I, the “background” (0, 3, 6, 9) symmetrically defined partitioning elements they do for Collection II, the “roots” of the (0 3 7/0 4 7/0 4 7 10) complexes of Model A or the “accented” tones of the (0 2 3 5) complexes of Model B). And so, too, Nos. 68–70 are ultimately interpretable in terms of a Collection II-Collection I interpenetration (despite Collection IPs “advantage”), an interpenetration which proceeds to the fully committed Collection I passage at Nos. 70–72 via Collection I’s contribution, its succession

Some Characteristics of Stravinsky’s Diatonic Music

of (0 2 5)’s at E, C♯, B♭, and G. And we might note, in passing, how impressively Nos. 68–70 demonstrate the (0, 3, 6, 9) octatonically conceived conditions of balance, “equilibrium”, “opposition”, and deadlock alluded to earlier. And the poised equilibrium exhibited by the varying rhythmic periods (e.g., the ostinato’s regular period versus the irregular (0 4 7 10) “dominant seventh” interruptions) is exquisite here, a triumph of the octatonic imagination. Indeed, there are few passages in the literature, that can match the invention here, the subtle play of symmetrical confinement, of locked confrontation and deadlock. Finally, Exx. 17 and 18 condense two passages from the second and third tableaux where the (A-G-F♯-E-D-C) hexachordal collection may be inferred as “central” to the activity, activity with respect to which a pivoting 7th pitch element may render the surroundings either fully diatonic or signal the intervention of octatonic relations as pitch number 11. Thus, at Nos. 78–80, I infer the (A-G-F♯-ED-C) hexachord despite the presence of—in my estimation—a “peripheral” pitch number 10, the B. (Note, in this connection, the “circle-of-fifths” articulation of the pairs of (0 2)’s which encircle the (A-G-F♯-E-D-C) collection: C-G-D-A.) And Collection II’s (0 4 7 10) complexes, introduced earlier at Nos. 68–70, “intrude”, so that Nos. 78–80 become interpretable in terms of a Collection II-(A-G-F♯-ED-C) interpenetration where, again, the “lower” (7 9 0) incomplete (7 9 10 0) tetrachord of the (0 2 3 5 7 9) hexachordal collection, D-C-A here, serves, along with the shared (0 4 7) on D, as the betweenreference connecting link. And, at No. 80, the reiterating (A-G-F♯E-D-C) fragment is articulated by way of (0 4 7) triads on D and C, with B—in my estimation—still “peripheral”. And, at Nos. 82–87, the “peripheral” B, pitch number 10, “becomes” B♭, pitch number 11, and the diatonic (A-G-F♯-E-D-C) framework of Nos. 78–82 gives way to a fully committed octatonic (Collection III) framework (explicit reference, List No. 1), with A and the “upper” A-G-E (0 2 5)—or the “upper” A-G-F♯-E complete (0 2 3 5)—serving as between-reference connecting links. And, while Berger, in his analysis of this Collection III material at Nos. 82–87, cites E’s presence as supportive of A as the pitch class of priority (over a contending E♭/D♯, a priority perhaps already established in the preceding “blocks”), his recourse to an ascending scale representation and pitch numbering from A again

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Example 17

Some Characteristics of Stravinsky’s Diatonic Music

misses the mark.28 For it is not E’s—irrelevant or anachronistically conceived, in my estimation—”support” of A which is of special significance here, but the preserved A-G-E (0 2 5) “basic cell” (or the preserved complete A-G-F♯-E (0 2 3 5) tetrachord) which E defines with the A and G, this A-G-E (0 2 5) “basic cell”—or (0 2 5) connecting link from the preceding (A-G-F♯-E-D-C) diatonic framework— standing, octatonically now, “in a certain ((0, 6) defined “fixed” or polarized) opposition” to the E♭-D♭-B♭ unit. Hence, the “intrusion” of pitch number 11, B♭, relates articulatively in this (0 2 5) “basic cell” conception to the E♭-D♭-B♭ unit (see brackets in Ex. 17), and the framework is fundamentally (0 2 3 5) tetrachordal (Model B). And these are the relations which seem to me of consequence (or most deserving of analytical attention) at Nos. 82–87.

Example 18

But the entire passage at Nos. 78–87 (Ex. 17) exemplifies, in a most telling fashion, the “summary” of Ex. 4a: the (0 2 3 5 7 9) 28Arthur

p. 18.

Berger, “Problems of Pitch Organization in Stravinsky”, PNM, Vol. 2, No. 1,

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hexachord or D-scale, via their two content-distinguishable (0 2 3 5) (7 9 (10) 0) tetrachords, may implicate two of the three contentdistinguishable octatonic collections. And here, A-G-F♯-E and D-C-A of the (A-G-F♯-E-D-C) hexachord implicate Collections III and II. And, as an additional “summary”, we may insert these (0 2 3 5) or (7 9 (10) 0) connecting links in the connecting link “slot” of Ex. 11, noting, of course, that Nos. 78–87 constitute a reading from right to left where the (A-G-F♯-E-D-C) diatonic framework moves toward— or is “intruded upon” by—octatonic relations. Noting, too, that the between-reference (0 3 7/0 4 7)’s would have to be included in this “insertion” so that, at No. 82, the connecting link “slot” would include, as that which is articulatively shared between Collection III and the (A-G-F♯-E-D-C) hexachord, not only the A-G-F♯-E (0 2 3 5) unit but the (0 4 7) triad on C and the (0 3 7) on A as well. And the reader should find the (A-G-F♯-E-E♭-D♭-C-B♭) Collection III-(A-G-F♯-E-D-C) hexachordal interpenetration at No. 59 (Ex. 18) reminiscent of the “blocks” at Nos. 7 and 11 in Petroushka, first tableau. For, apropos No. 11 in Petroushka, the (A-G-F♯-E-D-C) hexachord is implicated by a fragment outlining a (0 4 7) on D and a (0 3 7) on A; and, as at No. 7, this (0 4 7/0 3 7) articulation—or the (0 4 7) on D—stands “in a certain (“fixed” or polarized) opposition” to the “lower” referentially octatonic (Collection III) pitch number 11, the B♭. And while we may note the inclusion of pitch number 10, the B, in an accompanying tremolo, this inclusion in no way undermines (A-G-F♯-E-D-C) hexachordal integrity at No. 58. For the principal fragment’s (0 3 7/0 4 7) articulation of the (A-G-F♯-E-D-C) hexachord remains “central” to the activity at No. 58, with respect to which pitch number 10, the B, assumes a “peripheral” role; and the simultaneous appearance of both pitch numbers 10 and 11, the “diatonic B” and the “octatonic B♭”, underscores the previously noted “flexibility reserved for 7th pitch-class identity” in (0 2 3 5 7 9) hexachordal contexts, the “closing of the (0 2 3 5 7 9) gap” with pitch number 10 or 11. (And note that the (0 4 7 10) complex on E♭ in the simultaneity just prior to No. 59 enhances Collection III’s contribution to the octatonic-diatonic interpenetration.) Finally, at No. 59 (not shown), a Collection III (C-A-C♯/B♭/A ostinato is introduced in Piano IV which persists in the lengthy passage at Nos. 62–65 (and concludes the second tableau), interpenetrating with the (A-G-F♯f-E-D-C) hexachord which is

Some Characteristics of Stravinsky’s Diatonic Music

implicated by both the vocal contribution and by the material in Pianos I, II, and III (primarily an alternation between (0 4 7)’s on D and C, and an outlining of the (0 3 7) triad on A). And, in the lengthy vocal contribution at Nos. 62–65, there occurs not a single transgression of the (0 2 3 5 7 9) hexachord; not even a “peripheral” pitch number 10, the B, may here be inferred.

III

Now the question of pitch-class priority in many of these D-scale, (0 2 3 5 7 9) hexachordal or (0 2 3 5 6 9 11) octatonic-diatonic contexts of the “Russian” period strikes me as problematic. For, obviously, (0 2 3 5 79) or (0 2 3 5 6 8 9 11) confinement precludes tonally functional relations, many of the familiar harmonic progressions and cadential formulae associated with tonality and the C-scale becoming unavailable. And while the (0 3 7/0 4 7/0 4 7 10) triadic complexes are naturally a part of tonality and the C-scale (vis-à-vis “vocabulary”), their confinement to these references subjects them to behavior of a different sort, to a self-enclosed, repetitive, oscillating, circular, or symmetrical kind of construction which engenders the conditions of balance, “equilibrium”, “opposition”, “harmonic stasis”, and deadlock of which we have spoken, conditions which relate to those “deeply rooted” techniques of repetition, juxtaposition, and superimposition where “block” juxtaposition is defined as an abrupt shifting in the collectional reference (or in the partitioning thereof). And so priority (or centricity) becomes a matter of stress or metric accentuation, occasionally of octave reinforcement or “fifth” support, but perhaps most significantly of survival, a. matter of the persistence of a given pitch class or grouping from one “block” or section to the next, a persistence we have been interpreting in terms of shared or between-reference (or between-”block”) connecting links. Of course, in addition to the articulative partitioning cited in connection with (0 2 3 5 7 9) hexachordal reference (Ex. 2a), we have singled out the pairs of (0 2)’s which encircle this diatonic segment as exercising a critical role in the assertion of pitch-class priority. And, apropos the (0 2) reiterations of Petroushka, Le Sacre, Renard, and Les Noces, or the (0 2) (7 9) articulative contour of the opening

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G-F-C-B♭ fragment of Renard (Ex. 19),29 we may note, as before, that the relation expressed by these encircling (0 2) (7 9) units often acquires articulative cohesiveness and integrity. (In other words, (0 2) or (7 9) proximity, defined by the scalar ordering, is not merely “conceptual”.) And, this presented (0 2) (7 9) articulation naturally relates to the fundamental 2, 1 interval ordering of the octatonic scale (Model B, (0 2 3 5) partitioning) of the “Russian” category, an ordering appropriately expressed in the form of a descending 2, 1 scale representation. But the question as to which of these four encircling pitch elements “presides” varies from one (0 2 3 5 7 9) context to the next. Thus, from within the diatonic G-scale on B framework of The Firebird Finale at Nos. 11–14 and 17, we may infer a “foundational” (F♯-E-D♯-C♯-B-A) hexachordal collection owing to a “harmonization” of the borrowed folk melody in terms of a “foundational” alternation of (0 4 7) triads on B and A, with respect to which B, as pitch number 9, evidently assumes priority.30 Thus, in Petroushka at Nos. 0–2(–2), 29Apart

from this (0 2 7 9) articulative contour, note the G-F (0 2) reiteration in Renard’s ostinato (respecting either the (G-F-E-D-C-B♭) hexachord or the D-scale on G), and the referentially octatonic (Collection I) pitch number 11, the A♭. For these relations do prompt a fully octatonic (G-F-E-D-C♯-B-B♭-A♭) setting at Nos. 24–26 (explicit reference, List No. 1), with the seeds of this Collection I context thus embedded in the opening passage at Nos. 0–9 via pitch number 11— or via Collection I’s (and Model B’s) 0–11 interval span, G-A♭. Still, the ostinato’s A♭ could be heard and interpreted as a “downward” extension of (0 7) defined (0 2 3 5 7 9) overlapping, the (F-E♭-D-C-B♭-A♭) hexachord inferrable merely as the next (0 2 3 5 7 9) “in line” following the (C-B♭-A-G-F-E♭) hexachord implicated by the imitation of the opening G-F-C-B♭ (0 2 7 9) fragment, C-B♭-F-E♭ in the bass. But a more immediate “octatonic connection” materializes earlier: the A-G-E succession of the clarinet fragment as Nos. 0–9 “becomes” octatonic in the English horn at No. 9 + 1 owing to the F♯ and the E♭-D♭-C-B♭ (0 2 3 5) tetrachord articulated by the bassoon: (A-G-F♯-E-E♭-D♭-C-B♭), Collection III. 30Obviously, (0 2)-related (0 4 7) triads—(0 4 7)’s alternating a “whole-tone” apart— figure persistently as an articulative partitioning formula in Stravinsky’s (0 2 3 5 7 9) hexachordal contexts. And, in addition to the exemplification afforded by The Firebird Finale, Petroushka, Les Noces, and Histoire, see “Tilimbom” from Trois histoires pour enfants (1915–1917), where (0 4 7)’s alternating on D and C and a D-C-A (7 9 0) vocal fragment at mm. 1–5—with a “missing” pitch number 10, the B—implicate the (A-GF♯-E-D-C) collection. And this (A-G-F♯-E-D-C) reference is “superimposed” over the next “downward” (0 7)-defined overlapping (0 2 3 5 7 9), the (D-C-B-A-G-F) hexachord, implicated by the vocal part at m. 5 and by the G-C-G/F (7-2-7/9) ostinato in the bass, a (0 7)-defined (0 2 3 5 7 9) overlapping which prompts (0 3/0 4) “major-minor third” play respecting F/F♯, a “play” identical to that already noted in Petroushka at No. 11. And see, also, the first of the Four Russian Peasant Songs (“Saucers”), 1917. For while Stravinsky’s 1954 addition of fanfare-like flourishes (with four horns) implicates the

Some Characteristics of Stravinsky’s Diatonic Music

we may infer the (E-D-C♯-B-A-G) hexachord where, in contrast, the D, as pitch number 2, seems the most likely pitch class for priority status. And thus, too, in Renard at Nos. 0–9 (see Ex. 19), we may infer, from within a predominating D-scale on G framework, an opening (G-F-E-D-C-B♭) hexachordal “foundation”, where G, as pitch number 0, acquires a degree of pitch-class centricity. Consequently, quite apart from the ambiguity respecting pitch-class priority in many (0 2 3 5 7 9) contexts, there is this variance vis-à-vis those (0 2 3 5 7 9) contexts where a sense of pitch-class priority does seem to arise.

Example 19

And, while the encircling (0 2) (7 9) units may acquire articulative co-hesiveness as the (0 2 3 5 7 9) hexachord stands engaged, I suspect that it is ultimately to the (0 7) (7 2) (2 9) “circle-of-fifths”— or circle-of-(0 7)’s —conception of these units (see Ex. 2b), and to the (0 7)-denned overlapping of (0 2 3 5 7 9)’s (see Exx. 2 and 21), that we must turn in order further to probe this ambiguity or variance. Moreover, all these factors respecting (0 2 3 5 7 9) hexachordal reference—the partitioning formulae, the question of fragmental enclosure, the encircling (0 2) (7 9) units and their role in the expression (or confounding non-expression) of pitch-class priority—take on, it seems to me, a special urgency as we approach, finally, those interminable ostinatos of The Soldier’s March and the Music to Scene I (and their successive (near) repeats) in L’Histoire du Soldat. And, pursuant to the “circle-of-fifths” conception, we D-scale on D, the song outlines an alternation of (0 4 7)’s on G and F, this alternation implicating the (D-C-B-A-G-F) hexachord, this (D-C-B-A-G-F) hexachord naturally inferrable from within the fully accredited diatonic D-scale framework.

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might briefly entertain, via Wilfrid Mellers, the tonal approach to the ostinato of The Soldier’s March, an approach which, as we have indicated, Boulez evidently shares with Mellers in confronting Stravinsky’s music, but one which has at any rate been advanced in countless publications:31 Here, there is an unceasing ostinato in the bass consisting of the note G followed by D and E sounded together, a ninth apart. This seems to suggest the key of G. But the fragmentary tootling tune, nearly always out of step with the ostinato, is unambiguously in D. . . . This suggests that the D-E in the ostinato is really the tonic and dominant of D major elided together and that the G of the ostinato represents the subdominant. Traditional harmony revolves between the poles of tonic, dominant and subdominant. In telescoping two or even all three of these chords Stravinsky places in space, as it were, chords that would normally progress into one another. Instead of a resolved argument, we have a tension clinched, suspended in time.

For even were we, in the absence of anything remotely resembling tonally functional behavior, to shun the specter of “keys”, “chords”, and a subdominant-tonic-dominant relation (to shun, especially, that reference to the opening “tootling tune” being “unambiguously in D”, the concept of “D-major” not only wholly inapplicable here—C-scale on D would do—but, even if applicable, hardly “unambiguously” without cadential clarification, the “tootling tune” outlining—and coming to rest on—a (0 4 7) triad or (0 7) on A), and to replace this specter with the “circle of fifths” defined by the encircling (0 2) (7 9) units of the (0 2 3 5 7 9) hexachord, these (0 7)’s or “fifths” constituting an adequate “explanation” for the “harmonic stasis” or “tension clinched”), the point Mellers raises seems well taken: a fundamental ambiguity does manifest itself with respect to pitchclass priority, in the opening March at least until No. 5 where the ostinato pattern is temporarily discarded and there arises, for the first time, a sense of pitch-class priority inferrable on behalf of the D, this priority implicating, given the pitch content, the C-scale on D. Moreover, as Mellers notes, the “elision”, merging, or “coming 31Wilfrid

Mellers, Romanticism and the 20th Century (New Jersey: Essential Books, 1957), p. 202. Or, see Henry Boys, “Stravinsky: The Musical Materials”, The Score (January 1951), p. 15; Roman Vlad, Stravinsky (London: Oxford University Press, 1960), p. 51; or, G. W. Hopkins, “Stravinsky’s Chords”, Tempo (Spring 1966), p. 6.

Some Characteristics of Stravinsky’s Diatonic Music

together” of elements interpretable in terms of a subdominanttonic-dominant relation—all of which we re-interpret in terms of the “elision”, merging, or “coming together” of the four encircling pitch elements of the (0 2 3 5 7 9) hexachord—does constitute a kind of “superimposition”, with respect to which we might invoke the same kind of descriptive terminology invoked on behalf of Stravinsky’s octatonic settings: balance, “equilibrium”, “opposition”, “equal weight and independence”, “harmonic stasis”, deadlock, etc. But questions linger as to the enunciation of this “coming together”, the partitioning formulae which engender these conditions. And, in answer to these, I find it insightful (and reassuring) to interpret the ostinatos of Histoire in terms of the (0 2) (7 9) units of the (0 2 3 5 7 9) hexachord, a reference that will not only enable us to “situate” these phenomena—and the core of the “superimposed” material— within the wider “literature” framework we have been following, but to account, far more incisively than can the tonal approach, for peculiarity in the articulation. For it seems to me unquestionable that these ostinatos have as their origin Stravinsky’s (0 2 3 5 7 9) contexts, that their invention stems from Stravinsky’s “Russian” preoccupation with (0 2 3 5 7 9) hexachordal construction.32 Thus, as in Petroushka at Nos. 0–2(–2) and 2 + 3, I infer, straight away, the (E-D-C♯-B-A-G) hexachord (see Ex. 20). And Petroushka’s D-E (2 0) reiteration respecting this (0 2 3 5 7 9) hexachordal reference is here “sounded together” as E/D in the ostinato. And this E/D (0/2) “sounding together” alternates with a G, pitch number 9. And pitch number 7’s participation in this hexachordal (0 2) (7 9) encirclement is furnished by the “tootling tune” ’s outlining of a (0 4 7) triad on A and its “coming to rest” on a E-A (0 7) “fifth” at No. 3, at which point the bassoon reiterates A over the continuing G-E/D (9–0/2) ostinato. Thus, from within the fully accredited diatonic framework, I infer the (E-D-C♯-B-A-G) hexachordal segment— or the partitioning manifested on its behalf—as “central” to the 32Indeed,

prior to Histoire, pitch elements of the encircling (0 2) and (7 9) units of the (0 2 3 5 7 9) hexachord are on several occasions conceived as ostinatos. Thus, in addition to the (7-2-7/9) ostinato of “Tilimbom”—and apart from the (0 2) or (7 9) reiterations in Petroushka, Le Sacre, Renard, and Les Noces which, I suppose, are interpretable as ostinatos—see Stravinsky’s Berceuse of 1917, published in Expositions and Developments (London: Faber & Faber, 1962). And for further comment, see Eric Walter White, Stravinsky (Berkeley and Los Angeles: University of California Press, 1966), p. 225.

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activity; and, from within this hexachordal segment, I infer E, D, G, and A as pitch elements of priority, these elements constituting the encircling (0 2) (7 9) units of the (E-D-C♯-B-A-G) hexachord, an encirclement with an articulation nearly identical to that provided by the D-E and A-G (2–0 and 7–9) reiterations of Petroushka. And there is also exhibited, in the E/D “sounding together”, a degree of articulative cohesiveness on the part of the (0 2) unit in this (0 2) (7 9) encirclement or partitioning.

Example 20

Then, at No. 2 + 3, the second March fragment in the clarinet, by outlining (0 4 7)’s on A and B, implicates the (F♯-E-D♯-C♯-B-A)

Some Characteristics of Stravinsky’s Diatonic Music

hexachordal collection, so that, apropos the (0 7)-defined overlapping of (0 2 3 5 7 9)’s outlined in Ex. 2 on behalf of Petroushka, we might, in Ex. 21, outline another format for Nos. 0–5 in Histoire, noting, however, that the “lower” (E-D-C♯-B-A-G) hexachord “presides” with respect to which the (0 2 3 5 7 9)’s of the clarinet appear as “extensions”. For, at Nos. 4 and 7 (not shown), the clarinet fragment is transposed by the interval of 7 from A to E, so that, pursuant to a more “global” perspective, (0 7)-defined (0 2 3 5 7 9) overlapping would have to be extended further “upward” to include the (C♯-B-A♯G♯-F♯-E) hexachord as well.

Example 21

Still, while the marching tunes of The Soldier’s March and Scene I are fragmentary (left “open”) and repetitive in the same sense as are the “tunes” of Le Sacre, Renard, and Les Noces, they are, as Mellers notes, “related to clichés common to European art music”. And it may be indicative of this reference that, in place of the D-scale so often implicated by Stravinsky’s (0 2 3 5) fragments, the referential ordering of the fully accredited diatonic framework at No. 5 (not shown) appears to be that of the C-scale, the C-scale on D, D assuming a degree of pitch-class priority. For the G-E/D ostinato is replaced at No. 5 by a reiterating “low” D, while G’s participation seems diminished; and the accentuation of F♯ in the bassoon fragment— this F♯ merely a “peripheral” pitch number 10 respecting the earlier “tootling tune” ’s outlining of a (0 4 7) triad on A—appears to expose a predominating (0 4 7) triad on D at least through No. 7. Moreover, apropos the “circle-of-flfths” conception of (0 2) (7 9) encirclement (Ex. 2b), we can envision the A-D (7 2) “fifth” as centric (without necessarily invoking Mellers’s specter of a subdominant-tonicdominant relation). But note the qualification that must accompany the “C-scale on D” ruling at No. 5: 1) the (E-D-C♯-B-A-G) hexachordal

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outline in the bass over the reiterating “low” D; (2) the sustained “upper” E in the clarinet and in the violin jeté interruptions which continue to outline or accentuate E’s (0 2) affiliation with D; (3) the (0 4 7) triad on A “super-impositions” outlined by the clarinet and violin jeté interruptions; (4) the D-G (2 9) “fifths” in the violin accompaniment to the “chromatic” transformation of the “tootling tune” at No. 10. And so ambiguity respecting (single) pitchclass priority persists. And we may wonder whether we are not ultimately better off accepting and defining it in terms of this (0 2) (7 9) encirclement of the (0 2 3 5 7 9) hexachord—or the “circle-offifths” conception of this encirclement; resigning ourselves, in other words, to an inability to establish a referential ordering for the “fully accredited diatonic framework”. And, just prior to Scene I, the final simultaneity of the March, A/E/ G/C reading down, constitutes a transposition, by the interval of 7, of the corresponding simultaneity at No. 1, E/B/D/G (see Ex. 22); and this (0 7) transposition signals a transposition of the March’s “presiding” (E-D-C♯-B-A-G) hexachordal collection “down” to the next (0 7)-defined overlapping (0 2 3 5 7 9), (A-G-F♯-E-D-C). Accordingly, the (0 2) unit of the March’s ostinato, the E/D “sounding together”, becomes an A-G reiteration in Scene I’s ostinato; and pitch number 9, the G in the March, is replaced by a pitch number 7, the D respecting this new (A-G-F♯-E-D-C) hexachordal reference. But while the (A-G-F♯-E-D-C) hexachord “presides” at first, Scene I is ultimately more flexible respecting (0 2 3 5 7 9) hexachordal reference. And I attribute this flexibility—or greater (0 2 3 5 7 9) maneuverability—to Scene I’s ostinato. For in Scene I’s ostinato it is pitch number 7 which alternates with pitch numbers 0 and 2 (vis-à-vis the (A-G-F♯-E-D-C) collection), not pitch number 9 which alternates with pitch numbers 0 and 2 (vis-à-vis the (E-D-C♯-B-A-G) collection of the March). And these encircling pitch numbers 0, 2, and 7 of Scene I’s ((A-G-F♯-E-D-C) hexachordal) ostinato represent the encircling pitch numbers 7, 9, and 2 of the “presiding” (E-D-C♯B-A-G) hexachord of the March. Consequently, Scene I’s ostinato is really “open” or uncommitted respecting (0 2) (7 9) encirclement of these two (0 7)-defined overlapping (0 2 3 5 7 9) hexachordal

Some Characteristics of Stravinsky’s Diatonic Music

Example 22

collections, (E-D-C♯-B-A-G) and (A-G-F♯-E-D-C).33 Moreover, this 33In

other words, pitch number 9, along with pitch numbers 0 and 2, identifies or “fixes” a given (0 2 3 5 7 9) hexachord, as E, D, and G as pitch numbers 0, 2, and 9, do for the (E-D-C♯-B-A-G) hexachord of the March. And thus, had Stravinsky opted for a literal transposition of the March’s ostinato, C as pitch number 9, along with A and G as pitch numbers 0 and 2, would immediately have identified or “fixed” the (A-G-F♯E-D-C) hexachord in Scene I.

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encircling (0 2) (7 9) “neutrality” of Scene I’s ostinato allows for a ready alternation between (A-G-F♯-E-D-C) contexts—such as that noted just before No. 3, where C replaces C♯, where (0 4 7) triads are outlined on D and C, and where B, as pitch number 10, is either missing or “peripheral”—and (E-D-C♯-B-A-G) contexts—such as that noted at No. 5 + 1 where C becomes C♯, where a (0 4 7) triad on A “merges” with the ostinato’s D-G (2 9) “fifth”, and where F♯, as pitch number 10, is either missing or “peripheral”. And this (A-GF♯-E-D-C)-(E-D-C♯-B-A-G) alternation engenders an incessant (0 3/0 4) “major-minor” play respecting C/C♯, a “play” similar to that noted at No. 11 in Petroushka (see Exx. 1 and 2), and a “play” which can therefore similarly be attributed to (or can again best be heard and interpreted as a manifestation of) (0 7)-defined (0 2 3 5 7 9) adjacency or overlapping.

Example 22 (Continued)

Some Characteristics of Stravinsky’s Diatonic Music

But further. The bassoon’s F-G reiteration at No. 9, anticipated in the violin at Nos. 6–9, implicates an extension of (0 7)-defined (0 2 3 5 7 9) overlapping further “downward” to include the (D-C-B-A-G-F) hexachordal collection (F-G constituting the (7 9) unit of this (D-C-BA-G-F) hexachord), an extension which prompts additional (0 3/0 4) “major-minor” play vis-à-vis F♯/F. Thus, as in Exx. 2 and 22, we may again “compress” (0 2 3 5 7 9) strategy by sketching the “spread” of engaged (0 7)-defined (0 2 3 5 7 9) overlapping. And I need scarcely reiterate how very handily this “compression” (or conceptualization) reflects the circumstances surveyed: the “neutrality” of the ostinato pattern respecting (0 2) (7 9) encirclement of the (E-D-C♯-B-A-G) and (A-G-F♯-E-D-C) hexachordal collections; the various (E-D-C♯-BA-G) and (A-G-F♯-E-D-C) contexts to which this “neutrality” lends itself; and the C/C♯ “major-minor” play which this (0 7)-defined (0 2 3 5 7 9) alternation generates. Finally, note how the “spread” of (0 7)-defined (0 2 3 5 7 9) overlapping extends “upward” in the March via the clarinet fragment’s (0 2 3 5 7 9)’s, but “downward” in Scene I from the “presiding” (E-D-C♯-B-A-G) hexachord of the March. And, needless to say, it is, as always, the presented cohesiveness— the presented articulation and accentuation of the (0 2) and (7 9) overlapping defined by these “spreads” of (0 7)-defined (0 2 3 5 7 9)’s (notwithstanding the “circle-of-fifths” conception), and the presented articulation of (0 2 3 5)(7 9 0) and (0 3 7/0 4 7) partitioning manifested on behalf of the single (0 2 3 5 7 9) collections—that merits, as the most accommodating analytic-theoretical approach, the (0 2 3 5 7 9) perspective indicated. Finally, the tranquil sigh of the dejected soldier in Scene II— surely one of Stravinsky’s most poignant utterances—condenses the most pressing (0 2 3 5 7 9) relations of the preceding sections. For that lengthy, drawn-out A♭-G♭ (or G♯-F♯) (0 2) reiteration in the bassoon, articulated “below” an A♭-G♭-F-E♭ (0 2 3 5) tetrachordal fragment in the clarinet at Nos. 1-1 + 6 and 6-6 + 6, constitutes nothing but a continuation of the (0 2) reiterations of the preceding ostinatos; and a continuation, more determinately, of the G/A-E/GG/A (2/0-5/2-2/0) articulation of the A-G-E (0 2 5) fragment in the violin at Nos. 3–5 in Scene I (see brackets in Ex. 22) in terms now of a G♭/A♭-E♭/G♭-G♭/A♭ articulation of the A♭-G♭-E♭ (0 2 5) fragment (see brackets in Ex. 23).

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Example 23

But Scene II’s “sigh”—never to be repeated, a circumstance which invests it with special significance—opens with a (B-AG♯-F♯-) (F-C) Collection II octatonic-(B-A-G♯-F♯-E-D) hexachordal interpenetration, where the B-A (0 2) reiteration articulated jointly by the clarinet’s triplet figure and the violin’s sustained B (or the B-A-G♯-F♯ (0 2 3 5) fragment articulated by the clarinet and bassoon) is the between-reference connecting link. And the octatonic contribution to this interpenetration is once again conspicuously marked by the “intrusion” of a pitch number 11, Collection II’s C in the violin’s simultaneity; by the “intrusion” of Collection II’s (and Model B’s) 0–11 interval span, the B/C of the violin’s simultaneity; and by the “intrusion” of Collection II’s pitch number 6, the F in the bassoon. (How familiar are these circumstances now; with what consistency can we account for “chromaticism” in these works in

Some Characteristics of Stravinsky’s Diatonic Music

terms of the persistent “intrusion” of specific referentially octatonic pitch elements and intervals; and how remarkably consistent does Stravinsky now appear to have been in his “moving”, during the “Russian” era, from one piece to the next.)

Example 24

Then, in the third measure, the bassoon’s F♯-C♯-G♯ fragment and violin’s B delineate the encircling pitch numbers 0, 2, 7, and 9 of the (A♭-G♭-F-E♭-D♭-C♭ (B)) hexachordal collection, the B-A (0 2) reiteration of the opening measure thus being replaced by an A♭G♭ (or G♯-F♯) (0 2) reiteration. And, following this replacement, the clarinet and bassoon lapse into that lengthy A♭-G♭ (0 2) reiteration or A♭-G♭-F-E♭ (0 2 3 5) tetrachordal articulation noted above. Then, with the “intrusion” of a D at No. 1 + 6, pitch number 6 respecting the (A♭-G♭-F-E♭) (0 2 3 5) tetrachord, the clarinet descends by way of a D-C-B-A succession—by way of Collection II’s (0, 6) tritone-related (6 8 9 11) tetrachord—and returns in this manner to the B-A (0 2) reiteration of the opening triplet “sigh” and the inferred octatonicdiatonic interpenetration. In Ex. 24, I have merely indicated that the trumpet and clarinet at Nos. 3–5 (–2) articulate the A♭-G♭-E♭ (7 9 0) and the E♭-D♭-C-B♭ (0 2 3 5) partitioning units of the (E♭D♭-C-B♭-A♭-G♭) hexachordal collection, and that this articulation is “superimposed” over violin simultaneities which delineate the previously noted D-C-B-A tetrachord. Thus, with the A♭-G♭-E♭ (7 9 0) unit of the (E♭-D♭-C-B♭-A♭-G♭) hexachord as the articulative

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between-reference connecting link, Collection II may be inferred at Nos. 3–5 in terms of an (A♭-G♭-(F)-E♭) (D-C-B-A) articulation, Model B’s (0, 6) tritone-related (0 2 3 5) (6 8 9 11) tetrachords.

Example 25

And—as a final “finally”—I have wanted to draw the reader’s attention to a “neo-Classical” passage (see Ex. 25). For while it is my judgment that the articulative “habits” examined here on behalf of the D-scale, the (0 2 3 5 7 9) hexachord, and the (0 2 3 5 6 8 9 11) octatonic scale are characteristically “Russian”—that, indeed, Stravinsky’s “neo-Classicism” entailed a re-structuring (or “re-hearing”) of the octatonic scale in terms of its 1, 2 interval ordering, Model A, a re-structuring implicated by (0 3 7/0 4 7) triadic and (0 1 3 4) tetrachordal partitioning which coincided with an interpenetrating preoccupation with C-scale conventions and inflections (see Lists 1 and 2)—the (0 2 3 5 7 9) hexachord—its (0 2) (7 9), (0 2 3 5) (7 9 0) and (0 3 7/0 4 7) partitioning formulaemay still illuminate from time to time. Thus, were we to recognize G as the pitch class of priority at Nos. 78–80 in Les Noces (and to disregard, momentarily, the “presiding” A and “harmonization” of the reiterating fragment in terms of an alternation of (0 4 7) triads on C and D at No. 80, articulative circumstances which, far more readily than those inferrable at No. 22 in the final movement of the Symphony of Psalms, identify (0 2 3 5 7 9) hexachordal reference), the correspondence between this passage and No. 22 (or No. 26) from the final movement of the Symphony of Psalms becomes striking. And even were we, apropos Psalms, to interpret the “circle of fifths” defined by the encircling (0 2) (7 9) units of the (0 2 3 5 7 9) hexachord (the C-G-D-A articulation vis-à-vis the (A-G-F♯-E-

Some Characteristics of Stravinsky’s Diatonic Music

D-C) hexachord in Les Noces; the A♭-E♭-B♭-F articulation vis à vis the (F-E♭-D-C-B♭-A♭) hexachord in Psalms) as a subdominant-tonicdominant relation with the E♭-B♭ (2 7) “fourth” (or the B♭-E♭ (7 2) “fifth”) centric respecting this interpretation or a possible C-scale on E♭ or even “E♭-major” determination, this interpretation in no way qualifies the resemblance. For pitch organization remains fundamentally the same in these passages: a reiterating fragment— with pitch number 2 assuming a degree of pitch-class priority as the point of departure—is repeated over an ostinato “circle-of-fifths” articulation of the encircling (0 2) (7 9) units of the (0 2 3 5 7 9) hexachord. (Note the opening G/C (2 9) “fifth” of Les Noces which corresponds to the opening E♭/A♭ (2 9) “fifth” of Psalms, although A♭, pitch number 9, is not part of Psalms’ ostinato pattern but is merely sustained throughout.) And, upon each successive (near) repeat, the “point of departure”, the G in Les Noces and the E♭ in Psalms, takes on a slightly altered “harmonic complexion” as a result of the variance in rhythmic periods defined by the reiterating fragment and the “circleof-fifths” ostinato, a variance which allows for a different (0 7), (7 2), or (2 9) “sounding together” on each occasion, but a variance (or alteration in “harmonic complexion”) which is “local” within the larger self-enclosed, repetitive, circular, or deadlocked “circleof-fifths” framework, a framework with respect to which each of the “circle-of-fifths” pitch elements stands “in a certain (“fixed” or polarized) opposition” and assumes a degree of “equal weight and independence.”34 So we come to the end of a lengthy discourse: an approximation of one observer’s hearing and understanding of consistency, identity, or distinctiveness apropos Stravinsky’s diatonic writing. But I do not believe—as the title of this essay may suggest, but as its analytictheoretical perspective most assuredly contradicts—that pitch organization can be dealt with by treating the octatonic and diatonic “blocks” independent of each other, however much abrupt “block” juxtaposition may seem to tempt such an approach. (This approach 34Another

“neo-Classical” undertaking favorably approached in terms of (0 2 3 5 7 9) hexachordal reference is the opening Pas-de-Quatre of Agon. Read through the first nine measures with the (0 7)-defined overlapping (0 2 3 5 7 9)’s, (D-C-BA-G-F) and (A-G-F♯-E-D-C), in mind. And note the articulation, the singling out for special emphasis, of pitch numbers 0, 2, 7, and 9, the D, C, G, and F of the opening (D-C-B-A-G-F) hexachord, in the simultaneities at mm. 7 and 19 and in the concluding simultaneity of the Pas-de-Quatre.

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would have to forsake those many instances where the octatonic and diatonic pitch collections interpenetrate; and it is just such instances which provide the most valuable clues as to how Stravinsky’s octatonic perspective influences his diatonic perspective and vice versa.) The distinction with respect to reference exists, of course, as I believe it did for Stravinsky. Only, there is exhibited in so many of the “Russian” and “neo-Classical” works, by “block” juxtaposition or interpenetration, such a persistent and thorough going octatonicdiatonic interplay, that a satisfying and useful understanding of Stravinsky’s diatonic writing would seem to hinge on a corresponding (mutually arrived at) understanding of his “octatonicism”.

Chapter 2

Taruskin’s Angle

Professor Richard Taruskin’s (1985) essay on Stravinsky’s “angle” misconstrues some remarks of potential significance. Questioned by Robert Craft about the “musical manners” of Oedipus Rex, the composer spoke first of the “tarnished” reputation of his opera-oratorio. While conceding that its neo-classicism could be interpreted by “progressive-evolutionary standards” as a mere “husk of style,” as “cultured pearls,” he professed himself convinced of its enduring value as art. “I know, too,” he continued, “that I relate only from an angle to the German stem (Bach-Haydn-Mozart-BeethovenSchubert-Brahms-Wagner-Mahler-Schoenberg), which evaluates largely in terms of where a thing comes from and where it is going. But an angle may be an advantage” (Stravinsky and Craft 1963, 14). I submit that this reference to the “German stem” had nothing to do with octatonicism or symmetrical pitch relations. What Stravinsky sought to represent as a specific compositional issue, namely, the issue of neoclassicism and the peculiar discontinuity it posed, is taken by Taruskin to imply a scheme of octatonic ancestry

Reprinted from In Theory Only, vol. 10, no. 3 (1987). The Music of Stravinsky: Collected Essays Pieter C. van den Toorn Text Copyright © 1987 Michigan Music Theory Society Layout Copyright © 2023 Jenny Stanford Publishing Pte. Ltd. ISBN 978-981-4968-62-1 (Hardcover), 978-1-003-35916-6 (eBook) www.jennystanford.com

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that would never have occurred to the composer.1 Stravinsky depicts “angle”—the development of his own unique style during the early Swiss years, and “stem”—his sudden discovery of the distant past in baroque and classical music, as two separate and opposing forces. Taruskin interprets this opposition as signifying one and the same thing (or parts of the same thing): symmetrical pitch construction and its origin in the music of a few German romantics. This is bizarre. Taruskin overlooks what seems to me a serious attempt on Stravinsky’s part to describe the nature of his early “change of life” (as he later called neoclassicism; Stravinsky and Craft 1966, 23), the historical implications of which were no less crucial than the rather more obscure ones alluded to by Taruskin. By “angle” Stravinsky refers to his own accent: his manner of composing, the manner in which, as an outsider, he sought to accommodate his discovery of the past. That is to say, he refers to his own inventive processes (rhythmic, pitch-relational, an instrumental) and to the way in which he sought to make the past a compositional reality. To the extent that this accommodation entailed, in pitch-relational design, an interaction between symmetrical or octatonically derived elements and the harmonic procedures of the baroque and classical eras, Taruskin’s thesis might here acquire a certain pertinence. But I cannot for an instant believe that, in referring to the German stem, Stravinsky had in mind the overly ripe patches of purple cited by Taruskin from the music of Beethoven, Schubert, and Liszt.2 My impression is that the composer would have reacted to the Beethoven and Schubert passages (I exclude the cornier ones by Liszt) as he had when listening to a recording of Schumann’s Dictherliebe, remarking that this music was “much too beautiful” 1It

should be borne in mind that, notwithstanding the considerable role of the octatonic collection as a constructive or referential factor in Stravinsky’s music, the composer himself never mentioned the collection or scale (or anything like it) in his writings, including his six books of conversations with Craft (see van den Toorn 1983. 42, 328–29). 2These passages are: Beethoven: Symphony in F Major, No. 6, first movement, mm. 156–66 and 205–12; Schubert: Symphony in C Major, D944, fourth movement, letter N; Mass in E-flat Major, D950, Sanctus, mm. 1–8; Octet, D803, sixth movement, 6 measures before letter G; Liszt: Ce qu’on entend sur la montagne, mm. 1–65 and 16 measures before letter Y: Orpheus, mm. 1-14; Eine Faust-Symphonte, third movement, 3 measures after letters Xx.

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(Craft 1971, 24). We have it from Craft, who cannot automatically be dismissed as an unreliable Boswell, that remarks of this kind were typical of the composer. Taruskin might here interject that I am missing his point, that he wished merely to give Stravinsky’s remarks an ironic twist to fit other legitimate ends. I would counter that the remarks carry sufficient intent and that it might not always be advisable to adopt a relentlessly trigger-happy approach when confronting Stravinsky and his published conversations. Compositionally speaking, the German (or Austro-German) stem meant something that was both rudimentary and superficial. On an elementary level, it meant tonality and the major-scale ordering of the diatonic collection: tomes, dominants, keys, relative keys, sonata forms, fugal procedures—all that can be found documented in standard textbooks on tonal harmony and form. On a more superficial but no less significant level, it meant cliché and mannerism—all that was most stylized and conventional in surface gestures and figurations of the baroque and classical styles. Stravinsky sought a backdrop of blandness, a cultural ostinato, and all square metrical dance schemes against which he could exert the play of his own devices. The passages cited by Taruskin would have been too heated, too individual, and too original to have had an appeal in this more immediate compositional sense. It should be swiftly noted, however, that these liberties do not impinge on Taruskin’s primary concerns. Although prefaced by one of the oddest titles to hit the pages of JAMS (or any other scholarly musical journal for that matter), these concerns are straightforward and, from a musicological standpoint, entirely orthodox. Ever in quest of the Russian origins of Stravinsky’s music, and hence of a tradition that could confirm the composer’s octatonic credentials, Taruskin traces symmetrical pitch relations to Stravinsky’s teacher, Rimsky-Korsakov, and then further back to Liszt, Schubert, and Beethoven. One thing does appear to have led to another. Particularly noteworthy in his account are the melodic and harmonic formulas cited in Rimsky’s Kastchei the Immortal and Sadko: the (0235) “dorian” tetrachords, and the triads and dominant sevenths. The origin of the octatonic collection is also convincingly traced not to an embellishment of the diminished seventh chord but to a partitioning of the octave by triads a minor third apart filled in by passing tones.

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All this is pursued with insight, relish, and imaginative detail, leaving, at least for the present observer, very little room for disagreement. On the Other hand, whether these tracings can in some sense confirm the role or significance of the octatonic collection in Stravinsky’s music and presumably justify an analysis along these lines is a different matter. That Stravinsky inherited the collection along with a number of melodic and harmonic patterns from his predecessor is beyond dispute. This has been known for some time, although without the kind of documentation furnished by Taruskin. I must confess, however, that my own hearing and understanding of Stravinsky’s octatonicism remains unaffected by these disclosures. This is possibly because the weight of the octatonic evidence in his early music is already so conclusive. Beginning with pieces such as Zvezdoliki and The Rite of Spring, octatonic construction, by way of techniques of superimposition and rhythmic displacement, takes on a radically different complexion. The passages by Liszt and Rimsky seem tame and remote in comparison, as if conceived in a different age. And it is with this in mind that I still tend to take Stravinsky at his word when asked for an appraisal of his teacher’s music; its “modernistic’’ tendencies, he averred, had consisted of little more than a few “flimsy enharmonic devices” (Stravinsky and Craft 1960, 57). Indeed, Taruskin’s revelations are likely to have the opposite effect from what may have been intended. While it is unlikely that the music of Liszt and Rimsky can shed much light on Stravinsky, a study of the latter’s octatonic practices could well, as has here been the case with Taruskin, spur an interest in Liszt and Rimsky. Moreover, we can move sideways as well as backwards, and a comparison of the octatonicism of Stravinsky and Bartók, already touched upon by George Perle (1977, 10–15) and Elliott Antokoletz (1984, 313–20), seems in order. I would caution, however, that bridge-building by way of broad theoretical concepts (interval cycles, symmetrical sets, and the like) is useful only to the extent that critical distinctions are at some point brought to the fore. We are interested, above all, in what it is that distinguishes the music of Stravinsky from that of Bartók and in what distinguishes individual compositions. It is primarily in order to arrive at this kind of detail that we bother to concern ourselves with binding theoretical concepts—that is to say,

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with commonality. In the end, it seems doubtful that a convincing definition of ocatonic or octatonic-diatonic pitch structure in Stravinsky can be reached without a very careful consideration of the rhythmic issue. This may seem a bit harsh. The tradition of Rimsky and the Russian Nationalist School does occasionally yield telling passages. As a concession to Taruskin’s methods I offer a few examples of my own. Example 1 (pp. 32–33) is from the Coronation scene in Boris Godunov. Taruskin mentions this celebrated bell-ringing sequence in passing, but I quote it here because it seems so much closer to Stravinsky than the octatonic passages authored by Liszt or Rimsky. This may be, as Taruskin himself notes, because of the accordianlike, back-and-forth motion of the tritone-related dominant sevenths, although instrumental details—the use of the piano in particular— would also seem to play a role. Moreover, when a Russian folk song, introduced within a diatonic context (ex. 2, p. 34), is transposed to fit the octatonic implications of the alternating dominant sevenths (ex. 3, p. 35), the effect is striking indeed and not unlike many passages in Les Noces. Metrically, however, the music is rather stiff, and either by juxtaposing or by assigning varying rhythmic periods to the reiterating fragments, Stravinsky might well have been led to a form of triadic superimposition. Note, too, that with the return of the material somewhat transformed in act 2 (ex. 4, pp. 36–37), it is transposed by interval-class 3, enabling the com-pound figuration to remain confined to the initial octatonic collection.3 This little maneuver serves as a precedent for the “Petrushka” chord in Stravinsky’s ballet (ex. 5, p. 38). Toward the end of the third tableau (no. 77) the chord is transposed in like fashion with the same referential implications. I shall not venture further into the analytic details of ex. 6 (p. 39), except to mention that conditions of priority and triadic articulation suggest a scalar ordering so that the octatonic set has not been reduced to its “best normal order” or “prime form,” to use Allen Forte’s terminology.

3The clock scene in act 2 from which examples 4 and 6d are derived is not wholly octatonic. Initially, the tritone-related dominant sevenths on B and F are accompanied by C♯-C and G-F♯ motions of the bass clarinet. The symmetrical implications of these “outside” elements (C♯ and G) are briefly discussed in Antokoletz 1984, 4–5.

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Example 1  Mussorgsky, Boris Godunov, Prologue (continued)

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Example 1 (continued)

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Example 2  Mussorgsky, Boris Godunov, Prologue

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Example 3  Mussorgsky, Boris Godunov, Prologue

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Example 4  Mussorgsky, Boris Godunov, Act 2 (continued)

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Example 4 (continued)

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Example 5 Stravinsky, Petrushka

My final example is much weirder in that it resembles the more remote passages cited by Taruskin from the German romantics. This passage (ex. 7) is taken from the concluding measures of Brahms’s song “Immer leiser wird,” Op. 105, No. 2, and may be considered octatonic in that all four triads of the collection are present in succession without “outside” interference (mm. 41–47). I should add, however, that this clever innovation sounds worn and hackneyed to my ears and nearly ruinous to this otherwise most beautiful of songs. As an enthusiast of Brahms’s music, I am grateful that this is in fact the only instance in his oeuvre where the full minor-third cycle, unimpeded at a local level, is allowed to run its course. Several years ago Taruskin sought in a similar vein to instruct us on the nature of authentic Russian folk songs in his classic study of The Rite of Spring. In the process, Stravinsky was chided for having “busily revised his past” to suit his neoclassical preoccupations, his neoclassic “fealty to the values of ‘pure music’” (Taruskin 1980, 50).

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Taruskin’s claim was that, while composing this music, Stravinsky had been alert not only to the authenticity of his folk-song borrowings but to their ethnological character as well, and that the composer had deliberately sought material which, in seasonal and ceremonial character, was appropriate to the implications of the scenario. The idea behind this startling exposé was that “knowing that The Rite utilized many folk melodies; knowing something of the nature and function of these melodies in their natural habitat” (Taruskin 1980, 512) could alter our apprehension of the piece and, presumably, the nature of our appreciation as well. A similar approach was pursued in a fascinating study of the original scenario of The Rite (see Taruskin 1984).

Example 6  Analysis of examples 1–4

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Example 7  Brahms, “Immer leiser wird,” Op. 105, No. 2

Needless to say, all this came as news to those for whom this monumental slice of contemporary art had served for over half a century as the source of the most profound delight, for whom, one

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suspects, the descriptive title itself had borne sufficient weight, and for whom the phony Russian titles of the individual dance movements, or their French and English translations, had long been either dismissed or merely tolerated as a pretentious-sounding nuisance. No doubt the images that shaped the scenario and, to a certain extent, the music as well, can often clarify or at least confirm our sense of musical form. But whether a study of the handful of Lithuanian and Russian “source melodies” can provide similar illumination is surely open to question. The lines of contact are here too remote, the bits and pieces of melody too heavily obscured by the reality of all that is indeed profoundly new. There are fundamental differences between the use of folk songs in The Rite and the use of such material in The Firebird and Petrushka. It is revealing to compare Stravinsky’s version of an Easter song in Petrushka to Rimsky-Korsakov’s tonal adaptation of the same melody, or to acknowledge how the instrumentation and harmony of a French chanson ingeniously project a street flavor. But there is nothing comparable to this in The Rite. The original Lithuanian sources are without titles or harmony, and I seriously doubt that Stravinsky could have known all that much about their authentic character or function. The borrowings are of documentary interest only; musically, they are curiosities. Even with the Russian prototypes—where there is perhaps a greater certainty of the composer’s familiarity— character, function, and outline are radically transformed. In the end one is tempted to accept Stravinsky’s plea of forgetfulness or indifference on the whole matter of borrowing. On several occasions he did in fact confess that the question of originality, of “fabrication or ethnological authenticity,” was of no interest to him (Craft 1969, 16). In these elaborate reconstructions, these attempts to secure a credible Russian past for Stravinsky, Taruskin seems to me often to be battling against history itself. Undeniably, Stravinsky distorted or sought to revise the circumstances of the conception of The Rite. What is easily forgotten, however, is that these distortions or omissions were symptoms of evolving personal aesthetic impulses, and as such were no less genuinely legitimate than the assumptions which now appear to have shaped the origin of this piece. Taruskin might well agree on this point. There was nothing inherently “wrong” with Stravinsky’s changing aesthetic attitudes,

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notwithstanding the distortions to which they led. Early on he might well have sensed that by sidestepping the explicit symbolic confines of The Rite, the music could attain the kind of universal appeal it has now for so long enjoyed. But can the aesthetics of “musical abstraction,” or “pure” or “absolute music,” be isolated and depicted as a peculiarly Stravinskian hang-up? These ideas have been with us for some time, at the very least since the eighteenth century when, as a defense against the stolid, virtuous tradition of melody and the word, there arose an attempt to fashion a new philosophical and critical basis from which to support the growing popularity and prestige of the new instrumental forms. Taruskin might argue that this is precisely the point, that these ideas were foreign to the Russian symbolic climate in which The Rite was conceived, and were adopted only later by the composer as part of his neoclassical volteface. Yet, here too, one could argue quite differently. Given the fate of much ballet, incidental, and program music during the past century, the concert-hall career of The Rite can hardly be deemed exceptional. For better or worse, the reality in modern times has been stubbornly one-sided: with opera as the exception, music has succeeded as musical structure (that is, as “music”), or it has barely succeeded at all. One senses, too, in these appeals to a Russian past (a kind of “Evocation of the Ancestors,” as it were), an effort to fend off the incursions of pitch-class set analysis. The motive is not “territorial,” but stems from a suspicion that analytical preoccupations confined to such a high level of abstraction are not apt to yield much in the way of individuality. Taruskin would above all wish to preserve the particularity of Stravinsky’s music in all its quirkiness, and would prefer not to have it stuffed, along with the music of Scriabin, Schoenberg, Berg, Bartók, and Ives, into a single barrel of uniformity. I sympathize with many of these concerns. Of course, Taruskin knows fully well that to identify lengthy sections from The Rite, Les Noces, Symphony of Psalms, and Symphony in Three Movements as octatonic or octatonic-diatonicis to make a determination at a relatively high level of abstraction, namely, at the level of the unordered pitch-class set, a ruling roughly equivalent to one describing Mozart’s Jupiter Symphony as primarily diatonic. But I suspect that he is equally aware that it is just this kind of a referential determination that can guide the melodic and harmonic

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segmentation along a convincing path (one which would preserve the primacy of the triad) and from which one could descend the “ladder of abstraction” (Rahn 1980, 77) to those more immediate and determinate levels at which the peculiarity of individual pieces is to some extent ensured. Incompatibility is not the issue here. The notion of the pitch-class set and its attendant formulations (similarity, complementation, and so forth) can in no way be construed as incompatible with a more determined octatonic or octatonic-diatonic perspective. At issue, rather, is the referential character of much of Stravinsky’s music, the degree of hegemony exercised by the octatonic and diatonic sets, and, ultimately, the degree of abstraction that is deemed necessary or desirable in formulating rules of equivalence and association that can account for the coherence or consistency of the materials. Inevitably, one’s choices in this regard are guided to some extent by one’s preoccupations with other literatures and traditions. But this does not mean that the set-theoretic approach is awkwardly neutral or without a historical foundation. The Stravinsky pieces mentioned above are for the most part non-tonal,4 and frequently exhibit, as Allen Forte has claimed, the kinds of harmonic structures prevalent in the atonal music of Schoenberg, Berg, and Webern. Nonetheless, as an attempt to deal with a large number of seemingly intractable works, pitch-class set analysis represents a systematic retreat to more lenient and broadly defined terms of relatedness and 4Tonality

is viewed here in its restricted and historically oriented sense as a hierarchical system of pitch relations based referentially on the major-scale ordering of the diatonic set and encompassing an intricate yet fairly distinct set of harmonic and contrapuntal procedures commonly referred to as tonal functionality or triadic tonality. The by now classic formulation of this view is given by Arthur Bergen: Tonality ... is defined by those functional relations postulated by the structure of the major scale. A consequence of the fulfillment of such functional relations is, directly or indirectly, the assertion of one pitch class over the others within a given context—it being understood that context may be interpreted either locally or with respect to the totality, so that a hierarchy is thus established, determined in each case by what is taken as the context in terms of which priority is assessed. It is important to bear in mind, however, that there are other means besides functional ones for asserting pitch-class priority; from which it follows that follows that pitch-class priority per se: (1) is not a sufficient condition of that music which is tonal, and (2) is compatible with music that is not tonally functional. (1972, 123)

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association. The question, then, is whether, for its proper definition, the logic of much of Stravinsky’s music requires the greater generality of this retreat, or whether, by way of an octatonic-diatonic determination, it remains susceptible to the immediate rulings of a more familiar mode of reckoning, one characterized by scales, scalar orderings, triads, pitch-class priorities, and the like. In my own work I have stressed the second of these alternatives, namely, the octatonic-diatonic approach favored by Taruskin.5 And as Taruskin himself notes, the lines of communication here have been rewarding and reassuring. Often enough, too, we have enjoyed and profited from the disagreements as much as the agreements, although the latter have greatly overshadowed the few differences of opinion. This may not be immediately apparent from the present paper, but my ideas on the relationship of Stravinsky’s music to all sorts of trends and traditions has changed considerably. The world of Stravinsky has been made a good deal more interesting as a result of Taruskin’s formidable detective work, and I wish him well.

References

Antokoletz, Elliott 1984. The Music of Bela Bartók. Berkeley and Los Angeles: Univ. of California Press. Berger, Arthur. 1977. Problems of Pitch Organization. In Perspectives on Schoenberg and Stravinsky, ed. Benjamin Boretz and Edward T. Cone, 123–54. New York: W. W. Norton. Craft, Robert. 1969. Commentary to the Sketches for The Rite of Spring: Sketches 1911–1913, by Igor Stravinsky. London: Boosey and Hawkes. _____. 1971. Pages from a Chronicle. New York Review, Feb. 25, p. 24.

Perle, George. 1977. Berg’s Master Array of the Interval Cycles. Musical Quarterly 63 (1): 1–30. Rahn, John. 1980. Basic Atonal Theory. New York: Longman.

Stravinsky, Igor, and Robert Craft. 1960. Memories and Commentaries. New York: Doubleday. _____. 1963. Dialogues and a Diary. Garden City: Doubleday.

_____. 1966. Themes and Episodes. New York: Alfred A. Knopf.

5See van den Toorn 1983. For a more detailed discussion of The Rite of Spring, see van den Toorn, in press.

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Taruskin, Richard. 1980. Russian Folk Melodies in The Rite of Spring. Journal of the American Musicological Society 33 (3): 501–43.

_____. 1984. The Rite Revisited: The Idea and the Sources of its Scenario. In Music and Civilization: Essays in Honor of Paul Henry Lang, ed. Edmond Strainchamps and Maria Rika Maniates. New York: W. W. Norton. _____. 1985. Chernomor to Kastchei: Harmonic Sorcery: or, Stravinsky’s “Angle.” Journal of the American Musicological Society 38 (1): 72–142.

Van den Toorn, Pieter C. 1983. The Music of Igor Stravinsky. New Haven: Yale University Press.

_____. In press. Stravinsky and “The Rite of Spring.” Berkeley and Los Angeles: Univ. of California Press; Oxford: Oxford Univ. Press.

Reply to van den Toorn

My old friend van den Toorn is right. He has missed my point. My essay was not an explication de texte. I was not interested (at least in the present connection; in another it might be very interesting indeed) in establishing what Stravinsky meant by his “angle.” I was interested in defining it. I wanted to determine, to the best of my ability, what that angle was, not what Stravinsky said it was, though it was, or wished it thought it was. The Stravinsky on whom my sights were set, moreover, was neither the Stravinsky who wrote the words at issue, an octogenarian serialist who felt he had a lot to answer for, nor the Stravinsky about whom they were written, the arbiter extraordinaire of Parisian neoclassic chic and chief opposer of all he was later to embrace. I was writing about a fledgling composer In a far-eastern outpost of European culture who was taking his earliest, tentative, closely supervised steps in composition. (The only works I quoted were his Op. 1 and Op. 2.) I was interested in the fledgling’s patrimony, of course, because he was father to the Parisian neoclassic and grandfather to the Hollywood serialist. But the latter pair no longer knew him nor wished to know him, and had little light to shed upon him. On the contrary, for their various reasons they had repressed him and now wished to suppress him. My critic is correct in assuming that the titular allusion to the octogenarian Stravinsky’s recollections was ironic. And he is far from alone in chiding me for what he calls my “relentlessly trigger-happy approach” to Stravinsky’s

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autobiographical testimony. I have been living the life of a hunted desperado in everybody’s footnotes ever since I dared, to “Russian Folk Melodies in The Rite of Spring,” not only to the question the factual reliability of those famous texts but also (and, I thought, with all due respect and caution) to show that there were good and specific reasons not to accord Stravinsky’s memoirs any more credence a priori than a well-trained scholar accords anybody’s memoirs. The indignation with which this aspect of my work has been met has indeed surprised and saddened me; for it testifies, in my opinion, to a lack of maturity in our discipline. Writers or dictators of memoirs are witnesses, not oracles. Their testimony carries no privilege— that is, if we regard scholarly inquiry as a critical process, rather than an exegetical one. Unlike judicial inquiry (at least as practiced in this country), scholarly inquiry is not conducted through an adversarial procedure. Confronted with a piece of testimony our job is not to prove it true or prove it false, but simply (and etymologically) to prove it, that is, test it. This is done by a process of comparison with other witnesses. When witnesses contradict one another, a ruling must be made as to their veracity. And when testimony is rejected on such grounds, reasons must be stated in the form of a factual determination, a judgment of character, or an assessment of motive. I have recently said my piece at length on these matters as they pertain to Stravinsky and will not try the reader’s patience by rehearsing them again.6 Van den Toorn, on the contrary, evidently prefers the exegetical approach to Stravinskian texts, as we know implicitly from his otherwise admirable monograph, and as he affirms explicitly in his critique of my work. He also refuses to distinguish among Stravinskys. For him the composer is one and indivisible, now and forever. Anything one says about Stravinsky aged twenty must, in his view, be reconciled with what we know of Stravinsky aged eighty. As far as van den Toorn is concerned, it is sufficient to note that the Stravinsky of the memoirs reacted ironically to Schumann in order to conclude that the Stravinsky about whom I was writing would have found Liszt too corny and Rimsky too flimsy to be his mentors. He also believes that the eighty-year-old Stravinsky’s invocation of “the German stem” represented a “serious attempt. . . to describe 6See

17.

Richard Taruskin, “Stravinsky and the Traditions,” Opus, 3 (4) (June 1987): 10–

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the nature of his. . . neoclassicism.” This leads the old man’s exegete straightaway into tautology and fantasy. Oedipus Rex bears scant relationship to the “stem” composers named in 1963, whose work Stravinsky, like so many others in the Parisian modernist orbit between the wars, lost no opportunity to disparage in the twenties. With the exception of Bach, whose place on the “stem” list is a bit factitious anyway, the models for the neoclassic revival were Italian and French, and the movement itself amounted in large part to a reassertion of the aesthetic values of the aristocratic enlightenment against those of the Germanic romantic line with which Stravinsky later wished retroactively to claim common cause. His remarks in Dialogues and a Diary, far from a “serious” critique of Oedipus, were typically disingenuous and self-serving. Isn’t it time to get beyond them? Isn’t it time to drop the exegetical approach through which so much of the Stravinsky literature has become mired in perpetuated an reified fallacy, equivocation, not to mention yesterday’s partisan propaganda, and to take advantage of the aerial perspective historical methods can afford us? But here again we encounter resistance. Van den Toorn wants to stigmatize the approach adopted in my essay as “musicological orthodoxy” (musicological here understood to mean historical, as is regrettably customary). He doesn’t scare me off. “History is bunk” has become the equally orthodox battlecry of certain selfprofessed “theorists,” who are eager to declare, as van den Toorn so disappointingly does, that their “hearing and understanding” are impervious to historical “disclosure.” As in his way of viewing Stravinsky himself, van den Toorn betrays a strangely static view of the music. Are his hearing and understanding so fully formed and finished? I cannot see what is gained by sealing oneself off like this, since I find my hearing and understanding of music to be constantly and excitingly in flux, not only affected but immeasurably enriched by what I have learned both from my historical investigations and from exposure to the analytical insights theorists, Pieter van den Toorn prominent among them, have furnished over the years. History and theory are ideally symbiotic, or so it appears to me, and ultimately so intertwined as to become indistinguishable. Why dichotomize them? Why force scholars to choose between them as between two warring crowns? It only impoverishes musicology. I find my own work on Stravinsky to be getting more and more analytical

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as time goes by, that is, increasingly concerned with investigating the principles of coherence that operate within individual compositions, and with questions involving the relationship between surface detail (“style,” if you will) and structural background. But my historical investigations are what have given me the specific grounding in style and structure alike that permit the confident framing of generalizations. This is indeed an orthodoxy with “us musicologists.” It was framed with great economy by one of our sages a couple of decades ago in a text we still often spoonfeed our novices. “In the analysis of art-works,” wrote Leo Treitler, “we seek to distinguish the fortuitous from the significant, and the uniquely significant from the conventional, and . . . the evidence of the historian is directly relevant to that task.”7 To take the Henry Ford view currently fashionable in certain theoretical quarters is to render either of these discriminations Impossible, and it also divorces analysis from any consideration of value, which renders the whole exercise pointless. I would even go so far as to say that to the extent that theorists do engage with questions of value, and to the extent that they do attempt to isolate the unique features of the music they analyze, they are in fact making historical judgments, if only tacitly. The trouble with tacit judgments of any kind is that they are less likely to be safeguarded against error than overt ones. There are, after all, at least as many ways to segment a musical surface as there are to skin a cat. What shall guide our scalpel as we perform the dissection? How do we know our findings are significant and not fortuitous? The closer we remain to the concrete realities of the music the less the risk of fortuity, it is easy enough to say. But how are these realities to be determined? Those who resolutely exclude historical concerns from their purview are forced to define the “reality” of the music they analyze according to arbitrary, atomistic schemata (e. g., simple recurrence of pc sets) that have been increasingly recognized of late, even within the theoretical community for the self-validating, circular things they are. Practitioners of such methods are, moreover, notoriously defenseless in the face of textual corruptions. I am tempted here to generalize to the effect that the possibility of basing a textual 7Leo

Treitler, “On Historical Criticism,” Musical Quarterly 53 (1967): 190.

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criticism on it is the first prerequisite of any analytical approach and the first test of its validity. In support of this assertion I offer two examples involving Stravinsky, one positive, so to speak, the other negative:



1. The oboe cadenza at the end of the first of the Pribaoutki of 1914 would be referable to one of the octatonlc collections if it contained an E-flat instead of an E-natural—that is to say, if the part carried the three-flat signature found in all the other parts in the published score except the transposing clarinet. A sketch for the cadenza8 confirms the surmise, based on an analytical inference, that the oboe part was meant to carry the signature, which was inadvertently omitted from the Chester score, owing perhaps to the fact that the oboe does not play in the song until the cadenza and was consequently omitted from the initial brace of the MS, where the signatures were entered. 2. In his recent “Hymenopteran Response” to a letter to the editor of Music Analysis in which I questioned the appropriateness of pc set analysis to Stravinsky’s music, and in which I noted a number of instances where the method had not saved its practitioner from tabulating and analyzing misprints, Prof. Forte reproduced and analyzed according to his lights the chordal motto at the beginning of Zvezdolikii, meanwhile incorrectly transcribing the final chord.9 He then proceeded to base a number of very trenchant analytical points on the corruption he had thus introduced into the text (including a nonexistent relationship between the harmonic vocabularies of Zvezdolikii and Petrushka). Had the piece been analyzed within a properly historical perspective—one that took account, among other things, of its relationship to the nearly contemporaneous Seventh Sonata of Scriabin, to Stravinsky’s intense admiration for which historical documents testify, the analyst would have immediately spotted the faulty reading, which introduces a harmony quite out of keeping either with Scriabin’s tonal vocabulary or Stravinsky’s emulation of it.

8A facsimile of the cadenza is published in Vera Stravinsky and Robert Craft, Stravinsky

in Pictures and Documents (New York: Simon and Schuster, 1978), p. 131. Forte, “A Hymenopteran Response,” Music Analysis 5 (2-3) (1986): 331.

9Allen

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Of course, merely to establish “referability” to some theoretical construct like the octatonic scale does not protect one against fortuities and non sequiturs, either. The “level” of such an analysis, as van den Toorn puts it, is still excessively “abstract,” that is to say. far removed from the concrete properties of the music—its “realities,” as I put it above. Van den Toorn himself gives an example of the pitfalls of reifying “referability” in his analysis of the bell-ringing progression from Boris Godunov. I see no justification for calling this music octatonic merely because its two constituent harmonies happen to be referable to what van den Toorn calls octatonic Collection II. As he is quick to point out, moreover, judged as an example of octatonicism, the passage is of inferior quality. It is being measured against a superfluous and invidious standard. Musical “realities” have to do not only with the notes on the page—the same dozen pcs, after all, no matter who the composer (unless it’s Haba or Wyschnegradsky) or what his style—but also with how they got there. What is ideally uncovered by analysis is not just pitch or rhythmic configuration tout court but some insight into compositional practice. That is why I considered it so important to research the background of Stravinsky’s octatonicism not merely to terms of sheer local referability to the scale (for then, as I have shown, his octatonic ancestry would have to be widened to encompass Beethoven and Reicha, Mozart and Bach, and all useful specificity would be lost), but in terms of usage, routine, technique— all that goes into the make-up (in this case of an individual) of a style or (in case of a group) of a school. The main contribution of my essay, in my opinion, lay in setting the emergent Stravinsky within a relevant context of common practice, which I demonstrated by setting his music alongside that of his teacher and his fellow pupils, by showing the theoretical premises according to which “octatonicism” was conceptualized, rationalized, and pedagogically imparted, and—most important of all—distinguishing the specific partitioning strategies that mark octatonicism à la Rimsky-Korsakov off from that, say, of Scriabin, and showing that it was precisely the former that conditioned the young Stravinsky’s theoretical baggage and compositional routines. In terms of Tteitler’s formulation, this provides the background of the “conventional” against which the “uniquely significant” in Stravinsky can assume relief. And as we learn more about the background, much that appears unique on the

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surface often recedes into it, grounding Stravinsky’s practice to an ofttimes amazing extent in what were the conventions of his specific environment. As an example we might consider the famous “Petrushka” chord. Quite obviously, Stravinsky’s more radical octatonic usages do indeed cause their antecedents in Liszt and Rimsky to “seem tame and remote in comparison,” as van den Toorn puts it, “as if [why as if?—They were] conceived in a different age.” The mere observation of this fact ought not to give license lazily to call off the hunt, though, lest our understanding of Stravinsky’s innovations remain simplistic. Van den Toorn draws a decisive and in his view impassible line between Rimskian harmonic successions and Stravinskian “superimposition,” citing this distinction as a reason for his indifference to historical investigations like mine. Yet full-fledged instances of the “Petrushka” chord, the most famous Stravinskian “superimposition” of them all, can be found in works dated 1908 by Maximilian Steinberg, Rimsky’s star pupil and son-in-law, and even in Rimsky himself.10 So much, for the time being, for the unique vs. the conventional. Awareness of a common theoretical viewpoint and a common compositional practice in the background of any music (a quintessentially historical kind of awareness) is also what enables us to distinguish the fortuitous from the significant in any musical context—again whether we acknowledge the fact or not—and it is indeed what “justifies an analysis,” to use van den Toorn’s phrase, along octatonic or any other lines. Even the spokesmen of pc set theory, who are wont to dismiss the whole historian’s kit and caboodle as so much “intentionalism”—so much confusion, in other words, of insignificant author with autonomous work—nonetheless render historical judgments of precisely this kind every day of their working lives, when they decide whether to apply their methods to a given musical text in the first place. For “atonal” music is not the only kind of music that is made up of pitch-class sets: pitch classes, and hence pitch-class sets, can be found in all music, and there is 10See Taruskin, “Chez Pétrouchka: Harmony and Tonality chez Stravinsky,” Nineteenth-

Century Music 10 (3) (Spring 1987): 268–69. Omitted from example 2a, which shows a sketch by Rimsky-Korsakov that includes the Petrushka chord, is the composer’s note to himself, “The same in the interstices G♯ and D,” which demonstrates his explicit awareness of the octatonic pitch field within which he was working.

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no a priori reason why all music could not be construed according to the method Forte set forth in The Structure of Atonal Music. Why isn’t it, then? Why don’t we analyze the Eroica that way, or Lulu? It can only be for the reason that we have assigned these works to historical categories other than the “atonal,” and have therefore decided that their significant features can best be revealed by other means. Concomitantly, we have decided, therefore, that pc analysis would yield, for “tonal” or “serial” music, results that are more likely to be fortuitous than significant. Both of these, but particularly the first, are historical discriminations, and when it comes to drawing lines between the categories (as in James Baker’s recent book on Scriabin) the lines are drawn in traditional historical terms, right down to trusty historiographical fictions like “transitional” phases. But we have to take this further. If we have the choice between analyzing a piece this or that way and we choose to do it this way, there must be practical considerations at work as well as historical ones, especially if we profess no interest in history. In the case of tonal music, I suppose, we realize that all notion of function and voice leading would be lost in a pitch-class set analysis, and that the degree of “recurrence” and “inclusion”—held by practitioners of pc analysis to be the main, if not sole, arbiters of significance—would be so great as to become oceanic and meaninglessly redundant, given the fact that, owing to the a priori assumption of inversional identity,11 the chord qualities (major vs. minor, to begin with) on which our understanding, indeed our very perception of the music depends must go by the boards. In the case of serial music, 11Forte insists that he posits inversional “equivalence,” not identity (“A Hymenopteran

Response,” p. 332); but I persist in calling a spade a spade: in the practice of pc set analysis (unlike, e. g., the old “dualistic” theories of Hauptmann and Riemann, which also invoked and depended on inversional equivalence), the equivalence does Indeed amount to identity (to the extent that a single reference number is employed without qualification for inversionally related sets). Indeed, when exposition of his method was his object, rather than its polemical defense. Prof. Forte readily and explicitly acknowledged the interchangeability of the terms “equivalent” and “identical” for pc set analysis. In his very first description of his system, “Context and Continuity in an Atonal Work: A Set-Theoretic Approach” (Perspectives of New Music 1 [2] [1963]), we find the following statement under the heading “Equivalence” (p. 76): “Set A contains no two equivalent (identical) subsets.” Similarly, in The Structure of Atonal Music, the concept of equivalence is Introduced by means of the following rhetorical question (p. 5): “Given two pc sets to compare, one might ask: Are they the same, or do they differ?”

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we are equipped by our understanding of the method by which it was composed (“intentionalism” again) to perceive subtleties in the linear ordering of the pitch classes that go far beyond primitive observations about recurrences of configurations. In both kinds of music we rely on theoretical guides to segmentation that free us from the arbitrariness, the circularity, and the primitiveness (usually amount-tag to crude vertical slicing or the exhaustive and uncritical process of sampling known as imbrication) that continue to bedevil pc analysis. We invoke the latter method when the music falls outside categories for which we have reliable theoretical guides. In other words, and more accurately, it is the method we invoke when (and only when) we have no method. It is history that tells us whether we have one.12 Were a troop of Martian musicologists to descend on Earth (let us say, after World War III) and discover the Eroica, they would not know it was “tonal.” For them, pc analysis would suffice. But for us humans who have a history on this planet, the kinds of insights such an analysis affords should no more suffice for Stravinsky or Schoenberg than for Beethoven. Taken in conjunction, van den Toorn’s work and mine (both of us heavily indebted, of course, to the pioneering insights of Arthur Berger) suggest the beginnings of a bona fide analytical method for some of Stravinsky’s music, particularly that of his “Russian” period. Surely no one can take the purely taxonomic survey of pc sets on the surface of, say, The Rite of Spring seriously any more as an adequate account of a work’s “harmonic organization.” Van den Toorn chooses to claim he can do without me, and I can well understand his feeling so, since his own “hearing and understanding” is so steeped by now in octatonic lore that it could hardly become more so. For my part, I could just as easily claim that I can do without van den Toorn, in that the historical record I have uncovered has led me independently to all of van den Toorn’s discoveries. I’m glad, though, that I don’t have to do without the heartening confirmation his brilliant inferential work has given my investigations; and perhaps one day he will 12This

might be the place to enter a protest against recent applications of pc set analysis to the music of Brahms, Liszt, and Wagner. Where other analysts engage with the fascinating problems engendered by this music in its ambiguous relationship with the common practice, the pc set approach clears the slate of the common practice and reduces the music’s problematic features to a bunch of static, atomistic particles, easily manipulated because decontextualized. Analysis, when all is said and done, may in fact be only a game; but games are only interesting when the rules are hard.

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realize that the historical support I have provided has gained his analytical approach many formerly skeptical adherents (they have confessed as much to me, at any rate). In his eagerness to maintain the walls that separate “theorists” and “musicologists,” van den Toorn comes on as far more generous and conciliatory toward the work of the pitch-class set analysts than toward mine. He is quick to assure the reader that “incompatibility is not the issue,” that his methods can coexist peacefully with those of the Yale contingent. In this very gentlemanly way, however, he has (surely knowingly!—would that I could be so subtle) dealt their position the coup de grâce. Compatibility, not incompatibility, is the issue. For pc set “analysis” is incompatible with nothing, as the fact of its universal potential applicability already testifies. It begins not with observation of musical particulars but with a universe of possibilities. The comparison of any musical entity with such a universe yields an inexhaustible quarry of “true facts” but no criterion of relevance. As long as no such criterion has been established, whether inferentially or historically (and if the one approach is valid, its confirming counterpart can also be found), the endless stream of ostensible relations stemming from the pc survey can persuade us for a while that analysis is being accomplished. But in. fact it is only a tabulation that can just as well be carried on in the presence of analysis as in its absence (hence the universal “compatibility”). Nor is it really so innocuous as I may be making it seem, since in its anodyne effect (one never comes back from the fishing expedition empty-handed, there is always “something to say,” some “finding” to report) it can deflect attention away from the task at hand, which is to formulate analytical methods, not concoct a universal solvent. Richard Taruskin

Chapter 3

Stravinsky Re-barred

I In Emotion and Meaning in Music Leonard B. Meyer offered the view*—no doubt shared by many—that much contemporary music ‘looks more irregular than it actually sounds’.1 As illustration he cited a passage from the ‘Soldier’s March’ of Stravinsky’s L’Histoire du soldat (1918). Reproduced here as Exs 1a and b, the passage at bs 48-57 was re-barred by Meyer according to the steady 24 periodicity of the basso ostinato. This analysis raises interesting questions about Stravinsky’s methods, especially with reference to the (A)-B-C♯-D(E) upward sweep of the melody at bs 48-50, 51-3 and 55-7. Meyer’s point was that ‘the main beat of the melody’, which he identified as A at b.48, shifts in relation to the ostinato’s accentuation at b.51, but that at the end of the climactic stretch at b.55 the initial alignment is restored.2 In other words, at the point marked ‘y’ in Ex. 1b, A’s 1Leonard B. Meyer, Emotion and Meaning in Music (Chicago: University of Chicago, 1956), p. 119. 2Ibid., p. 120.

Reprinted from Music Analysis, vol. 7, no. 2 (July, 1988).

*A shorter version of this study was delivered at the Cambridge University Music Analysis Conference 1986. The Music of Stravinsky: Collected Essays Pieter C. van den Toorn Text Copyright © 1988 Wiley Layout Copyright © 2023 Jenny Stanford Publishing Pte. Ltd. ISBN 978-981-4968-62-1 (Hardcover), 978-1-003-35916-6 (eBook) www.jennystanford.com

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placement relative to the ostinato shifts, while further along at ‘z’ its original placement above the G of the ostinato is restored.

Example 1a  L’Histoire du soldat

Example 1b  L’Histoire du soldat, as re-barred by Meyer

Meyer misread ‘the main beat of the melody’. For as can be seen from the opening bars of the March as quoted in Exs 2a and b, it is the B rather than the A of the (A)-B-C♯-D-(E) sweep which, in accordance with the ostinato’s steady 24 frame of reference, is introduced as a metrically accented note, first at b.16 (Ex. 2a) and then at b.45 (Ex. 2b). Hence the details of accentuation are the opposite of what Meyer contended. The actual shift in placement occurs not at bs 51-3 but rather at bs 48-50, and then again at bs 55-7, where, paradoxically, it leads to the restoration of metrical coincidence and order at b.57.

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Example 2

This is in no way to question Meyer’s essential argument. At hand is a very clear demonstration of what is commonly termed ‘displacement’, that is, a shift in the accentual implications of a reiterated fragment. More precisely, the metric identity of the B-C♯-D upward sweep relative to the ostinato is contradicted: introduced on the beat at bs 16 and 45, it assumes an offbeat identity at bs 49 and 56. At the same time, the dependency of felt displacement on the ‘square metrical dance schemes’ of the tonal tradition is underscored3; displacement of this kind hinges necessarily on a steady, metric periodicity. And in this way, too, Meyer reveals himself as an essentially ‘conservative’ interpreter of this music, in the quasi-technical sense in which this term was introduced by Andrew 3See

Hans Keller, ‘Rhythm: Gershwin and Stravinsky’, Score, No. 20 (1957), p. 19. Many of Keller’s reflections on ‘the art of syncopation’ and the presence of steady background metres in Stravinsky’s music parallel those of Meyer.

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Imbrie several years ago.4 In the face of conflicting evidence, his instinct is evidently to hold on to a prevailing regularity for as long as possible, often with the consequence that the effect of disruption is all the more acutely felt. In the passage at bs 48-57 (see Ex. 1a) the metric scheme is thus heard as a series of ‘syncopations with minor irregularities rather than as a series of irregular meters’.5 The purpose of the shifting metre is to ‘enforce and guarantee the syncopation’.6 Nonetheless, as should be evident from even the most casual glance at Exs 2a, b, c and d, the issue is a good deal murkier than these introductory remarks imply. Indeed, Meyer’s curious slip— missing the melody’s ‘main beat’ and then mistaking its initially established accentuation for a subsequent displacement—is in this respect more defensible, and more telling, than might at first be imagined. Meyer has in fact fallen into a carefully disguised trap, laid with consummate skill by a composer for whom the laying of such traps had by the time of L’Histoire become a well-oiled routine. For Stravinsky’s invention presupposes a second, counteracting factor: the metric identity of the B-C♯-D sweep as an irregular 38 bar remains fixed throughout. And one could argue that these opposing forces of identity and displacement induce momentary states of disorientation in which cases of mistaken identity, such as experienced by Meyer, are not only understandable but an expected part of an informed response. Before looking ahead, however, it will be useful to consider in greater detail the nature of the displacement itself. 4Andrew Imbrie, ‘”Extra” Measures and Metrical Ambiguity in Beethoven’, in Beethoven Studies, ed. Alan Tyson (New York: Norton, 1973), pp. 45-66. In Beethoven, however, the ‘conservative’-’radical’ dichotomy entails reactions to metric irregularity and disturbance at levels of structure above that of the bar. The notion is reintroduced in Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge: MIT, 1983), pp. 23-5, in connection with the opening bars of Mozart’s G minor Symphony. At the two-bar level, the first movement of this work begins with accents on the down-beats of the odd-numbered bars, a formula which is clearly reversed with the restatement of the principal theme at b.20. The authors conclude that the conservative listener might hold on to the established framework until b.14, while the radical one might readjust his or her metrical bearings at the first signs of conflict at b.10. 5Meyer, Emotion and Meaning in Music, p. 120. 6Ibid.

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II The disruptive content of the March can be traced to the melody’s B-C♯-D upward sweep which, as already noted, is barred throughout as a 38 unit. In opposition to this barring, a steady 24 metre is imposed by the G-E/D ostinato whose connecting beam crosses the barline during stretches of foreground irregularity. The contradictions to which the B-C♯-D sweep is subjected can be apprehended simply by examining the alignment of subsequent repeats with the ostinato pattern. In Exs 2a, b, c and d these repeats are aligned and marked with a series of dotted lines. In Ex. 2a the B-C♯-D sweep is introduced with a minimum of disturbance. Here, of course, its onbeat identity in relation to the ostinato’s 24 pattern is first established and is as yet not subject to displacement. Moreover, the 38 bar of the sweep is followed by another 38 bar which immediately cancels its potential threat to the crotchet tactus.7 And with the earlier 34 bar at b. 14, the two 38 bars cancel each other out at b. 18. Hence the 38 bar at b.16 figures merely as a potential troublemaker. And the terminating E at b. 17 is likely to be heard as an offbeat element, as a syncopation in relation to the steady 24 framework of the ostinato. Moreover, at bs 45-6 (see Ex. 2b) this identity is not markedly affected. For while B-C♯-D is shifted to the first, ‘strong’ beat of the 24 frame of reference, E retains its syncopated, offbeat identity. But further along, at bs 49-50 (see Ex. 2c), this identity is indeed contradicted. For in accordance with the 24 metre the sweep now falls off the beat, which means that its terminating E assumes an onbeat identity, not, as earlier, an offbeat one. A contradiction is 7Tactus and pulse are here used interchangeably. Both refer to that particular level of metrical structure where, in tonal music of the past, regularity is most stringent, and according to which batons are commonly waved, floors are tapped and steps are danced. Tactus, a Renaissance term, encompasses both the notion of pulse and a standard marking of 70 beats per minute; in tonal music, the rate is commonly between 40 and 160 beats. In A Generative Theory of Tonal Music, Lerdahl and Jackendoff introduce these terms in the following manner: ‘Musical intuitions . . . clearly include at least one specially designated metrical level. . . the tactus. This is the level of beats that is conducted and with which one most naturally coordinates foottapping and dance steps. When one wonders whether to “feel” a piece “in 4” or “in 2”, the issue is which metrical level is the tactus. In short, the tactus is a perceptually prominent level of metrical structure . . .’ (p. 71).

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thus established, and one of the conspicuous offbeat-onbeat variety. Notwithstanding the preserved 38 bar of the B-C♯-D sweep, the initial offbeat identity of its terminating E is contradicted by an onbeat appearance. Finally, at bs 50-7 (see Ex. 2d), these conflicting identities are presented successively in a tutti summation. In the first occurrence (bs 52-3) the initial offbeat identity of the terminating E is restored; in accordance with the 24 metre, E resumes its syncopated identity. But instead of an immediate cancellation of the first 38 bar, as at bs 1617 (see Ex. 2a), a resolution of the 38 ‘troublemaker’ is delayed until bs 56-7, where B-C♯-D-(E) reappears in its displaced, contradicted version. Yet it may be prior to this final contradiction, at b.53 in fact, that doubt and uncertainty arise. Indeed, the contradiction at bs 56-7 may not be felt as such. For by now the reversals have become so persistent, and the irregular stresses in the percussion (not shown in Ex. 2d) have wrought such additional havoc, that the steady 24 periodicity of the ostinato itself is challenged.8 Listeners seeking to hold on to the initial onbeat identity of the B-C♯-D sweep—and to gauge subsequent displacement accordingly—are here likely to begin questioning the stability of the ostinato’s 24 pattern. In other words, the sense of a ‘true’ metric identity for the B-C♯D-(E) fragment is temporarily lost, as its point of departure can no longer be distinguished from subsequent displacement. And with the loss of such identity comes the simultaneous loss of periodicity and pulse (here the crotchet, with a marking of 112); offbeats are for a moment no longer distinguishable from onbeats. True, order is eventually restored, as this climactic stretch draws to a close at b.57; the foreground irregularity emerges ‘on target’ with the background 24 metre. Yet the overall effect is as follows: Identity is first established in relation to a steady periodicity, which (1) is subsequently displaced, (2) leads climactically to a temporary state of disorientation where the periodicity and tactus are disturbed, and (3) is followed by a resolution of the conflict as the foreground irregularity and background periodicity emerge ‘on target’. But note that, in direct opposition to displacement, the irregular barring stubbornly preserves fixed metric identity. B-C♯-D is always 8Missing from Exs 2c and d is the semiquaver clarinet fragment, which at bs 45-7 and 57-9 is likewise subjected to onbeat-offbeat reversals in relation to the ostinato’s 24 frame of reference.

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barred as a disruptive 38 unit, while its terminating E falls always on the first beats of the succeeding bars. Hence the purpose of the shifting metre is not, as Meyer has claimed, ‘to enforce and guarantee the syncopation’, but rather to preserve a fixed metric identity for the reiterated fragment. That Stravinsky was conscious of this counteraction seems indicated by the stress and slur markings at b.49 in Ex. 2c. These are introduced precisely at the point where the initial onbeat identity of B-C♯-D is first contradicted by an offbeat placement. In opposition to the strong current of displacement at this point, the markings attempt to hold down B-C♯-D’s initial onbeat identity as introduced at bs 16 and 45. The double edge here is critical. The invention consists on the one hand of a form of displacement, of an effort to contradict the accentual identity of a reiterated fragment (which naturally presupposes steady metric periodicity, even if of the concealed, background type as exemplified by the March), and on the other hand of an effort to counter this displacement by pressing for a fixed metric identity in repetition. And if, as has been alleged, this strategy entails an element of ‘sadism’,9 then this can best be understood as it relates to counteraction, to the attempt to press for a metric ‘sameness’ in the repetition of a fragment (and often, in effect, a static, downbeating kind of ‘sameness’), to compose, indeed, as if the repetition were metrically genuine. Still, questions may linger about the effectiveness of counteraction, of fixed metric identity in repetition, where it threatens the integrity of the preserved 38 bar, as in the March. At b.16 in Ex. 2a, for instance, just how authentic is the 38 ‘feel’? Obviously, the character of the 38 bar is quite different from what it would have been had it been situated within a 38 periodic mould—or, as might here have been more likely, within a 68 mould. Given the strong 24 current in the March, the irregular barring takes on the feel of a self-conscious ‘counting’, which replaces the automatic sense of a steady periodic undertow. In a more conventional setting, an overall 24 metre would have been imposed throughout, and the 38 bars would have been replaced by stress and slur markings. Yet a change in character does not signal an absence of purpose, and a respect for the preserved 38 bar is essential 9See

Theodor W. Adorno, Philosophy of Modern Music, trans. Anne G. Mitchell and Wesley V. Bloomster (New York: Seabury, 1973), p. 159.

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if counteraction is properly to be observed. This is important in a performance of this music, where a strict, metronomic, percussive approach is required. For the point of the invention, of its displacement and counteraction, is quite simply lost if the music is subjected to any fluctuation of the beat, to ‘any subjectively expressive flexibility of the beat’.10 Indeed, it is from this angle that Stravinsky’s ‘formalist’ convictions can best be understood; that is, not as pure philosophy but as a reaction to the special articulative demands of the music, demands patently at odds with the articulative conventions of the nineteenth-century symphonic literature.11 The March leaves little room for ‘interpretation’ along conventional lines. If counteraction is applied, then this can come only by way of a strictly mechanical reproduction of the metrically fixed elements. Hence, too, the rebarring of Stravinsky in this essay is analytical, designed to uncover the concealed side of the double edge, not to serve as a substitute for the printed page.12 Indeed, as is in this respect sufficiently evident, Stravinsky himself was a ‘radical’ interpreter of his music. As a conductor, too, he favoured a strict adherence to the barline, a fact borne out by a number of recorded rehearsals13 and by the following excerpt from 10Ibid.,

p .154. a more detailed discussion of the relationship between Stravinsky’s aesthetics, his demands for a ‘mechanical’ articulation and his habit of composing at the piano, see Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven: Yale, 1983), pp. 204–14 and 238–45. 12Meyer’s re-barring of bs 48-57 in the March (see Ex. 1b) is also analytical in purpose, a fact which seems to have eluded Mieczyslaw Kolinski in his ‘A Cross-Cultural Approach to Metro-Rhythmic Patterns’, Ethnomusicology, Vol. 17, No. 3 (1973), p. 498. Kolinski complains that Meyer’s interpretation ‘trivializes the refinement of Stravinsky’s texture’. And so it does, of course, though Kolinski provides no satisfactory explanation. In truth, neither Meyer nor Kolinski explores the rationale of the irregular barring, or, more precisely, the question as to why, given the conditions of displacement, the composer should have opted for the rapidly shifting metre. (Obviously, the irregular barring conceals the displacement.) While Meyer misses the point of fixed metric identity, of disorientation, Kolinski ignores displacement, which can only be understood in relation to a steady, background frame of reference. 13Especially apropos in this regard is a private recording made in the 1940s of the composer rehearsing the Symphonies of Wind Instruments. Stravinsky’s insistence 11For

3

on a very close reading of the shifting 28 and 8 bars of the opening pages eventually tried the patience of a number of musicians, who retaliated by mimicking some of the composer’s idiosyncracies. I am indebted to Richard Taruskin for lending me his tape of the original recording.

Stravinsky Re-barred

Conversations with Igor Stravinsky. Here, of course, ‘accent’ means ‘phenomenal accent’ or stress14: R.C.: Meters. Can the same effect be achieved by means of accents as by varying the meters? What are bar lines? I.S.: To the first question my answer is, up to a point, yes, but that point is the degree of real regularity in the music. The bar line is much, much more than a mere accent, and I don’t believe that it can be simulated by an accent, at least not in my music.15

Yet it seems inconceivable that he could at the same time have been oblivious to the contradictions in the metric identity of the reiterated components which, hinging on a steady periodicity, lie concealed beneath the imposition of a foreground irregularity. For the shifting metre can acknowledge only one side of the coin, only one side of the double edge, namely, counteraction, the effort to render the repetition metrically the same. And such an effort can be appreciated only in relation to the current against which it is directed. The surface of the music may be ‘radical’, but its meaning is subject to a deeply ‘conservative’ grain of musical thought.

III

The question remains whether the terms of this invention apply equally to those manifold contexts of irregular barring in which the crutch of a steady ostinato does not readily appear. In other words, does felt displacement, with the steady periodicity upon which it necessarily rests, play a role in contexts of this kind? The answer would seem to be that it does, but that its effect varies from one piece to the next. For illustration we turn first to the opening pages of Les Noces (1917-23), and then to the slightly more difficult contexts of 14In

A Generative Theory of Tonal Music, the term ‘phenomenal accent’ is used to distinguish local stresses like sforzandi, long notes and leaps from metrical accents and structural accents (p. 17). Earlier, in Grosvenor Cooper and Leonard B. Meyer, The Rhythmic Structure of Music (Chicago: University of Chicago, 1960), stress is defined as ‘a dynamic intensification of the beat’ (p. 8). 15Igor Stravinsky and Robert Craft, Conversations with Igor Stravinsky (Berkeley: University of California, 1981), p. 21.

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the ‘Evocation of the Ancestors’ and a section from the ‘Sacrificial Dance’ in The Rite of Spring (1913). It should be noted at this point that the barring in the early drafts and editions of these works differs from that of the later, and more widely used, revised editions. In general, the early sketches and drafts featured longer bars which were subsequently sliced up into smaller units. The composer offered the following explanation in Expositions and Developments: In at least two of the dances [of The Rite] the lengths of measures were longer in the 1913 original; at that time I tried to measure according to phrasing. By 1921, however, my performance experience had led me to prefer smaller divisions (cf. the ‘Evocation of the Ancestors’). The smaller measures proved more manageable for both conductor and orchestra, and they greatly simplified the scansion of the music.16

These remarks betray considerable confusion about the actual dates of the revisions. Stravinsky seems to have forgotten, in Expositions and Developments, that the ‘smaller divisions’ of the ‘Evocation of the Ancestors’ were not a later conception, but were already a part of the 1913 autograph (Ex. 3b),17 if in somewhat different form than in the revision of 1929 (Ex. 3c).18 His confusion may have stemmed from the innumerable changes that dot the chronology of the revisions of The Rite. The first edition of the score (1921) actually returned to the lengthy 74, 84 and 104 bars of the original sketchbook version of the ‘Evocation’ (Ex. 3a).19 In contrast, 16Stravinsky

and Craft, Expositions and Developments (Berkeley: University of California, 1981), p. 147. 17The autograph of The Rite is with the Paul Sacher Foundation in Basel, Switzerland. In essentials, the barring of the ‘Evocation’ in the autograph corresponds to the barring in Stravinsky’s four-hand piano arrangement, published by Russischer Musik Verlag in 1913 (RMV 196) and reissued without modifications by Boosey and Hawkes in 1952 (B & H 17271). The barring in the autograph is given in Volker Scherliess, ‘Bemerkungen zum Autograph des “Sacre du Printemps”’, Musikforschung, Vol. 35 (1982), pp. 241–2. 18The re-barring of both the ‘Evocation’ and the ‘Sacrifical Dance’ in the 1929 revised version of The Rite was completed in January and February 1926, and in anticipation of a celebrated performance date: Stravinsky conducted The Rite for the first time on 28 February 1926, with the Concertgebouw Orchestra in Amsterdam. 19Stravinsky, The Rite of Spring: Sketches 1911–1913 (London: Boosey and Hawkes, 1969), pp. 73–4. This is a complete draft of the ‘Evocation’, of which only the opening eight bars are transcribed in Ex. 3c.

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the barrings in the autograph and in the 1929 revision represent different approaches to the problem of subdivision.20 Nor could a concern for problems of performance have dictated the details of these adjustments. In the 1913 and 1929 re-barrings of the ‘Evocation’, the dimensions of the movement underwent considerable expansion. The opening block of material, with its F♯E-D♯ figure in the bass, spans seven crotchet beats in the sketchbook version (with a fermata beneath the D♯), while in the autograph and 1929 versions it spans thirteen and eighteen beats respectively. Such changes must have been linked in some fashion to an altered conception of the movement as a whole. Significantly, too, the ‘smaller divisions’ of the ‘Evocation’ in the 1913 autograph and the 1929 revision are quite different. Irrespective of these considerations, 20In

the quotation from Expositions and Developments, Stravinsky’s reference to ‘the 1913 original’ is evidently to the 1921 edition of the score, and his reference to the ‘smaller divisions’ of 1921 is evidently to the new subdivisions of the 1929 revised score, completed in January and February 1926 (see note 18 above). The actual chronology of the barring of the ‘Evocation’ runs as follows: 1) the sketchbook version, with lengthy 74, 84, 104 bars; 2) the 1913 autograph, with subdivisions; 3) the 1921 edition of the score, based on the sketchbook version; 4) the 1929 revised edition of the score, with new subdivisions. Published by Russischer Musik Verlag (RMV), the 1929 revised edition bore the same date (1921) and the same publisher’s number (RMV 197) as the 1921 edition. It is largely in its 1929 revised form that the barring of both the ‘Evocation’ and the ‘Sacrificial Dance’ has become known. The Boosey and Hawkes editions of 1948 (‘1947 revised version’) and 1965 (‘revised 1947 version’), both numbered B & H 16333, were essentially corrected reprints of the revised score of 1929. The real 1921 edition of The Rite is now virtually inaccessible; the copy uncovered by the present writer is at the Lincoln Center Branch of New York Public Library. For a more detailed study of the revised barrings of both the ‘Evocation’ and the ‘Sacrificial Dance’, see Pieter C. van den Toorn, Stravinsky and The Rite of Spring’ (London: OUP, 1988), pp. 42-56, 85-96. The most comprehensive report on The Rite’s manuscripts, revisions and printed editions is Louis Cyr, ‘Le Sacre Du Printemps: Petite histoire d’une grand partition’, in Stravinsky: Etudes et temoignages, ed. François Lesure (Paris: Lattès, 1982), pp. 89-147. A condensed version of this latter is Louis Cyr, ‘Writing The Rite Right’, in Confronting Stravinsky: Man, Musician, and Modernist, ed. Jann Pasler (Berkeley: University of California, 1987). Robert Craft has published three separate accounts of The Rite’s revisions, each correcting and expanding on the conclusions of its predecessor: ‘Le Sacre du printemps: The Revisions’, Tempo, No. 122 (1977), pp. 2-8; Appendix B, ‘The Revisions’, in Vera Stravinsky and Robert Craft, Stravinsky in Pictures and Documents (New York: Simon and Schuster, 1978), pp. 526–33; Appendix D, ‘Le Sacre du printemps: A Chronology of the Revisions’, in Stravinsky: Selected Correspondence, ed. Robert Craft, Vol. 1 (New York: Knopf, 1982), pp. 398–406.

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it can only be assumed that, at some point in the process of rebarring, method intervened. The subdivisions of the 1913 and 1929 versions doubtless proved, for conductor and orchestra alike, ‘more manageable’ than the longer bars of the sketchbook version and the 1921 edition. Yet it is with the rationale of these subdivisions that our concern rests. Why should the re-barring of the ‘Evocation’ have followed the particular course indicated in Exs 3b and c? Or, in the case of Les Noces, why were the lengthy bars of the early draft (Ex. 5) dissected in the manner indicated in Ex. 6? The answer rests squarely with the double edge of displacement and fixed metric identity in repetition. For just as with the B-Q-D sweep and its preserved 38 bar in the March of L’Histoire, individual motives are singled out and exposed as metrically fixed elements. These constancies condition the metric irregularity of the surrounding material. Nevertheless, Stravinsky’s recollection of having measured the ‘Evocation’ ’s longer bars ‘according to phrasing’ is an interesting one. He suggests that, with the longer bars of the sketchbook version, metre and phrase coincide; the shifts marked off by the notated metre represent a localized ‘phrasing’ or grouping of some sort. This idea could be construed as an acknowledgement on his part of that underlying metric periodicity on which an understanding of displacement hinges, a periodicity against which the notated barring (or ‘phrasing’) is in some sense set in motion. The problem here, however, is that the later subdivisions, being as irregular as the earlier, longer, divisions, are really no different in this respect. Consistent with our conception of a concealed metric periodicity, they too are a form of ‘phrasing’, even if the particulars differ from those of the early sketches, drafts or editions.21 21The

idea that the irregular metres in much twentieth-century music might often constitute a phrasing or a motivic delineation of some kind has been suggested elsewhere. See Edward T. Cone, Musical Form and Musical Performance (New York: Norton, 1968), p. 82. Cone remarks that ‘the composers of the early twentieth century move in the direction of much freer rhythmic articulation, governed less by metric than by motivic considerations. For many later composers, abstract meter seems not to exist: what meter there is expresses itself only through the actual rhythmic motifs of the musical surface and hence is in a state of constant flux.’ One of the points of this article, of course, is that a steady or ‘abstract’ metre does often lurk behind the fluctuating surface of Stravinsky’s music, and that an apprehension of this concealed periodicity is essential to an appreciation of the rhythmic ‘play’. Beyond this, however, Cone’s observations are consistent with the present argument, and indeed with Stravinsky’s recollections in Expositions and Developments, at least insofar as the sketchbook version of the ‘Evocation’ is concerned.

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Example 3 (continued)

Stravinsky’s notion of ‘phrasing’ is most clearly demonstrated by a passage in Act II of Oedipus Rex (1926). A melodic fragment is introduced at No. 139 and repeated at No. 140 (see Ex. 4). Here, as with the B-C♯-D sweep in the March, the repeat harbours a contradiction. For in accordance with a concealed 34 periodicity, the initial statement begins off the beat while the repeat at No. 140 begins on the downbeat. The highpoint of this passage occurs at No. 144, however, where the concealed 34 metre is brought to the surface and the irregular subdivisions are replaced by stress and slur markings. From the standpoint of the initial irregularity, the later conception exposes the background periodicity, while, from the standpoint of the later periodicity, the earlier irregularity slices up a periodic conception in accordance with its stress and slur articulation. Here,

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then, metre and a localized type of ‘phrasing’ coincide. The barring and ‘phrasing’ at Nos 139 and 140 are ‘in phase’, to borrow a term from Lerdahl and Jackendoff22:

Example 3  ‘Evocation of the Ancestors’ 22Page

30. See notes 4 and 28.

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Example 4  Oedipus Rex

IV Examples 5 and 6 reproduce the opening two blocks of Les Noces, labelled A and B; Ex. 5 is from an early draft scored for mezzo soprano, woodwinds and double string quintet (where the two blocks are set apart by a change in tempo),23 while Ex. 6 gives the final version of this material in condensed form. As is readily apparent, the early draft features bars of seven, six and five quaver beats which were later sliced up into ‘smaller divisions’ of two and three beats. Moreover, the proportions in these two versions are different. Block A is considerably shorter in the earlier version, while Block B, although very nearly intact, is a crotchet shorter here than in the final arrangement. The brackets in Exs 5 and 6 mark off the longer bars of the earlier sketch which were retained by the final version across the subdivisions: More critical distinctions between these two Noces texts relate to motivic identity, pulse and tempo. The two 58 and 68 bars which conclude Block A in the early draft were among those retained, with subdivisions, by the finished score. Noteworthy is the concluding 6 8 bar, with its crotchet-quaver-dotted crotchet rhythm for the E-D-E segment. For it appears that, in making the transition to the expanded dimensions of the later version, this particular figure was 23This early draft is part of the Stravinsky Archives with the Paul Sacher Foundation in

Basel, Switzerland. A facsimile of the first page appears in Vera Stravinsky and Robert Craft, Stravinsky in Pictures and Documents, p. 144.

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at some point singled out for special emphasis. Its triple implications are underscored by the later 38 subdivision, where, transferred to the opening of the piece, it serves a motivic point of departure and return for the block as a whole. Hence, from within a seemingly random series of pitch inflections involving E, D and B, there emerged the beginnings of a coherent repeat structure. Seized upon as a motivic focal point, E-D-E became a metrically fixed element, a constancy.

Example 5  Les Noces (early draft)

Example 6

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Some of these implications are detailed in Ex. 7, where the two versions of Block A are placed in vertical alignment. The retained 58 and 68 bars are marked by dotted lines, while an arrow indicates the later transfer of E-D-E to the opening of the piece. The two versions appear also to be distinguished by what little may be inferred as to long-range periodicity—or, in view of the successive 38 bars for the E-D-E motive, by what might already be sensed as a commitment on the part of the finished score to triple metre. For in the early draft the crotchet is assigned the metronome marking, a stipulation obviously at odds with these later implications. Still, as Ex. 7 shows, steady 38 and 68 metres are implied from the start of the early draft, metres which in turn arrive ‘on target’ with the concluding 68 bar and its E-D-E segment:

Example 7

More eventful from the standpoint of fixed metric identity, however, is the tiny D-E segment. Marked off by brackets underneath both versions of Block A in Ex. 7, D-E is a part of E-D-E and of subsequent extensions of this motive as well. Returns to E invariably come by way of D, and the succession is stressed by a doubling in the cello in the early draft (see Ex. 5) and by octave doublings in Pianos I and III in the final version (see Ex. 9 below). Note, however, that in accordance with the longer bars of the early draft, D-E is barred differently on each occasion, while in the finished score D-E is always barred as an over-the-barline succession; irrespective of the notated irregularity, D-E assumes the same metric identity. Hence, just as with the E-D-E motive, the finished score latches on to a fixed element or constancy, here the smaller but more pervasive D-E component. In addition, E, as the registrally fixed pitch of departure and return, falls always on the first beats of the irregular bars. Indeed, as can now be seen, the notated irregularity of the final arrangement is in large part determined by these metrically fixed components; these

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components tend, as it were, to regulate the irregularity. The shifting metre seeks, at least in part, to preserve fixed identity in repetition. A summary of these conclusions appears in Ex. 8, where a hypothetical scheme demonstrates just how regular the irregularity is. Notice how the shifting metre revolves around the aforementioned components, and in particular the fixed over-the-barline identity of D-E. Indeed, according to the hypothesized version, Block A contains but three motivically defined metrical units: a 38 bar for E-D-(E), another 38 bar for the dotted crotchet E and a 58 bar for E-D-B-D. And if we omit the dotted crotchet, the scheme reduces to two such units: E-D-(E) and an extension in the form of E-D-B-D-(E). (Marked by parentheses in the fifth bar of the hypothesized version, the dot of the dotted crotchet must yield to a quaver D to allow for complete motivic correlation.) So, too, there are only 38 and 58 bars: four 38 bars with a total of twelve quaver beats, and three 58 bars for a total of fifteen beats. (The implications of three as common denominator will be discussed shortly.) And since a 38 bar with the E-D-(E) motive serves as a point of departure and return for the block as a whole, the 58 bars are recognized as extensions of the latter (or as metrical ‘troublemakers’): each 58 bar delays, by two beats, the return of D to E:

Example 8

Note, too, that the natural stresses of the Russian syllables underscore D-E as a metrically fixed unit in the final version.24 As the stress markings for Block A in Ex. 6 show, these stresses coincide 24A

translation of the two lines of Blocks A and B reads as follows: ‘Braid, my dear little blond braid!/Yesterday my mother braided you, my dear little braid, my mother braided you!’ Most of the libretto of Les Noces was adopted from P. V. Kireevsky’s anthology of peasant wedding verses: Pesni sobrannye P. V. Kireevskim, Novaia seriia, ed. V. F. Miller and M. N. Speransky, Vol. 1 (Moscow, 1911). I am indebted to Simon Karlinsky for his assistance in the translation and transliteration of the above text.

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with the musically stressed D of the D-E unit for all D-E repeats except those of the final two bars. In contrast, the repeats of D-E in the draft (Ex. 5), though doubled by a solo cello, lack this support. In view of the tradition of flexible accentuation in the singing of Russian popular verse, the coincidence here of natural verbal stress and musical accent (for the upbeat D of the D-E unit) takes on an obvious significance.25 A peculiarly Stravinskian trait in these opening passages is the stutter effect, the repeat, in the fourth and fifth bars of the final version, of the individual syllable ko, for Kosal meaning ‘braid’. Within the framework of a bride’s ritualized lament, the stutter suggests a sob or sigh. Up to this point the logic of the barring has been pursued solely from the standpoint of metrically fixed elements. The opposite side of this coin is, of course, displacement. But, as can be seen from the irregular barring of the finished score, displacement is not graphically a part of the invention. On the contrary, and as suggested, each of the designated components assume, in relation to the shifting metre, a fixed identity: E-D-(E) is barred as a 38 bar, D-E as an overthe-barline succession, while E falls on the downbeats of the bars in question. Hence the notion of displacement implies the opposite of what is here notationally evident, namely, a change in the metric accentation of a reiterated component, chord or configuration. And while reference is frequently made to the shifting of accents, at times to the shifting merely of phenomenal accents or stresses, 25An

early discussion of the flexible or ‘movable’ accent in Russian folk songs is contained in the Introduction to Eugenie Lineff, The Peasant Songs of Great Russia, Vol. 1 (St. Petersburg, 1905), pp. xvi–xvii. In Expositions and Developments Stravinsky recalled that his own conscious recognition of this feature had come as a ‘rejoicing discovery’ while working on the libretto of Renard: ‘One important characteristic of Russian popular verse is that the accents of the spoken verse are ignored when the verse is sung. The recognition of the musical possibilities inherent in this fact was one of the most rejoicing discoveries of my life’ (p. 121). It need hardly be remarked in this connection that this folksong tradition of flexibility in verbal stress is analogous to the musical technique of displacement (of shifting the accentual identity of a reiterated fragment), and that the latter may well have had the former as its origin. At the same time, the technique of displacement always carries with it the opposing force of fixed metric identity, an element which lies at the root of metric irregularity in Stravinsky’s music. Both the flexible stress in Russian popular verse and its implications in Stravinsky’s early vocal music are pursued in Richard Taruskin, ‘Stravinsky’s “Rejoicing Discovery” and What It Meant: Some Observations on His Russian Text-Setting’, in Stravinsky Retrospectives, ed. Ethan Haimo and Paul Johnson (Lincoln: University of Nebraska, 1987).

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and at other times merely to the resultant design or pattern,26 the implications for the listener are more dramatic. They materialize in the form of a shift in the metric identity of a component; while interval order and note values remain intact, metrical placement is altered. (To emphasize accent or pattern at the expense of motivic identity is to emphasize cause at the expense of perceived effect.) Moreover, since shifts of this kind can be perceived only with reference to a periodic background, they materialize in the form of upbeat-downbeat (weak-strong) or offbeat-onbeat contradictions. A reiterated component, introduced on the upbeat, is contradicted by a subsequent downbeat appearance (or vice versa), while another such component, introduced off the beat, might be contradicted by a later onbeat appearance (or vice versa). There is little difficulty in rearranging the opening blocks of Les Noces accordingly. As the brackets in Ex. 9 indicate, a 38 metre is implied by the E-D-E motive of the opening bars and imposed on Block A as a whole. And it is with reference to this background periodicity that displacements in the metric identity of the aforementioned components materialize:

Example 9 (continued) 26I

refer specifically to Pierre Boulez’s well-known analysis of rhythm in The Rite of Spring, reprinted in Notes of An Apprenticeship, trans. Herbert Weinstock (New York: Knopf, 1968), pp. 72–145. The problem is that Boulez is too exclusively a ‘radical’ interpreter of this music, so that many of his analyses tend to degenerate into ‘abstract’ or somewhat lifeless patterns in which the element of disruption, and the periodicity upon which disruption hinges, are ignored. This is not to suggest that his outlines of motivic repetition are irrelevant to perception, but only that they cannot so summarily be removed from established and in some instances readily inferrable implications of pulse and metric periodicity.

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Example 9  Les Noces

Thus, in the opening two bars, the stressed D-E succession falls on the third beat of the 38 bar, with D-E assuming its over-the-barline, upbeat-downbeat identity. But subsequent repeats contradict this identity. For, in accordance with the 38 periodicity, the D in this

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succession falls on the second beat at b.3 and the first beat at b.6. Hence a carefully patterned cycle of displacement is exhibited: the D of the D-E succession is introduced on the third beat, is subsequently displaced to the second and first beats, and then, in the completion of the cycle, is displaced yet another notch back to the original third beat, at which point D-E resumes its over-the-barline identity in conjunction with the return of the E-D-E motive in the final bars of the block. Moreover, the 38 metre emerges ‘on target’ with the foreground irregularity in these final bars. The two conflicting metres are aligned as the block draws to a close. And this naturally intensifies the sense of a steady 38 periodicity, along with the displacements which, as indicated, depend for their apprehension on its presence. Similar inferences may be drawn from the material of Block B. Here, however, the periodicity is duple rather than triple. Moreover, the foreground irregularity comes by way of a subtactus unit, while in Block A it surfaces by way of the tactus. In other words, while Stravinsky doubles the marking for the quaver from 80 to 160 at Block B, the listener is far more apt to hold on to the marking of 80, which becomes the marking for the crotchet (as tactus). And with the quaver relegated to a subtactus unit (and given, as well, the brevity of Block B in relation to Block A), the 24 metre becomes far more conspicuous than the 38 scheme in Block A. Note, too, that, just as with Block A, the steady metre arrives ‘on target’ with the foreground irregularity, thus heightening the sense of periodicity. With Block C the dotted crotchet is given the marking of 80, which in turn stipulates a triple division of the retained pulse. And while the stressed F♯-E♯ figure falls on the downbeat of the first bar, F♯-E♯ is more readily heard as a stressed upbeat to the punctuating E; in both Blocks A and B, the inflection is stressed as an upbeat to E as the point of departure and return. Observe, too, that the 24 periodicity of Block B favours such an alternative, since, as the brackets show, an extension following the repeat sign emerges at Block C with an extra quaver beat to spare. Further on, the invention follows a familiar path. Subsequent repeats of F♯-E♯-(E) are irregularly spaced, a feature which tends gradually to undermine the implied 6 8 periodicity. (The irregular spacing comes nonetheless closest to a 6 2 8 scheme, which, in view of the 4 periodicity of Block B, would in any case have been the ‘preferred’ reading.) The result is a tension

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between the implied 68 mould and the irregular spacing of the F♯-E♯(E) repeats, which usually miss a 68 or 38 delineation by one or two quaver beats. Contradictions similar to those noted in connection with Block A could in fact have been plotted on behalf of F♯-E♯-(E). Moreover, the irregularity emerges ‘on target’ with the 68 metre at the conclusion of Block C. Block C is then followed by slightly varied repeats of Blocks A and B. Example 10 re-bars the material of Blocks A and B in accordance with the 38 and 24 periodicities bracketed in Ex. 9. In addition, the brackets underneath Block A refer to the stressed D-E succession whose patterned cycle of displacement was noted above:

Example 10

V The ‘Evocation of the Ancestors’ in The Rite of Spring consists of two alternating blocks of material, the first of which marks off successive appearances of the second, principal block. Attention here focuses primarily on the second of these two blocks, henceforth designated Block B. At issue are (1) fixed metric identity, and (2) displacement. These, of course, are the twin sides of the double edge referred to above. However, in the ‘Evocation’ the second of these edges surfaces with an inconvenient hitch: at strategic points of arrival and departure, the background periodicity upon which felt displacement hinges does not, as in the previous illustrations, flatten out the foreground irregularity. Except for the initial statement of Block B at Fig. 121 + 3, the periodic background that may be inferred does

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not as a rule arrive ‘on target’ with the shifting metre as subsequent Block B statements are concluded. At the same time, the sense of periodicity is inescapable. In the 1929 revision the minim is initially the tactus, with an assigned marking of 72. And with the minimcrotchet-minim motive of Block B’s initial bar, a 22 metre may be inferred, in relation to which the subsequent 34 bars assume the by now familiar role of disruptive troublemakers. Indeed, the ‘play’ of the ‘Evocation’ derives in large part from the stimulation of longterm periodic expectations and the stubborn, counteracting refusal of fixed metric identity, as defined by subsequent repeats of the initial motives and submotives of Block B, to comply. This, of course, is the familiar twist of the double edge. Yet for the reasons already indicated, hidden periodicity seems here at a greater disadvantage than in the passages examined from L’Histoire and Les Noces, with the result that displacement in the metric identity of the reiterated motives may not be as acutely felt. With subsequent repeats of Block B’s initial motives, the listener is more apt to readjust his or her metrical bearings than to perservere with the diminishing traces of a prevailing periodicity. Hence the opposing forces of identity and displacement are placed in a more balanced relationship. For the conservative listener, the radical implications of the shifting metre are more persuasively brought to the fore. Three versions of Block B’s initial statement at Fig. 121+3 are shown in condensed form in Exs 11a, b and c. These are taken from the sketchbook, the 1913 autograph and the 1929 revision. As with Les Noces, the early draft is characterized by longer bars which were subsequently dissected into ‘smaller divisions’. In the autograph (Ex. 11b), the sevens of the sketchbook version were carved up into two units of 4+3 crotchet beats. Highlighted in particular is the underlying repeat structure of the initial B statement. For while motive a7 is shortened by two notes at b.4, the initial 4+3 unit is retained. (The deleted notes are bracketed in Ex. 11b, where the a7 label is retained for the repeat.) Hence, motivically speaking, modified restatements of Block B derive in their entirety from the single motive a7 and its 4+3 subdivision. All subsequent extensions, contractions and reorderings emerge with reference to this single motivic point of departure. In contrast, the barring of the 1929 revision records the actual shortening of motive a7 at bs 3-4. As Ex. 11c shows, the final C falls

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on the downbeat at b.5. Since the downbeat here coincides with the return of Block A, the C is placed in a parallel relationship with the C at b.3. This in turn underscores a more separately realized identity for the repeat (labelled b5 in Ex. 11c), whose 2+3 subdivision will in turn differ from that of a7. In addition to a 24 bar for the minim C, a disruptive 34 bar will now accommodate C-C-D as well as D-C-D. Moreover, as barred in Ex. 11c, the a7-b5 succession will serve as the somewhat lengthier motivic point of departure according to which subsequent modifications in Block B statements are gauged:

Example 11

This is not to suggest, of course, that the repeat structure of a7 followed by b5, as exposed by the autograph version, is entirely obscured. On the contrary, a7 still contains b5, while a single inflection, the D, acts as a pivot in distinguishing subsequent repeats of the two motives (see boxes in Ex. 12). Indeed, by including the final C in the motivic definition, the boxed-off D in Ex. 12 divides Block B into two equal units of six crotchet beats:

Example 12  ‘Evocation’

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In this way, too, the ‘Evocation’ emerges as yet another example of that familiar addiction to pitch-stutter, to an alternation between two or three notes, here presented in the condensed form of a punctuation of C and its inflection D.27 Correspondences with the opening blocks of Les Noces need hardly be cited in this connection. Yet, perhaps especially in the ‘Evocation’, the very idea that so much could have been made of so little presses itself on the imagination in an unprecedented way, in a manner quite without equal among the many other similarly disposed passages in the composer’s work. Two restatements of Block B are shown in Exs 13 and 14. These feature extensions and reshufflings of the original a7-b5 motivic order as introduced at Fig. 121+3. In addition, there are hinges in these lengthier statements, slight infractions in terms of C-E♭-D and G-F♯-E which occasionally extend the motivic repeats by three crotchet beats. Additional variety is achieved by deleting the initial minim C of motive a7, so that a7 becomes a5:

Example 13  ‘Evocation’

Example 14  ‘Evocation’ 27In

Igor Stravinsky and Robert Craft, Themes and Episodes (New York: Knopf, 1966), the composer himself acknowledged this two- or three-note alternation as ‘a melodicrhythmic stutter characteristic of my speech from Les Noces to the Concerto in D, and earlier as well—a lifelong affliction in fact’ (p. 58). A number of pitch-relational implications of these alternations are drawn in van den Toorn, The Music of Igor Stravinsky, pp. 152–4, 182–91, 280, 439–40.

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Most extensive among these restatements, however, is that at Fig. 125-7(+1). This begins with a recapitulation of the original a7b5 order, which is then followed by a b5/a7 overlap; the barring here of b5 conceals the longer a7 repeat, which is then extended by the C-E♭-D hinge (see Ex. 14). The latter hinge adds considerable refinement to the ‘balancing act’ of these bars. Yet the omission of these hinges in the form of an a7-b5-a7-a7-b5 succession would not have made for an entirely improbable B statement, as the ‘recomposed’ version in Ex. 15 shows. That Ex. 15 could indeed have figured as a respectable alternative derives at least partly from the fact that, following the a7-b5 recapitulation, the motivic order is reshuffled. Still, the peculiar tension of these bars cannot be said to reside entirely with the repetition of a string of unchanging motives. For instance, at Figs 125-6 in Ex. 14, to what extent is the second of the two successive b5s heard as a ‘true’ repeat of the first? Or, in the recomposed version of Ex. 15, in what sense is the second of the two successive a7s perceived as a straightforward repeat of the first? The point would seem to be that these repeats raise expectations of periodicity which, in a delicate balance between compliance and forced readjustment, are either affirmed or rebuffed by subsequent motivic placement:

Example 15  ‘Evocation’

As mentioned already, similar inferences may be drawn from the initial a7-b5 succession itself (Fig. 121+3). For with the minim as tactus, the opening bars initiate a 22 periodicity in relation to which the 34 bars are the disruptive troublemakers. Hence the tension of the repeat motive b5 in relation to a7 may be traced to the fact that (1) seven misses eight by one, and that (2) b5 can in this sense be heard as a syncopation in relation to a7—that, in other words, b5 becomes an offbeat contradiction of the onbeat identity of a7.

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Example 16  ‘Evocation’

Here again the exposed repeat structure of the autograph version is instructive. For as outlined in Exs 16a and b,28 the two sevens and their 4+3 subdivisions are a condensation, by one crotchet beat for each 4+3 unit, of a square metrical scheme of two eights with subdivisions of 4+4. In other words, with the initial motive a7, a square periodic 4+4 unit is squeezed into an ‘irrational’ one of 4+3; at b.3, the shortened repeat of a7 arrives one crotchet beat too soon. And with the shrinkage of this 4+4 unit to 4+3, pressure tends to accumulate precisely at the juncture of the motivic repeats, that is, at the minim C which invariably initiates repeats of both a7 and b5. (Note that the minim C falls always on the downbeats of the irregular bars.) Thus while the initial C at b.3 serves first and foremost as the start of the shortened repeat motive, it never entirely severs its ties 28The

dots beneath Ex. 16b indicate the levels respectively of the minim (tactus), the bar and the two-bar spans. The method of using dots to specify the levels of a metrical structure is derived from A Generative Theory of Tonal Music, where beats are conceived not as durations but as points in time (analogous to ‘geometrical points’ in space) which, strongly or weakly accented, are organized hierarchically in a manner that is independent of grouping or phrasing (p. 18). The conception of beats as durationless points in time stems in turn from Arthur J. Komar, Theory of Suspensions (Princeton: Princeton University, 1971), p. 52, and from Imbrie, ‘”Extra” Measures and Metrical Ambiguity in Beethoven’, p. 53; the spatial analogy is Imbrie’s. It should be noted, however, that in A Generative Theory of Tonal Music, metre is viewed as ‘inherently periodic’ and as ‘a relatively local phenomenon’; Lerdahl and Jackendoff contend that at higher levels of structure, where the formulation is seldom regular, the sense of metre, of a strong-weak alternation, dims and gives way to large-scale grouping and ‘motivic parallelism’ (pp. 19–21). In contrast, Imbrie’s conception of metre allows for greater irregularity, so that, in their independent, interacting roles, metre and grouping continue to coexist at higher structural levels.

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to a7 as a terminating element; at b.3 a7 is cut short and remains in this respect ‘unfulfilled’. (The impact of the condensation could be represented by an interminable succession of elision loops at the juncture of all a7/b5 repeats.) Hence the motivic repetition of Block B assumes a tight, breathless quality. Arriving always a little too soon, the repeats within a particular succession appear hurried and impatiently realized, lacking the sense of true rhythmic finality or resolution: The second of the two factors mentioned above concerns b5 as a contradiction of a7. For with the trimming of 4+4 to an ‘irrational’ count of 4+3, the shortened b5 repeat at b.3 assumes, in relation to a7, a syncopated identity. In accordance with the 22 periodicity as inferred from a7 opening 22 bar, and in direct opposition to the fixed metric identity of the reiterated motives as defined by the shifting metre, the initial onbeat identity of motive a7 is contradicted by an offbeat placement at bs 3-4. These conclusions are in turn outlined in Exs 17a and b, where brackets outline the background 22 metre for the autograph and 1929 versions, and according to which the block is re-barred in Ex. 17c. And so, once again, fixed metric identity stands in opposition to displacement, the latter hinging for its apprehension on a steady, background frame of reference. And note that with the initial Block B statement at Fig. 121+3, the concealed periodicity arrives ‘on target’ with the foreground irregularity as the block is concluded four bars later.

Example 17  ‘Evocation’

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A final step in this analysis would be to situate these findings within the wider context of the two alternating Blocks A and B. As Ex. 18 shows, the total crotchet count for Block B is twelve. And Block B is flanked by A statements whose 2 divisions likewise total twelve crotchet beats. Almost immediately, however, this initial regularity is subjected to disruption. For in the echo statement of Block B at Fig. 122+1, the initial minim C of motive a7 is dropped, a7 becoming a5. And in accordance with the prevailing 22 arrangement, the second half of a7’s 22 bar falls on the first or strong beat rather than on the second, as at Fig. 121+3. Moreover, the 22 scheme fails to coincide with the foreground irregularity at the conclusion of the echo statement; indeed, with the entrance of a5 at Fig. 123, the original 22 sense has disappeared altogether. For at this point the initial fixed identity of a7 in its a5 condensed form holds sway, forcing the listener—indeed, perhaps already at the beginning of the echo statement—to readjust his or her periodic bearings. The ‘play’ of the ‘Evocation’ thus unfolds in the manner described above. A7’s initial bar stimulates expectations of periodicity which, with each displaced motivic repeat, are continually thwarted and then renewed in a kind of back-and-forth motion. This is the crux of the balancing act:

Example 18  ‘Evocation’

Of course, it could be argued that, at the higher level of structure in Ex. 18, the 1-2-3 triple count of Block B at Fig. 121+3 is inherently unstable. There can in fact be little doubt about this. For quite apart from the many psychological and physiological points that have been raised in support of the thesis of an innate duple preference in

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situations of this kind,29 Block B is an abbreviation of a conventional duple scheme. As Exs 16a and b show, the 7+7 and 7+5 schemes of the autograph and 1929 revision are both condensations of a square 8+8 scheme, so that, at the higher level in the 1929 revision, a potential 1-2-1-2 count shrinks to 1-2-3. Yet a duple alternative at this level at Fig. 121+3 would not appreciably have altered the disruptive effect as sketched in Ex. 17 on behalf of the triple metre. Beginning with the downbeat at Fig. 121+3, the entrance of a5 in the echo statement at Fig. 122+1 would still have fallen ‘incorrectly’ on a first, strong beat.

Example 19  ‘Evocation’

In Ex. 19 these implications are applied to the lengthy B statement at Figs 125-7+(1). Here, a 1-2 duple scheme is pursued at two levels of structure, while, underneath the excerpt, the brackets indicate the motivic repeats and hinges as surveyed already in Ex. 14. As is evident, the first major point of reckoning comes with motive a7 in the 32 bar at Fig. 126+2, just after the a7/b5 overlap and the C-E♭-D 29Reflections

on binary intuition can be traced back to the Renaissance theorist Franchinis Gafurius (1451-1522), Practica Musicae, trans. Irwin Young (Madison: University of Wisconsin, 1969). More recently correspondences have been drawn between the binary count and automatic functions like breathing and walking. Heinrich Schenker invoked ‘the principle of systole and diastole inherent in our very being’, as part of his own argument regarding the ‘natural’ two-ness of metrical structures. See Free Composition, trans, and ed. Ernst Oster (New York: Longman, 1979), p. 119. In A Generative Theory of Tonal Music, the duple bias is introduced as a ‘Metrical Preference Rule’ regarding higher levels of structure in tonal music (p. 101). It is briefly discussed and dismissed in a different context in David Lewin, ‘Some Investigations into Foreground Rhythmic and Metric Patterning’, in Music Theory: Special Topics, ed. Richard Browne (New York: Academic Press, 1981), pp. 101–3.

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hinge. For in accordance with the prevailing 22 metre, a7’s minim C enters ‘incorrectly’ on the second, weak beat rather than on the first. Here again, however, the listener is likely to switch metrical gears, opting in favour of a7’s fixed identity. But these implications are also short-lived. For the consequence of this readjustment is that b5 enters ‘incorrectly’ on the beat at Fig. 127, a contradiction which in turn fails to arrive ‘on target’ with the irregular barring as the entire block draws to a close two bars later30: As a final illustration, the ‘Evocation’ as a whole is outlined in Ex. 20. Here the design is similar to those introduced by Boulez in his discussion of The Rite.31 Note the sequential character of the format: within the alternation between Blocks A and B, principal statements of B alternate with the shorter echo statements. In addition, the echo statements retain a stable duration of five crotchet beats for the condensed motive a5, while the remaining, principal statements expand from twelve to twenty-two and finally to thirty-seven beats in the lengthy block surveyed in Ex. 19. As should by now be apparent, these measurements are far from ‘abstract’ in their perceptual implications. Understood with reference to the double edge of fixed metric identity and displacement, they take on a lively sense of the ‘play’ of this invention, its true raison d’être:

Example 20  ‘Evocation’ the fixed metric identity of a7, and in particular of its initial 22 bar, is likely to force readjustments in the 22 periodicity as traced at the minim level in Ex. 19. Accordingly, the Block B statement at Fig. 125 divides into three sections, defined motivically in terms of a7-b5, a7 (+ 3) and a7(+ 3) –b5. Thus, too, the total count of thirty-seven crotchet beats divides into three sections of twelve, ten and fifteen beats. 31Notes of An Apprenticeship, pp. 72–145. The most detailed analyses are those of the ‘Dance of the Earth’, the ‘Glorification of the Chosen One’ and the ‘Sacrificial Dance’. Boulez ignored the ‘Evocation’ altogether. See note 17 above. 30Actually,

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VI The kind of repeat structure that initiates Block B in the ‘Evocation’ is by no means unique in The Rite, Similar configurations are found in the opening two bars of the ‘Ritual of the Rival Tribes’, in the first two 58 bars of the ‘Glorification of the Chosen One’ and in the initial eight bars of the first section of the ‘Sacrificial Dance’. Indeed, in the ‘Sacrificial Dance’, a hidden 28 metre leads to a higher-level 1-2-3 triple count similar to that at Fig. 121+3 in the ‘Evocation’, and in connection with which similar implications of instability arise. In Ex. 21 attention is drawn to the two principal motives, a and b. As in Ex. 2, from L’Histoire, subsequent repeats of these two units are aligned vertically and marked off by dotted lines. Thus, too, fixed metric identity imposes itself along familiar lines. For 2 3 notwithstanding the irregular 16 and 16 bars of the tiny submotives, a punctuation of D or a semiquaver rest falls always on the downbeats of these irregular bars, while the reiterated chord follows on the second semiquaver beat. Hence, as earlier, fixed identity tends to regulate the irregularity. Nor, of course, are these graphs strictly ‘mechanical’ in conception, for the irregularity reflects an intention to retain a second-beat ‘feel’ for the reiterated chord—or, in relation to the quaver, an offbeat ‘feel’: Still, with the quaver implied initially as the tactus and with an assigned marking of 126, a concealed 28 periodicity emerges with little resistance, especially in view of the immediate, verbatim repeat of the a5-b7 succession and its higher-level 1-2-3 count. Indeed, with subsequent repeats of motive b7, the details of displacement are similar to those pursued on behalf of the B-C♯-D-(E) sweep in L’Histoire’s opening March. Here an initial identity is established for b7 at Figs 142 and 143, which at Fig. 144+4 is displaced by a quaver beat, the reversal thus coming by way of the tactus. Finally, at Fig. 145+4 the displacement surfaces more conspicuously, in the form of an offbeat-onbeat contradiction, and from this point on the struggle of identity and displacement assumes its relentless disposition. Of course, the ‘Sacrificial Dance’ has no basso ostinato. And without question the impact of the disruption, of a periodicity constantly lost in the modification and reshuffling of the metrically fixed elements, is ultimately far more severe. Yet the strategy itself

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remains unchanged. Even the more active role of the percussion in the climactic section (Figs 146-8) can be compared to that in L’Histoire, as already discussed apropos of Ex. 2d.

Example 21  ‘Sacrificial Dance’

VII As a final suggestion it might again be noted that the ‘play’ or double edge of Stravinsky’s invention is not as new or as exceptional as

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might at first be imagined. For if, in past tonal music, bars were routinely added or deleted at higher levels of metrical structure with expectations of periodicity, disruption and readjustment, then it can be seen that, in Stravinsky’s case, these same processes were merely shifted to different and more immediate structural levels. Thus, to take a famous example, in the first movement of Mozart’s G minor Symphony, thematic statements are introduced at bs 1 and 20, so that, at some point in these first twenty bars, the twobar module is broken as the accents shift from the odd to the evennumbered bars.32 And in the first movement of Beethoven’s Piano Sonata in D major, Op. 10, No. 3, the repeat of the entire exposition can be heard and understood as embodying a similar contradiction or reversal at the two-bar level, with the accents at the evennumbered bars shifting to the odd-numbered bars at some point during the exposition.33 To be sure, with Stravinsky the invention presumes a new conception of motivic repetition, of harmony and of formal outline. Yet the relationship is important because it points to underlying assumptions of conventional periodicity. So, too, the conservative-radical dichotomy in perception shifts to another level of metrical structure.

32See 33See

A Generative Theory of Tonal Music, pp. 23–5, and note 4 above. Imbrie, ‘“Extra” Measures and Metrical Ambiguity in Beethoven’, pp. 45–51.

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Neoclassicism and Its Definitions

How does neoclassicism manifest itself? Do parts or features readily identified as Baroque or Classical, tonal or adhering to tonally conceived forms and shapes, draw attention to themselves as such? And if they do, do they then defy integration? Are they then incapable of being assimilated by the individual context, incapable of acquiring a sense of motivation by way of that assimilation, a sense of integrity? (Are neoclassical wholes never wholes, in other words, never “organic”?) Or are questions of this kind questions of degree after all? Can neoclassical works have it both ways (which would seem to be the established view)? Some of these questions do not lend themselves all that well to analysis. They touch to too great an extent on the immediacy of the experiencing subject. The organic character of, say, Stravinsky’s neoclassical works cannot be proved one way or the other. Only as impressions do musical works manifest themselves in this way, do they become organically whole or “total” (as Schoenberg might

Reprinted from The Journal of Musicology, vol. 14, no. 3 (Summer 1996). The Music of Stravinsky: Collected Essays Pieter C. van den Toorn Text Copyright © 1997 University of Rochester Press Layout Copyright © 2023 Jenny Stanford Publishing Pte. Ltd. ISBN 978-981-4968-62-1 (Hardcover), 978-1-003-35916-6 (eBook) www.jennystanford.com

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have expressed it);1 only on the basis of what is sensed and felt, given directly in experience, can a musical train of thought appear as a whole rather than in parts, can parts assume a transparency in the service of that whole; only on such a basis is there a reciprocity with parts both defining and being defined by the whole. And even then, the manner in which such impressions are tied to aesthetic responses of one kind or another, favorable or not, adds yet another dimension to the puzzle. All of which is not to question the metaphor itself or its usefulness in practical analysis, the metaphor of organic unity or wholeness. Elusive and at times overly deterministic in its effect,2 it can nonetheless underscore the lifelike rather than mechanical quality of musical wholes, the natural and effortless rather than arbitrary or forced manner in which parts can be felt to cohere.3 It can help sustain a sense of the experience of music. But if analysis can offer little proof in these matters, it can offer evidence. And of immediate concern is the established view of neoclassicism, the contradiction embedded in that view, the idea, on the one hand, of an unbridgeable gap between the old and the new and that, on the other, of an assimilation or transcending 1Arnold Schoenberg, “Gustav Mahler” (1912, 1948), in Style and Idea, ed. Leonard Stein, trans. Leo Black (Berkeley and Los Angeles: University of California Press, 1984), 449. According to Schoenberg, a sense of the context as a whole, an “impression” of its “totality,” emerged gradually in the listening experience, even if it could be anticipated and later invoked in a moment’s time. For a survey of the origins of the metaphor of organic life, see Ruth A. Solie, “The Living Work: Organicism and Musical Analysis,” Nineteenth-Century Music 4 (1980): 147–56. Its application to Schoenberg’s writings is discussed in Severine Neff, “Schoenberg and Goethe: Organicism and Analysis,” in Music Theory and the Exploration of the Past, ed. Christopher Hatch and David W. Bernstein (Chicago: University of Chicago Press, 1993), 409–33; it is discussed with reference to Schenker’s writings in William Pastille, “Music and Morphology: Goethe’s Influence on Schenker’s Thought,” in Schenker Studies, ed. Hedi Siegel (Cambridge: Cambridge University Press, 1990), 29–44. 2See, for example, Joseph Kerman, “How We Got into Analysis, and How to Get Out,” Critical Inquiry 7 (1980): 311–331. Kerman’s critique of organicist thought in music analysis has been reprinted in Joseph Kerman, Write All These Down (Berkeley and Los Angeles: University of California Press, 1994), 12–32. 3These particular implications of the organic model were always an important part of its message: see Kevin Korsyn, “Schenker’s Organicism Reexamined,” Intégral 7 (1993): 91. Korsyn remarks that “organicism must also be seen in relation to mechanistic and materialistic trends, as a response to everything that threatened to reduce human beings to mere mechanisms.”

Neoclassicism and Its Definitions

contextuality.4 The assumption would seem to be that traditions both remote and long since spent, no longer capable of functioning authentically, only anachronistically, are put to use on behalf of the new; neoclassical works can make a point by way of that use and we as listeners can respond accordingly.5 But that point is made, bits and pieces of the nonimmediate past are revived even as the individual neoclassical context makes a point of its own, emits a sense of integrity that overrides the very traditions upon which rests the initial point of departure. This may oversimplify the established view, of course, by treating each side of the contradiction independently of the other. Applying the idea of a transformation of the old by the new, both sides could presumably be taken into account, nonimmediate tradition as well as newly constructed context. Viewing the latter as a transformation of the former, old and new could figure as part of the same overriding process. Observe, however, that such a perspective does not eliminate the contradiction. On the contrary, a before-and-after scenario remains in place, one in which the new is defined to some extent by the old, by an awareness of what it is that is being transformed. And the approach would therefore continue to segment and isolate 4For

a recent manifestation of this traditional view of neoclassical music, see Joseph N. Straus, Remaking the Past: Musical Modernism and the Influence of the Tonal Tradition (Cambridge: Harvard University Press, 1990), 44–73. Straus underscores the “non-organic” character of Stravinsky’s neoclassical “recompositions,” their “dual structures” of old and new, “continuous conflict,” and absence of “larger resolution or synthesis.” At the same time, however, he insists that a transcending “new meaning” is realized, one in which “traditional formations [are] heard in a novel way.” Moreover, according to Straus, the new or post-tonal in Stravinsky’s “recompositions” is distinguished by motivic processes involving abstract pitch-class sets and their relations. Here, however, such processes and relations are heard and understood to straddle the tonal and post-tonal worlds. See note 20. 5The extent to which aspects of the nonimmediate past manifest themselves anachronistically (and in this way neoclassically) in several contexts from the music of Stravinsky, Bartók, and Schoenberg is discussed in illuminating detail in Martha Hyde, “Neo-classic and Anachronistic Impulses in Twentieth-Century Music,” Music Theory Spectrum 18 (1996: 200–35). The influence of jazz may also be felt in the harmonic and rhythmic configurations in the first movement of Stravinsky’s Symphony in Three Movements, undoubtedly a product of the composer’s arrival in the United States in 1939 and of his reacquaintance at that time with varieties of American popular music. See, in this connection, the triplets and offbeat patterns of punctuation at Rehearsal 7–13, as condensed in Ex. 2.

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what for the critic stands isolated by its own accord, namely, the past which resists integration. So, too, application in analysis is likely to be partial and incomplete; not all of the data covered by, say, a tonal reading of a neoclassical context is likely to overlap or intersect with the data of the new, an interpretation of the new. (Here, the “data” might include the manner in which pitches, intervals, and rhythms are grouped as well as the pitches and intervals themselves. In passages to be examined here from Stravinsky’s Symphony in Three Movements, classes of pitches and intervals which figure as part of a diatonic and even tonal segmentation are not included in an octatonic arrangement—one, however, which is no less specific and cohesive in its articulation.) And this is where the difficulty lies, of course, in the apparent absence of a unifying design or synthesis, one specific enough to be of use in embracing conflicting components of this kind. Instead, such parts and the traditions they embody attract too much attention; they are felt as insufficiently transparent in a reading of the whole, insufficiently motivated from the standpoint of the whole. All of which has tended to manifest itself in the following practical terms: Analysis can either accept the high degree of non-integration or conflict as a defining attribute of this music, devoting its energies accordingly, or it can pursue a transcending ideal by retreating to relations of greater abstraction and, for the specifics of the conflict, less definition. It can either attend to the conflict or, pursuing the whole, adopt relations of an increasingly abstract nature precisely in order to override conflict. In the latter case, however, it will override that which defines the underlying rationale of its subject matter. And it is in the irreconcilable duplicity of these options that analysis reflects the contradiction that lies at the heart of the traditional approach to the study and understanding of neoclassical music. Indeed, many familiar forms of analysis have proceeded along just such lines. What may work with a convincing degree of specificity for the part is imposed on the whole; alternatively, a highly abstract reading of various parts, one involving, say, pitch-class sets and their relations, is imposed on the whole in like fashion, and with results too watered down to be of consequence. In each case, the issue of the whole is forced; parts which conflict at relatively low levels of abstraction (parts representing the old and the new, for

Neoclassicism and Its Definitions

example) are made to relate and intersect at higher levels (with the old either cancelling out the new or vice versa). And the larger issue thus becomes not relatedness as such but, rather, its kind and degree, not intersection but the manner of its articulation. (Given a sufficient degree of abstraction, in other words, all parts can be made to relate.) And what may therefore be sensed and felt of the past and present, what, indeed, may seem to define the character of Stravinsky’s neoclassical works, is lost. This is not to suggest that such a predicament is peculiar to the analysis of this particular music, only that its effects can seem unusually severe and problematic. Thus, theories of tonality as sophisticated as Schenker’s are apt to make for an uneasy fit. Many of Schenker’s terms work best as an outside foil, in fact, a way of setting neoclassical processes in relief; stretched beyond that point, they lose much of the explanatory power they wield for the repertory for which they were intended. Indeed, by way of a Schenkerian analysis, very little of Stravinsky’s neoclassical idiom is likely to come to the fore; by such means, a piece such as the Symphony in Three Movements can relate only rather poorly (or irrelevantly) to such exemplars of the tonal past as the symphonies of Haydn, Beethoven, and Brahms. But here again, to dismiss the tonal tradition altogether is to dismiss a point no less crucial to neoclassicism; the tonal tradition requires acknowledgment, even if the evidence in support of the Schenkerian model is too incomplete to allow for a convincing application. What tends to emerge from such application, in fact, is a residue, one manifesting itself discontinuously in bits and pieces, here and there, without much in the way of a connective tissue. (For Schenker himself, of course, fragmentary evidence of this kind would have ruled out the possibility of tonality or of an organic structure altogether.) And it is in just this fragmentary respect that Stravinsky’s (neoclassical) uses of the past can indeed seem far from disciplined, even within single, individual pieces; varied in their individual effects, they are scattered and too contextualized from one piece to the next to be judged the product of a methodically applied technique or system abstracted from the classics. The composer himself might have argued differently, to be sure, and by insisting repeatedly on the craftlike nature of his art, the need for received

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rules, discipline, and so forth.6 And there is little question but that, between the two world wars, Stravinsky’s aesthetic as well as political views grew increasingly conservative and even reactionary, driven apparently by images of a chaotic present and the need for the restoration of an idealized order. Richard Taruskin has documented a number of aesthetic and institutional implications that would seem to bear this out.7 Yet the music speaks very differently, it seems to me, not of method or system but of far-reaching freedom in both the borrowing and the uses to which that borrowing is put; it speaks of a great variety of references whose sources are numerous, varied and conflicting even within individual pieces and movements. On the other hand, analytical methods having to do with motives and pitch-class sets are capable of more extended treatment. In the case of motives and their development, this has to do with the highly contextualized nature of the motivic process. Defined by its rhythms and successions, the melodic life of a particular work can still be very much its own. And this is because, although relatively nondescript in and of themselves, motives can reflect all the various aspects of a context, including its melody, harmony, rhythm, and instrumentation. Motives can result from an interaction of those aspects, and can reflect not only the sum but the transcending context itself. And it is their initial nondescriptness that allows for such a reflection, allows motives both to mold and to be molded in such a comprehensive fashion, and to become so entirely both instruments and reflections of the individual context. It was Schoenberg who sought to define a repertory along such lines (his own repertory, of course, twelve-tone as well as tonally “extended”), identifying his music with the Classical and Romantic traditions of the eighteenth and nineteenth centuries— “homophonic” music, as he described it at one point, music which

6See, for example, Igor Stravinsky, Poetics of Music, trans. Arthur Knodel and Ingolf Dahl (Cambridge: Harvard University Press, 1947), 65. “My freedom will be so much the greater and more meaningful the more narrowly I limit my field of action and the more I surround myself with obstacles ... The more constraints one imposes, the more one frees one’s self of the chains that shackle the spirit.” 7See Richard Taruskin, “Back to Whom? Neoclassicism as Ideology,” NineteenthCentury Music 16 (1993): 287–93. Taruskin documents some of the conservative aesthetic and sociopolitical currents with which Stravinsky seems to have identified himself during the early years of his neoclassicism in France.

Neoclassicism and Its Definitions

adhered to “the style of ‘developing variation.’”8 And he identified his music accordingly, connecting it with various tonal traditions by way of the motive and its development, at the expense of other repertories, including Stravinsky’s neoclassical. In its relations with the past, neoclassicism was deemed a fraud, indeed, “fashionable foolishness.”9 In contrast, Schoenberg’s twelve-tone works escaped the neoclassical label for much of the century, notwithstanding the obvious and elaborate transfer they often entailed not only of Baroque and Classical forms but of various types of phrases, themes, and accompanimental figuration which were no less tonal in origin. Even today, with much of the earlier polemic subsided, efforts persist in the demonstration of the organic character of that transfer, the extent to which the inherited forms in Schoenberg’s music can be heard and understood as forming an integral part of the twelve-tone structures, indeed, as having been motivated by those structures.10 But other critics have continued to insist on the significance of that restoration, and on the extent to which Schoenberg’s twelve-tone idiom was made intelligible by it.11 The presumption motivating this view has been that, once made aware of the given forms and types, listeners can apply some of the logic that accompanied their tonal unfolding; in however incidental or qualified a fashion, listeners can impose a borrowed sense of location and direction. At the same time, the need for constraints on the part of both composer and listener can also be said to have been satisfied, so that, from any number

8Arnold Schoenberg, Fundamentals of Musical Composition, ed. Gerald Strang and Leonard Stein (London: Faber and Faber, 1970), 8. “Homophonic music can be called the style of developing variation. This means that in the succession of motive-forms produced through variation of the basic motive, there is something which can be compared to development, to growth.” 9Schoenberg, “Igor Stravinsky: Der Restaurateur” (1926), in Style and Idea, 482. In another article, Schoenberg referred specifically to Oedipus Rex: “I still believe this work is nothing,” he averred. (“Stravinsky’s Oedipus” [1928], in Style and Idea, 483.) 10See, for example, Andrew Mead, “‘Tonal’ Forms in Arnold Schoenberg’s Twelve-Tone Music,” Music Theory Spectrum 9 (1987): 67–92; and Martha Hyde, “Dodecaphony: Schoenberg,” in Models of Musical Analysis: Early Twentieth-Century Music, ed. Jonathan Dunsby (Oxford: Oxford University Press, 1993), 56–80. 11See Leonard Meyer, “A Pride of Prejudices; or, Delight in Diversity,” Music Theory Spectrum 13 (1991): 247. “Contemporary composers have employed ‘borrowed’ forms and procedures not solely (or even primarily) because they considered themselves to be heirs to the great tradition of European art music, but because they had virtually no alternative. They could not do without some way of deciding how the motivic variants they invented should be combined with or succeed one another.”

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of perspectives, the old forms and their employment become linked inextricably to their tonal origins. And it has been in opposition to this rationale that other enthusiasts, including Milton Babbitt, have chosen to sidestep the idea of a transformation altogether.12 If Schoenberg’s twelve-tone music was to prevail, then it would have to do so on its own—not, as was imagined in neoclassical music, through a logic that lay outside of itself, one which could not be made organically a part of itself. And so the familiar complaint about the non-organic character of Stravinsky’s neoclassical works, about the inability of such works to blend old and new in the interests of a whole, was also Schoenberg’s complaint. Parts or features were perceived as resisting assimilation, refusing an intrinsic role. Either the new was judged incapable of absorbing the old or, in reverse, the old was judged incapable of absorbing the “impurities” or “wrong notes” of the new. Either way, neoclassical works were little more than hybrids, neither tonal or atonal but “half-measures,” compromises destined to fall short; they followed a meek and nostalgic path, a “middle road,” to follow Schoenberg’s account, one which could never be expected to reach a suitable destination.13 (Here as elsewhere in his criticism, Schoenberg ignored the restored forms in his own twelve-tone music, the extent to which those forms were susceptible to the same kinds of arguments about assimilation and the demands of the individual context.) And analysis was made to fall short as well. Relying on tonal or atonal models, it could proceed only with a good deal of qualification; either analysis was judged incapable of doing justice to neoclassical works, or its inadequacy was judged the reflection of an inadequate music. In this way, too, the underlying issues of neoclassicism can be seen to lead back to immediate experience. For they involve our 12See

Milton Babbitt, “Some Aspects of Twelve-Tone Composition,” The Score 12 (1955): 55. Babbitt insists on “a completely autonomous conception of the twelvetone system . . . in which all components, in all dimensions, would be determined by the relations and operations of the system.” He ignores, therefore, the “transference to twelve-tone composition” of the forms (rondo, gigue, sonata, and the like) belonging to “triadic music.” 13Arnold Schoenberg, Foreword to Drei Satiren, op. 28. The Foreword is reproduced and translated in full in Scott Messing, Neoclassicism in Music from the Genesis of the Concept through the Schoenberg/Stravinsky Polemic (Ann Arbor, Mich.: UMI Research Press, 1988), 144.

Neoclassicism and Its Definitions

experience of the nonimmediate past as well as of the new and the individual context; even more crucially, they involve the extent to which we are obliged to recognize that nonimmediate past for what it might authentically have been. (Even with the evidence discontinuous and in bits and pieces, whole images of the past may be invoked in the mind of the listener.) How substantially are we compelled to look back in this music, to recall the old for the sake of the new? How extensive is this dependence on a familiarity with styles, idioms, and repertories long since past? And if indeed extensive (as has been implied), does it inhibit the individual context (as has also been implied)? Is this what neoclassicism is, in fact, inhibition with a distancing and alienating effect of this kind? Does the idea of a split between the tonal and atonal worlds, the pillarlike existence which those worlds have assumed in much critical discourse, encourage such an interpretation of neoclassicism? Has the suggestion been too pronounced, above all in the critical reception surrounding Schoenberg’s music and that of Schoenberg’s immediate and nonimmediate schools, that it is only the fully committed sides of that split that are capable of genuine musical expression, not the half-hearted spaces in between? Such questions can bring society and politics into play. What is more concretely apparent, however, is that, typically, the borrowing of tonal or stylistic features involves the nonimmediate past, traditions presumed dead rather than living; that the degree of relatedness and intersection, of unity sensed or demonstrated superficially, is far less than in the music of the various nonimmediate pasts; and that the resultant heightened sense of conflict is in no way eased by the idea of a transformation or that of the individual context, by the contradictory claim of an overriding sense of purpose. A more tangible consideration of these issues will be pursued in the analysis which follows.

Motives

The opening section of the Symphony in Three Movements, Rehearsal Nos. 0–34, is without question a “developing variation,” consistent with the many attempts to pin down this elusive if suggestive concept of Schoenberg’s. Illustrated in Ex. 1, the principal theme

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appears in two parts, the second as a “continuation” of the first. The first part, labeled Motive A, consists of a lower pitch G standing in opposition to its tritone-related triad (D♭–F–A♭); crucial is the upper-lower disposition of the two components, a fixed registral spacing that is transposed and repeated variously throughout the first movement and from which a quality of superimposition and ultimately of opposition emerges. Additional segments include the separate grouping of G with A♭, arising from the G–A♭ “minor ninth” span that opens the movement. G is grouped with F as well, forming the “minor seventh” G–F. And if we assume “octave displacement,” the latter three pitches may be joined as a descending “minor-third” motion A♭–G–F, a part not only of Motive A but of its “continuation” in the form of Motive B as well.

Example 1 Stravinsky: Symphony in Three Movements, I

Neoclassicism and Its Definitions

Examples 2a and 2b

The preceding segments are motivic, of course, and as such hinge on repetition, on what follows in the way of a continuing development. In the case of Motive A, subsequent transpositions and transformations project the idea of a Grundgestalt, or “basic shape,” along the lines indicated by Patricia Carpenter and Severine Neff in their recent studies of this elusive yet suggestive Schoenbergian

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concept.14 Reduced to the common thread of a pitch-interval succession, Motive A as “basic shape” may be defined by a lower pitch standing in tritone-related opposition to an upper triad, most often major, sometimes minor. Traced in Ex. 2, the transition at Nos. 5–7 leads to a further transposition at Nos. 7–13: the A of an A–C–A basso ostinato stands in opposition to an upper (E♭–G–B♭) triad. The configuration at No. 13 is less clear-cut in this regard, although it too involves a whole-step transposition, this time to B and (F–A–A♭–(C)); lacking its fifth, the triad has become incomplete. The conclusion of this section at No. 34 is marked by a similar configuration, only transposed to C♯ and (G–B–B♭–(D)). Tritonerelated to the initial thematic statement, this final transposition allows for a reversal of the initial opposition; C♯ (D♭) now stands opposed to its incomplete tritone-related triad (G–B–B♭–(D)). So, too, the successive transpositions of Motive A yield a larger pattern of ascending whole steps; as shown in Ex. 3, only the transposition back to G (D♭–F-A♭) at No. 22 upsets this pattern.

Example 2c 14Patricia

Carpenter, “Grundgestalt as Tonal Function,” Music Theory Spectrum 5 (1983): 15–38; Neff, “Schoenberg and Goethe.”

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Example 2d

Example 2e

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Example 2f

Example 3

Observe, too, that the sense of an opposition between tritonerelated components is far less evident at No. 34 than in earlier passages; the lower of the two components, C♯ (D♭) in the bass, is scarcely more than an inflection at this point, a V-of-V chromatic tendency tone (or chromatic neighbor) to the D; it asserts itself with

Neoclassicism and Its Definitions

far less independence. And while the C♯–B “minor seventh” at No. 34 + 3 is unmistakably motivic, referring back to the G–F “minor seventh” of Motive A in the opening measures, the opposition itself is defined not so much by the tritone relationship as by that most pervasive of all neoclassical “clashes,” the major-minor third, conceived here in terms of the two incomplete major and minor triads rooted on G. Incomplete with roots doubled and fifths missing, the two triads magnify the effect of a clash, reflecting at the same time an even more pervasive motivic function than that defined by Motive A and its segments. Motive B follows as a “continuation” of Motive A: shown in Ex. 1, it includes the entire thematic stretch beginning with the upbeat to m. 4 and ending with the upbeat to m. 9. Ultimately more significant, however, are the octaves contained within this scale-like stretch of material, octaves which are split on either side by a third, most often minor but occasionally major. Labeled motive x in Ex. 1 and 2, octaves split in this way (forms of the incomplete triad, as suggested already) permeate this music as “building blocks” or “basic motives,” to use Schoenberg’s terms, elementary units of vocabulary or “smallest common multiples.”15 In the transition at Nos. 5–7, motive x appears linearly in the horns and trumpets in terms of G–B♭–G and B♭–G– B♭; it identifies harmonically with the diminished-seventh chord, (C♯–E–G–B♭). Subsequently, at Nos. 7–13, it is transposed to A–C–A, appearing as a basso ostinato; the configurations at Nos. 7, 13, and 34 all make reference to the incomplete triad. In its final appearance at No. 38 it is transformed as the principal theme of a new section. In schematic form, then, such are the motivic paths of this music, to the extent that such paths lend themselves to systematic analysis. Briefly read, they can be shown to differ little from the more familiar paths traced by Schoenberg and others in the music of Beethoven, Brahms, and Schoenberg himself. And the manner of their developing variation can likewise be shown to differ little. Indeed, only very weakly can a distinction be drawn along these lines, can the concept of developing variation be used to distinguish the music of the earlier and more familiar sources from this present Symphony and other excluded repertories such as the neoclassical; 15Schoenberg,

Fundamentals, 8. “Since [the basic motive] includes elements, at least, of every subsequent musical figure, one could consider it the smallest common multiple.”

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only very weakly can the claim of a distinct critical tradition be made, in other words, confined as this has been to the “homophonic” music of Schoenberg’s particular choice.16 This would not be to dismiss the many other distinctions which have been brought to the fore in this connection. Schoenberg set the “style of developing variation” against that of the model and its sequence, against the unvaried repetition that was attributed to the music of Liszt, Wagner, and the New German School, or to composers such as Tchaikovsky and Rimsky-Korsakov. He judged the exact or merely embellished repetition in these latter repertories shallow and too easy for composers and listeners alike: “It was the Brahmsian School which fought violently against the sequences of the New German School. Their attitude was based on the opposite viewpoint that unvaried repetition is cheap.”17 And he set the same “style” against that of various “folkloristic symphonies” as well: he judged borrowed folk material unable to imply continuation, unable to remain incomplete so as to suggest eventual completion; he thought folk material unable to pose questions that required answers, answers that could lead to further elaborations.18 (The folksong was judged too complete in and of itself.) Yet, the motivic processes he examined are far more pervasive than he allowed, more integrally a part of a great many styles, idioms, and repertories. In the case of Stravinsky’s music, for example, the ostinato-like repetition characteristic of the melodic invention is unvarying only from the standpoint of pitch-interval succession. From that of accent and metrical placement, it is neither unvarying nor devoid of a sense of development.19 By way of illustration: as a basic motive, the idea of motive x, of an octave split on one side or the other by a minor or major third 16I refer specifically to Walter Frisch, Brahms and the Principle of Developing Variation

(Berkeley and Los Angeles: University of California Press, 1984). But see also the discussion of motives and motivic development in Straus, Remaking the Past, 21–73. 17Schoenberg, “Criteria for the Evaluation of Music” (1946), in Style and Idea, 129. 18Schoenberg, “Folkloristic Symphonies” (1947), in Style and Idea, 164. 19 See the discussion of accentual displacement as it effects two types of rhythmicmetric construction in Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven and London: Yale University Press, 1983), 214–51; and van den Toorn, Stravinsky and “The Rite of Spring” (Berkeley and Los Angeles: University of California Press, 1987), 97–114. More specifically, the subject concerns reiterated motives or fragments in Stravinsky’s music and their patterns of accentual displacement in relation to a steady meter, notated or concealed.

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(the idea of an incomplete triad, more traditionally), is no less active in the first movement of Stravinsky’s Symphony than, say, in the first movement of Brahms’s Third Symphony (see Ex. 4). It is no less the subject of a developing variation in the former than in the latter. What separates the two sides is not motivic process but tonal organization, the absence (or near absence) of tonal constraints in the post-tonal Stravinsky, their presence in the tonal Brahms. Indeed, constraints in Stravinsky’s music are more readily octatonic or octatonic-diatonic; in the principal theme of the opening measures (Ex. 1), both Motive A as the Grundgestalt G (D♭–F–A♭) and the “continuation” of Motive B are confined to a single transposition of the octatonic set; the successions of motive x in this stretch, octaves enclosing major or minor thirds, are constrained accordingly. Alternatively, in the Brahms symphony the motive’s minor third is chromatic in relation to the F-major tonality, a circumstance whose consequences are immediately at hand in the flat-side modal mixture of the opening measures, the common-tone diminished-seventh chord of m. 2, and the chord of the lowered submediant in m. 8. But neither, on an even broader scale, can motivic processes, Schoenbergian or other, be used to distinguish the post-tonal from the tonal. Defined by means of pitch, shape, interval, or rhythm, motives and their variants are no more pervasive in, say, Schoenberg’s atonal or twelve-tone music (indeed, in the first movement of Stravinsky’s Symphony) than in Bach’s chorale preludes, Beethoven’s symphonies, or Brahms’s chamber music. And when reduced to unordered pitch-class sets (sets of interval classes, for the most part), they do not figure as part of a post-tonal “common practice” which could distinguish the post-tonal from the tonal.20 Rather, sets tend to change while the motivic processes 20Such

a case is made in Straus, Remaking the Past, 22–27, 57–64. Straus argues that the manipulation of motives, reduced in turn to abstract pitch-class sets, became a “common practice” in post-tonal music, one that can distinguish the post-tonal period generally from the tonal. In my estimation, however, motives based on the recurrence of unordered sets of varying degrees of determinacy are no less prevalent in tonal music than they are in post-tonal music (which includes the music of Bartók and Stravinsky as well as that of the Second Viennese School); the distinction rests with a negative, in other words, with the absence, in varying degrees, of tonally functional relations, not with any increased motivic “saturation,” “density,” “richness,” or the like. The issue is discussed at greater length in Pieter C. van den Toorn, Music, Politics, and the Academy (Berkeley and Los Angeles: University of California Press, 1996), 157–68. See also Richard Taruskin, review of Straus, Remaking the Past, Journal of the American Musicological Society 46 (1993), 129–34.

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themselves remain intact; the latter processes overlap the post-tonal and tonal worlds, uniting rather than separating those worlds. This is the whole point of the ties Schoenberg sought to project in his own music, of course, the point of a tradition of motives and of motivic development preserved.

Example 4  Brahms: Symphony No. 3

In Stravinsky’s Symphony, the octaves of Motives A, B, and x do not allow for extensive reduction. Consisting of an upper-lower tritone opposition, Motive A is a registral idea. And the specifics of its articulation, of two components standing in a tritonedefined opposition or polarity, are deeply reflective not only of this present Symphony but of Stravinsky’s music as a whole. Relations

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of significance can thus be defined fairly determinately. For our purposes, that more determinate definition has seemed preferable to the further abstraction of the unordered pitch-class set—which in the case of Motive A would have involved reducing G (D♭–F–A♭) or A (E♭–G–♭♭) to [0137], set class 4–Z29, to follow Forte’s nomenclature.

Polychords; C-Major Tonalities; Octatonic Sets

The above analysis can point not only to a good deal of consistency in Stravinsky’s use of motives, but also, from the same standpoint, to a good deal of motivation on the part of the individual context. For if, as has been indicated, motives can be nondescript and a part of processes which are hugely general, they can also, in their ultimate realizations, reflect considerable detail and hence individuality; as part of a continuing development, they can reflect all aspects of a specific context. This is the nature of the process, of developing variation, properly speaking, not static or isolated identification but a process of dynamic framing, one of motives being joined to form larger configurations from which new motives are made to evolve. There is an element of growth, as Schoenberg insisted. Alternatively, however, motives carry no inherent sense of succession, no governing rationale as to why one variant would necessarily precede or follow another. Beyond general processes of liquidation, there is no syntax of motivic succession, however much Schoenberg might often have imagined that there was, treating motives as if they were units of vocabulary within larger phrases, sentences, and paragraphs. Tonal functions provide for such a sense, of course, one of “directed motion,” as has often been indicated. And this may be possible even when such functions are severely qualified. Tonality, then, stands somewhat apart from strictly “motivic” considerations, as becomes clear from an examination of Felix Salzer’s Schenkerian interpretation of Stravinsky’s first movement.21 Two of Salzer’s graphs are reproduced in Ex. 5 and 6: Example  5 refers to the theme itself and its accompaniment in the bass; a dissonant “polychord” (Salzer’s term) is prolonged, consisting in the main of the tritone-related major triads rooted on G and D♭.22 21Felix

Salzer, Structural Hearing (New York: Dover, 1982), 248, 296 (Exx. 417, 472). Structural Hearing, 218.

22Salzer,

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Of these triads, G is judged primary, D♭ secondary. Yet Salzer treats the polychord as a stable sonority; A♭ and F in the theme are “chord tones” while G and E are subsidiary. In the second graph of Ex. 6, a “gigantic prolongation of G” is inferred at Nos. 1–27.23 Enclosed are smaller prolongations, including a neighbor motion involving A (in the bass) at Nos. 7–13.

Example 5

To some extent, of course, the idea of a polychord prolonged corresponds to that of a basic shape transformed. Motive A in terms of G and its tritone-related triad (D♭–F–A♭) may be compared to Salzer’s polychord, successive transpositions of Motive A to various stages of Salzer’s prolongation. At Nos. 7–13, for example, Motive A is transposed up a whole step to A(E♭–G–B♭); A in the bass (see Ex. 2) stands in opposition to a reiteration of (E♭–G–B♭) in the strings. In Salzer’s account, this transposition is interpreted as a large-scale motion surrounding G and involving A as a neighbor note; a return to G and the (G–B–D) (D♭–F–A♭) polychord is noted at No. 22. In the large, then, motives and basic shapes are transformed into polychords, transpositions into prolongations. In turn, the latter prolongations may be reinterpreted as well. For the areas marked off for interpretation by Motive A coincide with transpositions of the octatonic set. 23Ibid.

Example 6

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Indeed, as mentioned already, the principal theme is octatonic, accountable to a single transposition of that set. Plotted in Ex. 1, Motive A followed by Motive B and its subsequent successions of motive x in the treble part are all confined to Collection I, one of three content-distinguishable transpositions of the octatonic set.24 So, too, the transposition up a step from G(D♭–F–A♭) to A(E♭–G– B♭) at Nos. 7–13 (see Exx. 2 and 3) involves not only Motive A or a neighbor motion but the octatonic set as well: Collection I is succeeded by Collection III. And the diminished-seventh chord (C♯, E, G, B♭) shared by those two collections is isolated in a passage of transition at Nos. 5–7. A smoother octatonic maneuver would be hard to imagine. Indeed, the octatonic relations which follow are extraordinarily evident. But such an octatonic reading brings us no closer to the nonimmediate traditions underlying this music than the motivic paths traced in Ex. 1–3 or, in Ex. 5 and 6, Salzer’s idea of a prolongation of a dissonant polychord. The octatonic interpretation refers only to the new, in other words, not to the old or, indeed, to the idea of a transformation of the old by the new; it ignores the context as a whole as, at the very least, an interaction of conflicting components. Prolongation is a Schenkerian term, to be sure, but Salzer’s polychord fuses and to some extent negates tonal function. Indeed, tonality can best be acknowledged by changing Salzer’s quasi-tonic from G to a C, interpreting G as the dominant in C major. In this way, and as illustrated in Ex. 7, an octatonic theme with G at its center is placed in interaction with the diatonic white-note collection centered on C, the latter represented most conspicuously in the opening measures by the G–A–B–C ascending motion in the bass. The tonal implications of this interaction are shown in Ex. 8: superimposed over G, a Neapolitan chord is succeeded by a dominant minor ninth with A♭ as the degree of the lowered submediant. And this interpretation would seem to be confirmed by the return of the opening theme at the end of the movement, a return which does in fact resolve to a type of C-ending. (See Ex. 9, where the continuation of the theme as 24See the discussion of the octatonic set in van den Toorn, The Music of Igor Stravinsky,

31–98; and in van den Toorn, Stravinsky and “The Rite of Spring,” 119–31,143–48. As a reflection of its symmetry, the set is limited to three transpositions, beginning at C♯ with the semitone-tone ordering of the scale. I have labeled these Collection I (at C♯), Collection II (at D), and Collection III (at E♭).

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Motive B is in augmentation.) There, the presence of tonal degrees is unmistakable.

Example 7

Example 8

But how convincingly does this C-ending work as a confirmation of the earlier suggestion of C major? To what extent do the later degrees confirm the earlier ones? By virtue of the C-ending, in other words, is the sustained G of the opening section that much more a dominant, (D♭–F–A♭) that much more a Neapolitan, and A♭ a lowered submediant? Is the C-major tonality that much more authentic, the movement as a whole that much more integrated from a tonal standpoint? Or does the C-ending fail as a resolution of conflict? Is it a convenience at this point?25 In a way typical of Stravinsky’s music, 25See

the discussion of this in my earlier treatment of Stravinsky’s Symphony (van den Toorn, The Music of Igor Stravinsky, 362–64).

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of the statically sustained blocks of material and of the abrupt shifts which can often replace a more traditional sense of progression, do the reiterations of Motives A and B followed by the C-ending merely rehearse what has been rehearsed all along, indeed, from the beginning of the Symphony? In concrete form, of course, problems of this kind are typical of those arising from Stravinsky’s neoclassicism. Specifically of concern here is the C-major tonality, the point at which tonal expectations conflict not only with the symphony’s octatonicism but also with the motivic paths traced in Ex. 1–3.

Example 9

The C-ending is anticipated to some extent by the principal theme of the opening measures, by the G-A-B-C motion in the bass at mm. 3–5 and by the repeated Cs at m. 5. It is not without impurity: Bs are positioned in such a way as to give vent to earlier assertions of priority on the part of both E and G (E and E/G/E at No. 29). (The large-scale relationship of G to E, the octatonic as well as diatonic C-scale implications of that relationship, can also bring to mind the first movements of the Symphony of Psalms (1930) and the Symphony in C (1940)). And this positioning can readily reflect the individual context, a form of assimilation. By such means, the transformation of the old by the new makes itself felt in the final measures of the movement. Not to acknowledge such assimilation and transformation, to interpret

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B as a true impurity, is to interpret solely in terms of the C-major tonality, an option which seems to have been followed not only by Schoenberg but also by early critics of similar passages in Stravinsky’s neoclassical works. That option rules out the possibility of a segmentation: as an integral component, B may be grouped with (E–G–B) and (G–B–D) within the final simultaneity, reflecting earlier assertions of priority and acquiring in this way a sense of motivation. As an impurity or “wrong note,” however, it is detached from the C-major triad, isolated and without the reflection of a context.

Continuing Conflicts

There are obvious hazards in dredging up the Stravinsky-Schoenberg wars of the 1920s and ’30s. Schoenberg viewed neoclassicism as merely facile and clever, an idiom lacking in substance or “idea,” wholly superficial in its relations with the past; Stravinsky complained of “modernists” who worked with “formulas instead of ideas.”26 Yet, with the exception of Pierrot Lunaire for Stravinsky and Oedipus Rex for Schoenberg, the two composers knew little of the music about which they expressed such contempt.27 Moreover, while we can point to the compelling nature of the motive and its developing variation in Stravinsky’s Symphony, we need not question the nature of the process itself or, indeed, the legitimacy of the ties Schoenberg sought to invoke. Indeed, were we to ignore motivic processes altogether, the first movement of Stravinsky’s Symphony would group only very awkwardly with Schoenberg’s “extended,” atonal, and twelve-tone repertories, or with the rhythmic and melodic aspects of those repertories; in their progressive and forward-moving impulses, the latter aspects can seem antithetical to the statically maintained blocks and sections characteristic of the Symphony. On a more comprehensive basis, the two sides are better distinguished than likened; the contrast they afford is more compelling than the similarity. 26Quoted

in Messing, Neoclassicism in Music, 141. Messing, Neoclassicism in Music, 145. “Like that of Stravinsky, Schoenberg’s assessment of his contemporary was gleaned from what he read, not from what he heard: contemporary reviews and essays of their music made up the evidence upon which the composers made their aesthetic conclusions.”

27See

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Moreover, the persuasiveness of the individual context is hard to miss in the present case. Parts or features identified as Baroque, Classical, or tonal do not draw a great deal of attention to themselves as such, the sort of attention likely to impede integration and prevent, on the part of the individual context, the emergence of an overriding sense of integrity. Rather, a sense of purpose is everywhere immediately felt; embedded in the context, bits and pieces of the past do not create the sorts of separations likely to force the listener into a distanced form of dependence. Consistent with the idea of a removed sense of the nonimmediate past, neoclassical issues of this kind can seem skirted for the most part. On the other hand, each of the four interpretations in the above analysis was given its due. As Motive A, for example, G was grouped with (D♭–F–A♭), a compound sonority which was first interpreted as a Grundgestalt, second as a polychord prolonged, and third, in C major, as the superimposition of a Neapolitan triad over a sustained dominant. Subsequently, the same sonority was located within an octatonic framework, a single transposition of that set, an interpretation which introduced yet another set of circumstances. The trick of such an analysis would be to avoid the piecemeal, presumably by pointing once again, however provisionally, to the idea of a transformation. Thus, as illustrated in Ex. 7, the boundaries of the two interacting octatonic and diatonic sets overlap: with G and its major triad as the principal points of intersection, the two sets intersect more readily than they conflict. Indeed, the only nonoctatonic pitch classes in the opening thematic section are A and C in the accompaniment in the bass; illustrated in Ex. 1, A–C–A is a form of motive x at m. 4 while C is reiterated at m. 5. And while A and C are involved in a variety of clashes—A against the A♭ at m. 4, C harshly against the D♭ at m. 5—there are mitigating circumstances. Apropos of the C-major interpretation of this passage, A♭ and D♭, however octatonic in relation to the principal theme, are not without tonal implications. But the intersection and transformation of these varying interpretations, of the segmentations implied in each case, cannot, it seems to me, erase the sense of conflict that is at the heart of this music, the sense of a superimposition of segmentations never entirely reconciled, of a clashing of forces locked in confrontation. And that conflict may be traced to the very first measure, indeed,

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to the opposition defined by Motive A, the lower G which stands in opposition to its upper tritone-related triad. For although Motive A’s two opposing components intersect with both the octatonic Collection I and the diatonic C-scale (the latter by virtue of the Neapolitan interpretation of (D♭–F–A♭)), they are kept apart registrally; in the bass, G groups with the diatonic motion G–A–B–C while, in the treble, (D♭–F–A♭) groups with the octatonic set (see Ex. 10). Hence the ensuing conflict between registers as well as sets, between lower diatonic components which move contrary to upper octatonic ones, reflects, at the outset, the compound nature of Motive A; although motivically whole (indeed, a Grundgestalt), Motive A is split into opposing components. And the ensuing separation of those components as referential sets is remarkably cohesive. In the opening thematic stretch shown in Ex. 10, the nonoctatonic pitches A and C are not isolated as such. In the bass at mm. 4 and 5, they are grouped first with G and then with the ascending motion G–A–B–C, above all with the successions of motive x that articulate that motion; they form relations with the pitch classes of that motion, with G and B, for example, relations which, although partially intersecting with the octatonic set of the theme above, are effected accordingly. Those nonoctatonic relations, including the reiteration of C at m. 5, are diatonic, even tonal apropos of C major, however extensive the intersection with the octatonic theme and the deployment of motive x on both sides of this referential fence. In other words, A and C group with other pitch classes in the accompaniment which, even if intersecting with the octatonic set, are affected by their non-octatonicism; larger diatonic C-scale components are formed. Indeed, the static and to some extent irreconcilable superimposition of an octatonic theme over a diatonic accompaniment is unmistakable at the outset of the Symphony, as it is in later sections: C and (C–E–G) are not accounted for—and are hence made to clash and conflict with—the octatonic Collection I at the outset (see Ex. 10), while, later at Nos. 4 and 22 (see Ex. 11), Collection I triads and motive x successions are superimposed over white-note, diatonic scale passages. These relations are typical of Stravinsky’s neoclassical contexts, from the variation movement of the Octet (1923), where an octatonic Collection III theme with A at its center is placed in opposition to a tonic D, to the third movement

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of this present symphony: while tonics and tonic triads tend to conflict with interacting octatonic sets, dominants and dominant triads intersect.28

Example 10

Inevitably, then, we are led back again to the contradiction of the conventional view of Stravinsky’s neoclassicism, even if the terms of that contradiction may be addressed more tangibly in terms of specific motives, sets, segments, and their interactions; an impression of conflict, of a high degree of nonintegration coexists with one of transcendence. The opposing forces in the Symphony, right and left hands of the principal theme at mm. 1–9, the octatonic Collection I theme and its diatonic, C-scale accompaniment, are kept apart registrally. At the outset, they assume the character of a superimposition which, as has been noted, is a matter of conflicting 28See

the further discussion of this in van den Toorn, The Music of Igor Stravinsky, 330–71.

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sets and of the cohesiveness exhibited by those sets. And although not examined here, there are rhythmic metric definitions as well: fixed in register and instrumentation, motives of the kind traced in Ex. 1–3 may repeat according to cycles which vary independently of each other; they can stand opposed in this respect, with a sense of movement coming only by way of the resultant shifts in their coincidence.

Example 11

On the other hand, it has also been noted that conflicts of this kind are not absolute. In addition to the intersections plotted in Ex. 7, the two forces sound together; the meaning of one derives in part from

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the relationship it forms with the other. The point of the octatonic top at mm. 1–9 is defined to some extent by its superimposition over a diatonic bottom. It is here, in matters having to do with opposition and superimposition, matters effecting all aspects of context, that Stravinsky’s music is most appropriately addressed, that it can be distinguished convincingly from, say, much of Schoenberg’s, a repertory which, in its vertical or harmonic grouping, tends to invite integration to a far greater extent. (By reason of that integration, the issue of segmentation, of determining the legitimate parts of Schoenberg’s music, is far more problematic). For the referential interaction detailed here can easily be related to other octatonicdiatonic interactions in Stravinsky’s music, indeed, to forms of conflict that operate at all levels of structure and as an integral part of each of the three celebrated stylistic periods: Russian, neoclassical, and serial. So, too, it may be best to confront the contradiction of Stravinsky’s neoclassical works, features of a familiar yet nonimmediate past and the problem of their assimilation, on the elementary basis of segments, sets, and their union or separation. Neoclassicism can thus be related to manifestations of conflict more generally. For the interaction between the octatonic Collection I and the diatonic C-scale in the Symphony figures as one of many interactions involving the octatonic and diatonic sets, while Motive A together with its subsequent transformations is but one of many tritone polarities that emerge from such interactions. To begin with segments and sets in this fashion, with what may be characteristic of their use in Stravinsky’s music as a whole, allows the analyst to move with greater certainty to the issue of tonality and its residue, inevitably, to the problem of assimilation. Thus, the tritone polarity between G and (D♭–F–A♭) need not be confined to the idea of a dominant and a Neapolitan chord. Its behavior can also be dealt with in terms of basic shapes (motivically, that is), prolongations, and transpositions of the octatonic set. While the impression gained of such an analysis is likely to be one of nonorganicism, there are, as has been suggested, few alternatives. In acknowledging neoclassicism, analysis must deal with ideas which are often partial in themselves or which can only be

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applied partially. But to deal differently is to ignore the issue itself, that of neoclassicism, its character and rationale. Hence the next step is likely to consist of another confrontation with the familiar contradiction, another attempt to reconcile partiality with the demands of the individual context. The solution may remain beyond the analyst’s grasp, yet one hopes that the process can serve as a continuing source of illumination.

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Chapter 5

Will Stravinsky Survive Postmodernism?

In a scene repeated often enough in Richard Taruskin’s more provocative writings, an unsuspecting public is led astray by the theory establishment (a pet peeve of his), or by the formalist, specialist “talk” of “cold-war” meanies such as Milton Babbitt, Igor Stravinsky, Robert Craft, and Allen Forte. The same public is nursed back to musical health and well-being, however, to an appreciation of its own best interests, by the sympathetic intervention of its friendly neighborhood historical musicologist. Such scenes are played out throughout a distinguished body of work on Stravinsky, Russian music, and twentieth-century aesthetics, all of which culminates in two of Taruskin’s important new publications: Stravinsky and the Russian Traditions: A Biography of the Works Through “Mavra” (Berkeley: University of California Press, 1996), and Defining Russia Musically: Historical and Hermeneutical Essays (Princeton: Princeton University Press, 1997). Consider, for example, Taruskin’s approach to Schoenberg and to twelve-tone music in general. He views the dissemination of this music in the United States in the 1960s and 70s as elitist, a kind of force-feeding in which a reluctant public, strung along by a cast of academic composers, is made to digest what would otherwise have Reprinted from Music Theory Spectrum, vol. 22, no. 1 (Spring, 2000). The Music of Stravinsky: Collected Essays Pieter C. van den Toorn Text Copyright © 2000 Oxford University Press Layout Copyright © 2023 Jenny Stanford Publishing Pte. Ltd. ISBN 978-981-4968-62-1 (Hardcover), 978-1-003-35916-6 (eBook) www.jennystanford.com

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been set aside.1 In an essay in Defining Russia Musically (349–59), the implication is that the reception of twelve-tone music would have been more sympathetic had the professional “talk” about it been broadly aesthetic and historical rather than “technocratic,” had it featured the “spiritual” origins of the twelve-tone idea rather than the technical details of its “manufacture.”2 But even then, evidently, obstacles would have remained, given the “cognitive opaqueness” of twelve-tone music (an argument Taruskin borrows from Fred Lerdahl),3 the “gap” it presupposes between compositional and listening “strategies.” Taruskin approaches Scriabin in much the same way. He writes that a more positive response to Scriabin’s music would have been forthcoming had the aesthetics surrounding its conception— in this instance, the long, gooey entanglements with intangibles such as “desire” and “ecstasy” (a kind of cosmic hocus-pocus)—not been brushed aside by “cold-war” formalists and composers, including Stravinsky (Defining Russia Musically, 308–19, 358–59).4 More comprehensively, Taruskin’s concern in these and similar accounts is with “reception history,” critical environments and their role in shaping both music and our (presumably immediate, passionate) response to it. His claim would seem to be that, for better or for worse, consciously or unconsciously, reception is bound up accordingly, tied to past receptions and above all to original conceptions and intentions (to the extent that they are imaginable).5 What matters is the critical life of a piece of music, “public discourse,” attitude, and “criticism.” (He is better at distinguishing the interests of the listening public from those of the professional than in distinguishing the public from the critic and the popular press, however. The latter 1See,

for example, Richard Taruskin, “Revising Revision,” Journal of the American Musicological Society 46/1 (1993): 114–38. 2“[Schoenberg] sulks in positivistic limbo, his methods venerated but his deeds ignored. But it is precisely the academic despiritualization of dodecophany—more broadly, of atonality—that has led to its widespread, and justified, rejection.” Defining Russia Musically, 358. 3Fred Lerdahl, “Cognitive Constraints on Compositional Systems,” in Generative Processes in Music, ed. John A. Sloboda (Oxford: Clarendon, 1988), 231–59. 4One could easily argue the contrary, of course, namely, that a greater familiarity with Scriabin’s aesthetics would have soured the public additionally. 5For a similar appreciation of the role of “public discourse” and “criticism,” argued from a different vantage point, see Carl Dahlhaus, Esthetics of Music. trans. William W. Austin (Cambridge: Cambridge University Press, 1982), 86–87.

Will Stravinsky Survive Postmodernism?

are often confounded, it seems to me, and in ways not always helpful to his arguments.)6 Stravinsky and his music come under a similar fold. The efforts of Stravinsky to downplay the role of his Russian past, the role above all of his teacher and mentor, Nikolai Rimsky-Korsakov, are regarded as Bloomian, examples of the many lies and deceptions that dot his early interviews, autobiography, and later “conversations” with Robert Craft.7 At the same time, his celebrated neoclassical aesthetics are attributed to a reactionary group of French journalists (on whom Stravinsky relied for praise and encouragement), not to an encounter with music, one which here might have involved the Pergolesi and Gallo texts that underlie Pulcinella (1919).8 (However quaintly or naively, Stravinsky claimed the latter to have been the case, of course, that his encounter with and subsequent “recomposition” of these texts had constituted the “epiphany through which the whole of my later work became possible.”)9 And this too is telling, for 6I

may be less willing than Taruskin to anoint public opinion (or the opinion of those who presume to speak for the musical inclinations of the public), to assume that truths underlying such opinion are not available to listeners who happen to be specialists or experts. On what basis is the public assigned this role of a final arbiter in matters of reception? On the basis of its numbers? Or do we assume that its listening is more completely one of disinterested “pure pleasure”? In Richard Taruskin, “Back to Whom? Neoclassicism as Ideology,” 19th-century Music 16/3 (1993): 288–91, “professional discourse,” as exemplified by the formalist analysis of twelve-tone music, is decried as “by nature conservative,” reflective of an “entrenched power,” while “public discourse” is praised for its “enormous illocutionary force” and ability “to make things happen.” But in what way is The New York Times and its critics less of an “entrenched power” than, say, Perspectives of New Music and its contributors? More to the point, however, I suspect that those who, like Taruskin, are now arguing for a critical reappraisal of twelve-tone music and its earlier treatment, are doing so as members not of the lay public but of another group of academic experts and specialists which, having been brushed aside during the twelve-tone heyday some years ago, are now seeking their revenge. 7See Taruskin, “Revising Revision,” 114–38. 8See Taruskin, “Back to Whom?,” 289. “There is no better illustration of the influence of public discourse, and its embodiment in music,” Taruskin writes, “than the story of the neoclassical Stravinsky.... The aesthetics that sought to describe and define neoclassicism ... virtually shaped that style.” I have addressed some of these points before: see Pieter C. van den Toorn, Music, Politics, and the Academy (Berkeley: University of California Press, 1995), 144–52. 9Igor Stravinsky and Robert Craft, Expositions and Developments (New York: Doubleday, 1962), 129. “I looked, and I fell in love,” was his later recollection of this encounter.

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Taruskin has thereby made music a follower of ideology or sociopolitical “reality,” whatever it is about the experience of music that can be translated and understood in such terms. At the very least, the musical and the extra-musical are made one and the same. And so why, Taruskin asks in Defining Russia Musically (366–68), the continued appearance in our discussions of music of a phrase such as “the music itself”?10 Why should we continue to claim that music could speak for itself, that it could create a “world unto itself,” entice a form of mental and physical engagement the meaning of which, however sensed and felt, lies beyond all available means of explanation? Here, of course, Taruskin joins other “New Musicologists” or “postmodernists” in their attack on notions of aesthetic autonomy or “relative autonomy.” To him, phrases such as “the music itself” and “music in its own terms” are phrases of “rejection,” phrases applied by formalists and other “cold-war” figures to suppress meaning and significance as being “extra-musical,” to dismiss expressive content that is in fact capable not only of being discovered and discussed, but, to an extent far greater than the technical accounts of experts and specialists, of offering real assistance to the listening public (Defining Russia Musically, 367–68). These tragic exclusions are said to include Schoenberg’s metaphysics, Scriabin and the occult, and Stravinsky and the reactionary politics of formalism, classicism, fascism, and anti-Semitism. I shall argue here that many of Taruskin’s arguments are too sweeping, that they fail to consider adequately the grains of truth embedded in many opposing perspectives. But this is in no way to diminish the achievement of his work, above all of these latest volumes, and the magical blend of history, criticism, and analysis that is at their core. Few scholars in any field today can match Taruskin’s range, in any case, his ability to draw substantively from a great many sources in and out of music. I doubt that musicology can get much better, in fact—sumptuous in its detail, accessible yet sophisticated, and with a willingness to confront large issues in ways that relate to a spectrum of scholars, musicians, composers, and listeners. The field has been enlivened immeasurably by his efforts, made a truer reflection of what music is and how it functions in the large. And the 10The subtitle of the chapter in question (Chapter 13) reads: “A Myth of the Twentieth

Century: The Rite of Spring, the Tradition of the New and ‘The Music Itself.’”

Will Stravinsky Survive Postmodernism?

world of music theory could well do with a similar injection, it seems to me—a few Taruskins to probe and question on a broadened front; its journals would be better off with the more varied format likely to result from such a stimulus. The rigor of its analytical disciplines need not be sacrificed, only the extreme isolation of that rigor. This is an old lament, no doubt, one framed by Joseph Kerman some years ago,11 but it bears repeating in light of Taruskin’s more recent arguments. Winner of the 1997 Kinkeldey Award, the two hefty volumes that constitute Stravinsky and the Russian Traditions have been the subject of extensive and for the most part raving reviews in the popular press.12 Readers familiar with Taruskin’s work will recognize earlier articles in many of the chapters of these volumes, above all those on the nineteenth-century origins of Rimsky-Korsakov’s octatonicism (“harmonic sorcery”), Petrushka, The Rite of Spring, and the nature of Stravinsky’s Russian text-setting.13 But they are here expanded, as well as framed by a wealth of reproduced examples, pictures, and documents of one kind or another. (The chapter on The Firebird includes an early 1912 photograph of Stravinsky in the nude.) As the subtitle suggests, only the Russian period is covered in Stravinsky and the Russian Traditions, stretching from the early years to the one-act opera Mavra (1922). Stressed throughout is the depth of the composer’s ties to his native land, the depth of his early musical ties to Rimsky-Korsakov. Even The Soldier’s Tale (1918), with its dances seemingly reflective of a more cosmopolitan turn (as the composer himself acknowledged), is approached in this way. Its ensemble, which Stravinsky likened to a jazz band minus the saxophone, is 11See

Joseph Kerman, Contemplating Music (Cambridge: Harvard University Press, 1985). 12See, for example, Caryl Emerson, “The Rite of Passage,” The New Republic, 18 November 1996, 34–42. The most musically informed of these reviews (unfortunately in Dutch) is Elmer Schönberg, “Stravinsky,” Algemeen Handelsblad, 15 August 1997, 13–15. 13See Richard Taruskin, “Chernomor to Kastchei; Harmonic Sorcery, or Stravinsky’s ‘Angle,’” Journal of the American Musicological Society 38/1 (1985): 72–145; “Chez Petrushka: Harmony and Tonality chez Stravinsky.” 19th-century Music 10/3 (1986): 265–86; “The Rite Revisited: The Idea and the Source of Its Scenario.” in Music and Civilization, ed. Edmond Strain-champs and Maria Rika Maniates (New York: Norton, 1984), 183–202; “Stravinsky’s Rejoicing Discovery and What it Meant; Some Observations on His Russian Text-Setting,” in Stravinsky Retrospectives, ed. Ethan Haimo and Paul Johnson (Lincoln: University of Nebraska Press, 1987), 162–99.

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traced to East European village bands, in particular, to various Jewish counterparts. No less of a treat is Defining Russia Musically, a large collection of essays on Russian composers and topics beginning with an interesting defense of the early folk-song arrangements of N. A. Lvov (1751–1803). (The Introduction includes a spirited defense of a different kind, one of the role of the scholar as outsider, of the advantages of looking in from the outside, as it were, looking in at “other” musics and cultures.) Here, too, much has already appeared in print, but is rounded off within a larger format. At the center of this volume are four lengthy chapters on “Tchaikovsky and the Human,” “Scriabin and the Superhuman,” “Stravinsky and the Subhuman,” and “Shostakovitch and the Inhuman”; the first three are revisions of lectures given as the Christian Gauss Seminars in Criticism at Princeton in 1993. The full title of the Stravinsky essay, mentioned above, is “A Myth of the Twentieth Century: The Rite of Spring, The Tradition of the New, and ‘The Music Itself.’”14 It is the first of two essays on “Stravinsky and the Subhuman.” The second is a lengthy discussion of Stravinsky’s Svadebka (Les Noces, 1917), much of which is taken from Stravinsky and the Russian Traditions, but supplemented with additional comment on the composer’s reactionary politics, his association with the Eurasian émigré movement during the 1920s and 30s (coinciding with the European phase of his neoclassical period), and the occasion of numerous anti-Semitic slurs, attempts, as I now read them, to curry favor with German publishers and agents during the 1930s, to secure continued access to German audiences and royalties.15 Were Stravinsky’s remarks reflective of a genuinely anti-Semitic mentality? Or were they opportunistic, as has been suggested here? Was his anti-Semitism shallow, in other words, reflective of the social mores of his time, those of “polite society”? Taruskin

14This was published earlier in Modernism/Modernity 2/1 (1995): 1–26. See also in this connection, Pieter C. van den Toorn, “In Response to Richard Taruskin,” Music Theory Online 5/1 (1995). 15A typical slur runs as follows: “Is it politically wise vis-à-vis Germany to identify myself with Jews like Klemperer and Walter, who are being exiled? ... I do not want to risk seeing my name beside such trash as Milhaud.” Letter to Gavriyil Païchadze, Russische Musikverlag in Berlin, 7 September 1933. See Defining Russia Musically, 458. Slurs of this kind were regularly deleted by Robert Craft from his three-volume edition of Stravinsky’s selected correspondence.

Will Stravinsky Survive Postmodernism?

thinks not, arguing at length that Stravinsky’s behavior reveals an anti-Semitism that was “enthusiastic,” deep-seated, and pervasive (Defining Russia Musically, 448–60.) And it may not be possible to argue differently, in fact, without seeming inhuman or, possibly worse, like one of today’s legal defense teams (Bill Clinton’s, for example), forever splitting hairs in strategies of evasion. To condemn Stravinsky for his anti-Semitic remarks while keeping to a historical perspective, one mindful of the differences of time and place and of the possible injustice of hindsight, of mixing the composer up with Nazi propagandists and worse—is such an ideal still possible?16 I shall return to these ugly subjects, to the “dark side of modern music,” as Taruskin has called it, if only to examine some of the musical implications that have been drawn. First in line, however, are Taruskin’s accounts of some of Stravinsky’s earlier works. We can then move on to a number of socio-political issues.

I

The mixed feelings Stravinsky professed to have had about his early years of apprenticeship with Rimsky-Korsakov may have been genuine. Looking back over the years, he may have felt grateful for the lessons in orchestration, less so for Rimsky’s knowledge of composition, which may indeed have struck him as “not at all what it should have been.”17 He recalled Rimsky belittling Debussy’s “modernism” at a time when Rimsky’s own “modernist” credentials had consisted of little more than “a few flimsy enharmonic devices.”18 (Stravinsky may well have been referring to Rimsky’s octatonic 16Taruskin’s

pursuit of Stravinsky’s anti-Semitism mirrors the efforts by presentday historians to come to terms with “ordinary citizens” at the time of the Nazi persecutions, in Germany and elsewhere. The hard-line taken in Daniel Goldhagen, Hitler’s Willing Executioners: Ordinary Germans and the Holocaust (New York: Random House, 1997) may be compared with the mixed experiences chronicled in Victor Klemperer, I Will Bear Witness: A Diary of the Nazi Years, 1933–1941 (New York: Random House, 1998). 17Igor Stravinsky and Robert Craft, Memories and Commentaries (Berkeley: University of California Press, 1981), 57. 18Ibid., 59.

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harmony in these latter remarks,19 a direct Rimsky-Stravinsky link Taruskin is quite naturally at pains to underscore.) Stravinsky regarded himself as instinctual and largely self-taught, in fact, an opinion which seems to have been shared by others. As late as 1967, Pierre Suvchinsky, a close émigré friend from the 1920s and 30s, spoke of the “backwardness” of musical life in St. Petersburg at the turn of the century: “if you had seen what he came from in Russia,” he reminded Robert Craft, “you would believe in genius.”20 And independently of the composer too, critics have questioned the musical significance of the early bond. In a recent study, Claudio Spies judges Rimsky’s music too uninteresting from a rhythmicmetric standpoint to have served even the young Stravinsky as an important source of ideas and techniques.21 And in earlier studies, similarly, appraisals of Rimsky’s music had tended to adopt Gerald Abraham’s complaints about its metrical squareness, its failure to break away from the mechanical repetition of four-square sequences and patterns.22 Some of this is one-sided, no doubt, and Taruskin’s rebuttals offer a necessary antidote. Early chapters in Stravinsky and the Russian Traditions are wonderfully informative along these lines, drawing a picture of the early years while correcting many of the errors and distortions that undoubtedly marred the composer’s own published recollections. In seeking thus to set the record straight, however, Taruskin too can overreach at times, allowing that record to overwhelm critical and aesthetic concerns. This is an old bone of contention in musicology, of course, the slighting of individual artworks and their appreciation by overriding historical narratives. But it bears keeping in mind all the same, even in musical biography as compelling as Taruskin’s. A case in point is the lengthy chapter on The Firebird in Stravinsky and the Russian Traditions, a chapter confined in large part to a 19The

possibility of such a reference is pursued briefly in Pieter C. van den Toorn, Stravinsky and The Rite of Spring (Berkeley: University of California Press, 1987), 129–31. 20Igor Stravinsky and Robert Craft, Retrospectives and Conclusions (New York: Knopf, 1969), 265. Quoted in Stravinsky and the Russian Traditions, 18. 21Claudio Spies, “Conundrums, Conjectures, Construals; or, 5 vs. 3: The Influence of Russian Composers on Stravinsky,” in Stravinsky Retrospectives, ed. Ethan Haimo and Paul Johnson (Lincoln: University of Nebraska Press, 1987), 76–140. 22Gerald Abraham, Studies in Russian Music (London: William Reeves, 1935).

Will Stravinsky Survive Postmodernism?

listing of the possible precedents for Stravinky’s ballet in Rimsky’s operas and symphonic poems. Few of these citations are pursued analytically and hence with a view toward gaining insight into the music of either The Firebird or Rimsky. Rather, they are pursued in the interests of a historical point, the one here of lineage. And The Firebird emerges in just that light, in fact, as little more than a piece of history, “a veritable monument to the still-revered Rimsky” (Stravinsky and the Russian Traditions, 590). Little is left to be viewed aesthetically, in other words, listened to for its own sake or, indeed, in the context of Stravinsky’s music as a whole. Thus, for example, the Finale of The Firebird, the last of the five or so numbers included in the concert suite of 1919, is cited for its use of an authentic Russian folk-song, borrowed from one of Rimsky’s anthologies. And the stretch of 74 bars in the middle, allegro section of the Finale, acknowledged by Stravinsky as “the first instance of metrical irregularity in my music,”23 is traced to Rimsky as well, specifically, to the concluding 11 4 bars of Snegurochka (Snow Maiden, 1881). Taruskin’s conclusion is that the concert suite contains “little music of interest from a stylistic and historical point of view,” and none at all “that gives any inkling of the Stravinsky to come” (Stravinsky and the Russian Traditions, 588). But this can hardly be the only way of listening to this early, celebrated music. Some of it can still breathe, certainly, even after a century of “destructive popularity.”24 And it can do so as a reflection of twists and turns that Stravinsky was able to manage even at this early stage. The Finale consists of twenty-nine repetitions, one right after the other, of two phrases of the borrowed folk tune. This is a remarkable repetitive construction by any standard, it seems to me, even if it is seldom remarked upon, so accustomed have we become not just to it but, I would insist, to Stravinsky’s methods more generally. For there can be no mistaking the latter. Masking the repetition are repeated shifts in the metrical alignment of the two phrases. At relatively shallow levels of the metrical structure (at the level of the tactus, for example, the half-note beat here), alignments of the two phrases are displaced, their spans are made irregular, and the metrical levels themselves, internalized to some degree by the listener, are 23Expositions 24Ibid.,

149.

and Developments, 151.

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upset. And there are few processes more immediately identifying of Stravinsky’s music than these: repeating as a way of displacing, displacing as a way of catching listeners off balance, causing their metrical bearings to be lost or nearly so. Much of the impact of Stravinsky’s music is felt accordingly.

Example 1  The Firebird, Finale: repetition of folksong phrases

Labeled A and B, the two phrases of the folksong are shown and tracked throughout the Finale in Ex. 1. They are repeated in alternation, although the repetition is not always strict; A-plus-B remains the standard succession, but there are sometimes two and even three Bs to an A and vice versa. And this anticipates, beginning with the opening tableau of Petrushka, the “block” structures of Stravinsky’s later works, the technique of slicing up thematic statements into smaller units and of repeating those units separately and independently of each other. The units themselves are made irregular as a result of this reshuffling, an irregularity which can in turn reflect displacement.

Will Stravinsky Survive Postmodernism?

Observe too that the A-plus-B structure of the song and its repetition are features of the original conception, at least as it appears in Rimsky-Korsakov’s collection: see Ex. 2a. New in The Firebird, however, is the quasi-glissando on the final beat of phrase B; see Ex. 2b. And still newer, of course, is the eventual displacement of this glissando from the third beat of phrase B (upbeat) to the first beat of phrase A (downbeat). This occurs in the allegro section beginning at Rehearsal No. 17; see Ex. 2c. (Note values are evened out into quarters at this point, while phrases A and B are squeezed into two successive 74 bars, each with irregular subdivisions.)

Example 2  The Firebird, Finale: folksong and its source

Yet this notated displacement of the glissando may not be felt as such. For the listener can too easily continue with the alignments of the previous lento section at this point, sensing the glissando on an upbeat, as if it is still occurring on the last beat of phrase B. And one can do this without switching to the difficult quarter-note beat as the tactus (with Stravinsky’s metronome count of 208 here), continuing instead with the half-note beat, thereby avoiding the notated sevens altogether. To demonstrate how this is done, the passage is given in its original form in Ex. 3a and rebarred accordingly in Ex. 3b; phrases A and B encompass 32 and 42 bars respectively in the rebarring, totalling seven half-note beats, as the lower brackets indicate. The glissando beat, accented by the tuba and bass drum, becomes a giant syncopation. Example 3b is “conservative” in nature, “conservative” in relation to the “radicalism” of Stravinsky’s notation. Retained—conserved— is the half-note beat as the tactus (at an increased count of 104) and the alignments previously associated with that beat. But for how long is this alternative barring likely to hold? Is there a point at which, disrupted, it could force a reconsideration of the sevens of Stravinsky’s radical notation?

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Example 3  The Firebird, Finale: opening bars of Allegro section, alternative barring

202 Will Stravinsky Survive Postmodernism?

Example 4  The Firebird, Finale: Allegro section, alternative barring.

Will Stravinsky Survive Postmodernism? 203

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No doubt, the half-note beat, the tactus of this alternative reading, could be disrupted without forcing an acceptance of the notated sevens. Listeners could suspend their metrical bearings temporarily, in anticipation of a return to the rebarred version of Ex. 3b. And the stage could be set for such an eventuality if either of the two phrases A or B were to be repeated “block”-like, that is, separately and independently of each other. Such a repetition occurs with the transposition up a semitone at No. 18; see Ex. 4a. The initial phrase A is repeated twice before a final return to the A-plus-B pattern. Although listeners could continue to hear the glissando as an upbeat to phrase A at this point (without yielding in this regard; see the rebarred version in Ex. 4b), their sense of the half-note beat as the tactus is likely to be disrupted, making a confrontation with the irregular sevens of the notated score all but inevitable. But how might the return of the standard A-plus-B succession be interpreted? Is it likely to encourage a switch back to the rebarred version of Ex. 3b? Great care seems to have been taken to block such a possibility. In the subsequent passage, shown in Ex. 5, not only is phrase B repeated singly after the A-plus-B succession, but the glissando and its eighth-note beat are eliminated, leaving the sevens of the two phrase B statements exposed and inescapable. This is likely to figure as a final turning point for the conservatively inclined listener, with the same rug pulled one too many times. The source of that listener’s response, the standard A-plus-B succession, can no longer be relied upon. And even for listeners with modest inclinations in the direction of a reasonable metrical pulse—the halfnote beat here, internalized and retained—the penultimate 74 bar, where B is repeated immediately, is likely to be the trickiest of them all. Performers are likely to experience real difficulty in remaining synchronized. The sadistic play of this invention, its splitting off of alignment from meter, with the listener pulled one way and then another, would remain a characteristic feature of Stravinsky’s music for years to come. Much of the impact of this allegro section would be lost without it. And there is nothing remotely like it in Rimsky’s output, including, as mentioned already in this connection, Snegurochka.25

25A single instance of displacement in Snegurochka, a change in the metrical alignment of a repeated folkish fragment, may be found at m. 202 in Act III. Fragmented and appearing at the end of a group of repetitions, however, the displacement could easily be heard and understood by the listener as being a part of a process of liquidation.

Example 5  The Firebird, Finale: Allegro section

Will Stravinsky Survive Postmodernism? 205

Example 6  Possible sources of The Firebird, Finale, Allegro section.

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In fact, if we strip the configuration at No. 17 of its rhythmic invention, the material itself could suggest a number of contexts unrelated to Rimsky. Ex. 6 shows excerpts from two of these: “Nuages,” the first of Debussy’s Nocturnes (Ex. 6a), and an earlier work of Stravinsky, the opera (composed in 1908) The Nightingale (Ex. 6b). Linking these two passages to the allegro (Ex. 6c) are twopart thematic structures, back-and-forth motions, and, above all, open fifths doubled at the octave. In the case of the Debussy, the first of these fifths is pitch-specific and, perhaps to some degree, centric with regard to pitch structure more specifically. The overall character of Stravinsky’s allegro is no doubt markedly different from that of the opening of “Nuages”: if Debussy’s configuration influenced Stravinsky, then it did so incidentally. The contexts of examples 6a and 6b are perhaps best regarded as having laid somewhere in the back of Stravinsky’s mind as he first discovered and then worked more deliberately on the idea of the allegro. Conversely, the allegro may well have emerged as a convergence or coming together of these contexts: Debussy’s “Nuages” relates to the allegro by way of the opening measures of The Nightingale, and by way of the borrowed folk tune itself, as arranged in Rimsky-Korsakov’s collection of 100 Russian National Folksongs (excerpted and transposed in Ex. 6d). Another precedent, not included here, involves the third song (“An End at Last to Senseless Day”) of Mussorgsky’s song cycle, Without Sun. The song’s piano accompaniment features a similar configuration of two phrases with back-and-forth motions and octave doublings. In fact, the influence of Debussy’s music is a good deal more conspicuous than Taruskin allows. The celebrated syncopated theme of The Firebird’s Infernal Dance is no doubt traceable to a similar outline in Act III of Rimsky’s Mlada, but the music that follows at Rehearsal No. 26 (in the concert suite), where the theme’s diminished seventh outline yields to major thirds and an open fifth, could not have been conceived (in my judgment) without a studied awareness of the second of Debussy’s Nocturnes, “Fêtes.” And while Kastchei’s motive of interlocking major and minor thirds within a tritone was no doubt taken from a passage in Rimsky’s Kastchei the Deathless, the system of motivic derivation in The Firebird is unlike anything in the earlier score. In fact, the sound of the chromatic elaboration of Kastchei’s motives, being a part of the “instrumental

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recitative” to which Taruskin devotes the bulk of his analysis, can often bring Debussy as well as Rimsky to mind. The Firebird is “of the styles of its time,” of course, as the composer himself insisted, but it is so in ways often richly varied and compelling. The net it casts both forward and backward is a good deal wider than the one to which Taruskin refers so relentlessly.

II

The role of Stravinsky’s Russian past figures no less prominently in accounts of the composer’s subsequent works, including The Rite of Spring. My own view has been that, once the various subsets of, say, the octatonic set are superimposed (mostly triads and (02(3)5) tetrachords [i.e., (0235) or its (025) subset]), melody, harmony, rhythm, and form tend to unite in ways which, if never entirely free of past reference, are new, different, and Stravinskian all the same. The tritone-related (02(3)5)s in Ex. 7 from The Rite may be inferred from a passage at No. 33 in Scene 1 of Kastchei the Deathless, but according to vastly different criteria. Superimposed, as in Ex. 7, these (02(3)5)s have as much in common with, say, passages in Bartók’s Mikrokosmos (“The Isle of Bali,” for example), as they do with Scene 1 in Kastchei. They identify with more contemporary practices, in other words, and it makes as much sense (and sometimes a good deal more) to acknowledge as much, to relate them sideways or forward into the twentieth century, as it does to refer them back to Rimsky and the nineteenth. This is not the perspective of Stravinsky and the Russian Traditions, of course, but it is a perspective no less capable of shedding light on Stravinsky’s idiom as a whole, Russian as well as neoclassical and serial. (Octatonic passages in still earlier works, including the Scherzo fantastique [1908], tend to follow the more traditional path of literal sequences, and can for this reason more easily be dealt with by way of Rimsky’s applications.)

Example 7  The Rite of Spring, “Ritual of the Rival Tribes,” principal fragments

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An account of The Rite’s scenario and its possible sources in Stravinsky and the Russian Traditions (881–91) is followed, in Defining Russian Musically (360–88), by the drawing of a number of socio-political implications, the substance of which could hardly be less attractive. Taruskin’s earlier complaint about Stravinsky and The Rite is well known.26 It focused on the composer’s attempt to sidestep the close, “interdisciplinary” conditions under which much of the music may well have been composed; consistent with his newly acquired neoclassical aesthetics, Stravinsky recast the piece as an “objective construction.” This was in 1920, at the time of Diaghilev’s revival of the ballet. But already in 1914, following the success of Pierre Monteux’s concert-hall performances, these tables had begun to turn. A new, more sympathetic venue had suggested itself. And on this most practical of levels, why should this not have been the case? Much of the music of The Rite had been drowned out at the premiere, overshadowed by Nijinsky’s choreography and the riot which, perhaps more than any other factor, it caused. Freed from these distractions, from the bar-by-bar specifications of a scenario, the music could attract as foreground rather than as background music. The mere suggestion of a fantasy on pagan rites could suffice under these circumstances. This is not to deny the possibility of a cross-fertilization, a musical understanding informed by details of the scenario and vice versa. Only, the conception of which those details were a part is in no way “privileged.” The formalist approach is not less “true” or “authentic” than the earlier one. Later impulses were no less genuine (and no less lasting, certainly) than the assumptions which may now appear to have marked the origins of The Rite. (Taruskin can seem a bit trigger-happy with the composer’s published remarks and statements, pouncing as a matter of habit. Formalism itself, the composer’s neoclassical aesthetics, can seem the object of his criticism, not the composer’s distortions and lapses of memory. In much of this, it seems to me, the difficulties Stravinsky faced as an émigré composer are overlooked, the difficulties of earning a living, for example, winning an audience, communicating his views, and living down early successes whose aesthetic assumptions bore little relationship to neoclassicism.) 26See

Richard Taruskin, “Russian Folk Melodies in The Rite of Spring,” Journal of the American Musicological Society 33/3 (1980): 501–25.

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The more recent complaint about “the music itself” in Defining Russia Musically is not far removed. It targets aesthetic autonomy, music as a world separate and resistant to translation. Taruskin complains here that Stravinsky and a great many note-crunching analysts and theorists have used this phrase as a refuge,27 a means of dodging the issue of expressive content, “purifying” a piece such as The Rite by stripping it of its scenario and choreography and relegating both to the “extra-musical.” The dark side of music has been skirted as well. According to Taruskin, it was not as a celebration of early humankind that The Rite won fame and controversy, not as a tribute to “our common prehistoric roots,” but as an ugly “anti-humanist” tract, one which found resonance later in the century. Mass movements characterized both the scenario and the choreography; both lacked human subjectivity as a result, a sense of compassion. Individuals submitted to a collective will, as with the Chosen One and her Sacrificial Dance. Taruskin sees all this as foreshadowing a host of twentiethcentury evils, including those of fascism and the Nazi regime. He links the same anti-humanist impulses to the composer’s formalist aesthetics: Stravinsky’s lifelong recoil from the personal in music, from self-expression; his rejection of “psychology” and insistence on music as a world cut off from everyday forces, including, evidently, those of morality. A more sinister reading of these aesthetics would be difficult to imagine. Adorno’s reading comes to mind, of course, but Adorno is less biographical in his approach, less in tune with Stravinsky the person. But an argument of this kind can unwind for only so long. The issue from which it derives its motivation, the issue of musical content, must be confronted at some point. The musical significance of these anti-humanist implications must be addressed, the manner in which they manifest themselves musically in The Rite. “Those who assert the critical relevance of the connection” are under an obligation in this regard, as Taruskin himself concedes; they share a “burden of proof” (Defining Russia Musically, 363). Yet it is just 27Just about everyone with anything published on The Rite is given the heave-ho at this

point, including this reviewer. The two exceptions are: Robert Moevs, review of Allen Forte, The Harmonic Organization of The Rite of Spring, in Journal of Music Theory 24/1 (1980): 97–107; and Arnold Whittall, “Music Analysis as Human Science? Le sacre du printemps in Theory and Practice,” Music Analysis 1/1 (1982): 33–53.

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here where his argument begins to break down. Crucial questions about content, perception, association, and the role of the individual listener are left hanging (indeed, as such questions invariably are in accounts of this kind). Taruskin concludes with the following: “Whether [the anti-humanist side] irrevocably taints Stravinsky and his work, as T. W. Adorno insisted, is something we have to decide in keeping with our own liberal traditions” (Defining Russia Musically, 391). We have to decide? But surely Taruskin himself is convinced of the “impurity” of this music, its “taintedness”? For him, surely, the notes are “impure”? The notes carry traces of the composer’s antihumanism, traces which are sensed and felt accordingly? He has led the reader to assume as much, it seems to me, and rather pointedly at that. The idea of “the music itself” and that of the “extra-musical” have been brushed aside, dismissed as so much artful dodging on the part of formalists and “autonomists,” the means by which The Rite has been “purified,” “sanitized,” “sterilized,” and so forth. Backing off at this point places these contentions in jeopardy. It tends to confirm the appropriateness of the very formalist terms (“the music itself”) that Taruskin has discarded with such gleeful contempt. If, apart from Taruskin, we ourselves were to decide on the matter of this music’s “impurity,” then we would have to do so with a sense of conviction and belief. And such a belief would have to come in response to something tangible in the music. We would not be activating our censoring “liberal traditions,” deciding in a manner consistent with those “traditions,” on a whim, the flimsiest of associations. We would be responding to something musically concrete and vital, not a fishing expedition. But how does music incriminate itself in this way? How does it speak to us in these terms? Taruskin points to the “long spans of unchanging content” in The Rite, the “long stretches of arrested root motion and pulsing rhythms” (Defining Russia Musically, 383, 385). These are cited as evidence of the musical presence of these implications. Or are they? A few lines on this most crucial of questions, on the point of contact with music, are unlikely to inspire much confidence. Presumably, “pulsing rhythms” (a cliché of nearly a century of talk about this music) embody the anti-humanist evil within, so to speak, the evil that has steadfastly refused to be tamed.

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Consciously or unconsciously, this is what draws us, an awful truth of some kind. (Actually, syncopations, displacements, and conflicting stratifications are what are likely to excite in The Rite, a highly sophisticated network of aroused and frustrated expectations, not the “pulsing rhythms” which are but a support, a piece of wallpaper.) All this may prove unsatisfactory, of course, in which case we could turn to an even cruder form of associationism. We could switch our attention from the music to the listener, from suppositions of musical content to suppositions of disposition and conditioning. More specifically, we could assume that it is the listener who is “tainted,” not the music. And we could associate the music with Stravinsky, Stravinsky with formalist aesthetics, formalist aesthetics with an impersonal, detached view of music, a detached view of music with anti-humanism, and anti-humanism with authoritarianism, anti-liberalism, fascism, and the like. We could inform the listeners of these associations, hoping to predispose them; they would read them into the music, moving back and forth accordingly, testing them out. And the strength of their “take” would depend to some degree on the strength of their “liberal traditions,” as Taruskin implies. (It might depend on their impressionability too, of course, but who knows?) With a satisfactory “take,” the music would be judged guilty by association. But interest might also rest with those for whom The Rite would continue to serve as a source of intense aesthetic pleasure. Who are these listeners? Are they practicing formalists? Or are they merely insensitive? Do they lack humanism, in other words, Taruskin’s “traditions”? (Some may actually resent Taruskin’s intrusion at this point, the implication that their relations with music, the pleasures that may have seemed so deeply rooted as to be off-bounds, pure and unadulterated, were fraught with complicity, a sharing in some of the century’s most repugnant impulses. The flip side of Taruskin’s dark side would assume the image of a watchful eye for these listeners, a “correcting” censor tending to their sensibilities.) And so our “liberal traditions” are not so easily defined either. Taruskin mentions individualism repeatedly, the role of the individual in Western, liberal society, the belief in its worth and integrity. But such a belief carries sanctions, of course, sanctions against prejudgement, for example, against acting with prejudice. Why not extend the same protections to the individual piece of

Will Stravinsky Survive Postmodernism?

music? Why not seek to protect it from the sorts of implications raised by Taruskin? Or, after the fact, why not seek to free it of the same? (Taruskin’s interpretation could be viewed as a form of abuse, in other words, an attempt to smear The Rite, prejudice our hearing of the music.) But what purpose is served by this encumbrance of music? Why should we seek so ferociously to battle its abstraction? Are we not, by so doing, forcing it to become something which inherently it is not? It is as if its stimulus could be enhanced if it were less abstract and more like a language; as if, too, there truly were “secrets” of the kind unearthed by Taruskin, “secrets” which could reveal the nature of our attraction, and by so doing, act to enhance it. (Taruskin and others have not stopped at Stravinsky, of course. Other musics have been found suspect in this way, reflective of the immorality of their composers.28) Stravinsky may well have cut an unsympathetic figure between the wars. His politics were reactionary (anti-communist, at the very least), pro-order, pro-tradition, and pro-established religion. He was an elitist with an unabashed fondness for the rich and famous, touting the latter as a way of gaining acceptance and patronage. He admired Mussolini and fascist Italy for a time. (Later, in the United States, he admired Harry Truman.) As a formalist, he often dodged questions about the expressive content of his music, but not out of a disbelief in deep, underlying meanings and significances. He distrusted verbal descriptions and explanations, fearing the lives such descriptions would assume on their own, their overshadowing of music. He feared music’s trivialization and “debasement,” its abuse and exploitation. “Music expresses itself,” he thought; music itself was a creation, not a mirroring of something else.29 Taruskin suspects moral indifference. If “great” music was immune, then so too was the composer. And he finds this 28T.

W. Adorno comes to mind again: see his Philosophy of Modern Music, trans. Anne G. Mitchell and Wesley V. Bloomster (New York: The Seabury Press, 1973). Adorno’s approach to both Stravinsky and Wagner is given a strong reading in Rose Subotnick, Developing Variations (Minneapolis: University of Minnesota Press, 1991), 7–90. Accounts of Beethoven’s Ninth and Tchaikovsky’s Fourth may be found in Susan McClary, Feminine Endings (Minneapolis: University of Minnesota Press, 1991), 128, 69–79. The taintedness of Die Meistersinger is discussed in Barry Millington, “Nuremberg Trial: Is there Anti-Semitism in Die Meistersinger?,” Cambridge Opera Journal 3/3 (1991): 247–60. 29Memories and Commentaries, 123.

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unacceptable. Try as he might, in fact, he cannot reconcile “great” music with flawed, anti-humanist composers. And so an adjustment is made. Stravinsky’s music is deemed less than great, contaminated, in fact. In effect, it is asked to pay for the sins of its maker. In the absence of Stravinsky, Taruskin would have the music take the stand to, as it were, answer to the composer’s sins. At the same time, the specifics of the musical contamination are left unexamined. For Taruskin, of course, it is Stravinsky who is tainted, Stravinsky whose taintedness taints the listener (Taruskin). Yet the final link in this trail of associations, the actual tainting of the music by the composer or the listener, is averted to some degree. As has been suggested already, something of a hasty retreat is beaten at this juncture. And much New Musicology or postmodernism in music scholarship is like this. Build-ups with extravagant claims are followed by hazy, ambiguous commitments to musical connections, leaps of faith that are rarely acknowledged as such.30 Much of this musicology fails not because it traffics in the duplicities of “correctness,” the officially sponsored sympathies of the day, but because of “the music itself,” the refusal of so much of what we perceive and understand in music to respond in the appropriate ways. In answer to accounts such as Taruskin’s, accounts with highly negative, inflammatory interpretations of musical meaning, listeners do not shrink in horror, proclaim themselves sinful and repentant, determined to resist further contact with taintedness. The accounts themselves stick to their claims, of course. At the very 30The

musical connections are drawn quite explicitly in some of Susan McClary’s accounts, however. See, in her Feminine Endings (69–79). the discussion of the second theme in the first movement of Tchaikovsky’s Fourth. Specific features of this music are discussed in terms of stereotypical homosexual behavior. But even here, it seems to me, the chain of associations is hazy. Although the reader is led to believe that (McClary herself believes that) the first movement of this symphony has indeed been tainted by the composer in the prescribed way, a hasty retreat is beaten toward the end of her analysis. For it is evidently only McClary who. by way of her knowledge of Tchaikovsky’s homosexuality, has tainted the music. And the music is tainted only for her, evidently. The first movement need not be read along these lines at all, she later admits. It can be heard “as portraying a more ‘universal’ Oedipal pattern, or as a nonspecific struggle with both power and sensual enticements, or in any number of ways” (77).

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least, their commitments must be feigned, their beliefs in the musical embodiment (taintedness) of whatever it is that music is supposed to represent or is to be associated with must be kept in line. Even Taruskin, clearly uneasy at this stage of the process, only hedges, only appears to back off. Backing off unequivocally would have led his argument to a collapse. The use and exploitation of music in the promotion of extraneous socio-political views would have been exposed. The issue of their musical significance would have been abandoned. Not just “pure instrumental music” but music in general “unlocks the marvelous realm of the infinite,” awakens within us an “endless” and “indefinite longing” (E. T. A. Hoffmann). Music is “insatiate desire forever hieing forth and turning back into itself” (Ludwig Tieck); it expresses the “inner life” of desire (Schopenhauer). We can ask about the ability of music to rehearse such themes—why we should be attracted so ecstatically to the rehearsal, why it should be this particular manifestation and not another, here rather than there, and so forth. But after hundreds of years of such questions, there are still few answers. And I suspect that when there are more, much of the attraction will have ceased. In the following recollection of (of all people) Hitler (grotesque because seemingly ordinary), the dictator is inspired by the Prelude to Wagner’s Die Meistersinger: I began with a Bach fugue on the badly out of tune piano which Hitler listened to with much interest, seated in an armchair, his head in his hands, until I felt my fingers had warmed up enough to launch myself in the Prelude to the Mastersingers. And with this, as I had hoped, I touched Hitler’s musical nerve at just the right point. He was on his feet immediately and began walking up and down the room waving his arms in the gestures of a conductor and whistling every note in a strangely penetrating vibrato which was absolutely in tune.

Wagner’s music had simply become second nature to him. I would even maintain that there were marked parallels between the structure of the Mastersingers Prelude and his speeches. In both cases the same interweaving of leitmotifs, wealth of embellishment, counterpoint and finally the powerful outburst like the sound of trombones at Wagner’s act endings and Liszt’s rhapsodic finales.

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When I had finished the Finale with gusto, a radiant and completely changed Hitler stood before me, praising my playing effusively and even going so far as to say, “You’re a complete orchestra, Hanfstaengel.”31

The nature of Hitler’s inspiration is left open. Its non-musical ends or uses, good or bad, are left undetermined. Hitler is tainted, of course, but the music is not tainted. Hitler does not taint the music, and his taintedness does not arise from the music. The music merely inspires. It has the potential of arousing, stimulating. Nor is the Prelude tainted by the composer. Out of disgust with Wagner’s immorality, his anti-Semitism, the listener may choose to set the music aside. But the implications of this are political, not musical. Even if listeners, overwhelmed by Wagner’s immorality, associated the music with that immorality (reading anti-Semitism into the notes, as it were), the music would remain untainted. For the tainting is theirs. And they themselves would acknowledge as much. The use of analogies and metaphors follows a similar path. While the structure of Wagner’s Prelude could suggest “parallels” with any number of ideas and processes associated with Hitler, these are abstract considerations which, once again, do not involve the substance of his arousal. The connection to music is non-conceptual, in other words. Our musical awareness is immediate and non-verbal. Such a perspective can seem a bit cut and dried, no doubt, but it is generous all the same, respectful of the power of music, its ability to connect in ways that circumvent and resist the sorts of associations alluded to above. The connection is physical as well as mental. We can internalize steady meters, reflexively synchronizing them with our “internal rhythms.” And music is made physically a part of us in this way. So, too, it can reflect what we are in this way, what we are deep, down, and under, even if it does so in ways that are indirect, non-specific, and abstract. The hitting of the bass drum at Rehearsal No. 103 in The Rite may, upon reflection, seem “brutal” or “vicious,” conjuring up a fleeting image of brutality, say, the striking of the percussionist’s mallet itself. But such an image need not be that of a striking mallet. Nor need it be that of a “Savage Dance,” act of nature, or fist struck in anger. For 31Ernst

Hanfstaengel, Zwischen Weissen unci Braunen Haus (Munich: Piper, 1970), 55. Quoted in Jeremy Tambling. Opera and the Culture of Fascism (Oxford: Clarendon, 1996), 4–5.

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it is not the specifics of such an image which are likely to move us. The specifics can serve as a metaphor, no doubt, a foil for whatever it is that does in fact happen at No. 103 in The Rite. They can assist in highlighting No. 103, bringing it into sharper focus. But they are not what happens, and they do not arouse us. What counts is the musical train of thought of which No. 103 is a part, and in relation to which, as a form of verbal description, terms such as “brutal” and “vicious” are not only incomplete but usher in impressions of indefiniteness. And so, too, of course, does the “longing” of music. The big tease has always been that this indefiniteness in description and translation attaches itself to musical structures of incomparable definition. Only very slight changes in a musical structure can bring about a complete reversal in a given listener’s response. And so we are moved by something very specific after all, something for which there may be no substitute.

III

Taruskin takes a final stab at all this with, of all pieces, Stravinsky’s Svadebka. On the “technical” side of his discussion, the octatonicdiatonic analysis he offers, with the (0235) tetrachord as a connecting link, is ingenious in places, a definite advance on previous attempts in this regard (Defining Russia Musically, 389–467).32 But his primary concern is with the socio-political implications of this framework and of Svadebka’s many “anhemitonic” (pentatonic) melodies and fragments. Taruskin compares these “anhemitonic” melodies in Svadebka to those of various ancient Turkic tribes, as transcribed in Nikolai Trubetskoy, k probleme russkogo samopoznaniya (Paris, 1927). Trubetskoy was a founder of the Eurasian movement, the dream of many Russian émigrés between the wars of an ideal homeland called “Turania.” (Turkic tribes were presumed to have been among the earliest inhabitants of Turania.) Evidence of Stravinsky’s ties to this group is circumstantial, given the absence of references 32See,

for example, my own account of Les Noces in Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven: Yale University Press. 1983). 155–77. There, too, the (0235) tetrachord figures as a connecting link, of course, but the analysis is less systematic all the same.

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in his correspondence and publications. Several close friends and acquaintances of his were Eurasianists, however, including Suvchinsky, Arthur Lourié, and Lev Kasavin. For Taruskin, the music of Stravinsky’s Russian period, written in Switzerland during World War I, is essentially “Turanian.” Svadebka, the culmination of this period, was a “deliberately crafted representation in unmediated musical terms of the Turanian world view described by Trubetskoy” (Defining Russia Musically, 400). And many Eurasianists at the time may have felt likewise, of course, even if Stravinsky’s own views remain something of a mystery. We do not know if the composer himself thought of his Russian-period music in this way; we cannot be sure of the degree to which his own musical, aesthetic, and sociopolitical ideals overlapped with those of his Eurasian colleagues. Eurasian politics tended to be anti-West as well as anti-Soviet; sympathetic publications were critical of the West’s “panromanoGermanic” origins, its liberal democracies, legalisms, individualism, materialism, and so forth. Eurasionists sought instead a “symphonic society,” one of homogeneity, balance, and religious fraternity. But the problem here again was the emergence of a dark side. Eurasian visions of Utopia became indistinguishable from fascist and Nazi ideas about race, nation, and society. Taruskin uncovers an antiSemitic slant as well, bringing Stravinsky’s affiliations to the fore. The composer’s early jealousies are recounted, among these an apparent envy of Maximilian Steinberg, a Jew and fellow pupil of Rimsky. Stravinsky’s anti-humanism is again contrasted with Rimsky’s tolerance, humanism, and progressive liberalism. Even after World War II, Taruskin insists, Stravinsky’s anti-Semitism continued unabated. Taruskin cites the vocal texts for the Cantata (1952) and A Sermon, a Narrative, and a Prayer (1961) as evidence of this; both incorporate “overtly anti-Semitic content” (Defining Russia Musically, 459). The Cantata text, derived from a fifteenthcentury “sacred history,” rehearses “the old guilt libel,” while that of the Narrative, taken from the Book of Acts, includes St. Stephen’s address to the High Priest of the Temple: “Ye do always resist the Holy Ghost,” and so forth. (It is at least plausible that Stravinsky did not use these texts anti-Semitically, of course, but Taruskin would likely respond to such a suggestion with a charge of indifference on the composer’s part, indifference toward the plight of Jews.)

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Can there be anything worse at this point in time? To be branded an anti-Semite (an “enthusiastic” one) with images of the Holocaust everywhere before us, with issues of race, ethnicity, prejudice, and victimhood so entirely current? (It can almost seem as if New Musicologists were in the business of upping the ante with each new foray, daring the formalist or “autonomist” not to be provoked or affected musically by an even more detestable revelation.) Will Stravinsky’s music withstand the threat of an association with these still uglier manifestations of what is now alleged to have been an anti-humanist mentality? Can it resist these new assaults on its “context”? Taruskin’s own conclusions are somewhat reserved. The attraction of Svadebka, he writes, rests with a tension between a Turanian, reactionary vision of society and our obligations as enlightened individuals (our “liberal traditions,” in other words). There is an “anxious thrill of a moral risk” at play in Svadebka (Defining Russian Musically, 391), the risk, evidently, of being sucked back into primitive license, anti-humanism, and collective indifference. Here, however, the familiar “puritanics” of postmodernism (as I like to call them) are all too evident, it seems to me, the prissiness with which postmodernists have tended to approach matters of attunement in music, matters of aesthetic pleasure. The listener is asked to hold back, in other words, not to “let go,” not to become too rapturously immersed. (The advocacy of a kind of permanent coitus interruptus is too close to miss here.) The loss of such conscious control is anathema to New Musicologists not only because of the images of seduction, submission, and exploitation that follow along the familiar routing system of “political correctness,” but also because of the fear, as with puritanical sects in general, of “nature” and instinct, of being caught off guard, as it were, caught in a “natural” yet ideologically inconsistent act, an incorrectness.33 There is another interpretation of the vocal texts of the Cantata and the Narrative. According to Lilian Libman, Stravinsky’s personal secretary and assistant for twelve years (1959–1971), the composer’s anti-Semitism was a “ridiculous fiction,” a kind of prejudice that “could hardly have entered his scope of thought.” In 33These

issues have been addressed before. See, for example, my letter in response to Judith Lochhead, Music Theory Spectrum 20/1 (1998): 160–68.

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fact, Stravinsky “never bothered to deny” the evidently frequently voiced “theory” that he himself was Jewish.34 And upon hearing of the offending passages in these texts, he and Craft immediately set about making revisions for a new edition. There will be more interpretations, of course, not just of these vocal texts of the later years but of Stravinsky’s politics and of the manner in which they do or do not find their way into the music. Scholars will continue to argue about these matters, as has most decidedly been the case here, even as they find much more from which to profit in these huge “musical biographies” of Taruskin’s. Nevertheless, such works are landmarks, in fact, achievements that will prove invaluable as guides to Stravinsky, to Russian music in general, and to the whole idea of “biographies of musical works.” Their mixture of analysis, biography, and criticism is brilliant at times, including something for every conceivable musical interest— compositional, historical, analytical, or critical. And the hope may be that scholarly ambitions will be stirred accordingly, stirred in the direction of combinations of history, aesthetics, criticism, and music analysis, combinations in which, as is so often and remarkably the case with Taruskin, the response of the individual listener is never ignored.

34Lilian

Libman, And Music at the Close: Stravinsky’s Last Years (New York: Norton, 1972), 304.

Chapter 6

Stravinsky, Les Noces (Svadebka), and the Prohibition against Expressive Timing

In Stravinsky’s Les Noces, folklike fragments are repeated relentlessly and literally (ritualistically). They are not varied or developed, strictly speaking, but are cut up and displaced metrically. Typically, displacement results in a disruption of the meter. Conflicting expectations of metrical parallelism are raised in the mind of the listener, expectations which catch the listener off guard. And if this disruptive effect is indeed to materialize, then the beat must be held firmly and without expressive nuance. This analytical perspective suggests a specifically musical rationale for exact, metronomic readings of the composer’s music, and it also offers a way out of the doomsday aesthetics of “antihumanism” (T. W. Adorno) with which the inflexible elements of the composer’s idiom have been identified. The psychology of metrical entrainment and disruption can speak to the vitality of Les Noces, the ability of this music to excite in ways unrelated to the familiar sociopolitical equations. Reprinted from The Journal of Musicology, Vol. 20, No. 2 (Spring 2003). The Music of Stravinsky: Collected Essays Pieter C. van den Toorn Text Copyright © 2003 University of California Press Layout Copyright © 2023 Jenny Stanford Publishing Pte. Ltd. ISBN 978-981-4968-62-1 (Hardcover), 978-1-003-35916-6 (eBook) www.jennystanford.com

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Scored for vocal soloists, chorus, four pianos, and percussion, the final 1923 version of Stravinsky’s Les Noces (Svadebka) remains to this day startling and problematic. Coming on the heels of a near decade-long search for a suitable instrumental guise (1913–23), the final arrangement was later described by the composer as “perfectly homogeneous, perfectly impersonal, and perfectly mechanical.”1 And there can be few qualms at least in principle with this description, the references to the “impersonal” and the “mechanical” perhaps above all. At the same time, however, there are practical considerations. After two or so tableaux, the four “elephantine” pianos (as Stravinsky described them),2 pounding away often chordally as a form of accompaniment to the vocal soloists and chorus, can sound monotonous. The effect can be like that of an arrangement, which is in fact what the final version is, at least in part: a rendition of something conceived earlier for very different instruments.3 Even the tempo changes are of little help in this regard. Often closely related and held metronomically in check, their effect on the listener is likely to be controlling rather than contrasting or releasing. In an interview dating from January 1925, the composer pointed to the “intransigent” quality of Les Noces, the demands of the material for a sharp, percussive approach, “nothing so human as strings.”4 Yet the many sacrifices are difficult to ignore, including the compositional detail in an early sketch of the octatonic passage

1Igor Stravinsky and Robert Craft, Expositions and Developments (New York: Double day, 1962),134. 2Ibid., 133. 3Several arrangements preceded the 1923 version of Les Noces, the most extensive of these having been a 1919 version of the first two tableaux for harmonium, pianola, and two cimbaloms. An account of these earlier arrangements, based on an extensive study of the available sketches and drafts, will be published in Stravinsky and “Les Noces”: Accent, Ritual, and the Secrets of Style, a book currently in its final stages of completion and authored by Margarita Mazo and myself. See also the following: the lengthy study of Les Noces in Richard Taruskin, Stravinsky and the Russian Traditions: A Biography of the Works through “Marva” (Berkeley: Univ. of California Press, 1996), 1319–86; the earlier discussions of Les Noces in Margarita Mazo, “Stravinsky’s Les Noces And Russian Village Wedding Ritual,” Journal of the American Musicological Society 43 ( 1990): 99–142 ; and Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven: Yale Univ. Press, 1983), 155–77. 4Musical America, January 10, 1925. Quoted in Vera Stravinsky and Robert Craft, Stravinsky in Pictures and Documents (New York: Simon and Schuster, 1978), 622.

Stravinsky, Les Noces (Svadebka), and the Prohibition against Expressive Timing

at rehearsal no. 11 in the first tableau, transcribed here in Ex. 2.5 The sketch is from the second version of Les Noces,6 dating from 1915 and scored for double string quintet; it may be compared in Ex. 3 to the final version. Missing in the latter is the detailed part writing of the early sketch. Consisting in the main of a superimposition of tritone-related (0 2 3 5) Dorian tetrachords, the passage includes B A G♯ F♯ in the accompanying parts, F E♭ (D) C in the bass solo. (The octatonicism here is slightly impaired; the B♭ lies outside of the octatonic transposition in question, namely, Collection II.) The intricate working out of the parts in the early draft is missing from the later version, which is not only more percussive and mechanical (like wallpaper, in fact), but also more plain and direct. In this respect, there is less invention in the final version. On the other hand, what may compel is precisely the hardness of this version, the stiff, percussive nature of the articulation, qualities of Stravinsky’s early music that lie at the heart of much of the criticism leveled over the past century or so; a relentless and often literal repetition of themes, motives, and chords combined with a demand for a metrical beat that was inflexible and without “expressive fluctuation” (as T. W. Adorno termed it), without a traditional sense of “nuance.”7 5The

vast majority of the available sketches and drafts of Les Noces are housed at the Paul Sacher Foundation in Basel, Switzerland. This includes the sketch transcribed here in Ex. 2. 6See n3. 7Theodor W. Adorno, Philosophy of Modern Music, trans. Anne G. Mitchell and Wesley V. Blomster (New York: Seaburg Press, 1973), 154. Among Adorno’s many complaints about the rhythmic-metric character of Stravinsky’s music was its apparent ban on expressive timing, the need in performance for a metronomic adherence of the beat, for an absence of any “subjectively expressive fluctuation of the beat.” Much of the specific criticism of Stravinsky’s music in Adorno’s writings, criticism above all of the repetitive features, the mechanical beat, static harmony, and lack of a traditional sense of development, is not altogether different from what it is in Cecil Gray, A Survey of Contemporary Music (Oxford: Oxford Univ. Press, 1924), or in Constant Lambert, Music Ho! A Study of Music in Decline (London: Faber and Faber, 1935). Criticism of the static quality of Stravinsky’s harmony is no less severe in Pierre Boulez’s writings of the 1950s. See Pierre Boulez, Notes of An Apprenticeship, trans. Herbert Weinstock (New York: Knopf, 1968), 74. Superimposition is viewed by Boulez as an “irreducible aggregation,” a “coagulation” which creates for the superimposed fragments a “false counterpoint,” all of this “eminently static in the sense that it coagulates the spacesound into a series of unvarying stages . . . and in the sense that it annuls the entire logic of the development.” For further discussion of these issues, see van den Toorn, The Music of Igor Stravinsky, 61–66.

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Table 1  Adorno’s representation of metrical displacement

metrical displacement “convulsive blows and shocks” ____________________________________

(1)

(2)

inflexibility of the beat; relative lack of expressive timing

literal (unvaried) repetition; relative lack of elaboration or developing variation

non-espressivo secco, mechanical, lacking “nuance” or “expressive fluctuation” (pianola)

incantatory style. ritualistic, “primitivistic patterns”, static quality immobility

non-individual impersonal, “depersonalization”, ,” unfeeling

non-individual impersonal, “collective” “murderous collective”

“anti-humanistic” “agents of destruction”

Shown in Table 1 is a sampling of the analytical descriptions contained in T. W. Adorno’s celebrated indictment of Stravinsky’s music. Drawn from Adorno’s Philosophy of Modern Music8 and a later 8See

n7 .

Stravinsky, Les Noces (Svadebka), and the Prohibition against Expressive Timing

article entitled “Stravinsky: A Dialectical Portrait,”9 the descriptions, often incomplete and fragmentary in the writings themselves, are here pieced together in the form of a single train of thought. Adorno himself avoided schemes of this kind, as has been noted in a number of recent publications,10 but they are hard to ignore when attempting a closer look at the description along lines that are more specifically musical. The stylistic features cited in Table 1 are traceable to a single musical condition, namely that of metrical displacement. Two subsidiary conditions result from displacement: 1) metrical beats which are maintained inflexibly (lacking in expressive timing, in other words), and 2 ) a repetition of themes, motives and chords that is relentless, literal, and lacking in the traditional modes of elaboration or “developing variation.”11 In turn, these conditions spawn a host of characterizations which, although relatively concrete, neutral, and observational to begin with, are increasingly less so further

9Theodor W. Adorno, “Stravinsky: A Dialectical Portrait” ( 1 9 6 2 ) , in Theodor W. Adorno, Quasi una Fantasia: Essays on Modern Music, trans. Rodney Livingstone (London: Verse 1 9 9 8 ) , 1 4 5 –7 5 . 10The unsystematic nature of Adorno’s approach is discussed in Max Paddison, Adorno’s Aesthetics of Music (Cambridge: Cambridge Univ. Press, 1 9 9 3 ) , 1 9 – 2 0 . See also Julian Johnson, “Analysis in Adorno’s Aesthetics of Music,” Music Analysis 1 4 ( 1 9 9 5 ) : 2 9 6 –9 7 . 11Championed in Adorno’s music criticism generally is the thematic-motivic model of the Classical style, or “developing variation” (as Schoenberg called it), whereby motivic particles, detached from thematic shapes, are varied, developed, and finally transformed. Adorno underscored the identity-nonidentity dialectic underlying the process, the way in which “the musical element subjects itself to logical dynamic change while simultaneously retaining its original identity”: see Rose Rosengard Subotnik, Developing Variations: Style and Ideology in Western Music (Minneapolis: Univ. of Minnesota Press, 1 9 9 1 ), 2 0 . Adorno’s own references to these dynamics are sketchy and scattered, however. See T. W. Adorno, Aesthetic Theory, trans. C. Lenhardt (London: Routledge, 1 9 8 9 ) , 4 7 7 – 7 8 , and “Vers une musique informelle” ( 1 9 6 1 ), in Adorno, Quasi una Fantasia, 2 8 3 – 8 4 . Adorno’s approach to analysis is discussed in Johnson, “Analysis in Adorno’s Aesthetics of Music,” 2 9 5 – 3 1 3 , while Adorno’s critique of Stravinsky’s music along these lines is discussed in Jonathan Cross, The Stravinsky Legacy (Cambridge: Cambridge Univ. Press, 1 9 9 8 ) , 2 2 7 – 3 4 . Adorno’s point of departure on matters of the motive and its “developing variation” was Schoenberg, as represented by the latter’s music and critical writings. See especially Arnold Schoenberg, Fundamentals of Musical Composition, ed. Gerald Strang and Leonard Stein (London: Faber and Faber, 1967), 1–19. See also Walter Frisch, Brahms and the Principle of Developing Variation (Berkeley: Univ. of California Press, 1983), and, most recently, Ethan Haimo, “Developing Variation and Schoenberg’s TwelveTone Music,” Music Analysis 16 (1997): 349–65.

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on down the line. The more specific the imagery, in fact, the less tangible and more speculative. On the left-hand side of Table 1, the need for strictly held meters is made to imply mechanization and impersonality, while mechanization leads to “anti-humanism” and a “collective” voice that stands in opposition to the individual.12 On the right-hand side, the lack of variation in the repetition of Stravinsky’s themes and motives is made to imply a similar identification with the “murderous collective,”13 as Adorno expressed it, with various “agents of destruction.”14 Stravinsky’s “identification with the collective” is thus “primitive” and pre-individual in Adorno’s imagination.15 The repetitive features of his music are ritualistic in this respect, symbolic of something stiff and unyielding, more specifically here, the refusal of the collective voice to give way to the variations of the individual. Locked in repetitive gesture, the “musical subject” is unable to move beyond the trance-like stupor of ritual. These conditions are contrasted with the developmental style of the Classical tradition which, drawn in large part from Schoenberg’s analytic-theoretical definitions, symbolized for Adorno the ability of the subject to mature with time, to meet the day’s challenges, and to develop accordingly.16 While ritual and ritual-like repetition represented a form of enslavement, developing variation represented relative freedom. This was the musical opposition Adorno sought to reveal, the split he attributed to Stravinsky’s music and its tear from tradition and traditional sensibility. While the descriptive terms in Table 1 are Adorno’s, the outline converts much of the description and characterization into stylistic features of one kind or another, features which are connected and arranged in the form of an explanatory path. A larger rationale has 12Adorno,

Philosophy of Modern Music, 160. “Stravinsky: A Dialectical Portrait,” 149. 14Ibid., 149. 15Adorno, Philosophy of Modern Music, 145–47, 157–60. 16Ibid., 154. Some of the aesthetic and sociological implications of these opposing worlds are addressed at greater length in Robert Adlington, “Musical Temporality: Perspectives from Adorno and de Man,” repercussions 6 (1997): 12–13. While, with the developmental style, “maturation implies the ability to cope with, and develop in response to, changing circumstances,” the “regressive” features of Stravinsky’s music denote “a reversion to infantilistic modes of behavior.” For Adorno, “repetition represents an infantile denial of time . . . while development signals proper recognition of the temporal condition.” 13Adorno,

Stravinsky, Les Noces (Svadebka), and the Prohibition against Expressive Timing

thus been sought for the stylistic features acknowledged in one way or another, an explanation in more specifically musical terms: What it is that binds the various features, motivates or triggers one in relation to the others. The features themselves are not isolated phenomena, in other words; they interact in ways that vary complexly from one context to the next. There are concrete reasons for the lack of traditional variation and development in Stravinsky’s music, just as there are reasons for the strict metricality often demanded in its performance. Consideration of Ex. 1 makes it clear that the rules and regulations governing the repetition in the opening two blocks of Les Noces could not be tighter. With the pitch E as the point of departure and return, melody consists of a reiteration of but three pitches, E, D, and B, pitches which together form the trichord (025); F♯ is sounded as a grace-note to the D. The confinement of this content extends to subsequent restatements of blocks A and B throughout the first tableau as well. More telling still is the tiny motive D-to-E, bracketed just beneath the soprano staff in Ex. 1. Falling over the bar line, repeats of this motive (five occurrences in block A) are without elaboration, transposition, or changes in dynamics or instrumental assignment. Each repeat is a carbon copy of the next. The D is inflected by the grace note F♯, enters fortissimo, and is doubled massively by the accompanying parts in the pianos and xylophone. There are no modifications to this routine. From start to finish, features of the motive are held rigidly in place. A partial explanation for this immobility rests with the pattern of displacement that lies concealed beneath the notation. Against the backdrop of the various components held in place, returns to E as the point of departure vary. With all other components held immobile, the spans between these returns number three or sometimes five eighth-note beats. This of course means that the alignment will vary. If the 38 meter of the opening measures is pursued through the whole of block A, repeats of the motive will be read as a series of displacements, as shown by the brackets in Ex. 1: For the main soprano line alone, the notated irregular meter is reproduced in Ex. 4a, while just below in Ex. 4b, the passage is rebarred by way of the steady 38 meter. Although irregular insofar as the spans are concerned, the series of displaced repeats forms a cycle: If the 38 bar line is considered by itself, the motive shifts from the third beat of a

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measure to the second and first beats, respectively, before arriving back on the third beat for two concluding repeats. Significantly, too, the two conflicting barrings arrive “on target” as the passage draws to a close. They intersect with the return of the original alignment of the motive, providing the downbeats of the concluding measures with a sense of resolution. The departures of the previous measures are thus followed by a return and arrival point.

Example 1 Stravinsky, Les Noces, first tableau, opening (continued)

This is the nature of the invention by which opposing forces are set in motion: metrical parallelism on one hand, displacement and the steady meter on which displacement hinges on the other. With

Stravinsky, Les Noces (Svadebka), and the Prohibition against Expressive Timing

the first of these forces, outlined in Ex. 4a, a motive and its repeats are aligned in a fashion that is metrically parallel; the meter shifts in order that the alignment of the D-to-E motive might be held constant. And constancies of this kind are the source of much of the notated metrical irregularity in Stravinsky’s music, above all in works of the early Russian period. With the second of the two forces, Ex. 4b, the steady meter is sustained with the motivic repeats heard and understood as displacements. The two readings are not reconcilable. Although listeners may switch from one reading to the other, or sense one in relation to the other, they cannot attend to both simultaneously.17 In pieces such as Les Noces, the repetition itself follows a different logic. Themes, motives, and chords are repeated not to be developed along traditional lines but to be displaced. And in seeking thus to displace a repeated theme, motive, or chord, the composer retains features other than alignment in order that alignment itself (and its shifts) might be set in relief. The literalness of the repetition acts as a foil in this respect. Features of pitch, duration, and articulation are retained, as the metrical alignment shifts for the given theme, motive, or chord. But literalness acts as a counterforce, too. Exact or near-exact repetition can have the effect of referring the listener back to the motive’s original placement. In direct opposition to displacement, it can raise expectations of metrical parallelism, the repetition of the original placement along with all else that is repeated literally. And the more that is repeated literally, the more fully reinforced are these conflicting expectations likely to be. 17In

earlier studies of metrical displacement in Stravinsky’s music, I described the two types of barrings pursued here in Exs. 4a and 4b as “radical” and “conservative,” respectively. Meter is interrupted in Ex. 4a, while in Ex. 4b it is maintained (conserved), with the repetition of the motive displaced as a result. See Pieter C. van den Toorn, Stravinsky and “The Rite of Spring” (Berkeley: Univ. of California Press, 1987), 67. These terms were first introduced in Andrew Imbrie, “ ‘Extra’ Measures and Metrical Ambiguity in Beethoven,” in Alan Tyson, ed., Beethoven Studies (New York: W. W. Norton, 1973), 45–66. They were introduced as a way of distinguishing alternative interpretations of hypermeter in Beethoven’s music. Subsequently they were applied somewhat similarly in Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge: MIT Press, 1983), 22–25. A further application to alternative interpretations of displacement in Stravinsky’s music may be found in Gretchen Horlacher, “Metric Irregularity in Les Noces: The Problem of Periodicity,” Journal of Music Theory 39 (1995): 285–310.

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Example 1 (continued)

In A Generative Theory of Tonal Music, Fred Lerdahl and Ray Jackendoff treat conflicts between meter and metrical parallelism as conflicting “well-formedness” and “preference” rules.18 In the common-practice contexts examined by these authors, the “preference” rule for metrical parallelism yields to the “wellformedness” rule for metrical regularity, the stipulation that a level of pulsation consist of equally spaced beats. Meter is maintained, in other words, while displacement is absorbed as a form of 18See

Lerdahl and Jackendoff, A Generative Theory, 74–75.

Stravinsky, Les Noces (Svadebka), and the Prohibition against Expressive Timing

syncopation. Typically in Stravinsky’s music, however, the two sides of this coin are more equally balanced. There is insufficient evidence for an automatic ruling in favor of one side or the other, so that the listener is left in the lurch, unable to commit wholeheartedly one way or the other. With varying degrees of intensity, the result is a form of metrical disruption. An inferred meter, internalized by the listener, is challenged, disrupted, and at times overturned.19

Example 2 Stravinsky, Les Noces, first tableau, early sketch (2nd version), transcription 19Crucially

in this regard, meter and metrical parallelism, although separable, interact. Recent studies of the psychology of this interaction have underscored the role played by parallelism in the formation of meter. See David Temperley and Christopher Bartlette, “Parallelism as a Factor in Metrical Analysis,” Music Perception 20 (2002): 117–49. Even in some of the common-practice instances of displacement examined by Lerdahl and Jackendoff, the potential for disruption is likely to be felt by the listener.

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Example 3 Stravinsky, Les Noces, first tableau

It should be noted, however, that conditions in the opening block A of Les Noces (Ex. 1) are not nearly so traumatic. Metrical parallelism is likely to be the “preferred” take here, as indeed Stravinsky’s notation implies, with the meter constantly interrupted in order that the D-to-E motive and its subsequent repeats might be

Stravinsky, Les Noces (Svadebka), and the Prohibition against Expressive Timing

aligned in parallel fashion. The tempo is slow, repeats of the motive are literal and pronounced, the 38 meter is likely to be established only very weakly at the beginning, and displacements occur at the level of the bar line, not at that of the tactus, i.e. the eighth-note beat with a metronome marking of 80. A sense of the varying spans and displacements is likely to occur only rather dimly in the mind of the listener, with the “preference” for a parallel reading of each D-to-E fragment likely to predominate.

Example 4  Stravinsky, Les Noces, first tableau, opening: “radical” (a) and “conservative” (b) barrings

But consider pitch structure. Midway through this passage, vertical coincidence or “harmony” is little different from what it is at the beginning or at the end. Missing altogether is a sense of harmonic change, movement, or progress, all of which becomes a function not of harmony strictly speaking, but of the varying spans of the repeated motive—of metrical alignment and displacement. What was once harmonic-contrapuntal in design becomes metrical, a function of metrical alignment and timing. Indeed, the contrast to the world of developing variation and the Classical style could not be starker. Displacement and its many and varied implications preclude the sympathetic give-and-take of that world, the way in which motivic particles, detached from themes, are exchanged between instrumental parts. In Ex. 1, the D-to-E motive is not tossed about from one instrument to the next in the manner of a dialogue, as it might be in a string quartet by Haydn or Mozart. It is not treated “humanistically” by such means (as the character of such treatment has often been imagined, at the very least, in modern times, since the dawn of instrumental chamber

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music).20 Nor is it treated expressively. If the forces of meter and metrical alignment are to make themselves felt, then the beat must be held evenly (mechanically) throughout, with little if any yielding to the conventions of expressive timing and nuance, traditionally the means by which performers have made their mediating presence felt. This latter prohibition could not have had a deeper or more profound effect on the critical reception of Stravinsky’s music throughout the past century. What had been implied by these conventions of expressive affect in terms of individual performance and interpretation was set aside or curtailed severely. The implications, consisting of small-scale deviations from the regular and the exact, cadential retardations and the like, had involved immediacy, spontaneity, and, as this equation seemed to suggest, truth. A sense of engagement on the part of the performer had been implied: true, authentic feeling, as it were, an indication of the human capacity for arousal. More specifically, the ritardandos and rallentandos had implied delay, added suspense, and by such means an intensification of the listener’s anticipation of the cadence. The cadence itself had represented a form of release from expectation. Among the most intimate terms known to music, in fact, the deviations of expressive timing were motivated not by affect alone, but also by structural considerations. They had served to clarify delineations of grouping and phrase, to impart an evolving sense of structure, with even the smallest departure heard and understood not as effect or caprice but as a means toward that larger end. Recent studies of the psychology of expressive affect by Eric Clarke,21 John 20The

association of the “humanistic” with chamber music, dialogue, and the developmental style generally is discussed in Carl Dahlhaus, Nineteenth-Century Music, trans. J. Bradford Robinson (Berkeley: Univ. of California Press, 1989), 252–61. “The idea of chamber music,” Dahlhaus concludes, “arose as a musical reflection of a humanistic-aristocratic culture primarily centered on conversation. The aesthetic of this genre may be derived from the constantly recurring comparison with educated discourse . . . that each party continuously shows regard for the other. In this way, the whole emerges from an interplay of voices sustained by an understanding of each participant for the overall context, and not as a mumbled amalgam of its parts” (260). 21See Eric Clarke, “Expression and Communication in Musical Performance,” in John Sunberg, Lennart Nord, and Rolf Carlson, eds., Music, Language, Speech and Brain (New York: Macmillan, 1991), 184–93; or Eric Clarke, “Expression in Performance: Generativity, Perception, and Semiosis,” in John Rink, ed., The Practice of Performance (Oxford: Oxford Univ. Press, 1998), 22–54.

Stravinsky, Les Noces (Svadebka), and the Prohibition against Expressive Timing

Sloboda,22 and Bruno Repp23 have borne this out by identifying connections between expressive timing and the projection of meter and phrase rhythm in the large. When applied to Stravinsky’s music, however, the same modifications weakened structure. They obscured the juxtapositions, stratifications, and metrical alignments of Stravinsky’s repeated themes, motives, and chords. And they were set aside quite deliberately by the composer and his adherents for these very reasons. They were dismissed as a form of liberty taken anachronistically and at the expense of structure. Identified with the interpreting performer alone, they were viewed accordingly as a form of display by which structure was sacrificed to give expression to the performer’s feelings. No greater sin could be imagined in relation to Stravinsky’s music and its articulation. For the composer himself, the personal in music could not have taken on a worse connotation. What traditionally had been a matter of structure as well as engagement had become one of engagement alone—indeed, one of self-indulgence. (Conductors were always the most heavily censored in Stravinsky’s many published remarks on the subject of interpretation; his own experiences had evidently convinced him that no indulgences on the part of performers were as severe in their consequences as those of the conductors.)24 The performance of Stravinsky’s repeated and displaced themes, motives, and chords required mechanical-like precision. Fidelity was mandatory, coolness with a sense of restraint. Notes were not to be slurred or tied into. In matters of articulation, of small-scale separation and grouping, a crisp, clean, secco approach was necessary if the bite of invention was to be given its due. Stravinsky’s lifelong battle with “interpretation” and “nuance” begins here, in fact—not necessarily with aesthetics nor with the formalist ideas he had encountered earlier in the century in Paris, but with these practical matters of performance. It begins with the need to temper “interpretation,” to counter the traditional flexibility with a beat whose metronomical precision highlighted to 22See

John Sloboda, “The Communication of Musical Meter in Piano Performance,” Quarterly Journal of Experimental Psychology 14 (1983): 377–96. 23Bruno Repp, “Pattern Typicality and Dimensional Interactions in Pianists’ Imitation of Expressive Timing and Dynamics,” Music Perception 18 (2001): 173–211. 24Igor Stravinsky and Robert Craft, Themes and Episodes (New York: Knopf, 1966), 145–56.

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a maximum degree elements of meter, metrical alignment, and the changes in alignment (i.e. displacements) that were at the heart of this new way of composing. Only then did it extend to the ways in which the traditional flexibility had been linked to expressivity and emotion, the personal, and transcending human value. At the same time, the implications of these strictures for straight, non-espressivo readings of Stravinsky’s music went well beyond performance practice and engagement. The requirements anticipated more general modernist trends in the 20th century, notably the mid-century preferences for straight, unnuanced readings of all manner of repertory. And yet they are not a passing fancy, a reflection merely of the times or of a conductor’s personality. They serve purposes that are deeply structural in origin. They are parts of the package as a whole, whether viewed from afar or from the details of the repetition in the opening passage of Les Noces. Indeed, questions of meaning and significance posed by Adorno and other critics can best be addressed not in the context of Stravinsky’s unvaried repetition of themes, motives, and chords (as indeed Adorno often addresses them), or even in the context of expressive timing and its absence. As shown by Table 1, conditions of this kind represent the effects of deeper, underlying forces, most notably those of meter and metrical alignment. Given Stravinsky’s predilection for metrical displacement, inclinations to repeat literally and to keep the tempo as exact as possible (with the conventions of expressive timing held to a minimum) are apt to follow readily. Thus the next step in an inquiry of this kind would be an examination of the various processes of metrical displacement, presumably from a perceptual, cognitive, and emotional standpoint as well as from a music-analytical one. In an earlier paper I attempted to do just that, surveying Adorno’s pointed objections to Stravinsky’s displaced accents and their disruptive effect.25 Given the irregularity in the spans defined by the displaced repeats in Stravinsky’s settings, disruption was inevitable, Adorno argued. With the irregularity of these spans, listeners were prevented from forming metrical patterns, and hence from anticipating and assimilating displacement. Their engagement 25See Pieter C. van den Toorn, “Stravinsky, Adorno, and the Art of Displacement,” paper

delivered at the 24th annual convention of the Society of Music Theory, Philadelphia, November 2001.

Stravinsky, Les Noces (Svadebka), and the Prohibition against Expressive Timing

with the music having been interrupted, they were left to fend for themselves. They had become victims of a kind of barrage, bobbing this way and that in reaction to what Adorno termed “convulsive blows and shocks.”26 I want to suggest here that experiences of metrical conflict in Stravinsky’s music need not be the debilitating, traumatic ones scorned by Adorno. As internalized meters are brought to the surface of consciousness in the most disruptive cases of displacement, a heightened sense of attention, engagement, and suspense may ensue. Indeed, as has been suggested already, conflict and disruption can bring implication and inhibition to the fore, along the lines pursued by Leonard Meyer some time ago. Derived in large part from John Dewey’s “conflict theory” of human emotion, Meyer’s idea was that emotion in music arose from the same set of circumstances encountered in everyday life, namely, from the blocking of expectations or tendencies.27 He suggested that inhibition, blockage, or arrest of tendency, when accompanied by a belief in the eventual resolution of the conflict (or clarification of the ambiguity) could have the effect of heightening a sense of anticipation and suspense.28 “Delay pleasures play,” Meyer reasoned.29 In much music of the 19th century, delay can seem to have taken on a life of its own, of course. The ways in which completion is averted or suspense sustained appear to have grown ever more elaborate as the century wore on, from both a harmonic and a melodic standpoint. In poetic terms, the outwardly fragmentary and incomplete nature of much music of this period can be identified with an endless yearning: “longing eternally renewed,” as Charles Rosen expressed it in his discussion of the opening song of Schumann’s Dichterliebe.30 The emphasis on the purely negative side of pleasure (“negative pleasure,” as some have termed it)31 can seem sadistic or sadomasochistic as well. Pleasure is being derived from 26Adorno,

Philosophy of Modern Music, 155. Meyer, Emotion and Meaning in Music (Chicago: Univ. of Chicago Press, 1956) 25–32. 28Ibid., 28–29. 29Ibid., 35. 30Charles Rosen, The Romantic Generation (Cambridge: Harvard Univ. Press, 1995), 41. 31See Jerold Levinson, Music, Art, and Metaphysics (Ithaca: Cornell Univ. Press, 1990), 306–35. 27Leonard

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the inhibition or blockage itself, the pain of want and desire, the withholding of a sense of arrival, completion, resumption, or release. Adorno himself identified “sadomasochistic” strains in Stravinsky’s music,32 noting the composer’s “perverse joy in self-denial” and the shocks of his metrically displaced accents.33 Implications of this kind have doubtless long been a part of music in the Western art tradition, perhaps since the dawn of tonality. And there has been no dearth of acknowledgment. Heinrich Schenker likened the circuitous routes of his linear progressions to real-life experiences of “delays, anticipations, retardations, interpolations, and interruptions”;34 famously, the half cadence at the close of an antecedent phrase was judged an “interruption” in the progress of such a progression.35 In recent studies of the psychology of anxiety, emotions have been identified more generally as “interrupt phenomena” which arise from the “interruption (blocking, inhibiting) of ongoing, organized thought or behavior.”36 More specific versions of this equation involve not one but several simultaneously aroused and conflicting implications or tendencies. Here, of course, the fit could not be tighter. Settings of metrical displacement in Stravinsky’s music involve the opposition of irreconcilable forces, those of meter and metrical displacement on the one hand, parallelism on the other. To inhibit, arrest, block, delay, or interrupt one of these forces (an “ongoing thought or behavior”) is to stir the emotions. To displace a repeated theme, motive, or chord metrically is to thwart implications of parallelism, disrupt the meter, and thus to invite the “convulsive blows and shocks” to which a sizable portion of Adorno’s criticism is directed. And so the question arises: If inhibition or interruption can be an accepted and even expected part of the listening experience of the tonal (or atonal) repertory to which Adorno adheres, why can 32Adorno,

Philosophy of Modern Music, 159. 153. 34Heinrich Schenker, Free Composition, trans. Ernst Oster (New York: Longman, 1979), 5. 35Ibid., 36. 36George Mandler, “The Generation of Emotion,” in Robert Plutchik and Henry Kellerman, eds., Emotion: Theory, Research, and Experience (New York: Academic Press, 1980), 225. More recent theories of anxiety and emotion are discussed in Renee Cox Lorraine, Music, Tendencies, and Inhibitions: Reflections on a Theory of Leonard Meyer (Lanham: Scarecrow Press, 2001), 406. 33Ibid.,

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it not be of the experience of Stravinsky’s? Even if we grant the distinction in application, the processes substantiate the same general psychology. Moreover, metrical disruption is not unique to Stravinsky’s music. The disruption may be less relentless in other works, as well as less immediate, with displacements generally confined to less immediate levels of metrical pulsation, i.e. the bar line and above. When they do occur, conflicting alternatives to an established meter and its continuation tend to surface in the form of alternative meters, usually hemiola-related, while in Stravinsky’s music they tend to surface in the form of outright disruptions. The spans between a series of displaced repeats are invariably patterned and regular in earlier contexts, while in Stravinsky’s music they are often irregular (as they are, indeed, in the opening pages of Les Noces). Nor is the repetition in earlier repertoires as literal as it is in Stravinsky’s music; instead motives are constantly transposed and elaborated as part of a process of developing variation. Such is the case with much of the metrical conflict in Schumann’s music, for example, as examined by Harold Krebs.37 Yet notwithstanding the severity of these qualifications, matters of musical expectation, tendency, inhibition, and disruption are not as cut and dried as Adorno suggests. It should also be noted that Adorno’s analytical descriptions of Stravinsky’s music, sampled and condensed in Table 1, are just as easily framed with positive sociopolitical images as they are with negative ones. The very features vilified in Adorno’s account may, from a different vantage point, represent what is most appealing. If the lack of expressive timing in the performance of Stravinsky’s music can spell coldness and indifference to the plight of the individual (as Adorno insists), then it can spell directness and unsentimentality, too, a determination to confront the world “as it is.” And if the lack of variation can imply intractability—the refusal of a collective voice to give way to the variations of the individual (a state of unfreedom, as Adorno understands it)—then it can also reveal something of the hardness of the outside world, and can do so without compromise 37See

Harold Krebs, “Some Extensions of the Concepts of Metrical Consonance and Dissonance,” Journal of Music Theory 31 (1987): 99–119. The application of these “concepts” to Schumann’s music in particular is pursued at length in Harold Krebs, Fantasy Pieces: Metrical Dissonance in the Music of Robert Schumann (Oxford: Oxford Univ. Press, 1999).

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or falsification.38 Whatever the claims of Adorno’s adherents about the “inseparable” nature of the various components of Adorno’s argument, they are not full proof. Much of the analytical description can be understood and appreciated irrespective of the larger philosophical or socio-political rationale. And it can be appreciated irrespective of the critical verdict as well.39 In this connection, ritual and the ritualistic need not be confined to the primitive, unthinking, or herd-like. The archaic wedding rituals that underlie the scenario and music of Les Noces are a specific case in point. From what is known of the early performing practices of these rituals, the separation between character and character type, and between genuine feeling and play-acting were by no means hard and fast.40 One of the aims of these rituals, even when enacted by hired professionals, was to awaken within both the bride and the other participants something of the “specific thoughts and emotions” to which reference was made.41 Genuine feeling and the feelings demanded by the ceremonial traditions were supposed to overlap. This is what ritual is, of course, not public exercise alone but public exercise mixed with the personal. It involves the expression, by means necessarily public or communal, of what are presumed to be an individual’s “thoughts and emotions.”42 Communication with the outside world is guaranteed, while a buffer is afforded against the perils of an individual’s isolation. The emphasis falls on commiseration and bonding, but this comes not wholly at the expense of the concerns of the individual. Ritual acts as a go-between in this regard, a way of easing the public strain of personal remorse as well as the community’s difficulty in relating to that remorse. The proxy performances associated with the wedding rituals were 38Such

a reversal was indeed briefly entertained by Adorno as a form of “negative truth,” but it was rejected all the same. No sense of an awareness of this “truth” or predicament could be detected by Adorno on the part of the “musical subject.” And the static implications of Stravinsky’s music are for Adorno not a style feature, but the negation of the medium of music itself. See Adorno, “Stravinsky: A Dialectical Portrait,” 149–55. And see the discussion of this in Paddison, Adorno’s Aesthetics of Music, 268. 39Matters of this kind are discussed in greater detail in van den Toorn, “Stravinsky, Adorno, and the Art of Displacement.” 40See the discussion of this in Mazo, “Stravinsky’s Les Noces,” 119–22. 41Y. M. Sokolov, Russian Folklore, trans. Catharine Ruth Smith (New York: Macmillan, 1950), 211–12. 42Ibid.

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not entirely formulaic or stereotypical. From the evidence it may be gathered that the formulas were mixed with improvisation, and that the latter was intended as a more immediate reflection the bride’s true feelings.43 By such means, the stock in trade merged with the personal. And successful performances were not only “emotionally infectious” (beckoning the participants in the appropriate way),44 but designed as a combination of the tradition and the individual. Inflecting the opening pages of Les Noces is the grace note F♯. This hint of a sob proves integral not only to the idea of a lament, but to the composer’s musical conception as well. The repetition is incantatory and ritualistic in character, imitating the highly stylized vocalizations that informed the early laments themselves. So too, in the first line of the text, is the stutter in the setting of the Russian word kosal, meaning “braid.” The isolated repetition of the first syllable of this word produces an effect similar to that of the grace note F♯, namely that of a gasp or sob, and this is likewise integral. The motivation is not only poetic in the sense of a ritual lament, but musical as well, an aspect of structure and musical understanding. And yet the effect is spontaneous and unrehearsed as well. Even in the strictest, most exacting performance of Les Noces, with the rigidities of the construction in full view, as it were, the experience of the single bride is apt not to be lost. The grace notes and stutter motives are still likely to be heard and understood as those of the single bride. Their effect is still likely to be that of an uncontrollable weeping, spontaneous and hence true to the individual, immediate and reflective of a personal anguish or anxiety—one that is shared and collective in one way or another, but not therefore “impersonal.” What we as participants sense and feel is thus likely to be derived from the experience of the bride. And the more stiff and intransigent the aspects of the construction seem, the more emphatically they succeed in setting off the circumstances of the individual bride. Much of this has been overlooked by the detractors of Stravinsky’s music who would equate the repetitious, percussive, and metronomic features of pieces such as Les Noces (i.e. the “mechanical”) not only with ritual and ritual action, but with a collective voice as well, one that is primitive, autocratic, and “anti-humanistic” in its opposition to the interests of the individual person. “Stravinsky’s music 43See

Mazo, “Stravinsky’s Les Noces,” 121–22. Russian Folklore, 213.

44Sokolov,

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identifies not with the victims,” T. W. Adorno argued in one of his most extravagant summations, “but with the agents of destruction.”45 Given the many rules governing repetition in the opening pages of Les Noces, the character of this music can indeed seem implacable. Yet the rigidities are balanced by counteraction. The repeats of the intoning pitch E and of the succession D-to-E over the bar line are spaced irregularly, in defiance of the registral confinement of the melodic invention, the literalness of the repetition, and the metronomically held tempos. The stiffness of the construction is countered by fluidity in matters of rhythm, timing, and alignment. Detail of this kind should not be ignored in studies of the philosophical and socio-political implications of Stravinsky’s music, studies that seek a broadened context from which to apprehend the specific nature of the music’s appeal.

45Adorno,

“Stravinsky: A Dialectical Portrait,” 149.

Chapter 7

Stravinsky and the Octatonic

A Reconsideration* Dmitri Tymoczko

The importance of the octatonic scale in Stravinsky’s music has consistently been overstated. While octatonicism is an aspect of Stravinsky’s technique, it is just one of a number of different components that jointly produce the “Stravinsky sound.” The article focuses on two techniques that have often been mistaken for octatonicism: modal uses of the non-diatonic minor scales; and the superimposition of elements that belong to different scalar collections. Recent and not-so-recent studies by Richard Taruskin, Pieter van den Toorn, and Arthur Berger have called attention to the importance of the octatonic scale in Stravinsky’s music.1 What began as a trickle has become a torrent, as claims made for the scale have grown more and more sweeping: Berger’s initial 1963 article 1See

Taruskin 1996, van den Toorn 1987 and 1983, and Berger [1963] 1968. This general point of view has also been endorsed by Antokoletz 1984, Craft 1984, Walsh 1984, and, in the case of The Rite of Spring, Moevs 1980. For more critical, but by no means dismissive, perspectives see Straus 1984 and Kielian-Gilbert 1991. *Reprinted from Music Theory Spectrum, Vol. 24, No. 1 (Spring 2002). The Music of Stravinsky: Collected Essays Pieter C. van den Toorn Text Copyright © 2002, 2003 Oxford University Press Layout Copyright © 2023 Jenny Stanford Publishing Pte. Ltd. ISBN 978-981-4968-62-1 (Hardcover), 978-1-003-35916-6 (eBook) www.jennystanford.com

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described a few salient octatonic passages in Stravinsky’s music; van den Toorn’s massive 1983 tome attempted to account for a vast swath of the composer’s work in terms of the octatonic and diatonic scales; while Taruskin’s even more massive two-volume 1996 opus echoed van den Toorn’s conclusions amid an astonishing wealth of musicological detail. These efforts aim at nothing less than a total reevaluation of our image of Stravinsky: the composer, once thought to epitomize the “unsystematic” type of musician, working at the piano and following the dictates of his ear, is here portrayed as a systematic rationalist, exploring with Schoenbergian rigor the implications of a single musical idea. And the octatonic scale, once thought to represent a distinctive surface color, occasionally used by Stravinsky and others, has now been promoted to the deepest level of musical structure, purportedly controlling extended lengths of musical time. I challenge this view in this paper. I do not question that the octatonic scale is an important component of Stravinsky’s vocabulary, nor that he made explicit, conscious use of the scale in many of his compositions. I will, however, argue that the octatonic scale is less central to Stravinsky’s work than it has been made out to be. In particular, I will suggest that many instances of purported octatonicism actually result from two other compositional techniques: modal use of non-diatonic minor scales, and superimposition of elements belonging to different scales. In Part I, I show that the first of these techniques links Stravinsky directly to the language of French Impressionism: the young Stravinsky, like Debussy and Ravel, made frequent use of a variety of collections, including whole-tone, octatonic, and the melodic and harmonic minor scales. The use of these latter two scales reaches a peak in the first sections of The Rite of Spring, where they—and not the octatonic scale—account for the majority of non-diatonic material in the piece. (I also show that these scales have been consistently misinterpreted by van den Toorn as instances of “octatonic-diatonic interaction.”) In Part II, I turn to the issue of triadic superimpositions and the scales that often accompany them. I will contrast two views: one, which sees scales (such as the octatonic) as analytically prior to chordal superimpositions (such as the C-major and F♯-major triads which comprise the “Petrouchka chord”); and the other, which sees the superimpositions themselves as prior to the scales they

Stravinsky and the Octatonic

produce. Drawing on previous work, where I have shown that triadic superimpositions invariably produce subsets of a small number of familiar scalar structures, I present analytical examples suggesting that we frequently need to understand Stravinsky’s scales as arising from his superimpositions, and not the other way around. In the conclusion, I take up the broader question of how we should think about Stravinsky’s compositional style. Taruskin and van den Toorn have both presented a picture of Stravinsky as a composer whose approach to music is dominated by a single guiding idea, a Stravinsky who is no less systematic in his musical thinking than Schenker or Schoenberg. This view has no doubt had some salutary consequences: certainly, it provided a way of defending Stravinsky against those who felt that systematicity and rigor were crucial components of musical value. Perhaps more importantly, it encouraged a kind of careful attention to analytical detail that was—it must be said—sorely lacking in many earlier attempts to understand Stravinsky’s music. Nevertheless, I believe that this picture is fundamentally mistaken. For Stravinsky was indeed a methodological pluralist, a bricoleur who used a variety of techniques that do not admit of easy categorization. This conclusion may seem like a return to an earlier way of thinking. But it is tempered by the understanding—ironically, gained in part through the work of Berger, van den Toorn, and Taruskin—that though Stravinsky’s music may be unsystematic, it is still intelligently constructed, and that the principles of its construction can be uncovered through close analytical scrutiny.

Scales in Stravinsky

The Four Locally Diatonic Scales Elsewhere I have argued that the diatonic and octatonic scales are part of a family of four scales which share some interesting properties. Each of these collections is capable of being arranged so that adjacent notes are separated by one or two chromatic semitones, while notes adjacent but-for-one-note are separated by three or four chromatic semitones. In other words: the “seconds” in these scales are (enharmonically equivalent to) diatonic seconds, while the “thirds” are (enharmonically equivalent to) diatonic thirds. These

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four scales are thus “locally diatonic” in that each of their three-note segments is enharmonically equivalent to some three-note span of some diatonic scale. Consequently, the four scales represent a natural avenue of exploration for composers interested in expanding the vocabulary of traditional tonal harmony: first, because they provide natural scalar counterparts to the extended triadic sonorities much beloved by early twentieth-century composers; and second, because as scales they are recognizably similar to the major and minor scales of the classical tradition.2 The four scales in question are the diatonic (trivially), octatonic, whole-tone, and the ascending form of the melodic minor scale. In my previous paper, I argued that they are central to the harmonic vocabulary of the Impressionists as well as to contemporary jazz. Here I want to suggest that this same collection of scales, inherited from both Russian and French sources, plays an important role in Stravinsky’s first three ballets. Whole-tone scales suffuse The Firebird and make important appearances in both Petrouchka and The Rite of Spring. Likewise, the latter two pieces contain substantial passages of the modal use of ascending melodic minor scales.3 The Rite of Spring also contains several prominent passages involving modes of the harmonic minor scale, as well as passages that alternate between harmonic and melodic minor collections. (The harmonic minor scale is not part of my collection of four scales, but it is part of a related seven-scale collection: see p. 88 below.) In these respects, the early ballets wear their Impressionist influences on their sleeves. It is perhaps for this reason that the scales appear less frequently in Stravinsky’s later music. Indeed, as we shall see, Stravinsky began even within the first three ballets to erase the most obvious signs of his debt to the French tradition. If my argument is sound, and if it can be established that Stravinsky made use of a variety of non-diatonic scales beyond the octatonic, then this should have important repercussions for analysis. For many of the collections that might have seemed to be “obviously” octatonic in origin turn out to belong to more than one 2For

a detailed account of this material see Tymoczko 1997. Debussy’s use of the modes of the ascending melodic minor scale, see Gervais 1971 (who also finds the scale in Fauré’s music) and Howat 1983. Debussy’s use of the scale is also mentioned in Steven Kostka and Dorothy Payne’s 1989 harmony textbook. 3For

Stravinsky and the Octatonic

type of scale. The 6-z23[023568] hexachord, for example, appears in the melodic minor scale as well as the octatonic. (Other “typically octatonic” collections, such as the 4-17[0347] tetrachord and the 6-27[013469] hexachord, belong to the harmonic minor scale.) Thus, widening our conception of Stravinsky’s scalar vocabulary prevents the easy inference from these smaller sets to an octatonic sourceset. This brings to mind the adage that when the only tool you have is a hammer, every problem starts to look like a nail: if, like Taruskin and van den Toorn, all you have are the octatonic and diatonic collections, then many sets will seem to be clearly octatonic, if only because they are clearly not diatonic. If, however, you are working with more than just two scales—and Stravinsky certainly knew more than two—then these same sets will be understood to have multiple potential derivations. Thus, for analysts, the key issue is not whether Stravinsky occasionally used ascending melodic minor or whole-tone scales. Rather, it is whether acknowledging that he did use these other scales forces us to rethink our ideas about what sets are or are not “obviously” octatonic in origin.

Whole-Tone Scales

Whole-tone scales clearly play a significant role in The Firebird. In Ex. 1(a), they control the vertical dimension, as parallel augmented triads move in contrary motion. (In general, any two subsets of the whole-tone scale can be transposed in contrary motion to produce subsets of the whole-tone set; the technique is much used in jazz arranging.) At (b), a Debussian whole-tone glissando punctuates a more-or-less whole-tone texture. And at (c), the “Firebird theme” (the melodic 6-7[012678] hexachord) appears against a whole-tone wash. These passages represent Stravinsky at his most Impressionist and could easily appear in the music of Debussy or Ravel. In Petrouchka, whole-tone scales appear less frequently, as Stravinsky begins to develop his own powerfully original pitch language. Ex. 2 shows one explicit passage of whole-tone material, representing the trained bear as it walks awkwardly on its hind legs.4 I hear this passage as a wry acknowledgement of Debussy’s influence: the bear trainer plays a high tootling tune on his clarinet/

4Where possible, I have used Stravinsky’s own two-piano reductions of Petrouchka and The Rite of Spring.

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pipe that sounds like a parodic quotation of the beginning of Debussy’s Faun. Influence is here being felt and rejected in a single gesture: the passage is at once Impressionist and anti-Impressionist, and it transmutes French elegance into lumbering Russian spectacle. 8,

4

Example 1  The whole-tone scale in The Firebird

Example 2  The whole-tone scale in Petrouchka, reh. 100, mm. 3–5

The Rite of Spring, and indeed all of Stravinsky’s later music, bids farewell to such explicit whole-tone sonorities. However, as Ex. 3 shows, the whole-tone scale does appear prominently—albeit in combination with other material—at the end of both parts of the ballet.5 As in Petrouchka, Stravinsky’s relationship to Debussy is ambiguous: on the one hand, the scale does appear—very explicitly and recognizably, and at crucial moments in the ballet. At the same time, its characteristic “floating” quality is neutralized by the presence of extra-scalar elements. Indeed, the blaring, fanfare-like

5Messiaen (1956, Chapter 16) describes this technique of blunting the distinctive sonic signature of the whole-tone scale by combining it with other scales.

Stravinsky and the Octatonic

quality of Ex. 3(b) hearkens back to Ex. 2, only without any of the humorous quality of the earlier excerpt. (a) reh. 75, mm. 7–9 Tpt., Vln.

(b) reh. 175, m. 3–reh. 176, m. 1

Example 3  The whole-tone scale in The Rite of Spring

Ascending Melodic Minor Scales The situation is just the opposite with regard to the ascending form of the melodic minor scale (henceforth referred to simply as “melodic minor” and abbreviated “mm” in the examples). It is not a prominent feature of The Firebird’s harmonic language, although it does make a brief appearance at rehearsal 1 (suggesting an incomplete melodic minor scale on A♭; see Ex. 4). It does, however, appear quite strikingly in a few places in Petrouchka, and in The Rite of Spring it plays a dominant role in the first two sections of Part I, as well as in the “Ritual Action of the Ancestors” section of Part II. Thus, while the

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use of the whole-tone scale declines over the course of the first three ballets, the melodic minor scale becomes increasingly important. Although Stravinsky may have started to remove Debussian wholetone sounds from his vocabulary, the prominence of the melodic minor scale in The Rite of Spring testifies to his continuing debt to the French tradition.6

Example 4  The melodic minor scale in The Firebird, reh. 1

Example 5 lists four places in Petrouchka where the complete melodic minor scale appears. Example 5(a), the most extensive of the three, occurs near the beginning of the “Russian Dance” of the first tableau and contains four different transpositions of the melodic minor scale in sequence. Of course, the passage does not particularly sound like it is in minor, since the scale has been modally rearranged to emphasize the oscillations between two “dominantseventh”7 chords a whole-step apart. Example 5(b) shows another passage from Petrouchka’s first tableau: here, the registration of the scale suggests an augmented triad on B♭ with a major seventh. (This sonority will reappear prominently in the Symphony of Psalms; see Example 14 below.) Example 5(c) shows the same sonority as it reappears just before the curtain rises in the fourth tableau. Example 5(d), from the third tableau, is taken from a passage that is notably indebted to Debussy in construction: it begins with a simple

6The Stravinsky of Expositions and Developments (1962, 163) was explicit about this: “Le Sacre owes more to Debussy than to anyone else except myself, the best music (the Prelude) as well as the weakest (the music of the second part between the first entrance of the two solo trumpets and the Glorification de l’Élue).” 7I use the term “dominant seventh chord” here to refer to a collection, and not to the functional chord of traditional tonality.

Stravinsky and the Octatonic

diatonic melody over a B♭ pedal, suggesting B♭ lydian, or perhaps D natural minor. (This music is not shown in the example.) When the melody repeats, the accompaniment adds a harmonic A♭, producing a mode of the F melodic minor scale. (a) reh. 35

(b) reh. 7

Example 5  The melodic minor scale in Petrouchka (continued) (c) reh. 87, mm. 3–6

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(d) reh. 65, mm. 5–8

Example 5 (continued)

Example 6 lists seven examples of modal uses of the melodic minor scale in The Rite of Spring. The clearest and most extensive is shown at (a), which takes up the last twenty-four measures of the “Augurs of Spring.” If we take the melody’s A to be the tonic of this section, then the mode in question is the one that begins on the sixth degree of the normal ordering of the C melodic minor scale. (Jazz theorists sometimes call this the “locrian #2” mode, since it is equivalent to the locrian mode with a raised second degree.) This passage is prefigured at (b), which is slightly more ambiguous in that the melodic minor scale (here in the string sections and horn) is superimposed atop a C-major scale fragment (in the trilling bassoons and solo strings) that is foreign to the scale. Example 6(c), from the “Ritual Action of the Ancestors,” represents another fairly clear passage. Bass D is the primary pitch of this section, so that the passage implies the seventh mode of the E♭ melodic minor scale. (Jazz musicians would call this the “altered scale.”) Note that I am considering the melodic B to be an embellishing tone, a chromatic neighbor to the sustained C.8 But it could well be taken to be harmonic, in which case the alto flute’s sinuous melody would represent an alternation between E♭ harmonic and melodic minor. This sort of alternation is actually common in the Rite, as Ex. 6(g), 7(a) and (b) below will show. Example 6(d) shows a passage from the Introduction to Part I, at rehearsal 7. Here, the mode is the same

8I am also considering the English horn’s initial chromatic glissando to be nonharmonic.

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as that of Ex. 6(a).9 As in the first three examples, the melodic minor scale accounts for virtually all of the pitches present. (a) reh. 32

(b) reh. 25

Example 6  The melodic minor scale in The Rite of Spring (Continued)

9I am considering the second note of the clarinet melody to be a passing tone, as I believe it is in almost all of the melody’s appearances; see Ex. 6(e) and 7(b). One potential exception is at rehearsal 10 ff., where it is arguably the D♯, rather than the E♯, that is non-harmonic. However, this is a passage that features a large number of superimposed musical layers, so that the very notion of an “underlying harmony” becomes problematic.

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(c) reh. 129, mm. 7–8

(d) reh. 7

Example 6 (continued) (e) reh. 8

(f) reh. 5

Example 6 (continued)

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In Ex. 6(e), which occurs a few measures after (d), the melodic minor scale appears superimposed on top of other material. The first measure presents all the pitches of the B melodic minor scale, again in the seventh mode, as in (c). (I am considering the second note of the D-clarinet melody, here a D♯, to be non-harmonic.) We clearly hear this material as a unit, as it is directly derived from the music of Ex. 6(d). In measure two of the example, however, the alto flute heads off in its own direction, playing a noodling line that suggests D minor and D mixolydian. It is joined a measure later by a flute figure (not shown in the example) that also does not belong to the B melodic minor collection. Such superimpositions of melodic minor and other material are also characteristic of the final two examples. In 6(f), we find a fascinating interplay of four different musical layers. What I consider the core material harmonic material is found in layer 2: a series of trills and rifles in the flutes (as well as in the third horn) that outline the pitches A–B–C♯–D♯–F♯–G♯, a gapped scale-fragment suggesting either the lydian mode on A or the third mode of F♯ melodic minor. The primary melodic material, in layer 3, exploits this ambiguity, alternating (and superimposing) the two notes that would naturally tend to fill the gap in layer 2. Consequently, this passage does not present a scale in the (relatively) clear fashion of Ex. 6(a)–(e); instead, it toys with scalar ideas, exploiting our tendency to hear (and analyze) music in scalar terms, while producing a characteristically ambiguous Stravinskian sonority. Furthermore, the outer layers—layers 1 and 4—present material that is foreign to both scales implied by layers 2–3, thus heightening the non-scalar sound of the passage as a whole. Example 6(g), which in the score follows immediately upon (f), intensifies this procedure. The alto flute melody contains a statement of the complete D melodic minor scale, here centering on B. Thus the mode is again “locrian #2,” as in Ex. 6(a), (b), and (d). (Note that the three sustained pitches also belong to this scale.) Against this, the bass clarinet presents a five-note fragment of the G melodic minor scale, while the English horn adds a transposed version of the tune first heard at rehearsal 2. In Ex. 6(h), I have shown how the registral partitioning of the pitches in this passage suggests that three separate scales are operative at once: in the top register, D harmonic minor; in the middle register, D melodic minor;10 and in the lowest 10Recall

in this connection the melodic/harmonic minor interplay of Ex. 6(c).

Stravinsky and the Octatonic

register, a six-note subset of the G melodic minor scale. Here, as elsewhere in Stravinsky’s music, register and timbre combine to keep different layers distinct, allowing us to understand the music as a construction of seemingly independent musical ideas.

Harmonic Minor

In Ex. 6(c), we saw a predominantly melodic-minor passage colored by a brief infiltration from the harmonic minor scale. Now I would like to consider two examples of the opposite phenomenon: a predominantly harmonic minor sound that is lightly colored by notes from the other minor scales. (g) reh. 6

Example 6 (continued) (h) Registral partitioning at reh. 6 of The Rite of Spring

Example 6 (continued)

The most obvious instance, Ex. 7(a), comes from the “Augurs of Spring” section and features the chord that has come to serve as a metonymy for the Rite’s harmonic innovations. This sonority, an E♭

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dominant seventh superimposed atop an E-major triad (spelled F♭) involves all the pitches of the G♯ melodic minor scale and no others. Although we may not hear it as “minor” in origin, it arguably results from just the same procedures that gave rise to Ex. 5 and 6. Note in this context that the bassoon’s melody can be understood as arising from the G♯ melodic minor scale. Thus, the passage as a whole involves the same kind of harmonic/melodic minor ambiguity that was found in Ex. 6(c). Here, however, the primary sonority comes from the pounding harmonic minor chords in the strings. Readers may well be skeptical about this proposed derivation of the “Augurs” chord, preferring instead to think of it as resulting from a superimposition of two (unrelated) tertian harmonies.11 I am somewhat sympathetic to this objection, and will address the relation between scales and superimpositions below. But Ex. 7(b) provides a measure of support for the derivation I have proposed. Here, we find the same modal use of the harmonic minor scale, indeed at the same pitch-level and with a very similar E-major triad in the bass. In 7(b), however, the harmonic minor colorings of the piccolo clarinet line are very explicit: the descent from G♯ to G to E, all over the oboe’s insistent D♯, outlines the characteristic 4–7[0145] sound of the harmonic minor scale. (This set is very distinctly nonoctatonic, and does not appear in that collection.) In mm. 4–5 of the example, Stravinsky gradually inserts notes from the other G♯ minor scales: first an F♯ (from G♯ natural minor) and then, in m. 5, the harmonic minor’s E♯. These infiltrations are again reminiscent of those in Ex. 7(a) and 6(c), and while they enrich the harmonic minor sonority of the passage, they do not, at least to my ear, fundamentally dislodge it. The preceding analyses lie along a continuum, ranging from explicit and, to my mind, clearly intentional uses of the scale (Ex. 5[a], 6[a], and 6[b]) to more subtle passages (Ex. 6[g]) that require a good deal of analytical interpretation. I do not expect that all of these interpretations will be convincing to every reader. I do, however, think that as a whole they demonstrate that non-diatonic minor scales are an important part of the vocabulary of both Petrouchka and The Rite of Spring. For both the number of the examples (thirteen 11Cf.

Frederick Smith (1979, 178), who writes of the chord: “there is no harmonic analysis called for; it is simply a question of how the composer placed his hands on the keyboard.” I have taken this quotation from Whittall 1982.

Stravinsky and the Octatonic

in all) and their concentration in just two pieces suggest that we are not dealing with coincidences here, but rather with matters of compositional technique.12 To this internal evidence, we may also add the historical fact that modally-conceived minor scales are common in the works of Debussy and Ravel, two composers whom Stravinsky knew and admired. Nevertheless, van den Toorn has analyzed most of these passages—specifically, Ex. 5(a) and (b), 6(a), (b), (e)–(g), and 7(a) and (b)—as resulting from the combination of octatonic and diatonic materials.13 This, I submit, is not just wrong, but wrong in a way that should make us suspicious of the underlying methodology. For Ex. 5(a) and 6(a) are near-incontrovertible instances of modal use of the melodic minor scale; if even these passages can be interpreted as the result of “octatonic-diatonic interaction,” then we should rightly ask whether there is any music that cannot be understood in this way. (a) reh. 19, mm. 2–5

Example 7  The harmonic minor scale in The Rite of Spring (continued) 12“Compositional technique” can be in part a subconscious matter: it is quite possible

that Stravinsky picked up the sound of these two scales by listening to other music, and used them without full awareness of what he was doing. 13For Ex. 5(a)–(b), see van den Toorn 1983, 84–6; for 6(a)–(b), see van den Toorn 1987, 153–5; Ex. 6(c) and (d) are not analyzed by van den Toorn; for (e)–(g), see van den Toorn 1983, 100–10; for 7(a), see van den Toorn 1983, 108; for 7(b), see van den Toorn 1987, 152. Richard Taruskin (1996, 939 and 942 [example]) also analyzes Ex. 5(b) in terms of “octatonic-diatonic interaction.” Peter Hill (2000, 61–2), who expresses some reservations about octatonic-centered readings of Stravinsky, nevertheless describes 7(b) as “the first ‘octatonic’ sound of the work.”

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Example 7 (continued)

Stravinsky and the Octatonic

(b) reh. 4

260

Stravinsky and the Octatonic

In a sense, there is not: any proper subset of the chromatic scale can be decomposed into octatonic and diatonic components. It is particularly tempting to analyze the non-diatonic minor scales in this way. For both scales share six notes with a diatonic collection and six notes with an octatonic collection, as Ex. 8 shows. Both scales can also be understood as combining the octatonic scale’s signature 4-3[0134] tetrachord with a diatonic scale-fragment, as in Ex. 9. Thus, the non-diatonic minor scales naturally tend to evaporate under the scrutiny of the analyst predisposed to interpret music in terms of diatonic and octatonic fragments.14 This tendency should be resisted, since both analytical and historical evidence suggest that in Stravinsky’s music the non-diatonic minor scales are entities in their own right, rather than mere derived (or “surface”) formations.

Example 8  Minor scales as composed of octatonic and diatonic components

Example 9  Minor scales as composed of octatonic and diatonic scalefragments

A Brief Overview of the First Two Sections of The Rite of Spring Readers will have noticed that most of Ex. 6 and 7 come from the first few sections of The Rite of Spring. The heavy concentration of modally-reconceived minor scales in these few minutes of music may prompt us to look for a higher-level analysis. In particular, we 14Since

the melodic minor scale shares five notes with the whole-tone collection, it is sometimes misinterpreted as a product of whole-tone/diatonic interaction. See, for example, Whittall 1975, particularly the analysis of mm. 26–8 of Des pas sur la neige.

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may want to know the relative importance of octatonic scales and minor passages in these opening sections of The Rite of Spring. This comparison will provide an important test of the notion that Stravinsky’s language is predominantly octatonic in derivation, especially in light of van den Toorn’s assertion that the Rite is “generally octatonic” and “without question the most thoroughly octatonic of all Stravinsky’s works.”15 Spring

10(a).

number elements

1–9, 13 1

10–12, 14–19 20– 4 2–3 4 bassoon E.h.: C minor G w/ pentachord accomp. accomp.)

Notes

min.

25–7 5 lyd./ F mm.

7(b) 42, 44–5 number (7) elements mm. harmonic?)

Notes

46–51 8 mm., by scales

6(g)

52–6 9 Superimposed diatonic fragments

28–31 6 harm/mm; mm. 6(f)

6(g)

32–8 39–41, 43 7 4-10[0235] E mm. flute melody/ accomp. 6(d)

57–65 10–11 superimposition elements,including scales, A pentatonic,G harmonic minor, others

66–75 12

ostinato, F ,E

melody, “Augurs” dominants

6(e)

Example 10(a)  Scalar structures in the Introduction to Part I of The Rite of Spring

Examples 10(a) and 10(b) provide such a comparison. In these tables, I have attempted to summarize scales used in all the different “blocks” of material in the first two sections. As one can see, minor scales play an important role in a third of the measures in the introduction (25 out of 75 measures). By contrast, the introduction contains not a single measure of incontrovertibly octatonic music.16 In the “Augurs of Spring,” the situation is even more extreme: more than half of the measures of the section (93 out of 172) potentially involve modal uses of minor scales. By contrast, there are just a few measures of explicit octatonicism: the eight measures of rehearsal 15“Generally

octatonic”: van den Toorn 1983, 101; “without question”: van den Toorn 1983, 470, n. 4. Cf. also Robert Moevs’s claim that “perhaps ninety percent of this composition can be referred directly to a matrix of alternate half and whole-tone steps” (1980, 100). 16Van den Toorn (1983, 42–4) claims that the material at rehearsals 6 (Ex. 6[g]) and 8 is “explicitly” octatonic (cf. their appearance on “List 1”), but his argument is undermined by the fact that his graphs of these passages consistently, and without comment, leave out non-octatonic grace notes. (For the analysis with the missing grace notes, see pp. 104–5.) Note that van den Toorn’s analyses do contain grace notes when they do not interfere with his octatonic readings.

Stravinsky and the Octatonic

30, and the five measures at rehearsal 23. These numbers strongly suggest that the octatonic scale is a relatively minor feature of the first two sections of The Rite. What emerges instead is a picture that is fundamentally at odds with previous analyses of this piece. In these first 247 measures, the primary musical materials—besides the diatonic collection—are not octatonic, but rather minor scales. 10(b).

“

76–83 number 13 elements G

min.

Spring”

84–7 14 Superimposed triads: C, E, e ostinato (G min. C?)

88–97 (14)–15 G min. chromatic melody)

Notes 153–7 158–73 number 23 24–5 elements octatonic B mm. major trills Notes

174–81 26 as 158–73, but chromatic melody

182–9 27 B dorian trills continue)

98–109 110–144 145–6 16–17 18–21 (21) Superimposed G min. Non-scalar G mm.) 145: diatonic elements possibly octatonic) register: B –C– D –E – register: mixolydian 7(a) 190–207 28–9 E dorian now suggest E mm.)

208–15 30 Octatonic diatonic low strings)

147–52 22 chromatic + trill

216–23 224–47 31 32–6 minor mm. chromatic chromatic bass) flurries)

6(b)

6(a)

Example 10(b)  Scalar structure in the “Augurs of Spring”

To be sure, these scales play a less important role in the rest of the Rite (although they are very prominent in the “Ritual Action of the Ancestors.”) And, starting in the “Ritual of Abduction,” octatonic materials do make an important appearance. But throughout the piece, the octatonic scale continues to be just one element of many: much of the music (“Spring Rounds,” “Evocation of the Ancestors”) is diatonic; some sections (“The Dancing Out of the Earth”) involve the superimposition of diatonic elements on other scales; some are octatonic (especially the “Ritual of Abduction,” the central part of the “Ritual Action of the Ancestors,” and some parts of the “Sacrificial Dance”), and still other parts (such the “Naming and Honoring of the Chosen One,” and much of the “Sacrificial Dance”) have no clearly identifiable scalar background. In a word, the music is heterogeneous, exhibiting a variety of techniques and compositional procedures. To my mind, this heterogeneity is a major feature of Stravinsky’s style. The challenge for the analyst, then, is to explain the music’s coherence while still doing justice to the variety of different techniques that animate it.

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Superimpositions Stravinsky, Polyscalarity, and the “Petrouchka” Chord Perhaps the most striking aspect of Stravinsky’s harmonic language is polyscalarity: the simultaneous use of musical objects which clearly suggest different source-collections. Polyscalarity is a kind of local heterogeneity, a willful combination of disparate and clashing musical elements. It is the feature that prompted the Italian composer Alfred Casella (1924) to compare Stravinsky’s musical style to the “cubist” technique of Picasso and Braque, in which single objects are portrayed from more than one vantage point. Whether this is an apt description of cubism is open to question, but the analogy is certainly useful in thinking about Stravinsky: here, the “different perspectives” are different scales, or radically different harmonic areas, and their simultaneous presentation represents a fundamental challenge to the traditional assumption that a single scale or key area (or “referential collection”) should govern music at any one time. One can speak of this, if one likes, as “polytonality.” This is a concept that has come in for much undeserved abuse. Some theorists, such as Benjamin Boretz and Allen Forte, have argued that the very notion of polytonality involves logical incoherence.17 Others have questioned whether it is possible for human beings to perceive two or more keys simultaneously.18 We can grant that a piece of music cannot, in the fullest and most robust sense of the term, be in two keys at once; indeed, it may be impossible for us to hear one and the same note as having two tonal functions simultaneously. Still, this should not cause us to jettison the notion of polytonality altogether. For many pieces—including many of Stravinsky’s— naturally segregate themselves into independent auditory streams, each of which, if heard in isolation, would suggest a different 17See

Forte 1955, 137, and Boretz [1972] 1995, 244. (Both passages are cited in van den Toorn 1983.) Boretz seems strangely to think both that the idea of polytonality is logically contradictory and that we can experience more than one tonality at once. This is delicate ground, but I am inclined to think that if a concept accurately describes a common, non-illusory experience, then it is probably not incoherent or contradictory. For an analysis (of a Milhaud work) that is sympathetic to polytonality, see Harrison 1997. Harrison helpfully suggests some reasons why analysts have been reluctant to take polytonality seriously. 18See Krumhansl 1990, 226–39, for an empirical discussion of the issue.

Stravinsky and the Octatonic

tonal region.19 Further, it seems clear that we can, in some more rudimentary sense of the term, hear more than one tonal area at once. (Imagine an oboist playing “My Country ‘Tis of Thee” in F, while across the room a pianist plays the Star-Spangled Banner in D♭ this is a musical situation that can reasonably be described as involving “polytonality,” and it is one in which I suspect most skilled listeners would have no problem discerning the presence of two independent tone-centers.) Out of deference to terminological sensibilities, I will use the word “polyscalarity” to refer to music of this sort. I intend the term to carry no implication that we can (in the most robust sense) perceive two keys at once.20 The desire to avoid “polytonality” seems to be have been one of the major motivations for octatonic-centered readings of Stravinsky.21 For it often happens that on an octatonic interpretation, what might at first sound like objects that belong to different scales—say a C-major triad and an F♯-major triad—are interpreted as sonorities that derive from a single octatonic collection. As Arthur Berger put it, apropos the Petrouchka chord: Since the entire configuration may now be subsumed under a single collection with a single referential order, i.e., the octatonic scale, the dubious concept of “polytonality” need no longer be invoked.22

Van den Toorn quotes this passage approvingly, adding

19I

questions regarding the “bitonality” or “polytonality” of certain passages in this literature can no longer be taken seriously within the context of this inquiry. Presumably implying the simultaneous (C-scale tonally functional) unfolding of separate “tonalities” or “keys,” these notions—real horrors of the musical imagination—have been widely (and mercifully) dismissed as too fantastic or illogical to be

use “tonal region” here in a very general sense that is not restricted to the voiceleading conventions of Western classical music. 20There is an old debater’s trick of refuting an opponent’s claim by interpreting it only in its extremest possible sense. The attack on the notion of polytonality sometimes seems to partake of this: theorists sometimes seems to suppose that by showing that we cannot “perceive two keys” in the richest possible sense, they have shown that there is no useful sense in which we can be said to perceive more than one key at a time. 21Taruskin ([1987] 1990, 1996) is the exception here. He, too, argues that polytonality is a useful notion, though he seems to think that Stravinsky’s use of “multiple keys” arises from deeper-level octatonicism. 22Berger [1963] 1968, 134–5.

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of assistance . . . There is [in the Petrouchka chord] no simultaneous (tonally functional) unfolding of “two keys,” but merely this oscillation or superimposition of the (0,6) tritone-related (0 4 7) triads of Collection III at C and F♯.23

Note the structure of the argument: beginning with the notion that we cannot (in some rich sense of the term) perceive two keys at once, van den Toorn concludes that the Petrouchka chord is mono-scalar in origin. But this is doubly problematic. First, although some seeming instances of polyscalarity can in fact be resolved by the octatonic scale, many others cannot.24 Thus, although the availability of the octatonic scale may provide the impression that we can do without the notion of polytonality (or its weaker cousin, polyscalarity), this is not the case: sooner or later, even the partisans of octatonicism will have to confront the fact of Stravinsky’s multiscalar superimpositions. The second problem is that even when we can interpret a given passage of music as deriving from the octatonic scale, it is not clear that we should necessarily do so. For in many places, Stravinsky clearly does make use of multiple scales at a single time. (Indeed, he explicitly spoke of the music of Petrouchka’s second tableau as being “in two keys.”25) While it might be possible to interpret the Petrouchka chord as monoscalar, it may be more fruitful to regard it as polyscalar, deriving from the superimposition of elements belonging to the C-major and F♯-major collections. Whatever scruples we may have about the notion of polytonality, the music itself will necessarily be our last court of appeal. Let us consider the various transformations of the Petrouchka chord in that ballet’s second tableau. The first is shown in Ex. 11(a). Notice that the chord is accompanied by a note (the bassoon’s G♯) foreign to the octatonic collection that contains it. (The bassoon’s complete melody, which is not shown in the example, is a six-note subset of the harmonic minor collection.) The second time the chord appears, 11(b), it is again in a polyscalar context: the piano’s F♯ arpeggio is now accompanied by a G-major arpeggio. (This association of F♯ major, G major, and C major continues throughout van den Toorn 1987, 63–4.

23

24For

example: the music at rehearsals 6, 8, 9, 10, 11 of the introduction of The Rite of Spring; the figure which is first heard at 43, and much of the music of the last section of Part I. 25Stravinsky 1962, 156.

Stravinsky and the Octatonic

the second and third tableaux, and is as characteristically a part of Petrouchka’s musical personality as is the bare juxtaposition of F♯ and C.) This development makes more sense if we understand the Petrouchka chord as a superimposition of two different scales, one white-note and the other black-note; if we see the original chord as wholly octatonic, then the appearance of the non-octatonic G major will have to be independently motivated. Consider now the material at rehearsal 59, shown in Ex. 11(c).26 Again, we find the same nonoctatonic pattern of superimposition of black notes and white notes: here, the white notes appear on the last three quintuplets (or on unaccented sextuplets), and contain all but one of the notes of the C major scale (E is missing). All five of the black notes are used (the A♯ will not be found in the example: it appears in measures 8–9 of rehearsal 59). What happens next is quite telling: at rehearsal 60 (Ex. 11[d]), the material of rehearsal 51 (“Petrouchka’s cries”) is transformed into a representation of Petrouchka’s despair. Again, we find the same trilling alternation of black notes and white notes, but here, instead of F♯ and C (the Petrouchka chord proper) F♯ is juxtaposed with D minor. This shifts the music completely out of the octatonic realm—the resultant sonority is an instance of the hexatonic 6-20[014589] set, structurally analogous to the octatonic collection (alternating half-steps with minor thirds, instead of half-steps and major seconds) but very different in its sonorous qualities. This hexatonic sonority alternates with the original Petrouchka chord in the first four measures of rehearsal 60. Finally, the hexatonic sound is transposed away from the white-note/black-note orbit at rehearsal 76 of the third tableau, shown in Ex. 11(e) (“The Moor and the Ballerina Prick Up Their Ears”), where E♭ major alternates with B minor. This sonority is the point of furthest remove from the “Petrouchka” chord proper. I summarize this process in Ex. 12. What should be clear is that the transformations applied to the Petrouchka chord are guided not by underlying octatonicism, but rather by the principle of blacknote/white-note superimposition. Indeed, the development of the Petrouchka chord represents a fairly systematic exploration of the possibilities of such superimposition. Initially a C-major triad is juxtaposed against an F♯-major triad, producing a clear octatonic 26Similar

material can also be found at rehearsal 50.

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Stravinsky and the Octatonic

sound (albeit distorted by the bassoon’s initial G♯). Gradually the number of white notes in the superimposition is increased—first, to include the notes of the G-major triad, and then to include those of the D-minor triad as well. Correspondingly, the number of black notes in the superimposition is increased, producing resultant sonorities that are ever more chromatic, and eventually including all but one of the twelve pitch classes. Once this maximum point of chromatic saturation is achieved, the initial C- and G-major triads disappear, while the black notes are reduced to their original F♯-major sound. This produces the hexatonic sonority, strongly contrasting with the original octatonic sound, and yet still recognizably Petrouchkaesque. Contrast this with Taruskin’s interpretation of Petrouchka’s second tableau (1996, 737–56). In Taruskin’s view, the octatonic scale is a stable tonic collection throughout the entire movement. Various departures from this collection—such as the extended diatonic episode beginning at rehearsal 52—are to be understood as analogous to modulations in traditional tonal music. Even the hexatonic collection of Ex. 11(d) above is seen in relation to the octatonic set: in Taruskin’s reading, the D-minor chord is an appoggiatura to the C-major portion of the Petrouchka chord proper. And although Taruskin does acknowledge that there are some grounds for thinking of this music—especially Ex. 11(b) and (c)— as “polytonal,” he writes that this is acceptable only “so long as it is borne in mind that the keys in question were chosen not simply ad libitum but from among the circumscribed and historically sanctioned wares of the octatonic complex.”27 The octatonic scale, in other words, produces the Petrouchka chord, rather than the other way around.

Example 11(a)  The first appearance of the Petrouchka Chord, reh. 49 27Taruskin 1996, 749. Taruskin’s original paper ([1987] 1990) argues more forcefully

in favor of the polytonal explanation of the chord.

Stravinsky and the Octatonic

Example 11(b)  The Petrouchka Chord, reh. 49, mm. 11–2

Example 11(c)  Development of the Petrouchka Chord, reh. 59

Example 11(d)  Development of the Petrouchka Chord, reh. 60

Example 11(e)  Development of the Petrouchka Chord, reh. 76, mm. 2–3

Rehearsal #1 #2 sonority Notes

49 triad F triad Octatonic

(49) C, triads F triad Chromatic notes) White-note/black-note superimposition

59 E notes Chromatic notes)

60 triad F triad Hexatonic 6-20[014589]

76 triad E triad Hexatonic 6-20[014589] _

Example 12  The development of the Petrouchka Chord: summary

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Stravinsky and the Octatonic

We can certainly accept Taruskin’s point that juxtapositions of tritone-related major triads are characteristic of the music of Stravinsky’s Russian precursors.28 But are we so sure, even in light of this history, that all such juxtapositions derive from the octatonic scale? And is it even clear that the Petrouchka chord itself arises out of the “octatonic complex”? There is surprisingly little in the music which might tell us this: if we set aside the appearances of the Petrouchka chord proper—since this is the entity that we are trying to understand—then we note that in the entire second tableau, there are only four other measures of octatonic material. (These are mm. 1 and 7, and the two-measure cadenza that precedes rehearsal 59.) At the same time, there are approximately thirty measures of music (including Ex. 11(b)–(d) above) that seem to derive from polyscalar black-note/white-note superimposition. Counting is, of course, no substitute for musical analysis, but here it does suggest that octatonicism is not the main technique in the second tableau. It is instead a foreground phenomenon, a surface manifestation of the more fundamental (“middleground”) principle of black-note/whitenote opposition. Granted, such juxtapositions can produce octatonic sonorities; but they can also, as Stravinsky shows us, produce chromatic or hexatonic sonorities.

Scales and Superimpositions

The appearance of octatonic and hexatonic sonorities in our analysis of the Petrouchka chord should not be surprising. As is well known, the superimposition of any two (major, minor, or diminished) triads whose roots are separated by a minor third or tritone will produce a subset of the octatonic scale. Similarly, the superimposition of any two (major, minor, or augmented) triads whose roots are separated by major third will produce a subset of the “hexatonic” scale.29 In analyzing a work where triadic superimpositions play an important role, we should therefore expect that octatonic and hexatonic sonorities will be produced as a natural byproduct of the superimpositions themselves. 28Taruskin

has done more than anyone else to uncover this history. See especially Taruskin 1996, Chapter 4. 29One can go further: superimposition of two (major or minor) triads separated by a half-step produces a subset of either the harmonic minor or its inversion. This fact is somewhat unfamiliar to theorists, and it perhaps accounts for their reluctance to see the harmonic minor scale in passages such as Ex. 7(a) or 18(b).

Stravinsky and the Octatonic

More generally, as I showed in a previous paper, there is a set of seven scales which has the remarkable property of containing as subsets all those pitch-class sets that do not themselves contain a 3-1[012] trichord.30 (These seven scales are the diatonic, melodic minor, whole-tone, octatonic, harmonic minor, its inversion [sometimes called the “harmonic major”], and the 6-20[014589] hexatonic scale.) As a consequence, any superimposition of two triads—major, minor, diminished, or augmented—will necessarily produce a subset of one of these seven scales.31 (A fortiori, the same holds for the superimposition of subsets of triads.) There is thus a deep link between the technique of triadic superimposition and harmonies that are recognizably scalar. But, crucially, this is an intrinsic feature of the twelve-tone universe and not a result of decisions made by individual composers. What this means is that we must take care in analyzing the work of a composer who, like Stravinsky, makes use both of scales and of superimposed triadic sonorities. Is it the scale that is analytically fundamental, determining the choice of the objects that are to be superimposed? Or, as I suggested in the case of the Petrouchka chord, does the superimposition lie at the deepest musical level, producing scales in the foreground? If the latter, are the surface scales even an important part of the musical development? Or are they merely the inevitable byproducts of the superimpositions involved? I do not think that there need be any one answer to these questions, and, indeed, I think we can find examples of a wide variety of procedures in Stravinsky’s work. At the same time, I think that it is important to take these questions seriously. For otherwise, we are in danger of mistaking scales that are the mere byproducts of triadic superimpositions for the entities which produce those superimpositions. In other words, we risk treating the constraints inherent in the twelve-tone universe as distinctive features of a composer’s style. By way of example, let us examine the set-classes that result from the superimposition of a triad with one other note. (I will call these sets the “triadic tetrachords”: triadic tetrachords containing 30Tymoczko

1997. See also Pressing 1978. be more accurate: any superimposition of any triad or diminished seventh chord with any other triad or diminished seventh chord will produce a subset of one of these seven scales. The reason is that triads and diminished seventh chords do not contain major or minor seconds, and thus it is impossible to superimpose two of them in such a way as to produce a set containing a 3-1[012] trichord.

31To

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Stravinsky and the Octatonic

a major triad will be “major triadic tetrachords”; those containing a minor triad will be “minor triadic tetrachords,” and so on.32) As Ex. 13 makes clear, six of the major triadic tetrachords belong to the diatonic scale; five of them belong to the octatonic scale; and only one belongs to neither. (Since the diatonic and octatonic scales are inversionally symmetrical, the situation is the same for the minor triadic tetrachords). That one set, 4-19[0148], contains the augmented trichord—one of only two trichords that belong neither to the diatonic nor the octatonic scale.33 Now consider Ex. 14, from the Symphony of Psalms, which shows the first climax of the last movement’s fast section. The first four measures of the passage involve all three major triadic tetrachords that do not belong to the diatonic scale, and only one other (4z29[0137], which belongs to both the diatonic and octatonic collections). The first chord, here an A-major triad over a bass F, is the one triadic tetrachord that is neither diatonic nor octatonic.34 The next chord, F major over a G♯, is octatonic, while the third, D major over a G♯, is both octatonic and diatonic. (Note, however, that this octatonic-flavored tetrachord has a distinctly non-traditional sound.) The last, F major over a G♯, again belongs to the octatonic scale. Each of these tetrachords is further associated with a different scalar region: the first two measures of the excerpt (mm. 46–7 of the piece) belong to both the D harmonic and melodic minor scales; while the second two measures belong to a single octatonic collection.35 (Note that the last two measures suggest the D “harmonic major” scale and include a fifth triadic tetrachord.) In short, the excerpt seems to involve a number of different major triadic tetrachords that produce a series of different scalar harmonies.36 32Obviously

these definitions are non-exclusive. 4-17[0347], for example, is both a major and minor triadic tetrachord. 33The other trichord is 3-1[012]. The only tetrachords which do not belong to either the octatonic or diatonic scales are 4-7[0145] and those which contain either a 3-1[012] or 3-12[048] trichord. 34I am considering the E, which appears only in the second bar, to be an implied part of the chord throughout. 35It is important to note that this passage is preceded by a series of E-major arpeggios over an F-G bass ostinato, a formation which can be attributed to the octatonic scale. 36Notice that in a van den Toorn-style interpretation, the first chord in the passage is anomalous since it belongs neither to the diatonic nor octatonic collection; it is only the middle two measures that count as truly characteristic of Stravinsky’s language. In the interpretation I am proposing, this sonority is by contrast just as typical of Stravinsky’s language as the rest of the passage.

Stravinsky and the Octatonic

Or does it? As analysts, we have a choice between taking the scales as the primary objects (determining the triadic tetrachords to be used) and seeing the tetrachords as occupying the fundamental musical level. In this case, I believe the choice is clear. If we see the tetrachords as producing the scales, then the first four measures of the passage are consistent and comprehensible: they present the various non-diatonic triadic tetrachords, and fill them out with scales that contain those sonorities. If, on the other hand, we see the scales as fundamental, then it is unclear what (other than the triadic tetrachords) could link them together. Furthermore, it is difficult to imagine that these scales could have been chosen first, and that Stravinsky only later realized that they provided the opportunity to explore the three non-diatonic triadic tetrachords.37 As in Petrouchka, it is superimpositions—here, superimpositions of a major triad with notes foreign to that triad—that determine the choice of scales, rather than the other way around. Triad

and Octatonic Only Diatonic Octatonic

CEG

Only

Note

D F B F A B C E A

T Set 4-22[0247] 4-14[0237] 4-20[0158] 4-z29[0137] 4-26[0358] 4-27[0258] 4-18[0147] 4-17[0347] 4-19[0148]

Example 13  Octatonic and diatonic set-membership of the major “triadic tetrachords”

The Symphony of Psalms, First Movement With these points in mind, let us look more closely at the outer two movements of the Symphony of Psalms. Van den Toorn describes the Symphony of Psalms, with Scherzo Fantastique, Petrouchka’s second 37I

would like to emphasize that I do not mean for these words to express undue concern with the way Stravinsky thought about this passage or the way he actually composed. Instead, I take analyses to represent a kind of hypothetical story about how a piece of music might have been logically and rationally composed. That a good analysis makes a piece of music look sensible, and that composers often work in intuitive or even irrational ways simply underscores the difference between analysis and history.

273

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tableau, The Rite of Spring, and the Symphony in Three Movements, as Stravinsky’s most octatonic works, but one could go further: the first movement of the Psalms is quite possibly the most thoroughly octatonic of all of Stravinsky’s mature compositions. As such it represents the strongest possible case for an octatonic-centered reading of Stravinsky’s oeuvre.

Example 14  Symphony of Psalms, III, m. 46–51 (mm. 5–10 of reh. 5)

I do not so much wish to deny as to qualify the claim that the octatonic scale is central to the first movement of the Psalms. For although the scale is present in forty-one of the piece’s seventy-eight measures, it often appears alongside other notes and scales foreign to the octatonic collection, as Ex. 15 demonstrates. Indeed, the scale appears on its own (“unimpeded”) in only eighteen measures of the piece. Of course, this is still a fairly high proportion by Stravinsky’s standards, but it is important to remember that there are pieces in the literature which are vastly more octatonic than this. Messiaen’s “Regard du Pere,” for example, the first piece of the Vingt Regards, is a work whose nineteen measures last more than twice as long as the first movement of the Psalms. This piece is almost entirely octatonic in derivation, save for one progression at the end that suggests functional tonality. Indeed, the movement contains only a single sonority (the second to last) which does not belong to an octatonic collection. Furthermore, the octatonic scale appears on its own, without interference from notes foreign to the collection, in almost every measure of the piece. This is true and explicit—some might even say excessive—octatonicism. By comparison, Stravinsky’s use of scales tends to be subtle, qualified, and ambiguous.

Stravinsky and the Octatonic 1–4 number elements

Octatonic

Notes 37–40 number 6 elements Diatonic 40: chromatic)

5–10 1 Polyscalar: “ 6th” of chords 16(a) 41–8 7–8 Octatonic

11–4

15–8 2 phrygian

Octatonic and dorian

49–52 9 phrygian

19–25 3 and phrygian

26–32 4 Octatonic

33–6 5 and minor

16(b) 53–9 10–11 Mostly phryg.

60–4 Mostly min.

65–7 12 phryg.

68–74 13 Octatonic and phryg.

75–8 min.

Example 15  Scalar structures in Symphony of Psalms, I

The opening of the Psalms is a case in point. The piece begins with the celebrated octatonic passage shown in Ex. 16(a): an E-minor triad, followed by dominant-seventh chords on B♭ and G. But having established this octatonic frame of reference, Stravinsky immediately begins to break it down: in m. 5 the B♭7 arpeggio is infiltrated by an A, a note foreign to the collection that suggests an outward (“augmented sixth”-style) resolution of the minor seventh. In m. 7, the G7 arpeggio is accompanied by an F♯, again suggesting an outward resolution of the seventh. These non-octatonic outward resolutions immediately create the recognizably Stravinskian sound of clashing scales. The point here is simply that Stravinsky, even at his most octatonic, is notably reluctant to use the scale for very long. In mm. 11–13, shown in Ex. 16(b), the octatonic scale reappears, this time underneath an ascending F dorian scale. In m. 20, it is accompanied by a melody in the horn and solo cello that suggests E phrygian. At rehearsal 4, it appears on its own for seven measures; but immediately thereafter, the full chorus, singing forte, superimposes notes from the key of C minor on top of it. Likewise, in mm. 68–74, the scale appears underneath notes from the E phrygian collection. So, while it is true that this movement can be well accounted-for in terms of octatonic and diatonic scales, it is equally true that it frequently blurs its own octatonicism, combining that scale with notes foreign to the collection. In this sense even Stravinsky’s most insistently octatonic work suggests that it is not octatonicism per se that characterizes the composer’s harmonic language, but rather polyscalar superimposition—which may or may not involve octatonic scales.

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Stravinsky and the Octatonic

Example 16(a)  The opening of the Symphony of Psalms

Example 16(b)  Scalar superimposition in Symphony of Psalms I, mm. 11–3

I do not think that van den Toorn would necessarily deny this. His analyses are filled with instances of “octatonic-diatonic interaction,” in which Stravinsky’s music is segregated into independent diatonic and octatonic streams. If we are to take these analyses as having perceptual relevance, rather than representing mere formalist decompositions of the music, then we are presumably supposed to hear such passages as involving independent diatonic and octatonic musical “layers.” But then we have not come so far from the pre-octatonic view of Stravinsky, with its multiple layers, superimpositions, and “bitonality.” Speaking loosely, we could say that for van den Toorn, “octatonic-diatonic interaction” is a species of “bitonality”—indeed, the only one his analytical methodology recognizes.38 (More properly, we could say that van den Toorn recognizes polyscalarity and superimposition as important aspects of Stravinsky’s vocabulary, but limits himself to superimpositions 38I

say “speaking loosely,” because I understand that there is no such thing as an “octatonic tonality.” Nevertheless, the phenomenon of superimposed scales, each with its own distinctive sonic identity, is the one which the word “polytonality,” however inaccurately, was meant to capture.

Stravinsky and the Octatonic

involving octatonic elements.) As we have seen, however, Stravinsky’s superimpositions come in many varieties, some of which involve the octatonic scale, and many of which do not.

The Symphony of Psalms, Third Movement

Superimpositions play an even more important role in the third movement of the Psalms. Some involve non-diatonic, non-octatonic elements; others involve diatonic fragments belonging to different collections; and still others involve diatonic elements belonging to a single scale. Example 17 shows two prominent superimpositions of the first type. Example 17(a), from the beginning of the fast section of the movement, has three seemingly independent components: a C-major triad, a set of interlocked diatonic thirds in the trumpet and harp, which suggests the C natural-minor scale, and a chromatic ostinato in the low bass. (Notice that if we were interested in attributing all of this material to a single collection, we could treat the low F♯ as a neighbor note; everything else would then belong to the F melodic minor scale.) At (b), we find a whole-tone scale in the trombone combined with parallel triads in the trumpets that bark out the “interlocked thirds” motive from the beginning of the movement’s fast section.

Example 17  Superimposition of non-diatonic elements in Symphony of Psalms, III

Example 18, by contrast, contains three instances of the combination of diatonic materials to form non-diatonic totalities. At (a), an F-major arpeggio is combined with an octave transposed version of the “interlocked-thirds” motive to form the inversionally symmetrical set 7-z17[0124569]. (Note that the registration of the

277

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Stravinsky and the Octatonic

English horn arpeggio recalls the lower half of the famous “Psalms chord” that opens the first movement.) At (b), a major triad in the lutes and trombone is juxtaposed with another major triad a half step above it. (Note that here the registration of the flute/trombone triad recalls the upper half of the “Psalms chord.”) The resultant sonority is a six-note subset of the harmonic minor scale. And at (c), we find a complicated series of typically Stravinskian chords. (The example omits the harp and chorus parts, which I think belong to different “strata” of music.) As the example should make clear, these chords are registrally partitioned into two halves, each of which on its own is diatonic. The upper part of the chords belongs to B♭ major (or C dorian), and consists of an E♭-major triad, an incomplete F-major triad, a stack of fifths beginning on B♭ (B♭–F–C), and another F-major triad. The lower half contains, respectively, a stack of fifths on C, a perfect fourth (D♭–G♭) that perhaps represents an incomplete G♭ triad, an incomplete E♭-major triad, and a 3-6[024] trichord {D, E, F♯}, in a registration that here suggests a D9 chord. Of the four resultant sonorities, the first and third are diatonic, both belonging to B♭ major/C dorian. The second chord forms a five-note subset of the actual pitches of Ex. 18(b). Similarly, the final sonority, typically Stravinskian in its clangorous beauty, is a six-note subset of the actual pitches of Ex. 18(a). The appearance in Ex. 18(c) of subsets of the actual pitches in both (a) and (b) suggests that Stravinsky was, if not conscious of the reuse of the sonorities themselves, at least acutely aware of the characteristic sounds of superimpositions of different diatonic materials. And while it is probably unrealistic to expect listeners to pick up the similarities of pitch content among Ex. 18(a)–(c), it is perhaps not unreasonable to expect that they would hear that these various examples all result from a characteristically Stravinskian superimposition of different scalar regions. Finally, in Ex. 19, I have listed some examples of another common form of Stravinskian superimposition: the combination of materials that belong within a single scale. The most striking of these sonorities are those that cannot easily be interpreted as extended tertian harmonies—9ths, 11ths, and 13ths. In particular, the combination of low-register dominant material with high-register pitches from the tonic triad produces a very bright and energetic sound of uncertain

Stravinsky and the Octatonic

tonal function, one that is typical of Stravinsky’s neoclassic period. Example 19 lists two such sonorities: At (a), the dominant chord in a relatively traditional i7–iv46–V 43–I progression appears underneath the tonic note in the melody, skewing the listener’s sense of tonal function. (The non-diatonic bass D♭ further contributes to this effect.) At (b), high oboes produce a similar sound, undermining a very explicit, neo-Baroque vi–ii–vii°–iii sequence in the low strings and bassoons. Viewed from a set-theoretic or scale-theoretic perspective, such superimpositions are unremarkable, since they produce only subsets of the major scale; but viewed in the light of Stravinsky’s technique as a whole, these all-diatonic formations demonstrate the variety and range of Stravinsky’s superimposition procedures.

Example 18  Superimposition of diatonic elements belonging to different collections in Symphony of Psalms, III

Example 19  Superimposition of diatonic elements belonging to the same collection in Symphony of Psalms, III

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In Ex. 20, I have catalogued all the different forms of superimposition that appear in Movement III of the Symphony of Psalms. In Ex. 21, I summarize Ex. 20. One hundred fifty-seven of the movement’s 212 measures contain some form of superimposition. Most of these superimpositions result in a chromatic sonority, although all of them involve diatonic elements. About a third of the superimpositions produce a diatonic result (and perforce involve only diatonic elements from the same key). Superimpositions are involved in thirteen measures (8%) of clearly octatonic music, while the remaining nine measures (6%) produce sonorities that suggest non-diatonic and non-octatonic scales. Admittedly, these classifications involve interpretation, and are therefore open to question. But even if we regard them as useful approximations, the lesson is clear: superimposition is an extremely characteristic feature of Stravinsky’s pitch organization in the third movement of the Psalms; the majority of these superimpositions produce a chromatic totality, although they often use diatonic materials to do so. Octatonicism, though present, is a relatively minor feature of Stravinsky’s harmonic procedures here; even less frequent, though not unimportant, are superimpositions that produce non-diatonic, non-octatonic, yet still recognizably scalar totalities. Putting aside the issue of superimpositions (since almost sixty measures of music do not involve this technique), we see that the same picture still holds. Eighty-nine of the 212 measures of the piece (42%) are clearly diatonic, while ninety-three (44%) are chromatic—although it should be emphasized that “chromatic” here encompasses quite a wide range that stretches from largelydiatonic yet chromatically-tinged music to extremely dissonant, nondiatonic music. Twenty (9%) measures involve potential examples of octatonicism, while 10 (5%) involve other scales. These results contrast strongly with van den Toorn’s claim that almost half of the movement (102 measures) betrays the signs of octatonic influence. With all due respect to van den Toorn, and in light of all that has been said above, I think we need to ask whether this rampant octatonicism might lie in the eye of the beholder. The octatonic scale is important in Stravinsky, but it is not so omnipresent as it has been made out to be.

3:

scale fragment

Octatonic? triad

Chromatic triad

scale fragment

Diatonic

Diatonic

?

E

G–D–

F

ostinatos

14

call

(harmonic melodic) triad

Diatonic

46–7

Diatonic

12–20 2 minor

44–5

major/minor triad triad

9–10

40–3 5 (?)

major

7–8, 11

37–39

1–6 1 minor

14

mix.

21–3

Octatonic F-major/Dtriads F /G

Diatonic

?

48–9

lengths

Example 20  Superimpositions in the third movement of the Symphony of Psalms (continued)

Notes:

2:

Measures: Rehearsal: area: Superimposition elements: Resultant sonority: 1:

Measures: Rehearsal: area: Superimposition elements: Resultant sonority: 1: 2: 3: Notes:

14

arpeggio

(?)

major

52 6 mm.)

fragment trichord 17(a)

triad

chromatic

major major F -minor7 arpeggio

Diatonic/

?

50–1

24–36 3–4 C

Stravinsky and the Octatonic 281

Notes:

3:

2:

Measures: Rehearsal: area: Superimposition elements: Resultant sonority: 1:

Notes:

3:

2:

Superimposition elements: Resultant sonority: 1:

Rehearsal: area:

Measures:

major

110–12 14 ?

superimpose low instruments’V 19(b)

Quasi-diatonic progression instruments lines winds

Diatonic/chromatic

9

scale motive” triads) 17(b)

Example 20 (continued)

“

18(a)

115–31 15–17 C/E

winds

28–45

Quasi-diatonic progression instruments

Diatonic/chromatic

10 major/ mixolydian 9, but B )

80–6

Chromatic major fragment F-major arpeggio

Chromatic

?

109, 113–14

(octatonic)

72–9

Quasi-diatonic progression instruments lines winds voice

104–8 13 phryg.

8

65–71

Whole-tone/diatonic Diatonic

99–103 12 min./ phryg.

18(c)

Quasi-diatonic in horns melody mixolydian?), others ostinato

Diatonic

(loosely)

61–4

Diatonic/chromatic

87–98 11 C9/A7

19(a)

ostinato

Various

Chromatic dorian

Diatonic (in harmony) (in T melody)

2)

Diatonic

56, 58–9

Diatonic

53–5, 57, 60 1) 6–7 minor

282 Stravinsky and the Octatonic

Notes:

2: 3:

Superimposition elements: Resultant sonority: 1:

Measures: Rehearsal: area:

Notes:

2:

Measures: Rehearsal: area: Superimposition elements: Resultant sonority: 1:

157–62 21 B mixolydian, others

B mixolydian

132–4

rpt.,

Chromatic

Diatonic “ Laudate” music

Example 20 (continued)

oboe (ostinato) E –B –F–B ostinato E –B –F–B ostinato

Diatonic/chromatic

175–82 24 B -minor

Diatonic

163–74 22–3 E

44–

18(b)

triad

oboe chords E –B –F–B ostinato

Chromatic

Diatonic/chromatic

183–6 25 Various

F

minor triad

B

Diatonic E horn melody scale low instruments

147–9 (19) ? Diatonic

138–46 18–19 ?

Diatonic

135–7 18 E

163–74

E –B –F–B ostinato

187–98 26–7

triad

Gprogression

Diatonic

Diatonic

150–6 20 G

Stravinsky and the Octatonic 283

284

Stravinsky and the Octatonic

Measures: Rehearsal: area: Superimposition elements: Resultant sonority: 1: 2: 3: Notes:

199–204 28 Various

205–12 29

Diatonic/chromatic Chromatic chords E –B –F–B ostinato V

2–8

Example 20 (continued)

this appears

sonority chromatic diatonic octatonic scales

elements) 13 9

Example 21  Summary of the different superimpositions in the last movement of the Symphony of Psalms

Conclusion This paper has drawn its examples from three pieces that by all accounts are among the most octatonic that Stravinsky wrote: Petrouchka (especially the second tableau), The Rite of Spring, and the Symphony of Psalms. I have tried to show that even these works are less octatonic than they have been made out to be. Very often the analyses that purport to uncover the octatonic basis of crucial passages make questionable assumptions about which tones are structural and which are not, or about the priority of scales over superimpositions. In short, they seem to require a prior commitment to the idea that the octatonic scale is fundamental to Stravinsky’s music. But, of course, it is just this that Berger, Taruskin, and van den Toorn’s analyses were supposed to be demonstrating. To my mind, the failure of the octatonic hypothesis, in these paradigm cases of Stravinskian technique, means we need to expand our ideas about Stravinsky’s compositional methods.

Stravinsky and the Octatonic

My own analyses have made free use of a variety of concepts, some (“in C minor,” “augmented sixth”) belonging to the tradition of tonal music, and others (“B♭ lydian,” “polyscalar superimposition”) more tangential to that tradition. It may seem, therefore, that I am producing a methodological hodge-podge, an undisciplined analysis that helps itself to an ad hoc set of unrelated concepts. Something very much like this sentiment seems to lie behind van den Toorn’s criticism of earlier Stravinsky scholarship: Here, a bewildering succession of descriptive terms and explanatory notions (e.g., “key,” “C-major,” “tonality,” “bitonality,” “atonality,” “pantonality,” “pandiatonicism,” “polyharmony,” “polychordal,” “superimposition”), invariably left undefined or underdefined, deprives the undertaking of all meaning and consequence. Stravinsky’s music, everywhere and at once, is made to embrace every conceivable musical technique.39

But I do not think that such methodological pluralism is necessarily a vice. Why should we think that we can analyze sophisticated music with just a few techniques? Why should it not be the case that Stravinsky’s music, sometimes bewildering in its complexity, multi-faceted in its influences and references, should not require a similarly complicated analytical apparatus? Granted, it would be gratifying if we were able to understand Stravinsky in terms of a few fundamental procedures. But we have no strong evidence that this is possible. After all, it may just be that Stravinsky’s music is by turns tonal, pantonal, bitonal, atonal, and many other things besides. Elsewhere, van den Toorn writes: Stravinsky’s music has seemed stubbornly to resist binding analytictheoretical legislation. This is curious because of the conviction voiced by those familiar with his music that there is a consistency, a remarkable identity or distinction in “sound” that certainly ought to lend itself to such legislation.40

Here, it seems to me, we come to the heart of the matter: Stravinsky’s music always sounds characteristically Stravinskian, 39van 40van

den Toorn 1983, xiv. den Toorn 1983, xiii.

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Stravinsky and the Octatonic

and therefore there should be some specifiable characteristic that accounts for this. This, I believe, represents a fundamental misconception of the nature of musical style, one that has been abetted by some of the century’s most prominent theorists. It is of a piece with the view that musical language is systematic and regular, a quasi-logical system that is grounded in a few surveyable principles. And it is the sort of view that naturally leads analysts to search for totalizing accounts of a composer’s individual “sound.” I agree that Stravinsky’s music sounds characteristically Stravinskian. But I do not think that there need be any single explanation of why this is so. (Similarly, I do not think there is any non-complex explanation of why Mozart sounds like Mozart, or why Charlie Parker sounds like Charlie Parker.) Instead, the “unity” that we perceive in Stravinsky’s music may be the result of a multitude of disparate factors which together constitute the “Stravinsky sound.” In place of van den Toorn’s essentialist account, I am therefore proposing something more like a family resemblance: an explanation in which the perceived unity of Stravinsky’s music is due to a cluster of different techniques, no one of which is truly central to the composer’s style. Octatonicism is one of these techniques, but so are polyscalar superimposition, modal use of the non-diatonic minor scales, and many others. It is in this spirit, then, that I would suggest we return to the familiar picture of Stravinsky as pluralist, a bricoleur who used a variety of materials possessing no systematic unity. This is a composer who—to use Isaiah Berlin’s tired but useful metaphor— was more fox than hedgehog, a man who knew many small musical tricks rather than a single large one. This is a musician who cared not a whit about technical explanations or theoretical concepts. He is the composer who never once spoke about the octatonic scale, and who described the Petrouchka chord as being in “two keys.” This Stravinsky worked at the piano, finding the note that was right (though most other composers would have heard it as “wrong”) through the power of one of the century’s great musical ears. Some may feel that this picture cannot account for the unity of Stravinsky’s language, the characteristic “Stravinsky sound” that persists across radical stylistic changes. But others can take heart in the thought that

Stravinsky and the Octatonic

“unity” need not be a matter of any one specifiable technique, much as a rope may be unified though no one thread runs along its length. Stravinsky’s musical style, one might say, is a family of practices, of mixed Russian and French heritage, a motley assemblage that still manages to produce the impression, if not the analytically obvious fact, of unity.

List of Works Cited

Antokoletz, Elliott. 1984. Review of The Music of Igor Stravinsky, by Pieter C. van den Toorn. Journal of the American Musicological Society 37: 428–36. Berger, Arthur. [1963] 1968. “Problems of Pitch Organization in Stravinsky.” In Perspectives on Schoenberg and Stravinsky. Edited by Benjamin Boretz and Edward T. Cone. New York: Norton, 123–54. Originally in Perspectives of New Music 2.1: 11– 42.

Boretz, Benjamin. [1972] 1995. “Meta-Variations, Part IV: Analytic Fallout (1).” In Volume 1 of Meta-variations/Compose Yourself. Red Hook: Open Space. Originally in Perspectives of New Music 11.1: 146–223.

Casella, Alfred. 1924. “Tone-Problems of Today.” Musical Quarterly 10: 159– 71.

Craft, Robert. 1984. “Pluralistic Stravinsky.” In Present Perspectives. New York: Alfred A. Knopf.

Forte, Allen. 1955. Contemporary Tone Structures. New York: Columbia University Press.

Gervais, Françoise. 1971. Etude comparée des langues harmoniques de Fauré et de Debussy. 2 volumes, special numbers 272–3 of La Revue Musicale.

Harrison, Daniel. 1997. “Bitonality, Pentatonicism, and Diatonicism in a Work by Milhaud.” In Music Theory in Concept and Practice. Edited by James M. Baker, David W. Beach, and Jonathan W. Bernard. Rochester: University of Rochester Press, 393–408. Hill, Peter. 2000. Stravinsky: The Rite of Spring. New York: Cambridge University Press.

Howat, Roy. 1983. Debussy in Proportion. New York: Cambridge University Press. Kielian-Gilbert, Marianne. 1991. Review of Stravinsky and The Rite of Spring: The Beginnings of a Musical Language, by Pieter van den Toorn. Music Theory Spectrum 13: 252–9.

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Kostka, Stefan and Payne, Dorothy. 1989. Tonal Harmony. Second Edition. New York: Alfred A. Knopf.

Krumhansl, Carol. 1990. Cognitive Foundations of Musical Pitch. New York: Oxford University Press.

Messiaen, Olivier. 1956. The Technique of My Musical Language. Translated by John Satterfield. Paris: A. Leduc. Moevs, Robert. 1980. Review of The Harmonic Organization of The Rite of Spring, by Allen Forte. Journal of Music Theory 24: 97–107.

Perle, George. 1977. “Berg’s Master Array of the Interval Cycles.” Musical Quarterly 63: 1–30.

Pressing, Jeff. 1978. “Towards an Understanding of Scales in Jazz.” Jazz Research 9:25–35. Smith, F. Joseph. 1979. The Experiencing of Musical Sound: Prelude to a Phenomenology of Music. New York: Gordon and Breach.

Straus, Joseph. 1984. Review of The Music of Igor Stravinsky, by Pieter van den Toorn. Journal of Music Theory 28: 129–34.

Stravinsky, Igor, and Craft, Robert. 1962. Expositions and Developments. New York: Doubleday.

Taruskin, Richard. [1987] 1990. “Chez Petrouchka: Harmony and Tonality chez Stravinsky.” In Music at the Turn of the Century. Edited by Joseph Kerman. Berkeley: University of California Press. Originally in Nineteenth Century Music 10: 265–86. ______. 1996. Stravinsky and the Russian Traditions. Berkeley: University of California Press. Tymoczko, Dmitri. 1997. “The Consecutive Semitone Constraint: A Link Between Impressionism and Jazz.” Intégral 11: 135–79.

van den Toorn, Pieter. 1983. The Music of Igor Stravinsky. New Haven: Yale University Press. ______. 1987. Stravinsky and the Rite of Spring: The Beginnings

of a Musical Language. Berkeley: University of California Press.

Walsh, Stephen. 1984. “Review-Survey: Some Recent Stravinsky Literature.” Music Analysis 3: 201–8.

Whittall, Arnold. 1975. “Tonality and the Whole-tone Scale in the Music of Debussy.” The Music Review 36: 261–71.

______. 1982. “Music Analysis as Human Science? Le Sacre du Printemps in Theory and Practice.” Music Analysis 1: 33–54.

Stravinsky and the Octatonic

The Sounds of Stravinsky* Pieter C. van den Toorn

Dmitri Tymoczko’s “Stravinsky and the Octatonic: A Reconsideration” (Music Theory Spectrum 24 [2002], 68–102) has left me more convinced than ever of the validity of the octatonic or octatonicdiatonic approach to sizable chunks of Stravinsky’s music, chunks that include the four works to which the author refers explicitly, The Firebird (1910), Petrouchka (1911), The Rite of Spring (1913), and the Symphony of Psalms (1930). Tymoczko has sought to puncture this approach in various ways in order to demonstrate that the octatonic set and its uses play a much smaller role in Stravinsky’s music than Arthur Berger, Richard Taruskin, or I have maintained. The problem, however, is that the approach itself is ignored. Tymoczko makes no mention of the (0, 3, 6, 9) symmetrical structure of the set, the issues of priority that ensue, Stravinsky’s octatonic vocabulary, the interval orderings (scales) implied by that vocabulary (Models A and B), the intersection and interaction of these scales with various diatonic scales, distinctions between Russian and neoclassical works, the three transpositions—in short, all that made the octatonic and the octatonic-diatonic a compelling analytic-theoretical rationale in the first place. It is as if the author had confined his reading of the relevant materials by Berger, Taruskin, and myself to a handful of pages. What Tymoczko offers is not an analysis but a new labeling service, one based almost entirely on the pitch-class counts of selected blocks or sections of material. He adds up the pitch-classes of selected passages (usually rehearsal numbers), and assigns sets or scales accordingly. “Overviews” or “summaries” are then constructed by stringing together the resultant set or scale labels. See his “overviews” of the Introduction and “Augurs of Spring” in The Rite of Spring, which were his Ex. 10(a) and (b) respectively (p. 83). *Reprinted from Music Theory Spectrum, Vol. 25, No. 1 (Spring 2003).

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The focus is entirely local and without regard to continuity or any larger train of thought. The sets or scales are the diatonic “(trivially),” the octatonic, and the whole-tone (p. 69). The harmonic minor and various modes of the ascending melodic minor are featured, and often in novel ways. The author’s intent is to show a great variety of sets and scales, apparently as evidence of the “heterogeneous” character of Stravinsky’s music (p. 84). Curiously, however, the octatonic and whole-tone categories, although invariably referred to as “scales” in the author’s account, are never treated as such analytically. Passages of octatonic or whole-tone content are labeled “octatonic” or “whole-tone,” without further elaboration. So, too, the same categories, assigned to specific passages, are never represented in musical notation, with pitch letters, numbers, and the like. And the reason for this is clear, it seems to me, even if it is never spelled out by the author. By avoiding musical notation in these cases, the author is able to avoid the details of analysis, above all, the messy details of priority, segmentation, and vocabulary—details that would ordinarily be of concern in any determination as to scale or referential ordering. These same concerns would normally guide a study of Stravinsky’s octatonic uses as well, above all, one would think, a “reconsideration” of those uses. And the author’s diatonic labels, even when accompanied by specific pitch-classes, are no different in these respects. They, too, are assigned with little or no consideration of priority or segmentation. The methodology is not unlike instances of pitch-class set analysis, but with an important qualification. Even the most superficial exercises in set-identification are obliged to confront issues of grouping or segmentation, subsets and their recurrences. Rarely if ever in the author’s treatment of The Firebird, The Rite of Spring, and much of Petrouchka does the discussion venture beyond rehearsal numbers, total pitch-class counts, and the assignment of sets and scales. Questions of priority are never raised. Priority is assigned occasionally, but without criteria or deliberation. With the possible exception of the Petrouchka chord and sections of the Symphony of

Stravinsky and the Octatonic

Psalms, Stravinsky’s melodic and harmonic materials are ignored.1 This includes the extraordinary vocabulary of (0 2 3 5) dorian tetrachords, triads, “dominant sevenths,” and 0–5/6–11 vertical spans that figures so prominently in The Rite of Spring—indeed, in Stravinsky’s Russian-period works generally. As a consequence, register, instrumentation, and chordal disposition are ignored as well. No mention is made of the three transpositions of the octatonic set (Collections I, II, and III), of the two possible scales or interval orderings, and of the explicit ways in which these scales interact with various diatonic scales in Russian and neoclassical works. Omissions of this kind can make for some very bizarre readings. The opening bassoon melody of The Rite of Spring, quoted here in Ex. 1(a), is assigned to the C-major scale. And the “Augurs of Spring” chord at rehearsal 13, shown in Ex. 2, is labeled “G♯ harmonic minor.” “We may not hear [the chord] as ‘minor’ in origin,” the author writes, but “the sonority, an E♭ dominant seventh superimposed atop a E-major triad (spelled F♭), involves all the pitches of the G♯ melodic minor scale, and no others” (p. 78). In other words, the actual sound of these two superimposed triadic entities is of little consequence.2 The two segments do not count. What matters is the total pitchclass content and the assignment of that content to one of the nondiatonic modal scales. At the same time, the priority assumed by G♯ in this latter assignment, surely questionable from any standpoint, is of no concern either. Tymoczko fails to apprehend, in succeeding passages at rehearsal 14, 16, and 23+3 (see Ex. 2), the frequent substitution of G for G♯ and C for B, substitutions that tend automatically to render

1Briefly and without reference to a specific passage, the author refers to (0, 1, 3, 4) as “the octatonic scale’s signature ... tetrachord” (p. 80), showing its possible connection to the harmonic and melodic minor scales. However, next to the (0, 2, 3, 5) Dorian tetrachord, (0, 1, 3, 4) plays only a very slight role in The Rite of Spring and in Russianperiod works generally. Only with neoclassical pieces such as the Octet (1924) does the (0, 1, 3, 4) tetrachord and the semitone-tone scale it implies come to the fore. See the discussion of these matters in van den Toorn 1983, 48–52, 261–70, van den Toorn 1995, 143–8. My concern in this response is primarily with the first three of the Stravinsky works cited; the third movement of the Symphony of Psalms is not treated in the cited texts by Berger, Taruskin, or myself. 2See, too, the author’s assignment of the melodic minor scale to rehearsal 35 in the first tableau of Petrouchka. “The passage does not particularly sound like it is in minor,” the author writes (p. 73), but, evidently, the pitch-class content is the required one all the same.

291

(c)

3

Bn.

(a)

5

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pocopiu`

E. Hn.

3

A1

3

3

3

3

3

B

I

3

3

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A2

5

3

Example 1  The Rite of Spring, opening bassoon melody, extensions

(b)

1

A soload lib.

6

292 Stravinsky and the Octatonic

23 +3

Strings

13

“Augurs of Spring”

25

E. Hn.

etc.

() 3

Fl.

27

Vla.

Obs.

3

()

Fl.

3

Example 2  The Rite of Spring, Analysis of rehearsals 13, 14, 16, 23+3, 25, and 27

Hn.

Bns.

etc.

14

16

3

3

3

()

etc.

etc.

Stravinsky and the Octatonic 293

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Stravinsky and the Octatonic

the E♭ dominant seventh and the D♭–B♭–E♭–B♭ ostinato, along with the E doubled in the bass (the only doubling in the chord), of greater persistence, stability, and, in just these respects, priority. Above all, the substitution of (C E G) for (E G♯ B) at rehearsal 14, 16, and 23+3 (with E often retained in the “bass”), yields one of the truly crucial octatonic relationships in The Rite of Spring, of particular prominence in the “Augurs of Spring” and the “Ritual of Abduction”; see the succession of blocks in Ex. 2, all culminating with the chord that opens the “Ritual of Abduction” at rehearsal 37+2. Example 3 reproduces the analysis of this opening passage of the “Ritual of Abduction” in van den Toorn 1987, p. 155.3 Help! Is this on the level? Has analysis been reduced to a counting game? And is this what a scale is—another unordered pc set? Heard and understood, Stravinsky’s music is generally assumed to be structured in some fashion. Not all pitches or pitch-classes are heard and understood to be of equal weight, to assume the same role or function. Some are clearly subsidiary, while others are grouped in different ways. Groups are formed which are repeated, transposed, and transformed. Shown in Ex. 1(a), the opening bassoon melody, divided into four phrases, admits to at least three main segments:

1. A descending C–B–A motion, common to all four phrases, and resembling a passing motion involving a minor third; 2. An (E G B) triad, shared by phrase A and its subsequent repetitions, attached to B as the passing tone; 3. The dorian tetrachord (D C B A), common only to phrase B, and consisting of the descending C–B–A motion and a descending fourth, D–A. The grace-note G is clearly subsidiary to the A and (D C B A) tetrachord at this point, the latter quite clearly articulated integrally. None of these segments implies the C-major scale. A seventh pitch-class is missing, and, as far as scales are concerned, the 3Notice

that the segmentation and analysis in Ex. 3 does not begin with the octatonic scale (as Tymoczko implies, p. 82), but with the (0, 2, 3, 5) Dorian tetrachord. Complete or incomplete, and nearly continuously operative throughout the whole of The Rite of Spring, the Dorian tetrachord is shared by the octatonic and diatonic sets, often serving, by way of this neutrality, as the principal connecting link between the tone-semitone ordering of the octatonic scale and various diatonic orderings, often dorian. See van den Toorn 1983, 100–24.

Stravinsky and the Octatonic

articulation is contradictory as well as incomplete. Although the melody is a subset of the diatonic set, insufficient evidence exists for a judgment call along more determinate lines. 37 +2

“Ritual of Abduction”

Tpts.

etc.

Hns. Timp.

0–5 (025/035/0235) tetrachord

[

]

0–5/6, 11 intervalspan

[

0, 3, 6, 9

(0 2 3 5); triads, dom. 7ths

[

]

]

((

)

)

(

)(

)

0 2 3 5 6 8 9 11 0 2 3 5 7 9 10 (0) D-Scale Collection III

D-scale on A

Example 3  Analysis of the opening passage of the “Ritual of Abduction,” from van den Toorn 1987, 155

In contrast to the melody and the C-major scale, however, the three segments just noted are full of implication and consequence insofar as the Introduction and The Rite of Spring as a whole are concerned. As shown in Ex. 1(b), the bassoon melody is immediately followed at rehearsal 1 by an extension of the descending motion C–B–A. B♭ is added as a passing tone between C and A; it replaces B in the repeat, yielding the octatonic succession C–B♭–A–G–G♭. Only

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B resists the octatonic Collection III at this point, and these octatonic implications are further underscored when, at rehearsal 3+1, the extension is transposed down a minor third to A–G–F♯–E–D♯ (see Ex. 1[c]). Meanwhile, the dorian tetrachord is also transposed to within Collection III. Initially incomplete in terms of C♯–F♯–D♯, E is added a few bars past rehearsal 3; the G♯, non-octatonic at this point, anticipates a form of diatonic intervention which is as yet incomplete and not fully formed. Crucial here is the 0–11 dissonant vertical span between the upper C of the bassoon fragment and the lower C♯ of the C♯–F♯–D♯ unit. In its most complete realization, the span contains (or is articulated by means of) two tritone-related dorian tetrachords. Less completely, the upper of these two tetrachords, complete or incomplete, is often made to stand in a fixed, polarized opposition to a lower pitch number 11. Throughout much of The Rite of Spring, such is the nature of the octatonic “sound.” The above-noted relationships in Ex. 1 represent a segmentation of a larger musical whole. There are a few additional lines not included here, subsidiary and accompanimental for the most part, some conforming to the octatonic implications drawn, some not. But the idea here has been to present the opening rehearsal numbers as continuous, the two leading fragments in turn as part of a musical narrative. Despite the juxtaposition of blocks, the cutting and pasting, as it were, lines connect in various ways, and the Introduction is heard and understood as a single train of thought. Rehearsal numbers are not the endings and beginnings of different pieces, with the music organizing itself anew at each turn. The next appearance of the C♯–F♯–D♯ segment is at rehearsal 6; The reader should consult Tymoczko’s Ex. 6(g) and (h); Ex. 4 reproduces my own analysis in Stravinsky and “The Rite of Spring,” p. 149. Transposed to F–B♭–G and hence to within Collection I, the fragment, still initially incomplete as a dorian tetrachord, is superimposed over a lower B sustained in the bassoon. Crucially, the octatonic context is transposed as well. The original interval span, C–(F♯, D♯, C♯), reading down, is transposed to (B♭, G, F)–B. The only difference here is that it is the upper of the octatonic scale’s tritonerelated dorian tetrachords that is contained within the 0–11 vertical span, not the lower.

Stravinsky and the Octatonic

6

Fls. Alto 3 3

3

3

3

3

E. Hn.

etc. Bn.

0–5 (025/035/0235) tetrachord

(

)

0–5/6, 11 intervalspan

0, 3, 6, 9 3

(0 2 3 5); triads, dom. 7ths

3

0 2 3 5 6 8 9 11 0 2 3 5 7 9 10 (0) D-Scale Collection I

Example 4  The Rite of Spring, Analysis of rehearsal 6, from van den Toorn 1987, 149

And so the octatonic “sound” of The Rite of Spring, introduced tentatively at rehearsal 3, is further underscored at rehearsal 6. A new fragment in the alto flute transposes the (0 2 3 5) dorian tetrachord from (B♭, A♭, G, F) to (G, F, E, D) and (E, D, C♯, E)—in other words, along Collection I’s (B♭, G, E, C♯) symmetrically defined path. The octatonicism of these transpositions is reinforced by the C♯–D span sustained in the flutes and bassoons. And although a non-

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octatonic (non-Collection I) A embellishes the alto flute fragment at points (first as a grace-note and then as a neighbor note to the lower B), the diatonic implications of this embellishment are clearly subsidiary to the main octatonic forces at work.4 But why should this be? Why are the principal octatonic segments at rehearsal 6, F–B♭–G, (G, F, E, D), and the B sustained in the bassoon, singled out in my own analysis as indeed principal (see Ex. 4)? 7 +3

E. Hn.

7 +5

Hn.

Bn. 3

3

Example 5  The Rite of Spring, rehearsals 7+3, 7+5

The answer here is that the three segments are singled out by Stravinsky himself. In two subsequent repetitions of the passage at rehearsal 7, he confines the repetition accordingly; see Ex. 5. Only the grace-note A lies outside Collection I in these repeats, implying, ever so slightly, an interacting diatonic reference, one that remains incomplete and indefinite at this point. Indeed, a more securely fastened octatonic framework would be difficult to imagine. Nonetheless, Tymoczko stakes his claim in the following terms: the Introduction “contains not a single measure of incontrovertibly octatonic music,” he writes (his italics, p. 82). But the modified repeats of the passage at rehearsal 6 (see Ex. 5) are ignored all the same, as is the persistence of the given octatonic transposition, Collection I. (Recall the author’s refusal to recognize specific transpositions of the octatonic set, anything beyond the label itself.) 4Tymoczko

quite rightly complains about the deletion of this grace-note A from the musical quotation accompanying the analysis of Ex. 3 (p. 82). Although clearly subsidiary, the diatonic implications of this grace-note might have been included in the analysis of Ex. 3 as a form of intervention at this point.

Stravinsky and the Octatonic

8

I

Fl.

Picc. Cl. in D

Cl. in A

6

3

Fl. c-a. in G

dim.

3

pocopiu`

3

3

3

3

3

3

3

3

3

3

3

3

3

3

Bn.

Cbn.

Cb. solo

Example 6  The Rite of Spring, rehearsal 8

And the repeats of Ex. 5 are immediately followed by another Collection I passage at rehearsal 8 (see Ex. 6); (G, F, E, D) in the alto flute, although eventually a part of a more determinate diatonic framework, is one of six superimposed fragments in the alto flute, piccolo clarinet, clarinets, bassoons, contrabassoon, and solo double bass, the pitch-class content of which, excluding F♯ as a grace-note in the clarinets and bassoons, is entirely accountable to Collection I. Only the D♯ in the flute fragment resists the octatonic order. And this is eventually followed by the climactic block at rehearsal 10 (see Ex. 7), whose opening measures pit the same Collection I orchestra against two diatonic fragments in the clarinet piccolo and oboetrumpet. The F–B♭–G fragment reappears atop a B sustained in the “bass,” thus articulating the 0–11 vertical span in terms of (B♭, G, F)– B; crucial in this regard is the disposition of the E dominant-seventh in the strings, second inversion, with B doubled in the double basses. And with the dorian tetrachord, often (0, 2, 5) incomplete,

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as an intersecting connecting link, two diatonic fragments are superimposed over this Collection I accumulation. Note that the diatonic articulation could have implied a five-note segment of the interval 5/7-cycle as well as the overlapping dorian scales shown in Ex. 7. Ob., Tpt.

10

Picc. Cl.

etc.

5

etc.

Cl. E. Hn.

etc.

3

Bns.

etc.

etc.

etc.

Cb.

0–5 (025/035/0235) tetrachord

(

)

0–5/6, 11 intervalspan

0, 3, 6, 9

(0 2 3 5); triads, dom. 7ths

5

0 2 3 5 6 8 9 11 0 2 3 5 7 9 10 (0) D-Scale Collection I

D-scales on F andB

Example 7  The Rite of Spring, rehearsal 10

And so the question arises: if the main superimposed fragments at rehearsal 6 and at subsequent repeats of this passage refer to a single octatonic transposition (Collection I), why infer a superimposition of three different diatonic scales, as the author does in his Ex. 6(h), the D harmonic minor, the D melodic minor “centered” on B, and the G melodic minor, the latter “incomplete”? In fact, the author’s “registral partitioning” in his Ex. 6(h) is misleading, suggesting, as it does, a succession of three scales, when, far more

Stravinsky and the Octatonic

problematically, the fragments from which these scales are inferred are superimposed. Why infer a superimposition of three more diatonic scales at rehearsal 8: D minor, D mixolydian, and B melodic minor, the latter “in the seventh mode” (p. 75)? Why not show the continuity between the blocks and passages at rehearsals 6, 8, and 10 (my Ex. 4–7) by singling out the role assumed by the octatonic Collection I? And why not connect this early train of thought, octatonic and octatonicdiatonic, to subsequent rehearsal numbers, such as those cited here in Ex. 8(a) and (b)? No explanation is given for the avoidance of these exposed continuities in The Rite of Spring, or indeed for the assignment of as many as nine different diatonic scales and modes, mostly superimposed, to the passages examined at rehearsals 6, 8, and 10. 64

Vn. 1

etc. Tba.

(

) (

)

(a) rehearsal64, reductionand analysis.

132

134

Tpts.

Bn.

()

[

]

(b) rehearsals132 and 134, reductionand analysis.

Example 8  The Rite of Spring

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Stravinsky and the Octatonic

Nearly all of the author’s examples suffer from the same extreme isolation, lacking context as well as any attempt to come to terms with the materials at hand. In my own The Music of Igor Stravinsky, the passages at rehearsals 6, 8, 16–18, and 22–4 are described as “explicitly octatonic” (see van den Toorn 1983, 44–6). All four passages are shown to be “of substantial duration, relatively unimpaired by outside interference, with the collection complete or nearly so” (p. 47). “This, I submit, is not just wrong,” Tymoczko asserts, “but wrong in a way that should make us suspicious of the underlying methodology” (p. 80). But the “methodology” is not just mine (or Berger’s, or Taruskin’s, for that matter), it is Stravinsky’s as well. Transcribed in Ex. 9 are two sketches from pages 5 and 6 of Stravinsky’s sketchbook of The Rite of Spring.5 Both sketches refer to the material at rehearsal 25 in the “Augurs of Spring” (see Ex. 2), and both are discussed in van den Toorn 1987, 180. The principal diatonic fragment, (C, B♭, A, G, F), reading down, is superimposed over a tritone-related ostinato, E♭– G♭–D♭–G♭, the latter another incomplete dorian tetrachord. Although never actually employed at rehearsal 25, the incomplete tetrachord is the inversion of the prevailing ostinato, D♭–B♭–E ♭–B♭; the context is entirely octatonic, Collection III, except for the pitch F. And it is the non-intersection of this “diatonic F” that defines the nature of the octatonic-diatonic interaction: F conflicts with the tritone of the octatonic order, G♭, reading down, signaling the intervention of diatonic relations. At the same time (C, B♭, A, G) of the main diatonic fragment is the shared connecting link.

(a) p. 5

(b) p. 6

Example 9  Transcription of Stravinsky 1969, pp. 5 and 6

The vocabulary of these sketches, with its (0, 3, 6, 9) partitioning of Collection III in terms of (C, B♭, A, G), (G♭, [F♭], E♭, D♭), (E♭, D♭, 5Stravinsky

1969.

Stravinsky and the Octatonic

[C], B♭), and its diatonic intervention is unmistakable. Stravinsky appears not only to have been thinking of this framework at the time, but to have been thinking of it along the specific lines traced above and, at greater length, in van den Toorn 1983 and 1987. And to insist, as Tymoczko does repeatedly, that the framework is “wrong” or is a “misinterpretation” (p. 68) is quite simply to avoid the obvious, to bury oneself ostrich-like in the sand. The author’s use of various diatonic or non-diatonic modal scales is no different from his use of the octatonic. Given that these scales are made to embody little if anything in the way of a tradition or established practice, their assignment by the author is virtually meaningless. Tymoczko makes repeated reference to “the language of French Impressionism” (p. 68), “Impressionist influences” (p. 69), and the composer’s “French heritage” (p. 101), but in fact no evidence is produced (1) that the influence of, say, Debussy’s music on a handful of rehearsal numbers in The Rite of Spring and Petrouchka came (or comes) by way of these scales, or (2) that the materials to which these scales are assigned connect in some tangible way to Debussy’s music. Nor is such evidence likely to materialize beyond a few isolated passages. Bear in mind the unique character of much of the material in question, the “Augurs of Spring” chord at rehearsal 13 in The Rite of Spring, for example, to which the “G♯ harmonic minor scale” is assigned.6 Diatonic or non-diatonic modal scales are applied informally by Jazz musicians and theorists as well, of course, as the author notes. Typically, however, the application of these scales in Jazz circles evokes a tradition of some kind, a characteristic sonority or harmonic use. The problem here, however, is that such uses postdate the three early Stravinsky works to which the author makes reference. The “locrian ♯2” mode, assigned to rehearsals 6, 25, and 32 in The Rite of Spring, seems to have come into existence among Jazz musicians during the bebop times of the 1950s. Tymoczko himself may sense a meaningful connection between a few scattered rehearsal numbers in The Rite of Spring and, say, Dizzy Gillespie’s music, but I personally 6Repeated

references to “G♯ harmonic minor” in the author’s “overview” of the “Augurs of Spring” (see Ex. 1[b]) are misleading. They refer exclusively to the “Augurs of Spring” chord and its repeats at rehearsals 13, 14, and 18, and hence in no way to a larger connection or continuity to the movement’s remaining blocks and sections.

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do not. The larger point, however, is that such connections, implied by the author, are never pursued or demonstrated. Tymoczko should know, too, that the few occasions of overt whole-tone use in The Rite of Spring and Petrouchka are not especially “Debussian” in sound (as he implies, p. 73), and in fact owe far more to Stravinsky’s Russian predecessors than they do to Debussy or Ravel. In van den Toorn 1983, for example, the whole-tone set is listed along with the octatonic as a source of the chromaticism that accompanies the supernatural element in The Firebird (p. 5); its role has been examined in several separate studies.7 The passage quoted in Ex. 10, taken from van den Toorn 1987, 118, is from the overture to Glinka’s opera Russlan and Ludmilla (1842). It shows a descending whole-tone scale undercut somewhat by the major triads of an intersecting 6–20[014589]. (In addition to the octatonic and whole-tone sets, the 6–20 hexachord is also a set with a history among Russian composers of the second half of the 19th century.) And so the idea, mentioned by the author (p. 70), of a blunting of the whole-tone quality by outside elements can also be traced back to practices in earlier Russian music.

Example 10  Glinka, Ruslan and Ludmilla, Overture

So, too, in the “Dance of the Earth” of The Rite of Spring, the use of a whole-tone scale as a basso ostinato is not Debussian in sound or conception, but is highly individual with respect to The Rite of Spring. More to the point, such an impression of individuality could never have come from the two or so measures of the author’s Ex. 3(a), so entirely divorced are they and the three superimposed scales assigned to them from the actual context. At rehearsals, 74, 75, and 76, Tymoczko fails to acknowledge: (1) the tritone relationship between F♯ in the “bass” and the reiterated 7See,

for example, McFarland 1994.

Stravinsky and the Octatonic

(C, E, [F♯], G) triads from which the whole-tone scale in question emerges; (2) the points of intersection between this F♯ (C, E, [F♯], G) tritone relationship and the given whole-tone scale; (3) the octatonic implications (Collection III) of the same tritone relationship and the introduction of the (E♭, D♭, C, B♭) dorian tetrachord in the horns; (4) the transposition of this tetrachord along the 5/7-interval cycle to B♭ and F; (5) the derivation of the D♭–C–B♭/E♭–B♭ outline of this tetrachordal fragment from the D♭–B♭–E♭–B♭ ostinato and (E♭, D♭, B♭, G) dominant seventh in the “Augurs of Spring,” as well as from the C–B–A/D–A outline of phrase B of the opening bassoon melody (consult Ex. 11). Only by way of such connections can something of the musical sense and motivation of the “Dance of the Earth” and its principal (E♭, D♭, C, B♭) tetrachordal fragment be demonstrated. The three scales assigned by the author in his Ex. 12 are too fleeting and abstract to be of any assistance in this regard. = 50

3

3

12 + 8

13

37

“Augurs of Spring”

“Ritual of Abduction

75 + 5 “Dance of the Earth” 3

3

3

Example 11  The Rite of Spring, some motivic connections.

305

306

Stravinsky and the Octatonic

Briefly for the record: the “abuse” to which the term “polytonality” has been subject in recent years (something Tymoczko bemoans, pp. 84–5) is entirely deserved, in my view, and the more general terms introduced by the author— “independent auditory streams” or “independent tone-centers” (p. 84)—are in no way equivalent. There is little reason why an analysis of The Rite of Spring or Petrouchka should have to saddle itself with “polytonality” when “the fullest and most robust sense of tonality” (p. 84) is impossible to shake. For Berger and myself, the special attraction of the octatonic set lay not so much in its ability to circumvent concepts such as “polytonality” (as the author claims, p. 85), as in its ability to account in concrete pitch-relational terms for something of the character or “sound” of Stravinsky’s music, its quality of “clashing,” “opposition,” “stasis,” “polarity,” and “superimposition.” Far from canceling or negating such terms, subsumption of configurations such as the Petrouchka chord by the octatonic set explained them further. Tymoczko has both Berger and myself believing just the opposite, however, and managing to do so by cutting Berger off in mid-sentence. He quotes from Berger as follows: the entire configuration may now be subsumed under a single collection with a single referential order, i.e., the octatonic scale, the dubious concept of “polytonality” need no longer be invoked.

However, Berger wrote the following:

Since the entire configuration may now be subsumed under a single collection with a single referential order, i.e., the octatonic scale, the dubious concept of “polytonality” need no longer be invoked; nor does such an interpretation make it impossible to acknowledge a certain compound nature of this configuration, since this can be done entirely within the referential collection of the octatonic scale, by means of the partitions.

In other words, the “compound nature” of the Petrouchka chord and the countless configurations like it in Stravinsky’s music (the polarized or superimposed quality of the “independent auditory streams”), is more fully explained by relating it to a (0, 3, 6, 9) symmetrically defined partitioning of the octatonic set (see van den Toorn 1983, 64). The author’s avoidance of these specific pitch-

Stravinsky and the Octatonic

relational issues is part of his avoidance of the octatonic or octatonicdiatonic approach and analysis generally. In regard to the Petrouchka chord itself, Tymoczko focuses on the non-octatonic (G, B, D) triad that substitutes occasionally for (C, E, G) in its interaction with (A♯, C♯, F♯). But he ignores accounts other than the tonally functional or “polyscalar,” including my own in van den Toorn 1983, 64–6. Thus, of the two triadic subcomplexes of the Petrouchka chord, (C, E, G) may often seem to assert priority over (A♯, C♯, F♯). And this can be traced less to the distinction in chordal disposition than to the chromatic tendency-tone potential of (A♯, C♯, F♯) in relation to both (C, E, G) and (G, B, D). Thus, as often happens in Stravinsky’s music, tonality imposes itself less by any genuine functional definition of a tonality or “key,” than by the borrowing of the surface conventions of the repertory, here, the conventions of chromatic tendency: the third and fifth of (G, B, D) and the fifth of (C, E, G) are embellished by their chromatic neighbors, F♯, A♯, and C♯. And in place of an intensification of the conflict between the two subcomplexes of the Petrouchka chord (as the author would have it), the substitution of (G, B, D) for (C, E, G) actually draws the two subcomplexes together under a single fold; by way of (G, B, D), (A♯, C♯, F♯) and (C, E, G), although at times securely octatonic in terms of Collection III, are joined by way of this chromatic tendency-tone convention. Crucial here are the arpeggios in the piano at rehearsal 50 and the tremolos at rehearsal 51. Both treatments are omitted from the author’s account and “summary,” the latter which is his Ex. 12; for the passages themselves, see the present Ex. 12, reproduced here from van den Toorn 1983, 32. In sum, ... the peculiar disposition of the “chord,” the manner in which, as a tremolo at No. 51, its (A♯ C♯ F♯) component in first inversion precedes its (C E G) component in root position, allows F♯ to be heard and understood as something like a chromatic V-of-V tendency tone to the G of the (C E G) triad. But these, surely, are the limits within which the conventions of tonal practice may be inferred, or within which such conventions may be said to interact with a partitioning of the octatonic set. (van den Toorn 1983, 64.)

In fact, Tymoczko finds little evidence of octatonicism in the Petrouchka chord:

307

308

Stravinsky and the Octatonic

And is it even clear that the Petrouchka chord itself arises out of the “octatonic complex”? There is surprisingly little in the music which might tell us this: if we set aside appearances of the Petrouchka chord proper—since this is the entity we are trying to understand—then we note that in the entire second tableau, there are only four other measures of octatonic material. (These are mm. 1 and 7, and the twomeasure cadenza that precedes rehearsal 59.) (p. 88; his italics.) 49

Cls.

= 50

3

3

50

3

Pn.

3

etc. 51

77

Hns. = 108

Tpts.

= 80

Hns.

Tpts.

etc. 3

3

3

3

Str., Pn.

etc.

()

()

()

3

3

3

3

etc.

3

etc.

Str.

()

Example 12  Analysis of Petrouchka, from van den Toorn 1983, 32

48

3

Fl.

3

3

3

Example 13  Petrouchka, second tableau, opening; encircled notes are nonoctatonic

But the Petrouchka chord does in fact arise quite clearly out of an octatonic context. Had the author included the opening eight measures of the second tableau at rehearsal 48 in his account and “summary” (those that precede the first appearance of the chord at rehearsal 49), he would have found sufficient evidence of just such an emergence. A condensation of these eight measures appears in Ex. 13; the boxed-off areas refer to an explicit octatonic content (Collection III), one that includes the opening G–C–G–F♯–E–D♯ motive and the main harmonies, chords that are either sustained or that initiate or end descending chromatic motions. Significantly, the

Stravinsky and the Octatonic

two octatonic pitch classes missing from the Petrouchka chord, E♭ (D♯) and A, are very much in evidence in these opening bars, above all, E♭ (D♯). In fact, the Petrouchka chord emerges from a much lengthier hexachordal path, one that may be traced back to the beginning of the first tableau. Example 14 condenses this path from a lengthy illustration in van den Toorn 1983, 77–81. It begins with the (D–E) (A–G) tremolos of the opening bars and ends with the tremolos of the Petrouchka chord itself at rehearsal 51 in the second tableau; but it could have been extended into the third and fourth tableaux as well. Notice how closely the diatonicism of the hexachordal tremolo at rehearsal 2 approximates the Petrouchka chord: B♭ (A♯) and the (C, E, G) triad in root position are present at this point; only D of the tremolo resists the oncoming octatonic Collection III. Crucially, the distinction in disposition, with (C, E, G) of the Petrouchka chord in root position and (A♯, C♯, F♯) in first inversion, may be traced back to the B♭/(A♯)–C unit of the first tableau at rehearsal 2. My own comments on these long-range octatonic-diatonic interactions are as follows: O

= 138

Fl.

Hns.

2

51

Pn. etc.

Example 14  Petrouchka, summary of Petrouchka-chord derivation, from van den Toorn 1983, 77–81

[Retreating] to a somewhat more long-term, global, or continuously operative perspective, ... it is illuminating to interpret Petrouchka as a piece in which two simultaneities oscillate or move back and forth (accordion like, as so many have observed), a movement by no means limited to Petrouchka [insofar as Stravinsky’s oeuvre as a whole is concerned], but one which may nonetheless seem unusually conspicuous and persistent all the same. The two simultanities very often number six pitch elements, three to each. Thus, in this global, number-of-elements approach, the (0 2 3 5 7 9) hexachord of the first tableau appears as just one of several hexachordal sets or orderings. (van den Toorn 1983, 78.)

309

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Stravinsky and the Octatonic

Had the author been willing to include Chapter 3 in The Music of Igor Stravinsky in his “reconsideration” of the octatonic approach, he would have found additional support for the idea of the octatonic set conceived as a “foreground phenomenon” (p. 88) relative to a hexachordal oscillation or superimposition at a background level. Neither Berger nor I made claims as far as the second tableau as a whole is concerned. In van den Toorn 1983, only the opening section at rehearsals 48–52 and the section at 76–8 in the third tableau are judged “securely octatonic” (p. 64). Nonetheless, Tymoczko’s figures are as misleading here as they are with The Rite of Spring. It is not true that, were the Petrouchka chord itself to be set aside, “only four other measures of octatonic material” would present themselves in the second tableau. If we include the Petrouchka chord in our calculations (a much more direct way of proceeding than the one proposed by the author), at least four of explicitly octatonic content (Collection III) would present themselves at rehearsal 48, six measures of such content at rehearsal 49, and nine at 51 (the tremolos). Out of a total of thirty-nine measures in the opening section at rehearsals 48–52, nineteen are inferable as explicitly octatonic. This is far from the whole of it, however. Omitted from the author’s account and “summary” is the passage at rehearsal 77 in the third tableau. And it is precisely this passage that manages to secure the octatonic set in Petrouchka. The two triadic subcomplexes of the Petrouchka chord are transposed to the remaining and— at rehearsals 49–52– missing (C, E♭, F♯, A) symmetrically defined partitioning elements of Collection III, namely, E♭ and A; see Ex. 12. In other words, the passage at rehearsal 76, cited as “Hexatonic, 6–20” in the author’s “summary” is immediately followed by five measures of the Petrouchka chord, transposed to (B♭, E♭, G)–(A, C♯, E) and hence to within Collection III. (Notice, in this transposition, the retention of B♭(A♯) in the “bass.”) Omitted passages of this kind are difficult to dismiss as oversights on the author’s part, given not only the prominence of the excluded configurations in the score and in my own analysis in van den Toorn 1983, especially 32, 65, but also the central role they play in substantiating the octatonic component. Further, Tymoczko’s characterization of rehearsal 60 in the second tableau as (again) “Hexatonic, 6–20” is equally misleading. There are only six measures at rehearsal 60, and only two of these bars are “Hexatonic, 6–20.” The remaining four are devoted entirely

Stravinsky and the Octatonic

to the Petrouchka chord. Moreover, in the tremolo at rehearsal 60, (D, F, A) is clearly subsidiary to (A♯, C♯, F♯); the latter, retained by the Petrouchka chord, is clearly the stabler segment. (Here again, omissions and mischaracterizations of this kind are not easily dismissed as oversights, given the prominence of the excluded material. Crucial evidence is withheld from the author’s “summary,” and in ways that greatly distort the context of the Petrouchka chord.) The “sophisticated,” “pluralist,” and “multifaceted” features to which Tymoczko refers in his concluding remarks (pp. 96–100) have been discussed at length by, among others, Berger, Taruskin, and myself. The problem with his account, however, is not that the four works in question are portrayed as “pluralist,” but that they are portrayed as utterly incoherent. Is it quite seriously the author’s contention that his account and “overview” of, say, the opening sections of The Rite of Spring bear on experience? Is it his contention that this is, in fact, how the listener as well as the analyst make sense of this music? Bear in mind, however, that my complaint is not perceptual alone. The author’s account has little if anything to do with the actual materials. It has little or no basis in perceptual, compositional, or historical fact. A piece such as The Rite of Spring may be unsystematic in the large, exhibit little in the way of an all-encompassing outline in its transpositional path (see my analytical sketch and concluding remarks on this subject in van den Toorn 1987, 186–9). But this does not mean that the piece is dysfunctional, that it is disorganized or unintelligible. On the contrary, much of The Rite of Spring exhibits a remarkable continuity (even progress in places), a remarkable consistency in its melodic and harmonic materials and in the referential bases of those materials. The author has chosen to ignore this, including the nature of the octatonic content. And it is therefore hardly surprising that the analytic-theoretical view that results should be insubstantial. Small wonder, then, the author’s sense of a lack of construction in Stravinsky’s music, a lack of structure or “system.” I cannot let pass the faddish buzz words that adorn the final pages of his argument, however—words to the effect that, next to his own appreciation of Stravinsky’s diversity and “pluralism,” my own account is “essentialist” (p. 100). Such words will excite today’s powers that be, I have little doubt, those purveyors of trendy academic socio-babble, but in reality they testify to his ignorance not only of

311

312

Stravinsky and the Octatonic

the octatonic and octatonic-diatonic approaches to Stravinsky’s music, but also of the analytical process and its relationship to perception generally. Berger’s essay of 1963 is still something of a miracle to me, a lucid oasis in what was at the time a mount of confusion and “polytonality.” I have criticized Taruskin 1996, but only in small ways (see van den Toorn 2000). The influence of Rimsky-Korsakov’s music seemed to me too heavily drawn by Taruskin in places, and there were a number of socio-political stands that seemed strained as well. Yet the depth and comprehension of Taruskin’s achievement is surely nothing short of spectacular. In my own The Music of Igor Stravinsky (van den Toorn 1983), the emphasis on the octatonic may have been drawn a bit too heavily where it concerns the composer’s neoclassical works—too heavily and at the expense of other important neoclassical concerns. But while this may be true with Stravinsky’s works of the 1920s and 30s, it is not true with those of the 1940s. Stravinsky’s arrival in America and especially in California triggered the octatonic imagination in new and unexpected ways, as is evident in works such as Babel (1944), The Symphony in Three Movements (1945), the Ebony Concerto (1945), the string Concerto in D (1946), and the ballet Orpheus (1947). As a parting sample of this final neoclassical epoch, see the configuration at rehearsal 56 in Danses Concertantes (1942), shown here as Ex. 15, so entirely evocative is this of the Petrouchka chord some thirty years earlier; see, especially, the B♭/ A♯ in the “bass.” I like to count this as an example of the composer’s “pluralism.” 56

etc.

etc.

Example 15  Stravinsky, Danses Concertantes (1942), rehearsal 56

etc.

etc.

Stravinsky and the Octatonic

Octatonicism Reconsidered Again* Dmitri Tymoczko

My earlier article made two central claims about Stravinsky’s music. First, I argued that Stravinsky, like Debussy and Ravel, used the modes of the non-diatonic minor scales. To this end I provided more than a dozen examples of such scales in Stravinsky’s early music, the longest of which rivals in length and explicitness any of the octatonic passages in The Rite of Spring. My second claim was that Stravinsky’s music is animated by a broad range of polyscalar superimpositions involving more than just the octatonic and diatonic scales. I further suggested that scales in Stravinsky are sometimes surface phenomena, produced by underlying superimpositions that do not conform to any single collection. Here I provided several examples where it seemed to me that focusing on scales (in particular, focusing on the octatonic scale) hindered real musical understanding. Finally, in the course of making these positive points, my article raised several methodological questions about Pieter van den Toorn’s analytical procedures. I pointed out, for example, that any proper subset of the chromatic scale can be decomposed into octatonic and diatonic components, and I challenged van den Toorn to explain when such decompositions are musically significant. Furthermore, I argued that the notion of “polytonality,” repeatedly dismissed as inconsistent by van den Toorn, has a perfectly useful meaning, and that it can be applied to actual music, Stravinsky’s included. Implicit in these points was a challenge that van den Toorn refine and develop his critique of polytonality, a critique which he has carried out mainly by way of citations to Benjamin Boretz and Allen Forte. I am disappointed that van den Toorn’s long response does not take up any of these issues. Instead, like a defense lawyer with a weak case, he chooses to impugn the witness’s credibility rather than deal with the substance of the testimony. I do not begrudge the aggressive tone of his reply; it is natural to become personally invested in one’s scholarship. And if I am right, then much of van den Toorn’s work is misdirected. I am, however, concerned about the numerous inconsistencies and misrepresentations in van den Toorn’s response. *Reprinted from Music Theory Spectrum, Vol. 25, No. 1 (Spring 2003).

313

314

Stravinsky and the Octatonic

For these muddy the intellectual waters, preventing readers from making a reasoned choice between my arguments and his. I will not try the reader’s patience by enumerating all the various ways in which van den Toorn manages to cloud the issues between us, but here are a few pertinent examples. 1. Referring to my discussion of Petrouchka’s second tableau, he writes: It is not true that, were the Petrouchka chord to be set aside, “only four other measures of octatonic material” would present themselves in the second tableau. If we include the Petrouchka chord in our calculations (a much more direct way of proceeding than the one proposed by the author), at least four measures of explicitly octatonic content (Collection III) would present themselves at rehearsal 48, six measures of such content at rehearsal 49, and nine at 51 (the tremolos). Out of a total of thirty-nine measures in the opening section at rehearsals 48–52, nineteen are inferable as explicitly octatonic.

I claim that, besides the Petrouchka chord, there are only four other measures of octatonic material in the ballet’s second tableau. Van den Toorn responds that this is false, arguing that if we count the Petrouchka chord, we find more than four measures of octatonic material. This is logically incoherent. Further, van den Toorn includes in his count, not just fifteen measures of the Petrouchka chord (rehearsals 49 and 51), but also several measures where almost half of the notes are non-octatonic (see his Ex. 13). None of this shows that I have said anything false.8 2. Writing about the sixth mode of the melodic minor scale, which Jazz theorists call the “locrian ♯2” scale, van den Toorn says: Diatonic or non-diatonic modal scales are applied informally by Jazz musicians and theorists as well, of course, as the author notes. Typically, however, the application of these scales in Jazz circles evokes a tradition of some kind, a characteristic sonority or harmonic use. The problem here, however, is that such uses postdate the three early

8It may be that van den Toorn wants me to include measures 2 and 8 as octatonic. My original account did not include them, since no actual pitches are attacked in these measures. However, I am happy to concede the point, in which case there would be six measures of octatonic material (other than the Petrouchka chord) in the scene. From the standpoint of my larger argument, the difference between four and six measures is not significant.

Stravinsky and the Octatonic

Stravinsky works to which the author makes reference. The “locrian ♯2” mode, assigned to rehearsals 6, 25, and 32 in The Rite of Spring, seems to have come into existence among Jazz musicians during the bebop times of the 1950s.

This confuses the name of a thing with the thing itself. It is probably true that the term “locrian ♯2” came into existence in the last fifty years. However, the object, the mode itself, has been in use for nearly a century. In his “Étude comparée des langages harmoniques de Fauré et de Debussy,” François Gervais finds the mode in Debussy’s Pelleas. In “The Consecutive Semitone Constraint: A Link Between Impressionism and Jazz,” I provide two other examples of impressionist use of the “locrian ♯2 mode,” both of which predate The Rite of Spring. That article explicitly discusses the relation between the impressionist and Jazz treatment of nondiatonic minor scales, and suggests that the former may have influenced the latter.9 3. Van den Toorn writes: In my own The Music of Igor Stravinsky, the passages at rehearsals 6, 8, 16–18, and 22–4 are described as “explicitly octatonic.” All four passages are shown to be “of substantial duration, relatively unimpaired by outside interference, with the collection complete or nearly so.” “This, I submit, is not just wrong,” Tymoczko asserts, “but wrong in a way that should make us suspicious of the underlying methodology.”

Van den Toorn quotes me completely out of context here, misrepresenting my point. The sentence he cites refers not at all to his analysis of rehearsals 16–18 and 22–4 of The Rite of Spring, and only secondarily to his analysis of rehearsals 6 and 8. What I wrote was: Nevertheless, van den Toorn has analyzed most of these passages [i.e., most of the passages in Stravinsky’s early music that involve modes of the nondiatonic minor scales10] as resulting from the combination of octatonic and diatonic materials. This, I submit, is not just wrong, but wrong in a way that should make us suspicious of the underlying methodology. For Examples 5(a) [rehearsal 35 of Petrouchka] and 6(a) [rehearsals 32–36 of The Rite of Spring] are near-incontrovertible instances of modal use of the melodic minor scale; if even these passages

9At

no point have I claimed that the locrian ♯2 mode entered jazz before 1940. 5(a) and (b), 6(a), (b), (e)–(g), 7(a), and 7(b) in my original article.

10Examples

315

316

Stravinsky and the Octatonic

can be interpreted as the result of “octatonic-diatonic interaction,” then we should rightly ask whether there is any music that cannot be understood in this way.

The last sentence is the crucial one, I should think. While my earlier article acknowledged that readers might not agree with all my analyses, I suggested that some of them—such as my analysis of rehearsal 35 of Petrouchka, and rehearsals 32–6 of The Rite of Spring—were “near-incontrovertible.” (For a justification of this claim, see below.) It was van den Toorn’s misreading of these explicitly melodic-minor passages that prompted my doubts about his analytical methodology. Under the circumstances, I am disappointed that he did not see fit to discuss either the doubts or the analyses that prompted them. 3

3

16 3

3

3

3

Example 1  Van den Toorn’s reduction of The Rite of Spring, rehearsals 16–17

Incidentally, van den Toorn is wrong to describe rehearsals 16–17 of The Rite of Spring as “explicitly octatonic.”11 Indeed this music is arguably not octatonic at all. Example 1 presents van den Toorn’s reduction of the passage, as it appears in The Music of Igor Stravinsky. Example 2 presents a more complete summary. Van den Toorn’s analysis silently leaves out every non-octatonic element in the music—the ostinato bass, the bassoon’s trilling C♮, and the blaring stacks of fifths in the brass and winds.12 Example 3 shows how these elements suggest two different diatonic collections. The upper-register fifths, coupled with the bassoon trill and the viola 11Van

den Toorn’s repeated description of rehearsal 18 as “explicitly octatonic” is a mistake. Rehearsal 18 is virtually identical to rehearsal 13, a passage which van den Toorn does not describe as explicitly octatonic. 12Van den Toorn 1987 continues to omit the ostinato bass, restoring the stack-of-fifth chords only in the last two measures of rehearsal 17.

Str.

E.Hn.

Bsn.

Vla.

(

16

)

3

3

3

3

Example 2  The Rite of Spring, rehearsals 16–17 (continued)

Ob.

Brass

Cl.

3

Fl.

3 3

3

3

3

Stravinsky and the Octatonic 317

7

(

)

(

)

3

3

17

3

3

3

3

3

3

Example 2  (continued)

3

3

3

3

3

3

Str., Brass

Str., Brass

3

3

3

3

318 Stravinsky and the Octatonic

Stravinsky and the Octatonic

arpeggios, set the descending flute tetrachord (C–B♭–A–G) in a C mixolydian context. The ostinato fifths in the low strings suggest an E♭ dorian reading of the English Horn figure. Example 3 further shows how the two scales are almost completely separated in register: the only points of overlap are the C-mixolydian notes C4 and D4, which lie below the E♭ dorian D♭4 and E♭4. Finally, the second measure of Ex. 3 represents the total pitch content of the passage as a gapped stack of fifths, with only a missing A♭ needed to connect the English Horn’s D♭ to the strings’ E♭.13 C mixolydian

E dorian

(

)

Example 3  An analysis of the pitch structure of rehearsals 16–17 of The Rite of Spring

Clearly, it is wrong to describe this (fifth-based) music as “explicitly octatonic,” where that description implies that the music is “relatively unimpaired by outside [i.e., nonoctatonic] interference.” If blaring diatonic trumpets do not constitute substantial outside interference, then nothing does. Van den Toorn also misreads me in a number of other, smaller ways. He seems to interpret my Ex. 12 as an attempt to provide a harmonic summary of the sort found in my Ex. 10, 15 and 20. But this table only attempts to chart the development of the Petrouchka chord proper, rather than summarize Petrouchka’s second tableau. Likewise, van den Toorn interprets my assignments of nondiatonic scales in Ex. 10, 15, and 20 (and in the example captions throughout the article) as implying judgments about pitch-class priority. They do not.14 There are many more misinterpretations to be found 13Harrison

1997 explores a similar passage in Milhaud that can be read as both a single stack of fifths, and as a combination of two different diatonic components. 14Here, I bear a good part of the responsibility for the misunderstanding. My assignment of diatonic scales in Ex. 10, 15, and 20 does attempt to indicate pitch-class priority through the use of mode names. My assignment of nondiatonic scales does not indicate pitch priority, that issue being either unresolved or discussed in the text. The inconsistency results from the fact that there are no agreed-upon names for the modes of the nondiatonic minor scales. I regret that I was not clearer about this issue in the original article.

319

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Stravinsky and the Octatonic

in the response, but I will not take up the reader’s time detailing them. Instead, I propose to turn to some of the larger, and more theoretically interesting, disagreements that separate the two of us.

Stravinsky’s Scales

My earlier article offered numerous examples to support the claim that Stravinsky used the modes of the nondiatonic minor scales. I had expected van den Toorn to concede the point, while challenging its significance. For example, he might have argued: 1. that Stravinsky’s use of the scales is relatively infrequent, and confined to his earlier works;15 or

2. that these scales themselves can be accounted for “at a deeper structural level” as combinations of octatonic and diatonic elements.

Instead, he chose a riskier path. He suggests that these scales do not appear in Stravinsky’s music, but are merely the products of my overheated analytical imagination.

Example 4  The “Infernal Dance of King Kastchei” (melody only)

Consider Ex. 4, which presents the melody of the first twentysix measures of the The Firebird’s “Infernal Dance.”16 Example 5 proposes three possible interpretations of this passage. The first, which I favor, portrays the music as involving the fourth mode of the E harmonic minor scale. The second, shown in Ex. 5(b), suggests that the passage involves the traditional dorian mode plus one “non-harmonic” D♮. (The postulated diatonic D♮ does not appear in the music.) Example 5(c) follows van den Toorn in analyzing the passage as resulting from the combination of the diatonic and octatonic scales.17 The pitches A, C, D♯, E, F♯, and G are interpreted 15This

is a point that I, in turn, am prepared to concede. example omits the accompanying A drone and the punctuating A–E orchestral chords. 17See van den Toorn 1983, 18. 16The

Stravinsky and the Octatonic

as belonging to octatonic Collection III; the pitches A, B, C, E, and G, are interpreted as belonging to the A natural minor scale. (Again, the diatonic D♮ and F♮ as well as the octatonic B♭ and C♯, do not appear in this passage.) (

)

Example 5  Three interpretations of the “Infernal Dance,” mm. 1–26

Readers may ask how we can decide among these interpretations. Following my original article, we might cite three different considerations. First, the harmonic-minor interpretation is more parsimonious than the others: it accounts for all the pitches in the passage, and postulates none that do not appear. Second, the harmonic-minor interpretation is supported on historical grounds: the harmonic minor scale is a familiar musical object, one that Stravinsky obviously knew; and he had available examples of modal uses of the non-diatonic minor scales in the music of Debussy and Ravel. Finally, the numerous examples that I provided in my original article provide a third sort of evidence. I hoped there to convince readers, by dint of sheer quantity, that the many occurrences of nondiatonic minor modes could be attributed neither to mere coincidence nor (as van den Toorn would have it) to incompetence on my part. Nevertheless, readers may still feel that these three types of evidence are not absolutely compelling. We may have reasons—for instance, van den Toorn’s analysis of the entire Stravinsky corpus— to favor the less parsimonious interpretations given by Ex. 5(b) and (c). Is there anything more definitive that can be said in this regard? There is. We need the concept “scale” because we need the notion of scalar transposition to explain how this passage works.18 As Ex. 6 shows, the second 8-measure phrase of the melody shifts the corresponding pitches of the first phrase up by two scale degrees. (The one exception is the last eighth note of the third bar of the example, where the upper melody would need an E♮ for the 18I

use “scalar transposition” as an alternative to the more typical “diatonic transposition,” since the underlying scale here is nondiatonic.

321

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Stravinsky and the Octatonic

scalar transposition to be exact.19) In order to express this fact, we need to treat the E harmonic minor scale as a genuine musical object. Specifically, we need to understand the scale’s E♭ as a fourth scale degree—as a D♯—rather than a non-harmonic tone or a tone belonging to a background octatonic collection.20 To do otherwise is to forgo our ability to account for the parallelism, the transpositionwithin-a-scale, that links the two phrases of Ex. 4. Scale degree: 2

3

1

3

5

4

1

3

5

4

3

4*

7

6

3

1

4

4

5

3

5

7

6

(3)

5

7

6

5

7*

2

1

5

3

6

( )

Example 6  Kastchei’s melody as scalar transposition

What is therefore lacking in the analyses given by Ex. 5(b) and (c) is the sense that the resultant pitch collection has any unity or structure of its own. As analysts, we need to be able to say that E♭ is a step above C♮, just as B is a step above A. But this is not true of Ex. 5(b)’s 8-note collection. Nor is it true of Ex. 5(c)’s octatonic and natural minor scales. Furthermore, it is not true that arbitrary superimpositions of octatonic and diatonic elements will produce a scalar resultant. Thus, even if we were to favor an analysis along the lines of Ex. 5(c), we would need to acknowledge that Stravinsky’s particular octatonic-diatonic superimposition is special precisely in that it has scalar qualities. This is tantamount to acknowledging that there is an important level of description in which this music involves the harmonic minor scale, rather than the octatonic and diatonic scales. Many of the same points can be made about the end of The Rite of Springs “Dance of the Adolescents.” I take it that no one would substitution of E ♭ for E in this passage produces a subtle musical pun. In measures 7–8 of Ex. 4, the E♭ produces an exact chromatic sequence: A–C–E–E♭ becomes C–E♭–G–F♯. But the diatonic sequence is destroyed, since scale degrees 1–3– 5–4 are now answered by 3–4–7–6. What permits this subtle play between diatonic and chromatic transposition is the fact that two (acoustic) triads can be built on the sixth degree of the harmonic minor scale. 20Note that Stravinsky consistently spells this “fourth scale degree” as an E♭. I do not take this to be a significant difficulty; what is important is how the note behaves, not how it is written. 19The

Stravinsky and the Octatonic

question that Ex. 7(a), which occurs after rehearsal 48, involves a scale—I hear it as B♭ natural minor, despite the low E♭ bass. We need the concept “scale” to explain that the trumpet part consists of parallel second-inversion seventh chords: what makes these chords “parallel” is that they are all related by diatonic transposition; and what makes them “seventh chords” is that they can all be expressed as a stack of three thirds relative to the underlying (B♭ natural minor/E♭ dorian) diatonic collection.21 In much the same way, we want to say that the viola part consists in a descending scale (a unidirectional pattern of notes, each related by scale-step to the one that comes before it), and that the second time this pattern occurs it is doubled at the third (i.e., it occurs in conjunction with its diatonic transposition). Without the concept “scale,” and its concomitants “scale-step” and “diatonic transposition,” we simply have no access to these analytically obvious facts. Likewise, I take it as completely uncontroversial that Ex. 7(b) involves two scales. The top four lines are in A natural-minor; they are a chromatic transposition of the immediately preceding Ex. 7(a). The lowest musical voice moves stepwise along the chromatic scale.22 Now consider Ex. 7(c). All the factors that lead us to see scales in Ex. 7(a) and (b) are present here as well. There are parallel seventh chords in the horns (and eventually, strings); ascending stepwise runs in the viola and violins (eventually doubled at the third, fifth, and seventh); and, most interestingly of all, there is octave-displaced stepwise bass motion of the sort found in Ex. 7(b). Here, however, the stepwise chromatic motion of (b) has become the stepwise melodic minor motion of (c). (Such scale-to-scale transformations are explored in Matthew Santa’s article “Defining Modular Transpositions.”23) Again, all of these notions—“parallel,” “doubled,” “seventh chord,” and “stepwise”—implicitly involve the concept of transposition-within-a-scale. In addition, we need the concept “scale” not just to explain the internal consistencies of the passage, but also to explain how this music relates to that of (a) and (b). For the parallel seventh chords in the horns in (c) are the same 21Note

that the notion of a “third” itself involves the notions of scale-step and scalar transposition. 22This stepwise chromatic motion is somewhat obscured by Stravinsky’s characteristic octave displacements. 23Santa 1999.

323

Hn., Cb.

Str.

Ob., E.Hn.

Ob.

Fl.

Str.

Tbn.

Tpt.

Fl.

Example 7(b)  The Rite of Spring, rehearsal 31

Example 7(a)  The Rite of Spring, rehearsal 28+4

Vla.

324 Stravinsky and the Octatonic

Vc., Cb.

Vla., Vln.

Hn.

Tpt., E.Hn.

Fl.

Example 7(c)  The Rite of Spring, rehearsal 32

Stravinsky and the Octatonic 325

326

Stravinsky and the Octatonic

sort of musical object as the parallel seventh chords in the trumpets in (a), just as the ascending scales (doubled at the third, fifth, and seventh) in the strings of (c) are the same sort of musical object as the descending scales (doubled at the third) of (a). Van den Toorn would evidently have us forgo all of these observations simply because the scale in (c) is neither diatonic nor octatonic. To me this is plainly unacceptable. It is obvious that (c) involves a scale, and the analyst can deny it only at the cost of his own credibility.

Polytonality and Superimpositions

The second major point at issue concerns the disputed notion “polytonality.” Van den Toorn has been very blunt in his attacks on this concept, describing it as a “real horror of the musical imagination,” one that is “too fantastic or illogical to be of assistance.”24 But it is not clear exactly why he thinks this. In large part, this is because he has never articulated his difficulties with the concept, preferring instead to cite other authors—Benjamin Boretz and Allen Forte, whose views on this question are by no means clear—rather than explaining his concerns directly.25 Arguments from authority, however, can be made on both sides of this issue: while it is true that some writers have dismissed the notion of polytonality, a much larger group of theorists, including Arthur Berger and Richard Taruskin, believe “polytonality” to be a coherent concept.26 Clearly, what is needed is not polemic, but a careful consideration of the underlying issues. Unfortunately, such consideration is beyond the scope of this response. What I suggested in my earlier article, and what I hope to argue at length elsewhere, is that the phenomenon of auditory stream-segregation is crucial to explaining polytonality.27 (Contrary to what van den Toorn suggests, I offered the term “independent auditory streams” not as a replacement for the notion of “polytonality,” 24Van

den Toorn 1983, 63–4.

25The passages van den Toorn cites are Forte 1955, 137 and Boretz [1972] 1995, 244. 26See

Taruskin [1987] 1990. Berger, in a personal communication, allows that “polytonality” is a legitimate analytic concept, and even agrees that it is reasonable to provide a polytonal analysis of the Petrouchka chord. He continues to prefer the octatonic explanation, however. In this context, I should mention that Berger has some serious reservations about van den Toorn’s views. I regret that my earlier article overstated the degree of agreement between them. 27Interested readers can view a summary of the argument at http://music.princeton. edu/~dmitri/polytonality.pdf

Stravinsky and the Octatonic

but as a component in the explanation of the phenomenon.) It seems to me that a reasonably flexible notion of “tonality,” coupled with a clear understanding of the facts of auditory perception, suffices to place the concept of “polytonality” on a firm footing. But this is a matter for another paper. Instead, let me focus on the specific analytical issues. Van den Toorn writes: For Berger and myself, the special attraction of the octatonic set lay not so much in its ability to circumvent concepts such as “polytonality” (as the author claims, p. 85), as in its ability to account in concrete pitch-relational terms for something of the character or “sound” of Stravinsky’s music, its quality of “clashing,” “opposition,” “stasis,” “polarity,” and “superimposition.” Far from canceling or negating such terms, subsumption of configurations such as the Petrouchka chord by the octatonic set explained them further. Tymoczko has both Berger and myself believing just the opposite.

This is yet another misrepresentation. The question was never whether van den Toorn’s analyses acknowledged the existence of superimposed pitch-centers, or multiple “polarities.” Rather, it was whether van den Toorn correctly understands the nature of Stravinsky’s superimposition technique. Here, there are a number of related points that need to be distinguished. The first has to do with the types of “polarities,” or superimposed pitch-centers, to be found in Stravinsky’s music. Because van den Toorn is concerned to “explain” Stravinsky’s superimpositions in terms of the octatonic scale, he almost always identifies contrasting pitch-centers that are a minor third or tritone apart. These are the intervals by which the octatonic scale can be transposed onto itself, and music that features such superimpositions can therefore be portrayed (rightly or wrongly) as expressing the symmetry of an underlying octatonic collection.28 The problem is that Stravinsky’s music contains superimpositions at many other intervals. Example 8, which occurs at rehearsal 94 of The Rite of Spring, involves five28It

was just this feature of van den Toorn’s analyses that led me to suggest that for him, scales precede superimpositions: the nature of the octatonic scale determines the types of superimpositions that he allows. So while it is true that his analyses often portray the octatonic scale as growing out of superimposed pitch-centers, it is also true that he tends to consider only superimpositions that conform to the octatonic scale’s symmetries.

327

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note minor-scale fragments that are a major seventh apart.29 This passage (which is not analyzed by van den Toorn) is to my mind an extremely clear example of non-octatonic polytonality. (One wonders: if Ex. 8 is not explained by the octatonic scale, then in what sense does the octatonic scale explain minor-third or tritone-related superimpositions? It seems that van den Toorn must forgo the project of providing a single, unified account of superimpositions in Stravinsky’s music.) Example 8  The Rite of Spring, rehearsal 94.

The second analytical issue concerns the content of Stravinsky’s superimpositions. Van den Toorn allows that Stravinsky’s music uses more than one scale at a time, but he limits himself to just a few possibilities: the combination of octatonic and diatonic elements, and (more rarely) the combination of multiple diatonic, or multiple octatonic, collections. By contrast, I think Stravinsky’s superimpositions involve a much broader range of material, including chromatic, whole-tone, pentatonic, and the nondiatonic minor scales. Crucially, I also believe that Stravinsky’s superimpositions often involve non-scalar elements. Example 9(a), from the end of The Rite of Spring, is perhaps intermediate between these two possibilities. Measures 1–3 and 6–7 are completely octatonic, as are the bottom two systems throughout. But on top of this is superimposed a contrasting layer, registrally and timbrally distinct from the octatonic material. As Ex. 9(b) shows, the pitch content of this layer consists of the notes B♭–C–D♭–E–F–G. These notes comprise six of the seven notes of the fourth mode of the harmonic minor scale, the very mode which we encountered earlier in The Firebird’s “Infernal Dance.” (Indeed, the harmonic-minor scale’s characteristic half step-augmented secondhalf step pattern is clearly articulated by the four highest pitches in the figure.) While we may not have conclusive reasons for treating this material as scalar, we can confidently declare that it is neither octatonic nor diatonic. This alone should convince us that van den Toorn’s categories are inadequate. similar superimposition appears at the beginning of Stravinsky’s Concertino for String Quartet.

29A

octatonic+ ?

octatonic+ ? octatonic

Example 9(b)

(similar to B dorianwith a raisedfourth degree)

gappedscalefragment

Example 9(a)  The Rite of Spring, rehearsal 194+2

octatonic

Stravinsky and the Octatonic 329

330

Stravinsky and the Octatonic

The final analytical point at issue concerns the relative priority of scales and superimpositions. I have argued that the appearance of scale-fragments in Stravinsky’s music is often a relatively unimportant musical phenomenon, the mere byproduct of a more fundamental process of superimposition. Example 10 demonstrates. Here, I have provided a reduction of the first forty-four measures of the third movement of the Symphony of Psalms. The reduction suggests that there are two independent musical processes in play: the melodic notes, given by the closed unstemmed note heads, consist almost entirely of pitches drawn from the C natural-minor scale. (The one exception is the strings’ low F♯, which can perhaps be heard as a chromatic lower neighbor.) The harmonic material, given by the open noteheads, involves a series of three major triads that ascend by whole step. It does not take too much in the way of Fernhören (or controversial quasi-Schenkerian thinking) to understand this passage as a unified gesture, superimposing a single C-minor scale with a series of triads foreign to that collection. As can be seen from Ex. 10, van den Toorn considers two passages in this music to be “explicitly octatonic.” The first involves the four notes C–E♭–E♮–G, a “minor/major” 4–17[0347] tetrachord; the second involves the five notes E–F–G–G♯–B. Two aspects of this identification are disturbing. First, the octatonic subsets in question are relatively small, and their identity as octatonic is open to question. (Remember that for van den Toorn, “explicitly octatonic” is supposed to imply that the octatonic collection in question is “complete or nearly so.” Four or five notes do not form a “nearly complete” octatonic collection, even under the most generous interpretation.) Second, and more importantly, it is not clear that the fact that these passages involve octatonic subsets is musically relevant. Consider, for example, the relation between the allegedly octatonic material at 40, and the music which immediately precedes it. The F–G bass alternation at 40 clearly grows out of the C–A♭ –D–G alternation in m. 39; likewise, the E-major triad at 40 is directly related to the D-major triad in mm. 37–9. Van den Toorn’s analysis seems to suggest that we should take seriously the total vertical sonority at m. 40, but not in the immediately preceding measures. I can see little reason for this, other than a prior theoretical commitment to the centrality of the octatonic scale in Stravinsky’s music. Here, such a commitment

Stravinsky and the Octatonic

distracts us from the more important, long-range processes at work in the music. m. 4

29

(

37

40

44

)

vdT: octatonic

vdT: octatonic

Example 10  Middle ground polyscalarity in the Symphony of Psalms III, mm. 1–44

In summary, I have argued that Stravinsky uses a much broader range of superimpositions than van den Toorn allows. Some of them involve polarities that do not suggest underlying octatonicism; some involve elements that are neither octatonic nor diatonic; and still others produce scalar subsets as a relatively unimportant byproduct of deeper musical processes. Unfortunately, there is nothing in van den Toorn’s response that leads me to think he has considered any of these points.

Conclusion: Stravinsky in History

The many disagreements between van den Toorn and myself coalesce into two distinct pictures of Stravinsky’s place in the history of music. Van den Toorn has portrayed Stravinsky as a relatively isolated figure, an idiosyncratic composer whose peculiarly Russian syntax bears little resemblance to that of other Europeans. By contrast, I am offering a picture of the composer that is more open, one that links Stravinsky backward to French impressionism, and forward to the music of the many musicians who were influenced by him. For example: van den Toorn has argued that the whole-tone music at rehearsal 100 of Petrouchka has little to do with Debussy, preferring to see it as the product of an indigenous Russian tradition that begins with Glinka.30 I find this doubly unconvincing. First, Glinka tends to use the whole-tone scale melodically, rather 30Taruskin

also denies that this passage owes anything to Debussy, arguing instead that it represents Stravinsky’s attempt to capture the sound of a six-note equaltempered Russian folk flute. See Taruskin 1996, 710.

331

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Stravinsky and the Octatonic

than harmonically, as van den Toorn’s own example shows.31 The Petrouchka music, however, follows Debussy’s practice, in which the whole-tone scale provides the total pitch-content for an extended passage of music. Second, van den Toorn acknowledges Debussy’s influence on The Firebird, including its several wholetone passages.32 This suggests a rather unsatisfying story in which the Firebird’s whole-tone music was influenced by Debussy, but Petrouchka’s was not. Common sense, to say nothing of Stravinsky’s explicit testimony, suggests that Debussy continued to influence the language of Stravinsky’s second and third ballets. 3

3

Example 11  Charlie Parker quoting The Rite of Spring

a) Rite ofSpring,R9

b) McCoy Tyner, PassionDance

5

Example 12  Fourths in Stravinsky and Jazz

Van den Toorn’s rejection of Debussy’s influence is symptomatic of his general tendency to isolate Stravinsky from the larger currents of twentieth-century music history. Particularly instructive is his inability to hear any relationship between Stravinsky and modern jazz. There is abundant evidence linking Stravinsky to jazz, including direct testimony (from musicians such as Coleman Hawkins, Charlie Parker, and Joe Henderson), explicit musical quotation (see Ex. 11), and internal musical evidence (such as Ex. 12, which compares a fourth-based passage from the Rite of Spring to a fourth-based 31In

Ex. 10 of his response, the whole-tone scale serves as a bass line for a triadic progression that includes numerous non-whole-tone notes. This has long been recognized as the hallmark of Russian whole-tone practice. 32Van den Toorn writes “Tymoczko should know, too, that the few occasions of overt whole-tone use in The Rite of Spring and Petrouchka are not especially ‘Debussian’ in sound.” I take this to concede that the whole-tone passages in The Firebird are indeed Debussian.

Stravinsky and the Octatonic

melody by McCoy Tyner).33 In addition, an equally large body of evidence suggests indirect links between Stravinsky and jazz. Stravinsky influenced Hindemith, who in turn influenced many seminal jazz musicians. Stravinsky’s music was an important source for Slonimsky’s Thesaurus of Scales and Melodic Patterns, a book that Coltrane, among others, studied.34 Finally, as I have argued, Stravinsky was influenced by Debussy and Ravel, composers who had an incalculable impact on the syntax of modern jazz.35 To the extent that we deny, or fail to hear these relationships, we miss out on a crucial part of the history of twentieth-century music. Consider also in this context the consequences of van den Toorn’s rejection of polytonality. It is a historical fact that many composers in the twentieth century took themselves to be composing polytonal music, and that many of these believed Stravinsky to be the inventor of the technique. Van den Toorn is forced to conclude that this whole compositional tradition is based on a misunderstanding. He would presumably argue that later twentieth-century composers misheard Stravinsky’s octatonicism as polytonality, producing music that had little do Stravinsky’s actual procedures. I find this view unpalatable. It seems to me that a passage like Ex. 13, from the end of Bartok’s Fifth String Quartet, may derive from passages like Ex. 8, above. In Ex. 8, Stravinsky superimposes two different versions of a diatonic tune at the interval of a major seventh; in Ex. 13, Bartok “harmonizes” a B♭-major tune with an accompaniment in A major. In my view, the similarity between these passages provides a potential example of Stravinsky’s influence on later composers. Yet this sort of influence does not sit easily within van den Toorn’s octatonic-centered framework. Indeed, by rejecting “polytonality,” and interpreting Stravinsky solely through the lens of “octatonic-diatonic interaction,” he has deprived himself of the resources to understand it. 33For

Coleman Hawkins and Stravinsky, see DeVeaux 1997, 449. Charlie Parker mentions both Hindemith and Stravinsky in Levin & Wilson 1949. For Joe Henderson, see The New Grove Dictionary of Jazz, s.v. “Joe Henderson.” For an interesting discussion of a Woody Herman quotation of Petrouchka, see Deveaux 1997, 360 n. 20. The Rite of Spring quotation in Ex. 13 is taken from a 1949 recording of “Cool Blues.” A transcription appears in Owens 1974, vol 2, 337. Finally, note that I do not mean to imply that Stravinsky’s Rite of Spring directly influenced McCoy Tyner’s Passion Dance, only that the two musicians shared musical concerns. 34See Demsy 1991. 35See Tymoczko 1997.

333

pizz.

Example 13  Bartók, Fifth String Quartet, movement 5, mm. 711–20

334 Stravinsky and the Octatonic

Stravinsky and the Octatonic

Ultimately, these historical issues will be decided by the theoretical community’s analytical conclusions about Stravinsky’s music. But it is also possible to let the historical issues influence our choice of analytical procedures. Van den Toorn’s Stravinsky is a composer largely concerned with his own idiosyncratic musical technique, engaged in a cryptic process of octatonic-diatonic synthesis, a process that remained almost completely misunderstood until van den Toorn decoded it. My Stravinsky is a much less complicated figure, a composer whose techniques are directly manifested on the surface of his music. This may mean that I am, in the end, a less original and sophisticated analyst than van den Toorn. But it also means that my Stravinsky is much closer to the one that had such a profound influence on the history of twentieth-century music.

References

Boretz, Benjamin. [1972] 1995. “Meta-Variations, Part IV: Analytic Fallout (1).” In Volume 1 of Meta-variations/ Compose Yourself. Red Hook: Open Space. Originally in Perspectives of New Music 11.1:146–223.

Bregman, Albert. 1990. Auditory Scene Analysis: The Perceptual Organization of Sound. Cambridge: MIT Press. Bregman, Albert and Jeffrey Campbell. 1971. “Primary auditory stream segregation and perception of order in rapid sequences of tones.” Journal of Experimental Psychology 89: 244–249.

Casella, Alfred. 1924. “Tone-Problems of Today.” Musical Quarterly 10:159– 71. Cowell, Henry and Sidney Cowell. 1969. Charles Ives and His Music. New York: Oxford.

Demsy, David. 1991. “Chromatic Third Relations in the Music of John Coltrane.” Annual Review of Jazz Studies 5: 145–180.

DeVeaux, Scott. 1997. The Birth of Bebop: A Social and Musical History. Berkeley: University of California Press. Forte, Allen. 1955. Contemporary Tone Structures. New York: Columbia University Press.

Gervais, Françoise. 1971. Etude comparée des langues harmoniques de Fauré et de Debussy. 2 volumes, special numbers 272–3 of La Revue Musicale.

Grout, Donald Jay and Claude V. Palisca. 1996. A History of Western Music. New York: W. W. Norton.

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Harrison, Daniel. 1997. “Bitonality, Pentatonicism, and Diatonicism in a Work by Milhaud.” In Music Theory in Concept and Practice. Edited by James M. Baker, David W. Beach, and Jonathan W. Bernard. Rochester: University of Rochester Press.

Levin, Michael and Wilson, John S. “No Bop Roots in Jazz: Parker.” Down Beat 16 (9 September): 1ff.

McFarland, Mark. 1994. “Leit-harmony, or Stravinsky’s Musical Characterization in The Firebird.” International Journal of Musicology 3: 203–33.

Owens, Thomas. 1974. “Charlie Parker: Techniques of Improvisation.” Ph.D. dissertation, University of California at Los Angeles. Santa, Matthew. 1999. “Defining Modular Transformations.” Music Theory Spectrum 20: 220–9.

Schoenberg, Arnold. [1941] 1984. “Composition with Twelve Tones (1).” In Style and Idea. Edited by Leonard Stein. Translated by Leo Black. Berkeley: University of California Press.

Stravinsky, Igor. 1969. The Rite of Spring: Sketches 1911– 1913. London: Boosey& Hawkes.

Stravinsky, Igor, and Craft, Robert. 1962. Expositions and Developments. New York: Doubleday.

Taruskin, Richard. [1987] 1990. “Chez Petrouchka: Harmony and Tonality chez Stravinsky.” In Music at the Turn of the Century. Edited by Joseph Kerman. Berkeley: University of California Press. Originally in Nineteenth Century Music 10: 265–86. _______. 1996. Stravinsky and the Russian Traditions. Berkeley: University of California Press.

Tymoczko, Dmitri. 1997. “The Consecutive Semitone Constraint: A Link Between Impressionism and Jazz.” Integral 11:135–79.

van den Toorn, Pieter C. 1983. The Music of Igor Stravinsky. New Haven: Yale University Press. _______ 1987. Stravinsky and the Rite of Spring: The Beginnings of a Musical Language. Berkeley: University of California Press.

_______ 1995. Music, Politics, and the Academy. Berkeley: University of California Press.

_______ 2000. “Will Stravinsky Survive Postmodernism?” Music Theory Spectrum 22: 104–21.

Wessel, David. 1979. “Timbre Space as a Musical Control Structure.” Computer Music Journal 3.2: 45–52.

Chapter 8

Stravinsky, Adorno, and the Art of Displacement

Much of what is characteristic of Igor Stravinsky’s music may be defined rhythmically in terms of displacement, shifts in the metrical alignment of repeated motives, themes, and chords. Stravinsky himself often began here, in fact, not necessarily with a committed set of pitch relations, one that is octatonic, for example, but with a phrase turned rhythmically, a motive or chord displaced in relation to a steady metrical framework. The many references in his published remarks to starting ideas bear this out, as do the works and sections of works themselves—Russian, neoclassical, and serial in origin. Even before the birth of concrete ideas, the composer would set himself in motion by “relating intervals rhythmically,” improvising on a set of “rhythmic units.” This initial exploration, he later confessed, “was always conducted at the piano.”1 Adorno began here, too. Targeted in his celebrated indictment of Stravinsky’s music are, above all, the composer’s rhythmic practices, 1Igor

Stravinsky and Robert Craft, Conversations with Stravinsky (New York: Doubleday, 1959), 11.

Reprinted from The Musical Quarterly, Vol. 87, No. 3 (Autumn, 2004) The Music of Stravinsky: Collected Essays Pieter C. van den Toorn Text Copyright © 2004 Oxford University Press Layout Copyright © 2023 Jenny Stanford Publishing Pte. Ltd. ISBN 978-981-4968-62-1 (Hardcover), 978-1-003-35916-6 (eBook) www.jennystanford.com

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Stravinsky, Adorno, and the Art of Displacement

the frequent displacement of accents, and the disruptive effect of displacement on the listener. The absence of expressive timing is bemoaned, the lack of any “subjectively expressive fluctuation of the beat.”2 And instead of the developmental style of the classical tradition (as defined by Arnold Schoenberg, Adorno’s point of departure musically and music-analytically), the repetition in Stravinsky’s music was relentless and literal. No development could be inferred, no elaboration of motives or “motive-forms.”3 So paradoxical in a music that could seem outwardly vital from a rhythmic standpoint, the overall effect was often one of standstill or stasis, an invention “incapable of any kind of forward motion.”4 “The repetition constantly presents the same thing as though it were something different,” Adorno complained. “Farcical and clownish, it has the effect of putting on airs, of straining without anything really happening.”5 Such characterizations form the liveliest part of Adorno’s critique. Descriptions of one kind or another, they address the psychological effect of Stravinsky’s music. At the same time, however, they are often incomplete and fragmentary, with the task of piecing them together left to the reader. Adorno’s approach is unsystematic to the point of being unintelligible (“anti-systematic,” as some have suggested more sympathetically),6 with the analytical descriptions themselves hemmed in by sweeping philosophical and sociological conjectures often no less fragmentary in character. The stream of consciousness can be explained by the dialectical processes at work, but only up to a point, and the suggestion of many of Adorno’s adherents to the effect that the critic-philosopher fetishized this

2Theodor W. Adorno, Philosophy of Modern Music, trans. Anne G. Mitchell and Wesley V. Blomster (New York: Seabury, 1973), 154. 3See Arnold Schoenberg, Fundamentals of Musical Composition, ed. Gerald Strang and Leonard Stein (London: Faber and Faber, 1967), 8. In Schoenberg’s analyses, “motivicforms” were the varied forms of a basic motive resulting from development. “Through substantial changes,” Schoenberg wrote, “a variety of motive-forms are produced.” 4Adorno, Philosophy of Modern Music, 178. 5Theodor W. Adorno, “Stravinsky: A Dialectical Portrait “(1962), in Quasi una Fantasia: Essays on Modern Music, trans. Rodney Livingstone (London: Verse, 1998), 152. 6The unsystematic nature of Adorno’s approach is discussed in Max Paddison, Adorno’s Aesthetics of Music (Cambridge: Cambridge University Press, 1993), 19–20. See also Julian Johnson, “Analysis in Adorno’s Aesthetics of Music,” Music Analysis 14, nos. 2–3 (1995): 296–97.

Stravinsky, Adorno, and the Art of Displacement

particular aspect of the process (its lack of finality) can seem real enough.7 Adorno acknowledged the “constellation”-like effect of his thought and prose,8 but the results can often seem like waywardness all the same, a poetic obscurity substituting for the more determined effort to address head-on the complexity of the issues raised. Indeed, there are problems with the analytical description as well. As Max Paddison has observed, “a strange disparity” exists between “the sophistication and radicality of [Adorno’s] aesthetics and sociology on the one hand and the lack of sophistication and traditional character of his music-analytical method on the other.”9 Actually, it is not so much the thematic-motivic model of analysis inherited from Schoenberg that lacks sophistication as it is its application (or lack of application). Missing not only in Adorno’s Philosophy of Modem Musk10 but also in a later essay on Stravinsky11 are definitions of every conceivable kind (elementary ones for terms such as “accent,” for example), identifications of passages and sections of works cited, and the analytical detail that must necessarily qualify generalization if generalization is not to lapse into polemic. The need for concrete detail—for the grounding of abstract terms and concepts “in the structure of the music itself—is acknowledged early on in the Philosophy of Modern Music,12 but is never allowed to materialize in the form of an effective supplement. Yet the bits and pieces of Adorno’s description are worth pursuing all the same. And they are so more for the musical illumination than for the larger philosophical and sociological ideas to which they are attached (and from which, as Adorno and his adherents have 7See

Johnson, “Analysis in Adorno’s Aesthetics of Music,” 298. Paddison, Adorno’s Aesthetics of Music, 19. “The academic treatise was rejected in favor of the idea of a ‘constellation’ of fragments,” Paddison writes, each of these fragments “equidistant from an unstated center, the object of the inquiry.” Adorno’s resistance to the idea of a “whole” in musical works and in systems of explanation generally (the equation of such a “whole” with “truth”) is at work in these predispositions for the fragment and the fragmentary, and this seems to have been the case even with the very earliest of his publications in the 1920s. 9Paddison, Adorno’s Aesthetics of Music, 169. 10See note 2. 11See note 5. 12Adorno, Philosophy of Modern Music, 5. 8See

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insisted, they not only derive their meaning but are “inseparable”).13 They are worth pursuing for the musical and music-historical sense that can be made of the juxtaposition of Schoenberg and Stravinsky, the juxtaposition of the classical or “homophonic” style as defined by Schoenberg (the style of “developing variation”)14 and Stravinsky’s processes of displacement. Where the construction of thematic material is concerned, the invention and use of such material, these two worlds can indeed seem to stand apart in ways that are immediately identifying, ways that can enliven experience and its reflection. Confronted in Adorno’s Philosophy, and in the later Stravinsky essay as well, is that single dimension in Stravinsky’s music that has 13Concerning

the “inseparability” of the various components of Adorno’s argument, see Johnson, “Analysis in Adorno’s Aesthetics of Music,” 296–97. The “interdisciplinary character” of Adorno’s writings is addressed at length in Paddison, Adorno’s Aesthetics of Music; see esp. 16–17. Common assumptions about the “self-sufficiency” of analysis in relation to aesthetics and sociological interpretation generally are questioned by Adorno in T. W. Adorno, Aesthetic Theory, trans. C. Lenhardt (London: Routledge, 1989), 477–78. Left unclear in Adorno’s remarks in Aesthetic Theory, however, is the precise nature of the “inseparability” that he alleges, the dependence of “technical” or “immanent analysis” (Adorno’s term) on social awareness and thought. Does analysis automatically presume sociopolitical awareness of this kind? Or does it merely invite philosophical or sociopolitical speculation? Left alone, analysis is “narrow-minded,” Adorno asserts, “positivistic” in its implications. Specific questions of this kind are addressed more fully in Julian Johnson, “The Nature of Abstraction: Analysis and the Webern Myth,” Music Analysis 17, no. 3 (1998): 267–71. 14See Schoenberg, Fundamentals, 8: “Homophonic music can be called the style of developing variation. This means that in the succession of motive-forms there is something that can be compared to development, to growth.” Or see the description of “developing variation” in Arnold Schoenberg, Style and Idea: Selected Writings of Arnold Schoenberg, ed. Leonard Stein, trans. Leo Black (Berkeley: University of California Press, 1984): “Criteria for the Evaluation of Music,” 129–31. Ideas encompassed by Schoen-berg’s use of the term “developing variation” underlie Carl Dahlhaus’s understanding not only of Schoenberg, but of tradition and the classical or “homophonic” style generally; see for example Dahlhaus, “What is ‘developing variation’?” in Dahlhaus, Schoenberg and the New Music, trans. Derrick Puffett and Alfred Clayton (Cambridge: Cambridge University Press, 1987), 128–34; and Dahlhaus, Between Romanticism and Modernism, trans. Mary Whittall (Berkeley: University of California Press, 1980), 40–52. The concept is further explored in Walter Frisch, Brahms and the Principle of Developing Variation (Berkeley: University of California Press, 1983). Its continuing relevance in Schoenberg’s twelve-tone music is examined in Jack Boss, “Schoenberg’s Radio Talk on Opus 22, and Developing Variation,” Music Theory Spectrum; and Ethan Haimo, “Developing Variation and Schoenberg’s TwelveTone Music,” Music Analysis 16, no. 3 (1997).

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seemed most to identify it in the ears and eyes of the listening public, namely that of rhythm and meter. The features that preoccupy Adorno are those that tend to stand out, in fact, perhaps in works of the early Russian period above all: the mechanical nature of the beat and its transmission, the displacement of accents, the rigidity of the juxtapositions, and the seemingly unvaried and relentless nature of the repetition. Touching on matters that pertain to the listener’s immediate response to Stravinsky’s music, Adorno’s concerns can be made to relate to wider and more tangible ones, to the listener’s “entrainment” of meter, for example, to the role of expectation in music, and to the way in which emotion (pleasureful or not) is aroused. In Leonard Meyer’s now classic formulation of “emotion and meaning” in the Western art tradition, emotions are stirred when implications or tendencies are inhibited or arrested, when established norms are broken.15 And the way in which expectations of metrical parallelism are thwarted by displacement in Stravinsky’s music, with the meter often disrupted as a result, figures as an instance of this type of interaction. Indeed, there is little reason why Adorno’s critique should not be scrutinized from perspectives of this kind, be made to relate to the world of music theory and analysis and its ties to issues of perception and cognition. Much of this can be pursued irrespective not only of Adorno’s philosophical ideas, but of the still larger framework (mainly Hegelian and Marxist) to which those ideas are attached. Indeed, it can be pursued irrespective of Adorno’s critical verdict. The latter need not be accepted in order for the analytical description, harnessed as a means of support, to be appreciated. Our understanding can be reasonably sympathetic, in fact, without in any way accepting the “no” of Adorno’s account. Indeed, as Virgil Thomson remarked some time ago, where matters of musical understanding and criticism are concerned, the actual opinions of critics need not concern us unduly.16 What counts is the musical understanding that is brought to bear, the features that are noticed, described, and commented upon in one way or another. The Schoenbergian model of the classical style can serve as a useful foil for Stravinsky’s music regardless of the larger 15See

Leonard Meyer, Emotion and Meaning in Music (Chicago: University of Chicago Press, 1956). 16In contexts of this kind, Thomson averred, “opinions are mostly worthless.” See Virgil Thomson, A Virgil Thomson Reader (Boston: Houghton Mifflin, 1981), 87.

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and less tangible philosophical and sociopolitical meanings to which, in Adorno’s account, that model is attached. On the more speculative side of Adorno’s argument, too, many of the negative images can be detached and replaced by positive ones. With this in mind we shall first be seeking to retrace the steps of Adorno’s critique, supplementing the analytical description with the detail and exemplification often missing in the Philosophy. Following this, a detailed definition of metrical displacement and its implications in Stravinsky’s music will be attempted, followed in turn by a number of rebuttals of Adorno’s argument. Conclusions will then lead to a somewhat less strident, less polarized view of the Schoenberg-Stravinsky divide, one in which the great variety of displacement in Stravinsky’s music can imply processes and psychologies that are not always at odds with those of more traditional tonal contexts.

Adorno Interpreted

Adorno is struck above all by the “concentration of accents and time relationships” in Stravinsky’s music. The “most elementary principle” of this “concentration” is displacement: melodic fragments and motives are constructed in such a way that “if they immediately reappear, the accents on their own accord fall upon notes other than they had upon their first appearance.”17 Because of their irregularity, the shifting accents “can appear to be the result of a game of chance.” They can seem to be “under a spell.”18 The game they play is an “arbitrary” one, according to Adorno, one whose rules lie beyond the control of the listener. And the arbitrariness of the game precludes participation and engagement on the part of the performer or listener. The listener’s role is reduced to that of a spectator. Stravinsky’s displaced accents resist assimilation. They cannot be anticipated, and so appear as “shock effects.”19 And while “shock” is accorded a legitimate place in the reception of much contemporary music (in that of Schoenberg’s atonal and twelve-tone music, above all, where Adorno identifies it with a sudden recognition of the horrors 17Adorno,

Philosophy of Modern Music, 178. Philosophy of Modern Music, 151. 19Adorno, Philosophy of Modern Music, 155. 18Adorno,

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of the modern world), its effect in Stravinsky’s music is viewed as debilitating. Deprived of the ability to anticipate, listeners cannot absorb the irregularly shifting accents of displacement. “Shock” overwhelms them, and they lose their “self-control.” “In Stravinsky, there is neither the anticipation of anxiety nor the resisting ego; it is rather simply assumed that shock cannot be appropriated by the individual for himself. The musical subject makes no attempt to assert itself, and contents itself with the reflective absorption of the blows. The subject behaves literally like a critically injured victim of an accident which he cannot absorb and which, therefore, he repeats in the hopeless tension of dreams.”20 Reference here and elsewhere in Adorno’s account to a “musical subject” implies dramatization. “The musical subject” rather than the listener falls victim to Stravinsky’s arbitrarily displaced accents. (The listener is seldom mentioned in Adorno’s account, in fact, although “listener” and “subject” are clearly interchangeable in this regard, with each viewed as the victim of the same set of musical circumstances.) Thus, the music lacks an overriding pattern according to which the irregularly shifting accents could be organized. In Adorno’s descriptions, the listener’s inability to organize these accents becomes the subject’s inability. Just as the listener loses his or her metrical bearings, so, too, the subject cannot “heroically reshape” the displaced accents in his or her image: the accents are experienced as “convulsive blows and shocks.”21 And although the specifics of this listener-to-subject translation are omitted from the record, they are an integral part of the equation. Without them, Adorno’s characterizations would make little sense. Central to Adorno’s argument is the idea of a balance in music of the highest quality, a balance between the four musical dimensions of melody, harmony, rhythm, and form. In Stravinsky’s music, this is overturned by an emphasis on rhythm and, more specifically, on displacement and its effect of shock. That “great” music could consist of such an ideal equilibrium—one good for all seasons, as it were— is an idea traceable to Schoenberg (Adorno’s likely source, in any case),22 although it appears in other guises early in the twentieth century as well. Schoenberg wrote of the need for music to develop 20Adorno,

Philosophy of Modern Music, 156–57. Philosophy of Modern Music, 155. 22See Schoenberg, Style and Idea, 39–41. 21Adorno,

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consistently and “equally” in all directions.23 Not only were these directions inseparable, but an emphasis on one could come only at the expense of the others. Ideas similar to these were expressed in a number of critical surveys during the 1920s and 1930s, including Cecil Gray’s A Survey of Contemporary Music (1924). There, each parameter is viewed similarly as being “at its highest when all are in complete equilibrium, when one does not predominate over the others.”24 Music “of the greatest masters” is neither harmonic, rhythmic, nor melodic, according to Gray; “it is all and it is none.”25 Adorno’s version of this ideal runs as follows: Stravinsky’s admirers have grown accustomed to declaring him a rhythmist and testifying that he has restored the rhythmic dimension of music—which had been overgrown by melodic-harmonic thinking— again to honor .... Rhythmic structure is, to be sure, blatantly prominent, but this is achieved at the expense of all the other aspects of rhythmic organization .... Rhythm is underscored, but it is split off from content, it results not in more, but rather in less rhythm than in compositions in which there is no fetish made of rhythm.26

Melody is the first casualty of these imbalances. Instead of a formation of shapes and contours, the melodies subjected to displacement in Stravinsky’s music are “truncated, primitivistic patterns.”27 No independent melodic life may be inferred from these “patterns,” no structure to speak of. Melodic, harmonic, and rhythmic features are not subjected to a “developing variation” along the lines implied by the Schoenbergian model, but are repeated literally and relentlessly. They are not varied, and without variation, progress and development are thwarted as well. For it is only by 23See

Schoenberg, Style and Idea, 41: “When composers have acquired the technique of filling one direction to the utmost capacity, they must do the same in the next direction, and finally in all directions in which music expands.” See the discussion of this aesthetic ideal in Carl Dahlhaus, Esthetics of Music, trans. William Mitchell (Cambridge: Cambridge University Press, 1982), 92–93. 24Cecil Gray, A Survey of Contemporary Music (Oxford: Oxford University Press, 1924), 141. The critical approach to Stravinsky’s music is similar in Constant Lambert, Music Ho: A Study of Music in Decline (London: Faber and Faber, 1935). 25Gray, A Survey of Contemporary Music, 140. 26Adorno, Philosophy of Modern Music, 154 27Adorno, Philosophy of Modern Music, 155.

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means of a process of elaboration that the repetition of motives and thematic segments can add up to an overreaching design or train of thought, something other than a mere sum or total. With Stravinsky’s “primitivistic patterns” and their repetition, there are only “fluctuations of something always constant and totally static.”28 The much ballyhooed rhythmic invention “consists of varied recurrence of the same; of the same melodic forms; of the same harmonic patterns, indeed, of the very same rhythmic patterns.”29 Evidence of a musical nightmare of this kind may be found on virtually any page of Stravinsky’s music, but see, as a starting point here, the repetition of the A–D–C–D fragment in the horns in the “Ritual of the Rival Tribes” and “Procession of the Sage” in The Rite of Spring (1913; see Ex. 9.1). Repeats of this “primitivistic pattern” (ten in all) are without elaboration, transposition, or changes in articulation, dynamics, or instrumental assignment. All is fixed from start to finish in these respects: the first two notes of the fragment are always accented, while the last three, D-C-D, are always slurred. What changes is the fragment’s alignment in relation to the steady 4/4 meter and the accompanying parts. Entering on the fourth, first, third, and second quarter-note beats, respectively, the fragment falls on and off the half-note beat, the likely tactus here with a metronome marking of 83. (The half-note beat, along with the sensation of falling on and off it, is likely to define the conditions of displacement in this passage. At a level of pulsation just below the tactus, the quarternote beat becomes a subtactus unit, the level of the pulse, as we shall presently be defining it.) In turn, the steady meter on which displacements of this kind hinge is likely to impose itself independently and prior to the 28Adorno,

Philosophy of Modern Music, 155.

29Adorno, Philosophy of Modern Music, 178. The static quality of Stravinsky’s harmony

and the lack of a traditional sense of development are subjected to criticism no less severe in Pierre Boulez’s writings of the 1950s. Techniques of superimposition in Stravinsky’s music are dismissed by Boulez as “irreducible aggregations,” a “coagulation” that creates for the superimposed fragments a “false counterpoint,” all of this “eminently static in the sense that it coagulates the space-sound into a series of unvarying stages ... and in the sense that it annuls the entire logic of the development.” See Pierre Boulez, Notes of an Apprenticeship, trans. Herbert Weinstock (New York: Knopf, 1968), 74.

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entrances of the horn fragment and its sustained Ds. The repetition of the G-F-E-D fragment in the first violins is crucial in this regard. As a point of departure and return, the pitch G in this fragment falls on the downbeat, while the fragment’s division into two segments, or “cells” (labeled A and B in Ex. 9.1), with each of these segments spanning the 4/4 bar line, lends further support for the 4/4 framework. Further along, repeats of the accompanying segments in the tuba, although irregularly spaced at rehearsal nos. 64–67, serve as an additional means of support—indeed, following the removal of the reiterated fragment in the violins at rehearsal no. 66, as a constant backdrop in this respect. The spans of these entrances are multiples of two and four; repeats of the segments G-sharp-F-sharp(G)-(Gsharp) and G-sharp-A-sharp-C-sharp-A-sharp-(G-sharp) are aligned in a metrically parallel fashion. In sum, while repeats of the various segments in the first violins and tubas are spaced irregularly, they are metrically parallel in relation to the 4/4 bar line. The two fragments are not ostinati, strictly speaking, but the displacement that results from the irregular spanning of their repeats is hypermetrical rather than metrical. Typical of the melodic invention in Stravinsky’s Russianperiod works, the reiterated G–F–E–D fragment in the first violins is sliced up into smaller segments. Labeled A and B in Ex. 9.1, these segments are reshuffled: after each repeat of segment A, segment B is repeated once, sometimes twice. Significantly, however, all repeats of these segments fall on the downbeat of the 4/4 bar line. And this parallelism is likely to reinforce the sense of a 4/4 hierarchy. At the outset of this passage, the effect is likely to be one of at least relative stability, and in preparation for the entrances of the sustained Ds and A–D–C–D segment in the horns. The latter are not only irregularly spaced, they are metrically nonparallel as well; the latter entrances are the troublemakers in this passage: the cause, as we shall see, of metrical conflict. (The conflicting cycle of the bass drum noted in Ex. 9.1 will come to the fore further along, and then only in the form of a challenge; even at rehearsal no. 70, where the notated meter changes to 6/4, the sense of a duple or 4/4 bar line is likely to persist.)

Stravinsky, Adorno, and the Art of Displacement

Example 9.1 Stravinsky, The Rite of Spring, “Ritual of the Rival Tribes,” “Procession of the Sage”; copyright 1912, 1921 by Hawkes & Son (London) Ltd., copyright renewed; reprinted by permission of Boosey and Hawkes, Inc. (continued)

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Example 9.1  (continued)

Pitch relations in this example follow an analogous path. The octatonicism at the outset is explicit and relatively unimpaired. Consisting in the main of the tritone-related 0–2–3–5 Dorian tetrachords G–F–E–D and C-sharp–(B)–A-sharp–G-sharp in the first violins and tubas, respectively, octatonic relations are qualified diatonically by the D-scale on G, implied by the accompanying parts in the strings (see Ex. 9.2: the dotted line beneath the quotation signifies octatonic-diatonic interaction in terms of the single octatonic transposition Collection II and the D-scale on G, shared by these two interacting orderings of reference is the G–F–E–D tetrachordal fragment, which serves as a connecting link).30 And this, too, would seem to be in preparation for the entrances of the A–D–C–D fragment in the horns. Articulating another 0–2–(3)–5 incomplete Dorian tetrachord, here in terms of D–C–(B)–A, the latter entrances are foreign to Collection II. The clash with the C-sharp– (B)–A-sharp–G-sharp tetrachord in the tubas is likely to be especially harsh in this regard. 30For a detailed discussion of referential interaction in Stravinsky’s music, of interplay

between a number of octatonic and diatonic scales, see Pieter C. van den Toorn, The Music of Igor Stravinsky (New Haven: Yale University Press, 1983), 66–91, 100–33, and 261–90. Or see van den Toorn, Stravinsky and “The Rite of Spring” (Berkeley: University of California Press, 1987), 143–86.

Stravinsky, Adorno, and the Art of Displacement

Typical of Stravinsky’s music as well is the layered or stratified structure that may be inferred. Fixed registrally as well as instrumentally, fragments in the first violins, tubas, and horns repeat according to cycles that vary independently of one another.31 The varying cycles in the horns and tubas result in an alignment or coincidence that changes vertically or “harmonically” as well as metrically. Yet the “harmonic” changes are locked into a limited set of variables from the start; harmony in the large is exceedingly static. The sound of the superimposed fragments midway through this passage is little different from what it is at the beginning or the end. As with the separately moving parts of a giant locomotive, the individual fragments churn away with little, if any, local, over-thebar-line sense of harmonic movement or progress.

Example 9.2  Stravinsky, The Rite of Spring, “Ritual of the Rival Tribes,” opening, © copyright 1912, 1921 by Hawkes & Son (London) Ltd., copyright renewed; reprinted by permission of Boosey& Hawkes, Inc.

A starker contrast to the world of developing variation would be difficult to imagine. There are motivic variations, as we have indicated, changes in motivic succession (reshuffling), durational spanning, and metrical placement. But the sort of melodic, harmonic, and rhythmic variations identified with the earlier developmental style are missing altogether. There are only “fluctuations of 31For

a detailed description of these structures in Stravinsky’s music, see van den Toorn, Stravinsky and “The Rite of Spring,” 97–108. Matters of stratification in Stravinsky’s music are pursued from a compositional standpoint in Lynn Rogers, “Rethinking Form: Stravinsky’s Eleventh-Hour Revision of his Violin Concerto,” Journal of Musicology 17, no. 2 (1999): 272–303. See also Gretchen Horlacher, “The Rhythms of Reiteration: Formal Development in Stravinsky’s Ostinati,” Music Theory Spectrum 14, no. 2 (1992): 171–87.

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something always constant and totally static,” as Adorno complained. The invention consists merely of “a varied recurrence” of the same melodic, harmonic, and rhythmic “patterns.” Indeed, processes of metrical displacement, along with the stratification of this passage, preclude the sympathetic give-andtake of the world of developing variation, in the way in which motivic particles, detached from themes, are exchanged between instrumental parts. In Ex. 9.1, the horn fragment is not tossed about from one instrument to the next, made the subject of a “dialogue” in this respect (as it might have been in, say, a string quartet of Haydn or Mozart). It is not treated “humanistically” by such means (as the character of such treatment has often been imagined, at the very least, in modern times, since the dawn of chamber music).32 And it is not treated expressively, either. If the displacement of the A–D–C–D fragment in the horns is to have its effect, then the beat must be held evenly (mechanically) throughout, with little if any yielding to the conventions of expressive timing and nuance, the means by which, traditionally, performers have made their mediating presence felt. So stark is the contrast, in fact, with so many of the familiar givens of the developmental style missing, that anything but the most negative of accounts on the part of a critic such as Adorno would have been difficult to imagine. It can almost seem as if the impression gained would have had to have been that of a cold, stiff, and unyielding music. Here, however, the point concerns the “protest” that, according to Adorno, music has always represented: “the protest, however ineffectual, against myth,” against “the inexorable bonds of fate.”33 No cry in the dark could be heard in Stravinsky’s music, no “inner self in its struggle with “outrageous fortune,” expressing the inexpressible. All this seemed missing as well, replaced by barking proclamations: “Thus it is, and not otherwise,” the composer seemed to be saying from one unvaried repeat to the 32The

association of the “humanistic” with chamber music, dialogue, and the developmental style generally is discussed in Carl Dahlhaus, Nineteenth-Century Music, trans. J. Bradford Robinson (Berkeley: University of California Press, 1989), 252–61. “The idea of chamber music,” Dahlhaus concludes, “arose as a musical reflection of a humanistic-aristocratic culture primarily centered on conversation. The aesthetic of this genre may be derived from the constantly recurring comparison with educated discourse that each part continuously shows regard for the other. In this way, the whole emerges from an interplay of voices sustained by an understanding of each participant for the overall context, and not as a jumbled amalgam of its parts” (260). 33Adorno, “Stravinsky,” 151.

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next. And the proclamations seemed to be those of an authority, of someone in charge, not those of the lone individual. “Stravinsky’s music identifies not with the victims,” Adorno complained in one of his more provocative pronouncements, “but with the agents of destruction.”34 Indeed, it identifies with the fascists who were just then appearing on Europe’s horizon.35 More generally, the “identification” of Stravinsky’s music “with the collective” admits of two interpretations: Adorno makes reference to a “primitive,” pre-individual age, and to a modern, industrial one.36 The musical subject behaves ritualistically in these worlds, “regressively” and in an “infantile” manner.37 Stravinsky’s music is “anti-humanistic” in these respects. Its sympathies are not with the “suffering subject,” but with the powers that be, various “agents of destruction.” In contrast, the developmental style symbolized for Adorno the ability of the subject to mature with time, to meet the day’s challenges and to develop accordingly.38 While the subject remained 34Adorno,

“Stravinsky,” 149.

35Adorno, “Stravinsky,” 157–58. “Not a small part of the collective effect of these pieces

by Stravinsky may be connected with the fact that in their own way, they schooled their listeners, unconsciously and at the aesthetic level, in something they were soon to experience systematically on the political plane.” Fascism is not identified explicitly in this allusion to what listeners “were soon to experience systematically on the political plane,” but the identification is implied all the same. For a spirited rebuttal of these particular claims, see Milan Kundera, Testaments Betrayed: An Essay in Nine Parts, trans. Linda Asher (New York: Harper Collins, 1995), 65–97. 36Adorno, Philosophy of Modern Music, 145–47, 157–60. 37Adorno, Philosophy of Modern Music, 160–67. 38Adorno’s understanding of the developmental process in Beethoven and the classical style generally is likewise scattered in a number of publications. See Adorno, Aesthetic Theory, 315–19. The role of “developing variation” in Adorno’s sociopolitical understanding of the classical style is discussed in Rose Rosengard Subotnik, Developing Variations: Style and Ideology in Western Music (Minneapolis: University of Minnesota Press, 1991), 20–24. The term defines that process “whereby a musical element subjects itself to logical dynamic change while simultaneously retaining its original identity” (20). Especially in Beethoven’s middle-period sonata allegros, “subjective freedom” is reconciled with “objective form.” Integrated “totalities” are formed in these allegros, with the individual able to “overtake” or to make his or her own received form, the “fixed, external order,” that represents the “world of object.” The continuation and intensification of the developmental style in Schoenberg’s application of the twelve-tone method is discussed in Theodor W. Adorno, “Vers une musique informelle” (1961), in Quasi una Fantasia, 283–84. Adorno’s understanding of this application is summarized in Jonathan Cross, The Stravinsky Legacy (Cambridge: Cambridge University Press, 1998), 229–32.

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locked in repetitive gesture in Stravinsky’s music, unable to move beyond the trancelike stupor of ritual, he was relatively free in the world of developing variation.39 This was the nature of the musical opposition Adorno sought to unravel, the split he attributed to Stravinsky’s music, its tear from tradition and traditional sensibility. A sampling of Adorno’s analytical descriptions appears in Figure 9.1. Incomplete and fragmentary in the writings themselves, they are here compressed into a single train of thought. All are ultimately traceable to a single musical condition, namely that of metrical displacement. Two subsidiary conditions result from displacement: 1) inflexibly held beats (beats lacking in expressive timing); and 2) a repetition of themes, motives, and chords that, apart from the displacement itself, is literal and lacking in the traditional modes of elaboration or developing variation. The characterizations triggered by these conditions are relatively concrete, neutral, and observational to begin with in Figure 9.1, increasingly less so further on down the line. Indeed, the more specific the imagery, the less tangible and the more speculative. On the left side of Figure 9.1, the need for strict metricality in the performance of Stravinsky’s music (the need for “expressive fluctuation” or nuance to be kept to a minimum) is made to imply mechanization and impersonality, which in turn are made to imply “anti-humanism” and a collective authority of one kind or another. On the right side, a lack of variation in the repetition of Stravinsky’s motives is made to imply a similar lack of “identification” with the individual, the plight of the musical subject. The descriptions and characterizations are Adorno’s, as has been suggested, while the outline converts both the description and the characterization into actual features of the music, features that are then connected in the form of an explanatory path. A larger rationale 39The more immediate aesthetic and sociological implications of these two worlds are

addressed at greater length in Robert Adlington, “Musical Temporality: Perspectives from Adorno and de Man,” repercussions 6, no. 1 (1997), 12–13. While “maturation implies the ability to cope with, and develop in response to, changing circumstances,” regression denotes “a reversion to infantilistic modes of behavior.” For Adorno, “repetition represents an infantile denial of time... while development signals proper recognition of the temporal condition.” In addition, Stravinsky’s “repetitive or nondevelopmental music had connotations of mechanized domination.”

Stravinsky, Adorno, and the Art of Displacement

is thus imposed along lines that are more specifically musical. (The outline is not Adorno’s, in other words, but represents an attempt to piece the various descriptions together as a single line of thought.)

Figure 9.1  Adorno’s Characterizations in the Form of an Explanation.

Displacement Defined Often missing from Adorno’s account, in fact, is precisely the sense of a larger rationale for Stravinsky’s music, what it is that connects the various musical components, motivates or triggers

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one factor in relation to the others. No doubt, as Adorno insists, the concern in Stravinsky’s music (and in his settings of displacement more specifically) is not with the features of a motive and their elaboration, but with just the opposite, namely the literal repetition of such features. Yet there are reasons for the unvaried nature of the repetition, reasons that are musically specific. The repetition in Stravinsky’s music follows a different logic. In works of the Russian period above all, Stravinsky repeats not to elaborate or to develop along traditional lines, but to displace. And in seeking metrically to displace a repeated theme, motive, or chord, the composer seeks to retain features other than alignment in order that alignment itself (and its shifts) might be set in relief. The literalness of the repetition acts as a foil in this respect. As features of pitch, duration, and articulation are retained, the metrical alignment of the given theme, motive, or chord shifts. This is not the whole of it, however. Literalness in the repetition of a fragment acts as a counterforce, too, a way of referring the listener back to the fragment’s original placement. In direct opposition to displacement, it implies metrical parallelism, a repetition of the original alignment along with all else that is repeated literally.40 And the more that is repeated literally, the more fully aroused are these conflicting expectations of metrical parallelism likely to be. The implications here are quite fiendish. To repeat a theme, motive, or chord literally and without variation so as to highlight and expose its metrical displacement is to undermine that displacement at the same time. It is to raise a conflicting signal of metrical parallelism. Typically, and with varying degrees of intensity, listeners are caught off guard. Unable to commit themselves initially one way or the other, to a reading of displacement or one of metrical 40See

Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge: MIT Press, 1983), 74–76, where implications of metrical parallelism are treated as a “metrical preference rule.” Given the repetition of a theme, motive, phrase, or other grouping, the “preference” is for the repetition to be aligned in a fashion that is metrically parallel to the original. The expectation is for the repetition and the original to be assigned the same metrical structure; hence the potential for disruption in cases of displacement.

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parallelism, they are apt to lose their metrical bearings.41 This is the origin of the disruptive effect of displacement, indeed, of the “convulsive blows and shocks” to which Adorno refers. It has to do not with one or the other of these two signals, not with metrical displacement or parallelism strictly speaking, but with their conflict, with the fact that there is insufficient evidence for an easy, automatic ruling in favor of one or the other. Crucially, too, the two sides are not reconcilable. Listeners cannot attend to both simultaneously.42 In Ex. 9.1 from The Rite of Spring, the horn fragment A–D–C–D is introduced on the fourth quarter-note beat of a 4/4 measure, only to be displaced to the first quarter-note beat several bars later. In half-note beats, it falls first off and then on the beat. How is this shift likely to be interpreted/ Will listeners read through the displacement with the steady 4/4 meter sustained as a frame of reference? Or, 41The idea of the “listener” invoked here is little different from that of the “experienced

and knowledgeable” listener referred to by Leonard Meyer in his study of expectation and the implication-realization process in music. See Leonard B. Meyer, Music, the Arts, and Ideas (Chicago: University of Chicago Press, 1967), 8. Although not necessarily trained academically or professionally, the “experienced” listener is alert to the implications of a steady meter, or to general features distinguishing idioms, periods, or composers. See also in this connection the references to “musical intuition” in Lerdahl and Jackendoff, A Generative Theory, 1–12, 53, and 281–83. The LerdahlJackendoff study addresses structure heard and understood, the listening experience generally, not “structure” pure and simple. The opening page of A Generative Theory refers to the “musical intuitions of a listener who is experienced in a musical idiom.” 42Conflicts involving meter and its continuation on the one hand, metrical parallelism on the other, occur in tonal works as well, of course, although, as we shall see, the effects of such conflicts tend to be less immediate and hence less disruptive of the listener’s metrical bearings. The two forces are treated as conflicting metrical “wellformedness” and “preference rules” in Lerdahl and Jackendoff, A Generative Theory, 72–75. The “well-formedness rule” stipulating that a level of metrical pulsation consist of equally spaced beats conflicts with the “preference rule” for metrical parallelism in the repetition of a theme, phrase, or other grouping. Most often in more traditional contexts, the latter “preference” gives way, with the repetition heard and understood as a form of syncopation. According to Lerdahl and Jackendoff, “the phenomenon of syncopation can be characterized as a situation in which the global demands for wellformedness [specifically here, the demands for equally spaced beats] conflict with and override local preferences [specifically, those for metrical parallelism]” (77). Often enough in Stravinsky’s music, however, metrically nonparallel relationships (displacements) result not merely in syncopation, but in outright disruptions or interruptions of established levels of pulsation. The disruptions may even involve the opposite of what Lerdahl and Jackendoff describe, namely, conditions in which the local “demand” for metrical parallelism overrides that for meter or equally spaced beats.

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alternatively, will they be taken in by the literalness of the repetition, by the fixed character of the articulation of accents and slurs? Will they attempt to match that literalness with the fragment’s original placement off the half-note beat? And will they do so by interrupting the meter at the half-note beat, adding an irregular (or “extra”) quarter-note beat to the count at rehearsal no. 68?43 The first of these alternatives is “conservative” in nature.44 An established meter is sustained (conserved) in order that the “same” fragment might be read through placed and displaced. The second alternative is “radical.” The meter is interrupted in order that the repeat of the fragment might be aligned as before, that is, in a fashion that is metrically parallel. The reciprocity of the relationship between these two metrical interpretations is summarized graphically in Figure 9.2. Reading from left to right, “conservative” listeners adjust the alignment of a repeated theme, motive, or chord (“change”) by holding on to an established meter (“no change”), while “radical” listeners do the reverse, adjusting their metrical bearings (“change”) 43The

notion of the “extra” beat is borrowed from Andrew Imbrie, “‘Extra’ Measures and Metrical Ambiguity in Beethoven,” in Beethoven Studies, ed. Alan Tyson (New York: Norton, 1973), 45–66. In Imbrie’s studies of metrical irregularity in Beethoven’s music, however, “extra” beats are beats at the level of the bar line and above (hypermeter), not, as here in The Rite of Spring, at the level of the tactus and below. The shallower levels of pulsation in Stravinsky’s case are a distinction worth pursuing more generally. As it concerns displacements of the sort illustrated in Ex.  9.1, the composer can indeed be imagined as having transferred to more immediate levels of metrical pulsation the displacements common in more traditional contexts at hypermetric levels. 44The distinction between “conservative” and “radical” responses (between allowing the meter to be sustained and allowing it to be interrupted) was first raised in Imbrie, “’Extra’ Measures and Metrical Ambiguity in Beethoven,” 45–66. In Imbrie’s studies, however, metrical irregularity and interruption in the form of “extra” beats occurs at the level of the bar line and above (hypermeter), while, here in Stravinsky’s music, the location is shallower. Imbrie stressed the “conservative force” of meter, the attempt by the listener to reduce to “law and order” the complexities of a musical surface. Subsequently, the distinction between “conservative” and “radical” interpretations was introduced in Lerdahl and Jackendoff, A Generative Theory, 23–25, and as a way of dealing with alternative readings of hypermeter in the opening of Mozart’s G-minor Symphony, K. 550. It has also been applied in the analytical rebarring of a number of Stravinsky contexts in van den Toorn, Stravinsky and “The Rite of Spring,” 67. See, too, Gretchen Horlacher, “Metric Irregularity in Les Noces: The Problem of Periodicity,” Journal of Music Theory 39, no. 2 (1995): 285–310.

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in order to persevere with an established alignment. A measure of conservation thus underlies both interpretations, whether it be meter, in the case of the conservative response, or alignment, in that of the radical one.

Figure 9.2  Alternative Responses to Displacement.

Stravinsky’s notation will tend to reflect one or the other of these responses. It may not always reflect the one to which a given listener is drawn, but it will tend to reflect one or the other all the same. And it will do so categorically. If, at any given moment of the listening experience, the repetition of a fragment may be heard as placed or displaced but not both, then the notation is no less categorical. It, too, acknowledges either the displacement or the fixed placement of a repeated fragment. The principal fragment in the clarinet in the opening allegro of Renard (1916) can serve as an additional illustration. The alternative barrings in Ex. 9.3a and 3b are derived from the finished score and an early sketch of Stravinsky’s, respectively. Typical of Stravinsky’s music, the fragment is sliced up into smaller segments or “cells,” units that are then repeated independently of one another; the series of irregularly spaced entrances that results is 5 + 2 + 5 quarter-note beats. (The quarter-note beat is the likely tactus here with a marking of 84.) In the finished score (see Ex. 9.3a), the resultant displacements lie exposed to the eye. The assumption here is that the passage will be heard and understood conservatively,

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that is, with the clarinet fragment newly placed at m. 9 and m. 10. Introduced on the bar line or half-note beat, the fragment falls off the beat twice and then on the beat again at m. 13. The steady 2/4 meter on which these displacements hinge is introduced and then maintained in large part by the basso ostinato, which acts as a metrical backdrop.

Example 9.3a–c  Stravinsky, Renard, opening allegro, mm. 7–13, score (conservative), early sketch (radical), and rebarred (still more radical), © copyright 1917 by J. & W. Chester, Ltd. (Chester Music), London; reprinted by permission of G. Schirmer, Inc.

The radical alternative, shown in Ex. 9.3b, stem from an early sketch of Renard.45 One of many in the sketchbook that would seem to indicate the composer’s awareness of these conservative and radical options, the sketch follows several drafts in which the conservative solution of the finished score is in place. (The sketch may have arisen as an afterthought, in fact, with the composer having wanted to test the radical option on paper.) Here, the meter shifts in order that the repeats of the clarinet fragment might be aligned 45The

available sketches of Renardare housed at the Paul Sacher Foundation in Basel, Switzerland. The passage in Ex. 9.3b is transcribed from p. 5 of the composer’s sketchbook of Renard. Used by permission of the Paul Sacher Foundation, Basel, Switzerland.

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in parallel fashion. All repeats fall on the downbeat. And much of the motivation for the notated metrical irregularity in Stravinsky’s music may be traced accordingly, that is, to attempts to expose these opposing forces of metrical parallelism. The parallel alignment in the analytical notation of Ex. 9.3c is still more radical from this standpoint. (Like the passage cited in Ex. 9.1 from The Rite of Spring, the opening allegro of Renard is a layered structure.) No doubt, compromises can sometimes be worked out in the notation, often by crossing the bar line with beams—attempts, at least on paper, to preserve both an established meter and an established alignment. But such solutions cannot alter perception or, indeed, the role played by an orientation, a frame of reference against which “events” are located, timed, and weighed. Listeners orient themselves as a matter of course, seeking a reliable groove, a context in this respect, a backdrop against which to organize “events.” They can respond conservatively or radically to a displacement, but not in both ways simultaneously (however much, by means of a crossing of the bar line, the notation may imply the possibility of such an option). Opposing forces are set in motion, forces that are ultimately not reconcilable. Yet the equivocation implied by the crossing of a bar line is not without perceptual implications. At least initially, the experience is likely to be conflicted, subject to a good deal of qualification or sensed opposition. A displacement is felt not in isolation, obviously, but as it relates to previously established placements. It implies those earlier placements, intimations of which surface not as part of an evolving sense of structure (an overriding pattern, in other words), but as something that conflicts. And this is crucial. The feeling is that of a prevailing assumption gone amiss, and of being taken unaware by this. Assumptions about meter and the metrical alignment of the repeated fragment or chord, inferred reflexively and internalized at some earlier point, cannot be sustained.46 The process may be 46The

process whereby, reflexively, a metrical hierarchy is internalized by the listener (subjected to a form of entrainment, as psychologists have described it, a form of embodiment), is discussed in Mari Riess Jones, “Only Time Can Tell: On the Topology of Mental Space and Time,” Critical Inquiry 7, no. 3 (1981): 571–76. See also in this connection Justin London, “Metric Ambiguity (?) in J. S. Bach’s Third Brandenburg Concerto: A Reply to Botelho,” In Theory Only 9, nos. 7–8 (1991): 27; and Candace Brower, “Memory and the Perception of Rhythm,” Music Theory Spectrum 15, no. 1 (1993): 27–33.

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likened to that of a rug being pulled suddenly and unexpectedly from under the listener’s feet. And this is likely to be the case even with highly conservative readings, in which established levels of metrical pulsation may be clung to tenaciously. If only for a split second, a change in the metrical alignment of a repeated theme, motive, or chord is likely to bring about a disruption of that which underlies alignment, namely meter. As depicted in Figure 9.2, the reciprocal nature of meter and metrical alignment is crucial. For it is not as if meter arose independently of placement and displacement, as if the materials of Stravinsky’s music fell automatically (or mechanically) into place, wholly at the mercy of such a design. Themes, fragments, and motives may be introduced within an established metrical hierarchy, to be sure, acquiring, as a result of that introduction, a strong sense of placement (or location). Yet the processes themselves are reciprocal and work both ways. If alignment emerges from meter, so, too, in the mind of the listener, does meter emerge from alignment. The renewed parallel alignment of a given fragment may confirm and reinforce an established sense of meter, just as a change in alignment (displacement) may disrupt that sense.47 At the first signs of change, in fact, confusion is likely to reign. A repeated fragment familiar to the listener is treated in an unfamiliar way, and the listener may be uncertain as to how to proceed. The specific nature of the change may not be known at first, but it may be sensed all the same. Figure 9.3 traces a possible response-pattern from an initial point of contact. Lasting anywhere from a split second to the lifetime of a listener’s engagement with the context in question, an initial state of confusion is followed by a retrospective scramble to reestablish the lost frame of reference. Since the feeling is indeed likely to be that of an assumption gone amiss, assumptions in general are put to the test. Was the fragment’s earlier alignment correctly inferred? Was the meter correctly inferred? Should it be sustained, allowing for a perception of displacement? Alternatively, should it be interrupted, allowing for a parallel alignment? Much of this can pass in a few seconds. 47Recent

studies of the psychology of this interaction have underscored the role of metrical parallelism in the formation of meter. See David Temperley and Christopher Bartlette, “Parallelism as a Factor in Metrical Analysis,” Music Perception 20, no. 2 (2002): 117–49.

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What listeners seek is a relationship, a way of relating the old with the new. Sought is a means of connecting the various placements, acknowledging all as part of a single train of thought. At some point in their retrospective analyses, however, listeners are likely to read through the repeated fragment conservatively or radically. An attempt of this kind is likely to proceed with a good deal of sensed opposition, however. One response is likely to qualify the other.48 And although retrospective analyses can facilitate subsequent readings, the stages outlined in Figure 9.3 are unlikely to be eliminated altogether. Listeners may proceed in an automatic, unconscious, or “bottom-up” way,49 according to which they are free to renew their initial experiences, including those of displacement and its disruption. They may proceed free of conscious memory, in other words, and in a way that allows them to go through “pretty much the same motions” from one hearing to the next, as Ray Jackendoff has phrased it in a related study of the cognitive implications of renewed hearings; listeners can continue to hear the piece “as if for the first time.”50 Hearings of this kind stand in contrast to “top-bottom” approaches, in which prior or immediate 48The general premise here is that, while oriented or focused on a given interpretation

or structure, whether conservative or radical in nature, listeners are able to hold competing interpretations or structures at bay. Not only are they able to sense the challenge of an opposing interpretation or structure and be interrupted by it, but they can switch “in midstream” without having to backtrack to a beginning. See in this connection Ray Jackendoff, “Musical Parsing and Musical Affect,” Music Perception 9, no. 2 (1991): 214–17, 220–28. According to Jackendoff, listeners keep “multiple” or “parallel” interpretations at bay unconsciously while attending to one interpretation alone. “If subsequent events in the musical surface lead to a relative reweighing of the analyses,” he writes, the selection process “can change horses in the midstream, jumping to a different analysis” (223). What Jackendoff overlooks, however, is the uncertainty and disruption the opposition of alternative metrical interpretations or structures can cause. Listeners may switch “in midstream” from one conservative or radical interpretation to another, but not without conflict or, often enough, real confusion and disorientation. It is not solely a matter of switching interpretations, in other words. 49See Eugene Narmour, “The Top-Down and Bottom-Up Systems of Musical Implication: Building on Meyer’s Theory of Emotional Syntax,” Music Perception 9, no. 1 (1991): 8–10. 50Jackendoff, “Musical Parsing and Musical Affect,” 229. Drawing on J. A. Fodor, The Modularity of Mind (Cambridge: MIT Press, 1983), Jackendoff suggests that on-the-spot processing of the “bottom-up” type “is modular and ‘informationally encapsulated’ from musical memory. [The parser] does not care whether the piece is familiar or not; it goes through pretty much the same motions regardless.”

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learning intervenes. Two systems of listening are thus at stake, each interacting yet independent of the other.51

Figure 9.3  Responses to Replacement

And so the timings of the various stages outlined in Figure 9.3 are left open. They are likely to vary considerably not only from one context to the next, but from one listener to the next as well. Some displacements may be sensed fairly readily. Evidence in their support may be overwhelming, and the listener’s initial doubt may be momentary and scarcely conscious. At other times, however, considerable thought and analysis may be required before the listener, retrospectively and with repeated hearings, “live” as well as “in his or her head,” is able to arrive at a conservative or radical reading, an integration of the disputed passage with an evolving sense of structure. (Worst-case scenarios involve outright dismissals, cases in which a passage of disruption is never made a part of such an emerging sense. Radical responses can often arise by default in this way, the result of a listener’s inability to follow through conservatively by sustaining an established meter against the forces of parallel alignment.) So, too, details are likely to vary from one listener to the next. The same listener may react conservatively to one context, radically 51See

Narmour, “The Top-Down and Bottom-Up Systems,” 3.

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to another. And still another listener may switch in midstream, succumbing quite suddenly to the conflicting evidence that, up to that point, had served merely as a form of opposition. And the possibility of a conservative or radical predisposition cannot be discounted either. The degree to which steady meters are internalized and made physically a part of the listener (the degree to which they are entrained, to use the terminology of the psychologist,52 synchronized with our biological and cognitive functions, our “internal clock mechanisms”),53 may vary. Some listeners may be more susceptible than others in this regard. And their conservative responses may be a function of that susceptibility. Quite apart from the musical context in question, in other words, listeners may be predisposed to respond in the way they do. Figure 9.4 takes this possibility into account, rearranging Figure 9.3 accordingly. Listeners arrive on the scene inclined to react conservatively or radically, to sustain an established meter or to yield in this respect.

Figure 9.4  Responses to Displacement (with predisposition) 52See

note 46.

53See the additional discussion of entrainment and “biological timing mechanisms” in

David Epstein, Shaping Time: Music, the Brain, and Performance (Cambridge: Schirmer Books, 1995), 135–49.

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The variables are numerous and complexity interwoven. Firmly established metrical frameworks favor conservative reactions, obviously, while literalness in the displaced repeat of a theme, motive, or chord will tend to favor the radical alternative, metrical parallelism and an interruption of the meter. Size can make a difference, too. With lengthier fragments, the difficulties in adjusting to a new metrical alignment are likely to increase: displaced chords are more easily assimilated. Tempo plays a decisive role in the disruptive potential of a displacement, as does metrical location. And both these factors are open to measurement.

Figure 9.5  Displacement and Metrical Location (Renard, Nos. 0–9)

Figure 9.5 shows a way of classifying displacements on the basis of their location within a given metrical hierarchy or grid. (The given hierarchy here derives from the opening allegro of Renard. The signature is 2/4, and the likely tactus is the quarter-note beat with a marking of 84). Location is defined by two interacting levels of pulsation, a slower level that “interprets,” “groups,” or marks off the beats of a faster, “pulse” level.54 The pulse level is the highest level 54Some

of these terms are borrowed from Harold Krebs, “Some Extensions of Concepts of Metrical Consonance and Dissonance,” Journal of Music Theory 31, no. 1 (1987): 101. “The levels of motion... break down into a ‘pulse level’ and one or more ‘interpretative levels.’ The pulse level is the fastest level. The slower levels are interpretative in the sense that they impose a metrical interpretation on the pulse level.”

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at which the placed and displaced entrances of a given fragment are beats, while the interpretative level is the next highest level at which those beats are marked off as onbeats or offbeats. In this way, displacement follows meter.55 At least two levels of pulsation must interact to meet its conditions, even if the effect of a given displacement may be felt at levels above and beyond that initial interaction. The levels of pulsation in Figure 9.5 are grouped in overlapping twos. At a degree marked 0, beats at the level of the tactus “interpret” beats at the subtactus level just below. Here, the potential for disruption is at its highest: repeated fragments fall on and off the tactus, specifically in Figure 9.5, the quarter-note beat. At the degree marked +1, beats at the level just above the tactus “interpret” the tactus. Here, repeated fragments fall on and off the half-note beat rather than the quarter-note beat. In Ex. 9.3a, entrances of the clarinet fragment are defined in this way, falling on and off the halfnote beat (or bar line). Beats of the half note rather than the quarter note are subject to interruption (quarter-note beats may continue uninterrupted), the disruptive effect of which is likely to be milder. This concerns time and timing as well as human psychology. The actual disturbance of the half-note beat at the degree of +1 may equal that of the quarter-note beat at the degree of 0. At a slower pace, however, displacement or the radical alternative of adding “extra” beats to the meter may be negotiated with greater ease. Traditionally, too, this is where meter is centered, namely, with the regularity of the tactus and the identification of that regularity with the human pulse. This where “the beat” is, so to speak, where the sense of a steady alternation between downbeats and upbeats or onbeats and offbeats is likely to be most vivid. Meter’s internalization is likely to be at its most sensitive, with immediate contact of this kind manifesting itself outwardly as well; at the level of the tactus or 55Krebs,

“Some Extensions of Concepts of Metrical Consonance and Dissonance,” 101–02. Or see Maury Yeston, The Stratification of Musical Rhythm (New Haven: Yale University Press, 1976), 66. Yeston defines meter as “an outgrowth of the interaction of two levels—two differently-rated strata, the faster of which provides the elements and the slower of which groups them.” A similar definition is given in Victor Zuckerkandl, Sound and Symbol: Music and the External World, trans. William R. Trask (Princeton: Princeton University Press, 1956), 162: “The metrical arrangement does not simply divide the temporal flux into many particles of equal length. In addition, it collects the particles together into little groups.”

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just above, with beats synchronized with the “rhythmic” character of biological or cognitive processes, feet are tapped, steps taken, and so forth.

Example 9.4a–d  Stravinsky, Renard, opening allegro

Then, as this acute sense of meter fades when moving away from the tactus, displacement fades, too. Extended beyond the degrees of 0 and +1 in the direction of hypermeter, displacements are felt less keenly. Internalization or entrainment is less marked, so that when a fragment is displaced and the meter threatened or interrupted as a result, the sense of disruption is less severe. With more time, the

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listener is likely to have less of a struggle with what may indeed have become entrained, made physically a part of him or her. Conservative or radical adjustments or readjustments are made more easily. Examples 9.4a–d show the displaced repeats of another fragment from the opening allegro in Renard, arranged here according to the graduated scale of locations of Figure 9.5. The initial placement is followed by three displacements at increasingly shallow locations: introduced on the beat of a twomeasure span in Ex. 9.4a, the fragment falls off the beat of that span in Ex. 9.4b, off the half-note beat or bar line in Ex. 9.4c, and finally off the quarter-note beat in Ex. 9.4d. While the last of these alignments is purely analytical in conception, the first three do indeed occur in Renard, and in the order given in Ex. 9.4a–c: following the initial placement, the degrees are progressively shallower, the displacements themselves progressively more disruptive in their potential.

Rebuttals

But is there no interaction at all between the style of developing variation and that of metrical displacement? Is the music of Schoenberg and Stravinsky wholly antithetical, as Adorno implies? And are Adorno’s “convulsive blows and shocks” altogether unforgiving? Is there no merit in displacement and the disruption it can cause? Even in the passage quoted from The Rite of Spring (see Ex. 9.1), where displacements in the repetition of the horn fragment A–D–C–D are likely to be disruptive of the meter, the experience can be mixed. Introduced off the half-note beat at rehearsal no. 67, the A–D–C–D fragment falls on the beat just before no. 68. Assuming that the shock of this initial shift can be absorbed without too much hesitation (assimilated either as a form of displacement or, by interrupting the meter with an “extra” quarter-note beat, as a parallel alignment), a second displacement on the beat a few bars later is likely to be more destructive. The uncertainty caused by the initial shift is likely to be renewed and strengthened. The possibility of such a second displacement is likely to be questioned first; the meter underlying it, second. While the quarter-note beat (here, at the pulse level) may

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continue uninterrupted, its interpretation by the half-note beat is likely to be the subject of a breakdown, with the distinction between onbeats and offbeats lost. In the listener’s scramble to reestablish his or her bearings (to reclaim, above all, a sense of the interpreting half-note beat), even the metrical character of the accompanying tuba fragment, otherwise consistent and in phase up to this point, is likely to be questioned. Indeed, the breakdowns are likely to continue through much of this passage. Introduced off the beat and on the fourth quarter-note beat of the 4/4 bar line, the horn fragment shifts to the first, third, and second quarter-note beats, respectively. Although effectively “spotting” each quarter-note beat in this way, the displaced repeats are not strictly cyclical in relation to the bar line, and the spans they define are highly irregular (see the brackets in Ex. 9.1). Yet the disturbances may remain temporary. Although irregularly spaced at first, repeats of the horn fragment reach the stable duration of eight quarter-note beats at rehearsal no. 70; seven successive repeats follow off the beat and on the second quarternote beat. (Although the notated meter shifts to 6/4 at this point to accommodate a number of conflicting periods in the accompanying parts, the 4/4 framework is likely to persist in the mind of the listener.) And the accompanying tuba fragment is stabilized even earlier, with repeats reaching the duration of sixteen quarter-note beats. Something of a resolution is thus forged as the two dance movements in question draw to a close. Alignment and harmonic coincidence are stabilized, with the disruption of the earlier bars (Adorno’s “shocks”) capable of being heard and understood as part of a larger plan of action, one with a beginning and an end. Far from being isolated and isolating, the disturbances may be reconciled within a larger, evolving structure. More specifically, at rehearsal no. 70, the final placement on the second quarter-note beat of the 4/4 bar line may be heard and understood as the “correct” reading of the horn fragment A–D–C–D. In turn, earlier alignments on the fourth, first, and third beats, respectively, may be read as displacements. Crucial here is the fragment’s concluding pitch D and the agogic accent of this pitch. The final placement on the second quarter-note beat allows D to

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fall on the downbeat of the 4/4 bar line, and in this way to acquire the metrical acknowledgment and support withheld from earlier repeats at rehearsal nos. 64–70. This, too, may contribute to the sense of resolution at rehearsal no. 70. It is as if, after much trial and error, the horn fragment had finally stumbled into place, finding the metrical location from which a maximum degree of stability could be derived. Indeed, displacements in Stravinsky’s music are not typically as disruptive in their potential as the ones cited in Ex. 9.1. Examples 9.5a–c show thematic statements from three works of the Russian era. Each of these statements consists of a displacement, whether notated or concealed by the radical notation; a short motive falls first on and then off the likely tactus, the half-note beat in Ex. 9.5a, the quarter-note beat in Ex. 9.5b and 5c. And despite the shallowness of the location and the disruptive potential (the degree of location is 0 in all three cases), a conservative reading is likely to fare with little resistance, with the displacements read as a form of syncopation.

Example 9.5a  Thematic Statements. Stravinsky, The Rite of Spring (1913), autograph

Example 9.5b  Thematic Statements. Stravinsky, Les Noces, IV (1917–23)

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Example 9.5c  Thematic Statements. Stravinsky, Symphonies of Wind Instruments (1920; 1947 version)

There are qualifications, no doubt. In Ex. 9.5a and 5c, not only are the displaced repeats concealed by the radical notation (which retains a single, fixed alignment for the repeated fragments), but the repetition is also somewhat shortened. In Ex. 9.5c, the motive D–D– D–B is shortened to D–D–B. And instead of a series of displacements, there is but one immediate shift. Yet the radical resistance to a conservative reading is still likely to be minimal. The evidence can still seem to be tipped heavily in favor of the effect of syncopation. And this has mainly to do with the strength of the meter that may be inferred in each case. In Ex. 9.5c from the opening of the Symphonies of Wind Instruments, the 2/4 meter of the rebarred, conservative reading is above all a product of the bell-like repetition of the pitch D in the opening bars. The regularity of this attack-pattern could not have been more forceful in this respect.56 In fact, the displacements in Ex. 9.5a–c are more likely to be binding than disruptive. The syncopation is likely to allow for a smoother and more continuous connection between the motives and 56See

the sets of metrical rules involving “events” and “attack-patterns” in Lerdahl and Jackendoff, A Generative Theory, 80–85. The reader may wish to compare the conservative rebarring of the opening block of the Symphonies in Ex. 9.5c to the analysis of this same material in Jonathan Kramer, The Time of Music (New York: Schirmer Books, 1988), 224–26. As in Ex. 9.5c, Kramer slices the thematic statement into two halves, with the second of these halves acknowledged as the modified repeat of the first. No meter is inferred, however, no quarter-note or half-note beat capable of interpreting or “grouping” the eighth-note beat. As a result, no syncopation is inferred either, no displacement of the first half of the statement by the second. Focusing almost exclusively on the collagelike structures of the Symphonies, the discontinuities posed by these structures, Kramer’s analysis is thus acutely radical in conception. No “normal beat” is inferred from works such as the Symphonies, no “reliable sequence of evenly spaced strong beats on any hierarchic level but the shallowest” (257).

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their subsequent repeats. With the initial spans of the three motives reduced to seven beats (see the brackets in Ex. 9.5a–c), the repeats arrive “too soon” and may actually have the effect of increasing the listener’s anticipation of the bar line. The reduced and irregular spans are a part of a process of compression.

Example 9.6a–d Stravinsky, Symphonies of Wind Instruments, opening

Examples 9.6a–d show an analysis of the opening statement of the Symphonies alone. Example 9.6a reproduces the notated barring of Ex. 9.5c; Ex. 9.6b rebars the statement conservatively with a steady 2/4 meter, exposing the displacement concealed by the irregular barring (the motive [D]–D–D–B falls first on and then off the quarternote beat); Ex. 9.6c eliminates the displacement by adding an eighthnote beat to the initial span (expanding the span from seven to eight quarter-note beats); and Ex. 9.6d eliminates both the displacement and the shortening of the repeat. With the repetition of the bell-like motive stripped of its invention in this way, something of the nature of that invention is revealed. The displacement of the motive may be heard and understood as a departure from an underlying stereotype, a variation in this respect. Significantly, too, at the end of the thematic statement at m. 6 (see Ex. 6a and 6b), the conservative reading arrives “on target” with the radical notation, a point of intersection

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that is likely to enhance the sense not only of a downbeat, but of an arrival as well. The pitch D returns at this point, with E likely to be interpreted as a metrically accented neighbor note. The syncopation of the repeat can heighten the listener’s sense of anticipation as the thematic statement as a whole draws to a close. Indeed, why not interpret the displacements in Ex. 9.5a–c as variations (even as developing ones), metrical alignment itself as a feature of the motive along with other such features identified in Schoenberg’s Fundamentals of Musical Composition?57 Conservative responses would seem to invite such a consideration, in any case, the idea of a motivic profile followed by its variants (displacements, in this case). The psychology of the conservative response would seem to correspond to that of the motive and its apprehension: reading through the displacement of a motive as it relates to an earlier alignment, listeners are likely to be struck above all by the change or relationship itself, not necessarily by the alignments considered separately or in an idealized adjacency or juxtaposition. Something of the transformation itself is sensed automatically (effortlessly), and this is what is likely to excite and to direct their attention conservatively. In these respects, the experience is little different from what we know of the phenomenology accompanying the perception of more traditional motivic relations.58 No doubt, there are qualifications here as well. In a lengthy study of metrical nonparallelism and the varied repetition of motives in traditional, tonal contexts, David Temperley has compared the difficulties of the former with the fast, automatic way in which ordinary motivic relationships are assimilated.59 When reinforced

57Schoenberg, Fundamentals of Musical Composition, 8–10. The various features of the motive cited and discussed are of four types, namely, rhythm, interval, melody, and harmony. Under rhythm, Schoenberg does in fact mention metrical displacement, describing it as “the shifting of rhythms to different beats” (10). But the few examples he provides are perfunctory and full of mediation, in fact, changes in many other dimensions. They are not likely to produce even the mildest effect of syncopation. 58The phenomenology of motivic detection and recognition is discussed in Dahlhaus, Esthetics of Music, 76–77. “The connection between the motivic variant, occupying the present, and the model it recalls is not ‘open to inspection’,” Dahlhaus writes. “The two motives are not side by side in the same sense as two phrases may be called ‘adjacent’ .... The fact of similarity between model and variant is clearer than the motive announced to begin with. The general existence of some connection is more striking than what specifically is being connected with what.” 59See David Temperley, “Motivic Perception and Modularity,” Music Perception 13, no. 2 (1995): 141–64.

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metrically by parallelism, motivic relationships “tend to be detected automatically,” he concludes, while, when not so enforced, they tend to be detected “only with difficulty” if at all.60 J. A. Fodor’s theories of perception are invoked as a means of explanation, the idea being that the detection of nonparallel relationships is “non-modular” in character; that of parallel relationships, “modular.”61 Yet the analogy with ordinary motivic variation is difficult to dispel. In the listener’s attempt to read through the displacement of a motive as it relates to an earlier placement (doing so by sustaining the meter against the forces of parallelism), it would indeed seem as if he or she were attempting to read through the displacement as a variation or modification. Attempts of this kind are difficult to explain in terms other than these. The displacement is read through motivically, in other words, as if metrical placement were indeed a feature of the motive. And to interpret a displacement conservatively in this way would indeed seem to be to interpret it motivically. With Adorno’s negative account of disruption generally, however, the concern is less with the variety of displacements in Stravinsky’s music and the severity of the disruption than with the nature of the experience itself. If meter is a “mode of attending,” as one theorist has claimed,62 a way of focusing the listener’s attention, what are we to make of its disruption? If there is satisfaction in letting go, in giving up and breaking away for a time (allowing, radically, for the regularity of a higher level of pulsation to take effect), what of the initial confusion of displacement, the disorientation into which, with varying degrees of intensity, the listener may be plunged? Theorists engaged with perceptual/cognitive issues have long stressed the emotional arousal that expectation can bring when inhibited or interrupted. And it has been some time now since Leonard Meyer first began discussing the affective experiences that “the deviation of a particular event from the archetype of which it is an instance” can cause.63 Surely the disruption of an established meter fits behavior of this kind. 60Temperley,

“Motivic Perception and Modularity,” 153–54. “Motivic Perception and Modularity,” 157. 62See Robert Gjerdingen, “Meter as a Mode of Attending: A Network Simulation of Attentional Rhythmicity in Music,” Integral 3 (1989): 67–92. 63Leonard Meyer, Explaining Music (Berkeley: University of California Press, 1973), 213. 61Temperley,

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At the same time, however, the larger psychological and aesthetic question has to do not with arousal as such, not with the state of alertness to which the listener may be propelled, but with the nature of the emotions stirred in one way or another. Are Stravinsky’s displacements and the disruption they can cause traumatic and psychologically damaging, as Adorno insists, or can they be “exciting” and a “delight,” as Meyer contends in his description of implication and delay more generally?64 And if displacement can be a “delight,” why should this be? Why should listeners of Stravinsky’s music be attracted to processes of displacement that disrupt their metrical bearings? Not just meter but meter internalized is the subject of the disruption. That to which meter attaches itself physically is affected and, in this way, brought to the surface of consciousness. (As we have suggested, even if the source of the disturbance is not known at first, it is likely to be sensed and felt all the same.) And this may be what alertness is, of course: the heightened sense of engagement brought about by disruption. By means of disruption, we are brought into closer contact with what we are internally, so to speak, with what we are, deep, down, and under. Meyer’s theory of arousal in music was derived in large part from John Dewey’s “conflict theory” of human emotion.65 The idea here was that emotion in music arose from the same general set of circumstances, namely, from the blocking of expectations, implications, or tendencies. Accompanied by a belief in the eventual resolution of the conflict (or clarification of the ambiguity), the inhibition, blockage, or arrest had the effect of heightening a sense of anticipation and suspense.66 “Delay pleasures play,” Meyer reasoned.67 “Expectation and reverie” could indeed be imagined as being “better than actuality.” In much music of the nineteenth century, delay can seem to have taken on a life of its own. The ways in which completion or closure is averted, suspense sustained, can seem to have grown ever more elaborate, and from both a harmonic and melodic standpoint. In poetic terms, the outwardly fragmentary and incomplete nature 64See

Meyer, Explaining Music, 213. Meyer, Emotion and Meaning, 14. 66See Meyer, Emotion and Meaning, 28–29. 67See Meyer, Explaining Music, 211. 65See

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of much music of this period can be identified with a yearning that is endless, “longing eternally renewed,” as Charles Rosen has expressed it in his discussion of the opening song of Schumann’s Dichterliebe.68 The emphasis on the purely negative side of pleasure (“negative pleasure,” as some have termed it)69 can seem sadistic or sadomasochistic as well. Pleasure is derived from the inhibition or blockage itself, the pain of want and desire, in other words, the withholding of a sense of arrival, completion, resumption, or release. Adorno himself acknowledged the “sadomasochistic” strains in Stravinsky’s music,70 in the composer’s “perverse joy in self-denial,” and in the shocks of his metrically displaced accents.71 Implications of this kind have doubtless been a part of music in the Western art tradition since, at the very least, the dawn of tonality itself. And there has been no dearth of acknowledgment. Heinrich Schenker likened the circuitous routes of his linear progressions to real-life experiences of “obstacles, reverses, detours, retardations, interpolations, and interruptions”;72 famously, the half-cadence at the close of an antecedent phrase was dubbed an “interruption” in the progress of such a progression.73 In recent studies of the psychology of anxiety, emotions have been identified more generally as “interrupt phenomena” that arise from the “interruption (blocking, inhibiting) of ongoing, organized thought or behavior.”74 More specific versions of this equation involve not one but simultaneously aroused and conflicting tendencies. Here, of course, the fit could not be tighter. Settings of metrical displacement in Stravinsky’s music involve the opposition of 68Charles

Rosen, The Romantic Generation (Cambridge: Harvard University Press, 1995), 41. 69See Jerold Levinson, Music, Art, and Metaphysics (Ithaca: Cornell University Press, 1990), 306–35. 70Adorno, Philosophy of Music, 159. 71Adorno, Philosophy of Music, 153. 72Heinrich Schenker, Free Composition, trans. Ernst Oster (New York: Longman, 1979), 5. “Therein lies the source of all artistic delaying,” Schenker wrote, “from which the creative mind can derive pleasure that is ever new.” 73Schenker, Free Composition, 36. 74George Mandler, “The Generation of Emotion,” in Emotion: Theory, Research, and Experience, ed. Robert Plutchik and Henry Kellerman (New York: Academic Press, 1980), 225. Recent theories of anxiety and emotion are discussed in Renee Cox Lorraine, Music, Tendencies, and Inhibitions: Reflections on a Theory of Leonard Meyer (Lanham: Scarecrow Press, 2001), 4–6.

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irreconcilable forces, those of meter and metrical displacement on the one hand, metrical parallelism on the other. To inhibit, arrest, block, delay, or interrupt one of these forces (an “ongoing thought or behavior”) is to stir the emotions. To displace a repeated theme, motive, or chord metrically is to thwart implications of parallelism and to disrupt the meter. It is to invite the “convulsive blows and shocks” to which a sizable portion of Adorno’s more specific criticism is directed. And so the question arises: if interruption and inhibition can be an accepted and even expected part of the listening experience of the tonal (or atonal) repertory to which Adorno adheres, why can it not be of the experience of Stravinsky’s music? Even if we grant the distinction in application—the emphasis on pitch structure in the tonal repertory, on rhythm and meter in Stravinsky’s—the processes substantiate the same general psychology. Moreover, metrical disruption is not unique to Stravinsky’s music. The disruption is less relentless in tonal works, as well as less immediate. There are fewer displacements, which in turn tend to be confined to less immediate levels of metrical pulsation, specifically to the bar line and above. Crucially, too, conflicting alternatives to meter and its continuation tend to surface in the form of alternative meters, ones that are often hemiola-related, while in Stravinsky’s music alternative meters of this kind are seldom an option, the conflict materializing in the form of an outright disruption or interruption of a prevailing scheme. A series of displaced repeats is invariably patterned and regular in earlier contexts, while in Stravinsky’s music it is often highly irregular (as it is in the passage from The Rite of Spring quoted in Ex.  9.1). And the repetition is far less literal in earlier settings; motives are transposed and varied melodically and harmonically as part of a more extensive process of developing variation. In the opening theme of the “Minuet” in Mozart’s Eine kleine Nachtmusik, K. 525 (see Ex. 9.7a), a rising two-note motive, straddling the 3/4 bar line at mm. 1–2 and 2–3, is displaced at m. 3. In the consequent phrase at mm. 5–7, the same motive, entering once again on the third quarter-note beat of the 3/4 bar line, is subjected to a cycle of displacement as part of a hemiola cadence (see the brackets in Ex. 9.7a). (Hemiolas in traditional contexts are

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often punctuated in this way by cycles of displacement.)75 In the “Preambule” from Schumann’s Carnaval, another two-note motive, starting on the downbeat in the left hand of the piano part, runs through two full cycles of displacement (see the brackets in Ex. 9.8).76

Example 9.7a–b Mozart, Einekleine Nachtmusik, Minuetto

Example 9.8  Schumann, “Preambule,” Carnaval

And in Ex. 9.9, from the second movement of Brahms’s Piano Quartet, op. 25, no. 2, a thematic phrase introduced and repeated on the third dotted quarter-note beat of the 9/8 meter (the likely tactus; see Ex. 9.9a) is subsequently displaced to the second beat (Ex. 9.9b) and to the first (Ex. 9.9c). In this third illustration, the displaced repeats do not make for an immediately patterned sequence, as they do in Ex. 9.7a and 75For

further discussion of the hemiola in the classical tradition, see Floyd Grave, “Metrical Dissonance in Haydn,” Journal of Musicology 17, no. 3 (1995): 168–202. 76Hemiola patterns of this kind in Schumann’s music are examined in Harold Krebs, Fantasy Pieces: Metrical Dissonance in the Music of Schumann (Oxford: Oxford University Press, 1999), 22–61.

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8. Yet they exemplify large-scale development all the same.77 The ambiguity of the tonic harmony over the bar line at mm. 1–2 (see Ex. 9.9a; the pitch B on the downbeat is most likely nonharmonic) is clarified by the motive’s subsequent displacement to the second beat of the 9/8 bar line (see Ex. 9.9b), a variation accompanied in turn by a modulation. Accordingly, extensive melodic and harmonic changes accompany the metrical dislocation, serving in this way as a form of mediation. There are mitigating circumstances, in other words, with metrical alignment, but it is one of many features affected in a more comprehensive process of development.

Example 9.9a–c  Brahms, Piano Quartet, op. 25/11

77Processes of metrical displacement (or metrical “relocation”) in Brahms’s music are

discussed briefly in Susan L. Kim, “Rhythmic Development in the Motivic Process of Brahms’s Chamber Music” (PhD diss., University of California at Santa Barbara, 2003), 114–30. See also Peter Smith, “Brahms and the Shifting Bar Line: Metric Displacement and Formal Process in the Trios with Wind Instruments,” in David Brodbeck, ed. Brahms Studies 3 (Lincoln: University of Nebraska Press, 2001), 91–129. I am indebted to Gordon Root for his many keen insights on the passages in Ex. 7, 8, and 9.

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In all three of these examples, the repetition, apart from the displacement itself, is far from literal. The motive is transposed and subjected to a variety of melodic and harmonic changes, all in keeping with an overreaching pattern of development and growth. In Ex. 9.7a, the cycle of displacement in the consequent phrase of the theme is a further development of the earlier motivic occurrences at mm. 1–2 and 2–3. More specifically, the earlier occurrences are compressed. As can be seen by the Schenkerian graph in Ex. 9.7b, the cycle defines a descending-third progression from scale degree 3 to 1, a B–A–G passing motion that, interrupted by the half-cadence of the antecedent phrase, is completed by the consequent. The descriptive terms here are in themselves reflective of the larger distinctions that can be brought to bear. At the same time, however, and notwithstanding differences of this kind, the many points of overlap cannot be ignored. Processes of implication, inhibition, and delay are as much a part of Stravinsky’s displacements as they are of the world of developing variation. As we have seen, significant overlapping occurs even in matters of metrical displacement. The effect of syncopation that typically accompanies hemiola patterns such as those illustrated in Ex. 7a and 8 may accompany Stravinsky’s displacements as well. Displacement, read conservatively, can be read motivically, in other words, as a form of variation. A pattern of displacements, even when highly irregular, as with the lengthy passage from The Rite of Spring in Ex. 9.1, can map out a form of development of its own, one capable of creating a sense of initial stability, departure, conflict, and resolution.78 So, too, just as with Adorno’s critical verdicts, the larger philosophical and sociopolitical images can often be set aside and reversed. They, too, are among the attached yet detachable components of his analytical description. The same features deplored and dismissed can be interpreted in a positive light. If the lack of expressive timing in the performance of Stravinsky’s music can spell coldness and indifference to the plight of the individual (Adorno’s musical subject), then it can spell directness 78See

in this connection Horlacher, “The Rhythms of Reiteration,” 171–87, where similar conclusions are reached from a different angle. Horlacher targets a number of patterned, superimposed cycles of displacement in the Symphony of Psalms, concluding that, even within a narrowly controlled set of variables, vertical or “harmonic” coincidence can exhibit a remarkable degree of variation.

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and unsentimentality, too, a determination to confront the world “as it is.” And if the lack of variation can imply intractability as well, the refusal of a collective voice to give way to the variations of the individual (a state of unfreedom, as Adorno understands it), then it can also reveal something of the hardness of the outside world, doing so without compromise or falsification. The possibility of such a “negative truth” was entertained briefly by Adorno himself in a later confirmation of the Philosophy.79 He asked whether, in the face of our “impotence” in confronting “the murderous collective,” a state of affairs “in which everyone is reduced to the status of potential victim,” a direct statement “about the way things are” would not be more persuasive than any “expression of musical subjectivity,” any “vain lament”:80 “Critics might insist that... the spirit of the age is deeply inscribed in Stravinsky’s art with its dominant gesture of ‘This is how it is.’ A higher criticism would have to consider whether this gesture does not give shape to an implicit truth which the spirit of the age denies and which history has rendered dubious in itself.”81 The cool objectivity (Sachlichkeit) so often attributed to Stravinsky’s neoclassicism was, of course, seen early on as a reaction to the nineteenth century, to the optimism and sense of belief that by the time of the Great War had grown suspect and even intolerable. Even later in the century, Lawrence Morton, Stravinsky’s friend and benefactor in Los Angeles, wrote of the spirit of contrariness in the composer’s music, the deflationary effect of its economy and concision.82 Instrumentation was a key issue here. The heavy pedals and doublings of Wagner’s orchestras (and Debussy’s) had been avoided even in relatively early works such as the finale of The Firebird and Petrushka, and replaced by the bouncy, soloistic, and transparent approach that would become Stravinsky’s trademark. Could Stravinsky’s lifelong recoil from the personal in music, from traditional notions of the self and self-expression (his “perverse joy in self-denial,” as Adorno phrased it),83 signal a recoil from vanity 79See

Adorno, “Stravinsky,” 149. Adorno, “Stravinsky,” 149. 81See Adorno, “Stravinsky,” 148–49. 82Lawrence Morton, “Incongruity and Faith,” in Igor Stravinsky, ed., Edwin Corle (New York: Duell, Sloane, and Pearce, 1949), 193–200. On the matter of Stravinsky’s “cool objectivity,” see Maureen Carr, Multiple Masks: Neoclassicism in Stravinsky’s Dramatic Works on Greek Subjects (Lincoln: University of Nebraska Press, 2002), 197–99. 83Adorno, Philosophy of Modern Music, 153. 80See

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and its conceits? Could the static quality of his music announce a more sober view of humankind and its prospects? And could the collective authority Adorno professes to hear so resoundingly in Stravinsky’s music, the collective will heard over against that of the individual, be that of an enduring truth or a demanding God rather than that of a fascist? Again, ideas similar to these were entertained briefly by Adorno, but rejected all the same. No sense of an awareness of this predicament could be detected by Adorno on the part of the musical subject.84 And the static implications of Stravinsky’s invention are for Adorno not just a style feature, but the negation of the medium of music itself. Being a temporal art, music must commit itself to “succession,” he insists, to becoming something new, to “developing.”85 What we may conceive of as musical transcendence, namely, the fact that at any given moment [music] has become something and something other than it was, that it points beyond itself—all that is no mere metaphysical imperative dictated by some external authority. It lies in the nature of music and will not be denied .... [Stravinsky] is beset by the crisis of the timeless products of a time-based art which constantly pose the question of how to repeat something without developing it and yet avoid monotony ... The sections he strings together may not be identical and yet may never be anything qualitatively different .... [Stravinsky] permanently wrote music about music, because he wrote music against music.86

As we continue to insist, however, the distinctive features of Stravinsky’s style are not so easily or so straightforwardly defined. The contrasts afforded by the model of developing variation, however insightful, are more often a matter of emphasis than of outright polarity or antithesis. They involve stress and frequency of occurrence. The literal and relentless nature of the repetition is not without parallel in nineteenth- and twentieth-century music, and there are a great variety of displacements in Stravinsky’s music, not all of which involve the disruption of an established meter. As we have seen, some may actually contribute to a sense of anticipation and engagement (see Ex. 5a-c). 84See

Padisson, Adorno’s Musical Aesthetics, 268. “Stravinsky,” 152. 86Adorno, “Stravinsky,” 153. 85Adorno,

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If Adorno’s approach to Stravinsky and his music can serve as a reminder of the hazards general observation is likely to incur when not sufficiently buttressed by analysis that is sufficiently concrete, then it can say something of the rewards of immediate impressions as well, of instincts pursued to the fullest. Displacement and its disruption are more varied and complicated than Adorno cared to admit. And the relationship between the developmental style and that of displacement in Stravinsky’s music is not as polarized as he imagined (or as he may have exaggerated, quite possibly for the sake of the argument). Rarely missing from his account, however, is a sense of struggle with what Stravinsky’s music is on an immediate level of contact, a determination to come to terms with that level. And it is this that is likely to excite and move the reader-listener to further reflection. Today’s tendency has been to applaud Adorno’s philosophy and sociology as sophisticated and radical, and to reject his analytical descriptions as half-hearted, crude, and dated.87 This is in part a reflection of postmodern trends in musicology. As it concerns Stravinsky and the Schoenberg-Stravinsky divide, however, the equation could be reversed. A motivic approach to music of the developmental style can hardly be judged inappropriate, and not all of Adorno’s analytical attempts along these lines are as piecemeal as those in the Philosophy or the later Stravinsky article.88 Surely the atonal and twelve-tone repertories of Schoenberg and his immediate predecessors can be viewed as intensely motivic in conception. And the juxtaposition of that style with processes of metrical displacement in Stravinsky’s music, qualified by the reservations noted here, is surely an appropriate way of proceeding analytictheoretically. In contrast, what can seem old-fashioned and even absurdly naive in Adorno’s writings about Stravinsky is a critical judgment that fixes musical value with a single style (with all other styles weighed 87See

Paddison, Adorno’s Musical Aesthetics, 9; or Johnson, “Analysis in Adorno’s Aesthetics,” 299–300. 88See for example Adorno’s thematic-motivic analysis of Berg’s Piano Sonata in Willi Reich, Alban Berg: Mit Bergs eigenen Schriften und Beitragen von Theodor Wiesengrund Adorno und Ernst Krenek_(Vienna: Herbert Reichner, 1937), 21–26. Adorno’s analysis is discussed in great detail in Paddison, Adorno’s Musical Aesthetics, 158–74, and Johnson, “Analysis in Adorno’s Aesthetics of Music,” 303–11.

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accordingly), verification with a single method of analysis (drawn from the single style), and musical expression with the terms and concepts laid down by that single style. Add to this a view of metrical displacement and its implications that are invariably one-sided (Adorno is steadfastly a radical interpreter of Stravinsky’s music, never a conservative one), and an aesthetics and sociology that, even if ultimately detachable from his critical judgments, purport to be founded on those judgments all the same, and the making of a large critical and aesthetic edifice in deep, wobbly trouble is surely unmistakable. Here again, however, the music to which Adorno refers may end up rescuing both the criticism and the philosophy. As long as the music continues to wield the sort of magic it has in the past, the speculative sides of his account are likely to be of interest and concern. This is not how Adorno himself might have envisioned the future, but for anyone less convinced about the nature of music’s sociopolitical content, it may be what we end up with all the same. For it allows an appreciation of both the music and Adorno’s analytical descriptions, setting aside all the while the necessity of having to subscribe to the larger sociopolitical convictions or to a belief in their musical embodiment (precisely what, as has been argued here, the coming years are likely to find increasingly problematic). Such an outcome can only work to the benefit of both music and its critical reception.

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Chapter 9

The Rite of Spring Briefly Revisited: Thoughts on Stravinsky’s Stratifications, the Psychology of Meter, and African Polyrhythm

Many of the dance movements of The Rite are stratifications, layered or polyrhythmic structures in which there is a superimposition of melodic fragments and rhythmic patterns that repeat according to varying cycles or spans. Another form of superimposition, stratification is static in its harmonic, registral, and instrumental implications. And so the question is posed: what accounts for the vitality of The Rite, the ability of this music to excite? Dynamic qualities in The Rite include the irregular accents and spans that mark off the repeats of fragments and chords, the displacement of these irregularly spaced repeats in relation to a steady pulse and meter, and the disruptions of the meter that are in turn brought about by displacement. I trace the physical impact of this invention to entrainment, the internalization of meter. The cognitive and biological implications of entrainment are discussed, including the evolutionary ones. Reprinted from Music Theory Spectrum, vol. 39, no. 2 (Fall 2017) The Music of Stravinsky: Collected Essays Pieter C. van den Toorn Text Copyright © 2017 Society for Music Theory Layout Copyright © 2023 Jenny Stanford Publishing Pte. Ltd. ISBN 978-981-4968-62-1 (Hardcover), 978-1-003-35916-6 (eBook) www.jennystanford.com

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Stratification of the kind found in The Rite is without precedent in the art music of Russia and the West. I turn therefore to the polyrhythmic textures of African drumming, in particular, Gahu, a well-known dance of the Southern Ewe in West Africa. Made up of six layers of distinct rhythmic patterns, the cyclic, repetitive features of Gahu are useful as a means of setting both sides of this comparison in relief. I make reference here to the aesthetic and analytical commentary of Reich (1973), Locke (1987), and Agawu (2003).

I

For all the celebrated complexity of Stravinsky’s ballet score of 1911–13, the materials are today not as analytically impenetrable as they appear once to have been.1 While the orchestration can still confound in places, the harmonic and melodic vocabulary is straightforward and consistent, as are many of the uses to which that vocabulary is put. Harmony in The Rite consists in large part of triads and dominant-seventh chords, melody of the (0 2 3 5) Dorian tetrachord, the latter often gapped by a minor third, with the four pitches reduced to three as a (0 2 5) or (0 3 5) trichord. (Pitch notation here follows conventions in van den Toorn [1987].) The tetrachordal melodies in The Rite, whether gapped or complete, are short, fragmentary, and open-ended, inviting the extensive and often quite literal repetition typical of the music of Stravinsky’s Russian period generally. Constrained by their range and repetitive treatment, they assume a folk-like character. We can get even more selective in these matters of vocabulary. The triads of The Rite are mostly major, while the dominant sevenths are mostly in first inversion and usually confined to within the octave— the (0 2 5 8) arrangement, in other words, reading down, with the chord’s root, seventh, and fifth bunched together and exposed as a 1Much the same can be said of the difficulties in timing, execution, and balance that for

so long plagued performances of The Rite. Many of today’s orchestras have overcome these difficulties, but often with the unfortunate consequence that their performances of The Rite can sound streamlined to the point of slickness; see Taruskin (2017).

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gapped (0 2 (3) 5) Dorian tetrachord.2 (See, at the outset of Ex. 1, the registrally fixed persistence of the pitches E♭, D♭, and B♭ of the (E♭ D♭ B♭ G) dominant seventh and the D♭–B♭–E♭–B♭ ostinato of the “Augurs of Spring.”)3 The Dorian tetrachord itself is also typically in closed position, bounded by a perfect fourth. Melody and harmony 2The (0 2 3 5) tetrachordal melodies of The Rite and other works of Stravinsky’s Russian

period implicate the whole step—half step or 2–1 ordering of the octatonic scale with a pitch numbering of (0 2 3 5) 6 8 9 11(0). The rationale behind the descending form of this 2–1 ordering is discussed extensively in van den Toorn (1987, 143–45) and van den Toorn and McGinness (2012, 42–44). One concrete reason for the descending approach involves the issue of priority or centricity. When moving from one block or section to the next in The Rite of Spring and other works of the Russian period, it is often an “upper” pitch and grouping that assume priority by means of doubling, metrical accentuation, and persistence. In the opening blocks of the “Augurs of Spring,” for example, the pitch E♭ along with (E♭ D♭ (C) B♭) and (E♭ D♭ B♭ G) assert priority by virtue of their predominance (see Ex. 1). If the pitch numbering and ordering are to reflect these conditions, the descending (E♭–D♭–C–B♭)–A–G–F♯–E–(E♭) scale, with E♭ as pitch number 0 and (E♭ D♭ C B♭) as (0 2 3 5), is the logical choice. Three recent publications on The Rite of Spring make use of a top-to-bottom reading of Stravinsky’s materials. In Chua (2007, 69), the author underscores the upside-down character of the E♭-major key signature and the “Augurs of Spring” chord at Rehearsal no. 13 (see Ex. 1). In McDonald (2010, 511), attempts to link the interval orderings of various configurations in The Rite to “durational patterns” also employ a descending form of representation. Joseph Straus letters the (0 2 3 5) melodies in The Rite and elsewhere in Stravinsky’s music in descending order, primarily as a way of emphasizing the polarity between melody and harmony, top and bottom; see Straus (2014). The letters assigned to the harmonic fifths and triads in the bass ascend in Straus’s study, just as they do in van den Toorn (1987), van den Toorn and McGinness (2012), and here above. 3The analytical formats of Ex. 1, 2, 3, and 4 are derived from van den Toorn (1987, 149–74) and van den Toorn and McGinness (2012, 48–50). Briefly, as it relates to the opening blocks of the “Augurs of Spring” (see Ex. 1): the first group of staves consists of quotations from the score (important fragments, chords), while the second group consists of the relevant (0, 3, 6, 9) octatonic partitioning elements, followed by a vocabulary of mostly (0 2 3 5)s, triads, and dominant sevenths. (The commas separating pitch numbers 0, 3, 6, and 9 in the (0, 3, 6, 9) designation distinguish this sequence of numbers as a cycle or transpositional path. (0, 3, 6, 9) is not a unit of vocabulary, in other words, as a tetrachord or diminished-seventh chord.) The final level features the octatonic and diatonic scales of reference, which, by means of stems and beams, are made to incorporate something of the segmentation of the upper levels. Dotted vertical lines through the analysis signal octatonic-diatonic interaction. The octatonic set is limited to three collections (or transpositions) of distinguishable content, which are labeled I, II, and III in accord with van den Toorn (1987, 143–44), Taruskin (1996), and van den Toorn and McGinness (2012, 42–43). An account ofthe intervallic redundancy and symmetry of the octatonic set (set-class 8–28) may be found in Berger (1972, 130–35) and van den Toorn and McGinness (2012, 42–47).

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are tightly knit in this way, as is pitch-relatedness generally in The Rite. Indeed, it is easy to imagine The Rite as having been composed in the fashion later recalled by Stravinsky himself, that is, “quickly” and in one fell swoop from September 1911 to early January 1912.4 Location and instrument of choice were locked in as well; nearly all of The Rite was composed on a muted upright piano in a small closetlike space in Clarens, Switzerland. This is not to ignore all manner of prefigurement in the form of early improvisations in the mind of the composer and at the piano. Conceived in a dream of a “pagan ritual” while Stravinsky was still at work on The Firebird (a “vision” in which “a sacrificial virgin danced herself to death”),5 The Rite actually began with a few sketches (now lost) in the summer of 1910. This project was soon interrupted for the “sort of Konzertstuck” that would become the second tableau of Petrushka.6 The orientation for the vocabulary mentioned above is typically octatonic, sometimes diatonic or octatonic-diatonic in combination, with the diatonic decidedly modal rather than tonal, often coming in the form of the D scale or Dorian mode.7 The fourth- or fifth-related Dorian tetrachords of the D scale, in their intersection with the minorthird and tritone-related (0 2 5) tetrachords of the octatonic set, are sometimes extended beyond the D scale along the circle of fourths/ fifths. But there is nothing particularly new about these collectional or scalar orientations, either. As Richard Taruskin has detailed on several occasions,8 Stravinsky inherited the references along with the accompanying vocabulary from his teacher and mentor, Nicholai Rimsky-Korsakov. Rimsky-Korsakov’s source for the octatonic was undoubtedly Liszt’s octatonic passages such as those featured at the close of the third movement of the Faust Symphony. 4Stravinsky

(1962b, 161–62). 159. 6Stravinsky (1962a, 82). 7To rephrase this question of a referential orientation from the standpoint of the vocabulary itself: triads, dominant sevenths, and (0 2 3 5) tetra-chords related by a minor third or tritone are octatonic in terms of a single transposition or a (0, 3, 6, 9) partitioning of the set. (0 2 3 5) tetrachords related by a fourth or fifth implicate the D scale. 8Taruskin (1996, 272–306); Taruskin (2011). 5Ibid.,

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Example 1  The Rite of Spring, Part I: excerpts, analytical reduction (continued)

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Example 1 (continued)

Stravinsky, Adorno, and the Art of Displacement

What dramatically sets Stravinsky’s octatonic uses apart, however, is his practice of superimposing the triads, dominant sevenths, and Dorian tetrachords of the octatonic set. Thus, in Ex. 1, (E♭ D♭ B♭ G) is superimposed over (E G♯ B), while the ostinato of the “Augurs of Spring” is superimposed over the triadic outlines (E G B) and (E G C);9 or, in Ex. 2, a D-scale-on-A melody is superimposed over (E♭ D♭ B♭ G) and (C E G) at the opening of the “Ritual of Abduction.” (The triadic configuration in Ex. 2 is derived from the superimposition of the ostinato over (C E G) in triplets at Rehearsal no. 15.) The dissonant “bite” of this invention, from which startling melodic, instrumental, and rhythmic implications were to accrue,

9The half step that relates (E♭ D♭ B♭ G) to (E G♯ B) and the D♭–B♭–E♭–B♭ ostinato to (E G D) is non-octatonic; (E♭ D♭ B♭ G) implies Collection III, while (E G♯ B) and (E G B) imply Collection I. Nevertheless, this half-step relationship between the triads and dominant sevenths of a compound sonority reappears in the opening and closing sections of the “Sacrificial Dance,” transposed to (D C A F♯) and (E♭ Gb B♭) and subsequently to (A G E C♯) and (B♭ D♭ (F)), respectively; see the analysis of the concluding four pages of the “Sacrificial Dance” in Ex. 7 and 8. In van den Toorn (1987, 151, 174), the bass pitch E at Rehearsal no. 13 is isolated from (E G♯ B), (E G B), and (C E G) as the most stable member ofthese accompanying triads (the only member shared by all three triads). The resultant (E♭ D♭ B♭ G) (E) configuration, abridged to E♭–B♭, E, substantiates the 0–5, 11 basic sonority of The Rite; see note 11. Dmitri Tymoczko, solely on the basis of a “note count,” assigns the configuration at Rehearsal no. 13 to the harmonic-minor scale on G♯; see Tymoczko (2002, 78). This assignment is in lieu of musical reality, however, since it ignores the triadic content of the configuration, the registrally defined superimposition of (E♭ D♭ B♭ G) over (E G♯ B), and the issue of priority or centricity for the context as a whole. The abundance of successive and overlapping scales in Tymoczko (2002) may be compared to the pitchclass sets in Forte (1978). The selection, grouping, or segmentation in both studies is too often at odds with (or indifferent to) the obvious in this music from the standpoint of analysis, perception, composition, and history. Straus assigns the configuration at Rehearsal no. 13 to his “Model 1,” given the semitone that relates the melodic span E♭–B♭ to the E–B fifth in the bass; see Straus (2014, 9–11). Compare Straus’s E♭–B♭/ E–B “bi-quintal” structure at Rehearsal no. 13 to the E♭–B♭, E or 0–5, 11 basic sonority cited above and in note 11. The latter sonority is intended to “cover” non-octatonic as well as octatonic passages in The Rite (Straus’s Models 3 [when articulated by major triads] and 6 as well as 1), serving in this way an analytic-theoretical purpose different from the one outlined by Straus. Often enough, Straus’s literature-wide models and accompanying descriptive analysis intersect in significant ways with van den Toorn (1987) and van den Toorn and McGinness (2012).

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opened up a new universe for Stravinsky, one that he was to render peculiarly his own.10

Example 2  The Rite of Spring, “Ritual of Abduction,” opening

The harshness of the dissonance in The Rite of Spring is for the most part octatonic in conception. It lies highly exposed, owing to the lengthy stretches in which the interval of a major seventh enclosing a perfect fourth or tritone (again, reading down, from 10See

Taruskin (1996, 407) and (2011, 176). On several occasions Taruskin has pointed to a possible precedent for Stravinsky’s methods of triadic superimposition in a late sketchbook of Rimsky-Korsakov. Among the sketches for an opera that was never completed (penned in 1908, evidently, the year of Rimsky-Korsakov’s death), several measures feature a superimposition of the tritone-related triads (B D♯ F♯) and (F A C). And it may well be, as Taruskin has insisted, that, along with the octatonic triads and (0235) tetrachords, the idea of superimposing these units of vocabulary arose with Stravinsky’s teacher. Still likely to startle, however, is the immense distance that separates, by only a few years, Rimsky-Korsakov’s late sketches from The Rite of Spring. When combined with methods of displacement, juxtaposition, and, above all, stratification, superimposition takes on a radically different complexion. Not only octatonic triads, but also all manner of repeated, stratified entities are placed in superimposition. The technique becomes integrated into a newly constructed whole.

Stravinsky, Adorno, and the Art of Displacement

top to bottom) is sustained without a sense of progression or resolution.11 Crucially, in Part I and much of Part II of The Rite, the dissonant seventh operates between rather than within melodic fragments; thus, in Ex. 1, the stretch from E♭ to E between (E♭ D♭ B♭ G) on top and the pitch E in the bass; in Ex. 3, the top-to-bottom stretch from G to G♯ that encloses the tritone-related tetrachords, (G F E D) and (C♯ (B) A♯ G♯), the upper tetra-chord extracted from a diatonic D scale on G framework, the lower one gapped; or, in Ex. 4, the same superimposed tetrachords in the “Ritual Action of the Ancestors.” Taken individually, the fragments in these sections are for the most part diatonic and even archaically so. Typically in The Rite of Spring, as Pierre Boulez decreed some years ago, a “horizontal diatonicism” stands poised against a “vertical chromaticism.”12 But this description of The Rite overlooks a key detail in pitch relations, namely, the shared status of the Dorian tetrachord where the octatonic and diatonic sets are concerned and its subsequent ability to serve as a connecting link, qualifying the nature of the referential interaction. 11The

octatonic pitch-numbering of this configuration is 0–5, 11, where 0–5 signifies the “upper” (0 2 3 5) tetrachord, and pitch number 11 signifies the “lower” major seventh. At the final level of analysis in Ex. 1, 2, 3, and 4, the reader will find some of the octatonic scales of reference bracketed in accord with this 0–5, 11 vertical interval span. Interestingly, further along in the “Glorification of the Chosen One” and the “Sacrificial Dance,” the 0–5, 11 span is detached from its earlier triadic and tetrachordal superimpositions, becoming an independent sonority, a unit of octatonic vocabulary in its own right. Later, too, a pitch number 6 may substitute for the 5, an “upper” tritone replacing the perfect fourth. On the role of the 0–5, 11 vertical span in The Rite, see van den Toorn (1987, 145–74) and Taruskin (1996, 939–65); Taruskin views the span as the “harmonic source chord” of The Rite, its “global unifier”; and see note 9 above. In Straus (2014), 0–5, 11 is a segment of the “bi-quintal” structures of Models 1, 3 (major triads) and 6; obviously, triadic and (0 2 3 5) tetrachordal elaborations of Straus’s Models 3 and 6 abound in The Rite. See, in connection with Model 6, the tritone-related (0 2 3 5)s outlined in the analytical portions of Ex. 3 and 4. Crucially, Straus’s ideas about the “bi-quintal” nature of Stravinsky’s harmony incorporate the notion of a super-imposition involving opposing halves—melody and harmony, in Straus’s view. 12Boulez (1991).

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Example 3  The Rite of Spring, “Ritual of the Rival Tribes,” stratification, principal fragments

The subsumption of Stravinsky’s superimposed triads, dominant sevenths, and Dorian tetrachords by a single transposition or a (0, 3, 6, 9) partitioning of the octatonic set does not cancel altogether the compound nature of the superimposition, the ability of the encompassed components, as Arthur Berger explained some years ago, to acquire “equal and thus independent weight” and “to stand in a certain opposition.”13 Just as with the tritone-related triads of the notorious “Petrushka chord,” the composer-pianist’s right and left hands, representing the upper and lower components of the configuration as a whole, appear to have played an essential role in this conception of triads and (0 2 3 5) tetrachords standing “in a certain opposition.” Stravinsky composed at the piano, it should be recalled in this connection, preferring not only to test everything out in actual sound, but also to profit from the chance discoveries of improvisation. “Fingers are not to be despised,” he confided in his 1935 autobiography; “they are great inspirers and, in contact with 13Berger

(1972, 133). The opposite is also true, namely, that the compound nature of a configuration need not erase the sense in which the two components coalesce or mesh as a single, independent sonority. See, in Ex. 2, the superimposition of (E♭ D♭ B♭ G) over (C E G); transposed and repeated extensively in subsequent passages of the “Ritual of Abduction,” the configuration becomes a unit of vocabulary in much the same fashion as its embedded 0–5, 11 vertical span in terms of E♭–B♭, E. See note 11.

Stravinsky, Adorno, and the Art of Displacement

a musical instrument, often give birth to subconscious ideas which might otherwise never come to life."14

Example 4

"Ritual Action of the Ancestors," stratification, Reh. nos. 134, 138

The assumption here is that superimposition and its confrontational nature in The Rite form an integral part of the listener's experience of this music. Nearly all dimensions of Stravinsky's score are brought to bear in this connection. At Rehearsal no. 37 + 2, for example, the two superimposed entities, (Eb Db Bb G) in the trumpets and (C E G) in the horns, are kept apart in their registers and instrumental assignments (see Ex. 2). They are kept 14Stravinsky (1962a. 31). The composer's use ofthe piano as a compositional tool in articulating polarized halves of a compound sonority (or "polychord") is discussed in Straus (2014, 9). Stravinsky's habits in this regard may be compared to those of his nemesis across town for about ten years in Los Angeles, Arnold Schoenberg. In a letter dated 29 July 1944, Schoenberg sternly advised that "a real composer is not one who plays first on the piano and writes down what he has played. A real composer conceives his ideas, his entire music, in his mind, in his imagination, and does not need an instrument"; see Schoenberg (1965, 218).

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apart instrumentally and as separate layers in the opening pages of the “Augurs of Spring” as well. In some fashion, then, listeners are apt to hear superimposition.15 The triads, dominant sevenths, and (0 2 3 5)s brought together in the form of a clash in The Rite are the entities that, earlier in the music of Stravinsky’s immediate past, succeeded one another expressively in the form a progression. Something of a shock may thus accompany the listener’s experience of these techniques of superimposition, the sense, quite possibly along with it, of an old and familiar vocabulary turned on itself. (We can imagine The Rite as aggressive music in these respects, as we can where the convulsive effects of metrical disruption are concerned. The latter will occupy our attention in subsequent sections.) 15The

results of experiments with the “Petrushka” chord in Krumhansl (1990, 226– 39) are somewhat equivocal as to whether, in controlled circumstances, listeners hear the clashing of two separate entities or a single octatonic sonority. But surely there are listeners who hear Stravinsky’s “chord” in more ways than one, possibly at different split-seconds; they hear something of the ambiguous, conflicted nature of the tritonerelated triads (A♯ C♯ F♯) and (C E G), triads which are sometimes superimposed in Stravinsky’s score, sometimes separated, and sometimes arpeggiated in such a way as to expose the F♯ as a chromatic tendency tone to the G (or A♯, C♯, and F♯ as tendency tones to B, D, and G, respectively); see note 13 above. In Agawu (2011, 187–89), the author voices considerable skepticism about the possibility of the (0, 3, 6, 9) symmetrically defined, octa-tonic triads and their superimposition in The Rite and other Stravinsky works entering the everyday listening experience (unprodded by theory or analysis, in other words). But hearing is a complex matter, as Agawu himself admits. The inability of the layman (or professional, for that matter) to identify or define explicitly or in music-theoretical terms the Stravinsky phenomena cited above is no reason to believe that these phenomena do not impose themselves on the listener’s imagination in one way or another. As reasoned by Kendall Walton many years ago, much theory and analysis may well be a specification of what is heard by ordinary listeners, subconsciously or without acknowledgment. Furthermore, analysis and hearing are two sides of the same coin. “Noticing” a revealed relationship—“perceiving [the relationship] while acknowledging one’s perceiving of it”—can have a profound effect on appreciation or “aesthetic gratification” (Walton [1993, 42]). “Immediacy [as in aesthetic immediacy] knows nothing of itself,” Carl Dahlhaus mused some time ago. What counts is a “second immediacy,” he averred, one conditioned by reflection, however informal; see Dahlhaus (1982). Dahlhaus’s “second immediacy” encompasses Edward Cone’s Second and Third Readings, the first of these consisting of analysis, the contemplation of a “static art-object,” the second of an experience made more vivid by reflection; see Cone (1977, 79–81). Milton Babbitt tried to reassure the more skeptical of his twelve-tone students that they could in fact “hear these different notes.” “It’s not a matter of hearing,” Babbitt insisted; “it’s a matter of the way you think it through conceptually with your musical mind” (Babbitt [1987, 23]).

Stravinsky, Adorno, and the Art of Displacement

At the same time, the clashing of triads undermines harmonic implication, the sense of movement that each component may embody individually within a tonal framework. Stravinsky’s superimpositions are static “coagulations,” as Boulez described them, annulling a true sense of development.16 To follow Theodor Adorno here as well, Stravinsky wrote “music against music” in the sense that he sought to defy what is musically inherent, namely, “succession.” “As a temporal art,” Adorno explained, music is bound to the fact of succession and is hence as irreversible as time itself. By starting it commits itself by carrying on, to becoming something new, to developing. What we may conceive of as musically transcendent, namely the fact that at any given moment it has become something and something other than it was, that it points beyond itself— all that is no mere physical imperative dictated by some external authority. It lies in the nature of music and will not be denied.17

The combination of an octatonic vocabulary, superimposition, dissonance, and stasis, unknown to audiences in 1913, is without parallel in the music of Stravinsky’s contemporaries. No equivalent to the sound of this combination can be found in Schoenberg’s works of “extended tonality,” for example, or in the freely dissonant music of the Second Viennese School.18 The traditions enveloping the atonal and serial repertories of this School are for the most part foreign to The Rite. As we have seen, the spread of a major seventh at Rehearsal no. 13 in the “Augurs of Spring” lies between the individual, reiterated fragments (see Ex. 1). The origin of this dissonance rests not with the chromatically altered chords in the music of Liszt or Wagner, but rather with the superimposing of unadulterated triads, dominant sevenths, and Dorian tetrachords, the latter a mostly octatonic vocabulary inherited directly from Rimsky-Korsakov. 16Boulez

(1991, 57). (1998, 151). 18This is not to overlook the existence of octatonic moments in the music of, say, Schoenberg. In the “Tanzscene” of his Serenade (1924), the tri-tone-related triads (G B D) and (D♭ F A♭) are superimposed in the Landler episode; the two triads emerge as subsets of the octatonic set-class 6–30, the hexachord of the “Petrushka” chord. Perhaps not coincidentally, the Serenade was one of Stravinsky’s favorite Schoenberg works; its use of the mandolin inspired his own use of this instrument in Agon (1953– 57). Stravinsky thought the spirit of the Serenade (with its opening March) akin to his own “Soldier’s Tale”; personal communication with Robert Craft, July 2013. 17Adorno

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Moreover, what Schoenberg called developing variation— the processes of motivic development this composer associated with Brahms and the music of the Classical style more generally—has even less relevance in this context. In developing variation, motivic features are altered as part of an overreaching train of thought.19 Yet the very melodic, harmonic, and rhythmic characteristics heavily engaged by the developmental processes traced by Schoenberg are precisely those that, in The Rite of Spring, are often retained literally from one motivic repeat to the next. The passages illustrated by Ex. 1, 3, and 4 are stratifications; the superimposed fragments and chords may repeat polyrhythmically according to varying spans or cycles.20 The fragments are not transposed or developed; in other words, they are not tossed about from one instrument to the next in the form of a sympathetic dialogue (as they are, typically, in works of the Classical style from, say, Haydn’s “Farewell” Symphony to the beginning of the twentieth century).21 Rather, each fragment, fixed registrally and instrumentally, is repeated quite literally from a melodic, rhythmic, and articulative standpoint. Missing is thus not only a sense of forward motion, but of harmony as well, at least insofar as harmony is understood as encompassing chords leading to and away from each other. The stratifications in these examples are virtually immobile. They lead not to climactic moments, but tend rather to be cut off abruptly, often as separate blocks within larger formations of such blocks. 19See Schoenberg (1967, 8): “Homophonic music can be called the style of developing

variation. This means that in the succession of motive-forms produced through variation of the basic motive, there is something that can be compared to development, to growth.” Ideas encompassed by Schoenberg’s use of the term “developing variation” underlie much current understanding of the Classical style generally; see Dahlhaus (1980, 40–52), and Frisch (1983). 20In connection with Stravinsky’s music, the term stratification first appeared in Cone (1972) as a way of describing the block structures in three Stravinsky works, one from each of the three stylistic periods. Cone used the term to describe the vertical slicing-up of the materials into discrete blocks which, repeated, are placed in a kind of juxtaposition with one another. Here, however, stratification refers to the horizontal, polyrhythmic layering of fragments and chords whose spans or cycles of repetition may vary independently of each other. The latter use appears in Cross (1998, 18– 104), van den Toorn and McGinness (2012, 4), and Straus (2014, 5). 21For a highly detailed account of motives and their developing variations in Haydn’s “Farewell” Symphony, see Webster (2004).

Stravinsky, Adorno, and the Art of Displacement

II No doubt, altered chords are not the only source of chromaticism in the music of Lizst, Wagner, and the nineteenth century. As we have suggested, the chromatic (octatonic) chains of minor-third related triads and dominant sevenths in this nineteenth-century music are linked quite explicitly to the superimposition of this vocabulary in The Rite; we can trace the octatonicism in The Rite back to the octatonic sequences in Rimsky-Korsakov’s operas and symphonic poems, as well as to those in Lizst’s music. We might acknowledge as much with the construction of a few appropriately designed Tonnetze. Such a move would allow the materials of The Rite to be angled somewhat more abstractly: intersecting interval cycles would replace the octatonic and diatonic scales of Ex. 1–4 (stems, beams, and all), and the vocabulary would be allowed to float free of any consideration of priority. Tonnetze can seem to imply succession rather than superimposition, but the geometry is far from clear-cut in this regard. If we assign the minor-third cycle to the vertical axis, the triads and (0 2 3 5)s running up and down this column could just as easily imply superimposition as succession. Beyond these considerations, however, it is the panoramic view afforded by this retreat into greater abstraction that attracts; the vocabulary of a given octatonic transposition and its interaction with the circle of fourths/fifths can be seen and heard within the larger universe of such interactions. A glimpse can be caught, in other words, of what belongs and what does not where the vocabulary and interacting references of an individual context are concerned. Vast abstractions from the concrete, then, atemporal and with little sense of registral location, Tonnetze are “less real than imaginary.”22 Yet the ones sketched in Ex. 5 and 6 are useful as summaries or encapsulations of two repeats of the principal block of the “Ritual Action of the Ancestors” and the main section of the “Dance of the Earth.” Both blocks or sections are stratifications; the reader will find them condensed and analyzed as such in Ex. 4 and 1, respectively. 22Hyer

(1995, 101–2).

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The Tonnetze in Ex. 5 and 6 feature an intersection between the (octatonic) minor-third cycle along the vertical axis and the descending circle of fourths along the northwest-to-southeast diagonal. The (0 2 3 5) tetrachord and its gapped trichordal subsets, (0 2 5) and (0 3 5), traverse these two main arteries, the former represented graphically by squares, the latter by triangles within the squares. (See the short prefacing graphs in Ex. 5 and 6; the shaded triangles represent the (0 2 5)s, while the (0 3 5)s are left blank).23

Example 5  Tonnetz, (0 2 3 5) tetrachords; “Ritual Action of the Ancestors,” Reh. nos. 134, 138 (see Ex. 4)

Inversionally related, (0 2 5) and (0 3 5) mirror the parallel relationship between minor and major triads sharing a root: in moving from one to the other, the outer pitches enclosing the fourth are retained while the inner pitch moves by semitone. In The Rite and other Russian-period works, however, the (0 2 5)s predominate over the (0 3 5)s to such an extent that the potential for a form of 23Tonnetze

featuring the (0 2 3 5) tetrachord and its (0 2 5) (0 3 5) subsets are examined in van den Toorn and McGinness (2012, 144–46). These models are pursued in connection with Les Noces, however, and their designs vary.

Stravinsky, Adorno, and the Art of Displacement

smooth voice leading—with (0 3 5) serving as an intermediary between transpositions of (0 2 5) along the minor-third cycle—is rarely if ever realized.24

Example 6  Tonnetz, (0 2 3 5) tetrachords; “Dance of the Earth,” Reh. nos. 74– 79 (see Ex. 1)

Finally, along the vertical axis in Ex. 5 and 6, transpositions of the minor-third cycle yield the three overlapping transpositions of the octatonic set, which are labeled I, II, and III. 24In

transposing from, say, (G F D) to (G E D) and then to (E D B), the intermediary (G E D) ensures the retention of two pitches at each step. However, in the second step from (G E D) to (E D B), the third pitch is unable to proceed incrementally by tone or semitone. See Richard Cohn’s arguments about “parsimonious” voice leading and the privileged status of the triad; Cohn (1997, 1–15) and Cohn (2012). Also privileged, to follow Cohn, is the major-third over the minor-third cycle as a transpositional path in the chromatic music of the nineteenth century. Cohn cites the contrary or “bidirectional” motion in the semitonal voice leading between triads of a single 4-cycle, along with enharmony and its association with magic and the supernatural; Cohn (2012, 17–25).

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Given the density and extent of the stratification at Rehearsal nos. 134 and 138 (see Ex. 4), the reduction of this octatonic (Collection I) block to the tritone-related (0 2 3 5)s outlined in Ex. 5 (see the shaded squares between the Collection I columns) might strike the listener as scarcely credible, at least at first blush. The (B♭ D F) in the timpani is not represented in Ex. 5. This triad, together with (D♭ C♭ (A♭) F) in the horns, yields the familiar superimposition inherited from the opening pages of the “Augurs of Spring” and the “Ritual of Abduction” (see Ex. 1 and 2); (E♭ D♭ B♭ G) (C E G) is transposed (D♭ C♭ [A♭] F) (B♭ D F), inside Collection I.25 Moreover, at Rehearsal no. 134, the pitch F♯ in a new sequence in the trumpets conflicts with Collection I, as does, at Rehearsal no. 138, the open string C in the cellos and double basses, which replaces the C♯ at Rehearsal no. 134. The extra resonance of the open string was likely the deciding factor in this replacement; the circle of fifths is extended downward by a notch, D–G–C.

Example 7  “Sacrificial Dance,” Reh. nos. 192–201 + 1 (end); octatonic triads, dominant sevenths; (B♭, D♭, F) 25At Rehearsal no. 138 (Ex. 4), see the additional superimposition of (B♭ A♭ D) between

the trumpets and horns over (G B D) in the lower strings. The chordal disposition of this configuration, with a dominant seventh superimposed over a major triad related by a minor third, assumes a prominent role throughout much of The Rite. In addition to the examples cited here, see the “Ritual of Abduction” at Rehearsal nos. 40 + 6 – 43 and the stratification at Rehearsal nos. 87–89 in the Introduction to Part II. The 0–5, 11 vertical interval span lies embedded within the sonority; see note 11.

Stravinsky, Adorno, and the Art of Displacement

In contrast to the octatonicism of the “Ritual Action of the Ancestors,” (0 2 3 5)s are transposed along the circle of fourths in the main section of the “Dance of the Earth” (see the quotations and analysis in Ex. 1). Beginning at the northwest corner of the Tonnetz in Ex. 6, (E♭ D♭ C B♭) is followed by (B♭ A♭ G F) and (F E♭ D C) along the northwest-to-southeast corridor (see the shaded squares). These (0 2 3 5)s enter separately in the order designated but are subsequently superimposed and repeated in the by-now familiar manner of a stratification. (E♭ D♭ C B♭) assumes priority here by virtue of its persistence (or survival) from one dance movement to the next, as it does in much of Part I. The opening blocks of the “Augurs of Spring” and “Ritual of Abduction,” as condensed in Ex. 1 and 2, are especially relevant in this connection. In an unmistakable nod to the octatonic, however, (B♭ A♭ G F) and (F E♭ D C) are extended downward by a single pitch to include E and B, respectively, outlining the tritone relationship in each case. In Ex. 6, dotted lines along the octa-tonic Collection I and II columns dip down to include the two pitches in question. Related octatonically to (E♭ D♭ C B♭) is the punctuating chord (C E G/F♯), which, together with (E♭ D♭ (C) B♭) in the upper parts, yields the triadic superimposition cited just above. The tritone motive C–F♯ in the timpani is also octatonic in relation to (E♭ D♭ C B♭), and it splits the whole-tone scale in half, the latter making a rare appearance not only here in The Rite of Spring but also in Stravinsky’s music as a whole. The rising whole-tone scale is repeated as a basso ostinato in the lower strings throughout the “Dance of the Earth”; in Ex. 6, half of it is shown running along the horizontal axis, reading from right to left.

III

The four concluding pages of the “Sacrificial Dance” (and hence of The Rite itself) are among The Rite’s most octatonic (see Ex. 7). In the scope and intensity of the octatonic commitment, these pages match lengthy sections of the “Ritual of Abduction” and the “Ritual Action of the Ancestors.” The section of which they are a part is both a transposition and extension of the opening passages of the “Sacrificial Dance.”

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Setting the octatonic in motion in these closing pages is, once again, the dominant-seventh chord in its closed, 65 position—the (0 2 5 8) top to bottom arrangement, with the chord’s root, seventh, and fifth exposed as an (0 2 5) trichord. To the left of the reduction in Ex. 7 is (A G E C♯), here with the root doubled and with a lower B♭ marking off the critical stretch of a major seventh.26 Numbered in circles are the four layers of superimposed, reiterating dominant sevenths and triadic outlines, of which the first and third layers are derived directly from (A G E C♯/B♭); as the stems and beams show, the pitch F joins C♯ (D♭) and B♭ to form the (B♭ D♭ F) outline of the first layer, while (A G E C♯) initiates a descending series consisting of the four dominant sevenths of Collection III. Layers 2, 3, and 4 are wholly octatonic in terms of Collection III, while (B♭ D♭ F) is foreign to that collection. Pitch-wise, however, only the fifth of (B♭ D♭ F), the F, lies outside Collection III.

Example 8  Tonnetz, triads; “Sacrificial Dance,” Reh. nos. 192–201 (see Ex. 7) 26See

note 11.

Stravinsky, Adorno, and the Art of Displacement

The four superimposed layers of Ex. 7 are not only fixed in their registers and instruments, but are rhythmically locked into each other as well, synchronized unvaryingly from start to finish. In the Tonnetz sketched in Ex. 8, major and minor triads replace the (0 2 5) s and (0 3 5)s of the previous Tonnetze. And while, as before, minor thirds and the descending circle of fourths run along the vertical and northwest-to-southeast arteries, respectively, major thirds rather than whole steps occupy the horizontal axis. The shaded triangles between the Collection III columns represent the triads of the octatonic layers 2, 3, and 4; (A C E) is inferred from the A–C motive in the timpani, layer 4. Lying to the right of the Collection III columns and encircled by dotted lines is (B♭ D♭ F) and the pitch F. In the entirety of these closing pages of the “Sacrificial Dance,” vertical slices of varying length from the superimposition outlined in Ex. 7 are repeated again and again. Only the pitch F clashes with the octatonic vocabulary of layers 2, 3, and 4.

IV

Questions are likely to arise at this point about the aesthetic attraction of the superimposed and stratified textures of The Rite of Spring, radically new in 1913 and perhaps to this day still capable of startling and even shocking first-time listeners. If these textures are indeed as static and deadlocked harmonically as we have suggested (lacking in a traditional sense of harmony, progression, and variation), to what can we attribute their vitality? The extraordinary popular and critical success of The Rite from the moment of its first concert-hall performance (19 May 1914, in Paris) to the present day constitutes a true rarity in the annals of the avant-garde of the past century.27 What accounts for the resilience of this music, the ability of The Rite to excite all these years? success of the initial concert performance of The Rite was repeated virtually without exception in the remaining capitals of Europe and North America, and even in Soviet Russia, in Leningrad and Moscow in 1926. Indeed, it now appears that, far more than Stravinsky’s score, it was the unorthodox character of Vaslav Nijinsky’s choreography that caused members of the audience to erupt in protest on the evening of 29 May 1913, at the Theatre des Champs-Elysees in Paris; see Taruskin (2016). In the critical reviews that followed this production on the morning after, attention was focused almost entirely on the ballet. Some of these reviews, as reproduced in Lesure (1980), acknowledge the composer but make no mention of the music.

27The

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Reproduced in Ex. 9 is an excerpt from the massive stratification that begins in “The Ritual of the Rival Tribes” at Rehearsal no. 64 and ends at the close of “The Procession of the Sage” at no. 71. Seven layers of reiterating fragments and rhythmic patterns are superimposed at this stage of the stratification, several of which repeat according to cycles or spans that vary independently of one another. The brackets in this example mark off the spans separating repeats of the segments, while the numbers represent the number of quarter-note beats encompassed by each bracket.

Example 9  “Ritual of the Rival Tribes,” stratification, Reh. nos. 67–68 + 2

Example 10 singles out the two most prominent layers of the stratification excerpted in Ex. 9. In the horns and tubas, the two fragments are Dorian tetrachords, the lower of which is gapped. These two reiterating fragments, related by a semitone (the

Stravinsky, Adorno, and the Art of Displacement

relationship is non-octatonic),28 grind against one another like the heavily rusted gears of a locomotive. As the brackets show in Ex. 10, the spans between successive repeats of the horn fragment are irregular. They number six, eight, thirteen (repeated three times), seventeen, six, and finally eight quarter-note beats. Something like a resolution to this conflict is forged at Rehearsal no. 70, as the repeats of the tuba fragment attain the stable and metrically reinforcing duration of eight quarter-note beats. (The notated meter shifts to 4 at this point to accommodate a number of conflicting strands in the accompanying parts, but the 44 framework is likely to persist in the listener’s mind.) In turn, repeats of the A–D–C–D fragment in the horns are displaced metrically (see Ex. 10); beginning just before Rehearsal no. 67, these repeats enter on the fourth, first, third, and second quarternote beats of the 44 bar line, falling off and on the half-note beat as the likely tactus at 83 beats per minute.29 The changes in metrical location and in the length of the spans are highlighted by what does not change, namely, everything else. Pitch, register, dynamics, and instrumentation are held constant, as the vertical alignment of the fragment shifts in relation to the other fragments and to the meter. (Even the articulation of the horn fragment, with the pitches A and D accented and D-C-D slurred, is fixed from one displaced repeat to the next.) This dynamic applies to the remaining fragments in Ex. 9 as well; the literalness of the repetition serves as a foil for the changes in alignment. 28See

note 9. introduced here, metrical displacement differs from the idea of a “displacement dissonance”; see Krebs (1999, 31–39). Displacement dissonances are the products of recurring off-beat patterns: a recurring motive, equal in length to the measure, may begin off the beat or bar line. Such a motive is not metrically displaced in the current view because its alignment relative to the bar line never changes; in other words, repeats of the motive are aligned identically. On the other hand, Krebs’s “grouping dissonances” frequently involve the metrical displacement of a recurring motive, although there are important distinctions here as well. In The Rite, the repetition of a metrically displaced motive is most often literal in all other ways—in its pitch, register, instrumentation, and articulation. Moreover, the spans separating motivic repeats are often irregular; see the spans between the repeats of the horn fragment as bracketed in Ex. 9 and 10. These and other distinctions are pursued in greater detail in van den Toorn and McGinness (2012, 38–41).

29As

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Example 10  The Rite of Spring, “Ritual of the Rival Tribes,” “Procession of the Sage,” stratification, principal fragments, Reh. nos. 64–71

Stravinsky, Adorno, and the Art of Displacement

And so the attraction (or vitality) of The Rite of Spring would seem to lie first and foremost with its rhythms (or patterns of duration), as these rhythms are played out against a mostly static landscape of stratified, reiterating melodic fragments and polarized, dammed-up harmonies. More specifically, the attraction lies with the irregular accents and spans that mark off the repeats of fragments and chords, in part with the displacement of these irregularly spaced repeats in relation to a steady pulse and a meter, and in part with the expectations of metrical parallelism that are in turn thwarted by displacement.30 It also lies, presumably, with the disruptions of the meter that may be brought about by thwarted expectation. When a fragment such as the one featured in the horns in Ex. 10 is displaced relative to a meter, the listener’s expectations that the fragment will be repeated at a metrically parallel location are frustrated. Since metrical parallelism can play a role in the actual establishment and subsequent confirmation of a meter, frustrating the listener’s expectations in this regard can have the effect of challenging and even disrupting the meter. In Ex. 10, expectations of this kind are foiled when the repeat of the horn fragment just prior to Rehearsal no. 68 is displaced from the fourth to the first quarternote beat (downbeat) of the 44 measure. The listener is likely to respond to this displacement in one of the following ways:



1. Conservatively, with the 44 meter sustained or conserved (quite possibly after a split-second jolt); the displacement of the repeated fragment, exposed by Stravinsky’s conservative notation, is heard and understood as such; 2. Radically, with the 44 meter disrupted; retroactively, the listener adds an extra quarter-note beat to the count just prior to the repeat, allowing the repeat to be heard and understood in a metrically parallel fashion (on the fourth beat of the 44 bar

30See

Lerdahl and Jackendoff (1983, 74–76). The authors treat metrical parallelism as a “metrical preference rule.” In passages of displacement or non-parallelism, this rule comes into conflict with “well-formedness rules” stipulating that the beats of a metrical level of pulsation must be equally spaced. Most often in the traditional contexts examined by Lerdahl and Jackendoff, the latter trumps the former; the more “global” demand for meter and equally spaced beats overrides the “local” one for metrical parallelism. In other words, the repeated motive, melody, or chord is read as metrically displaced or non-parallel.

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line); the conservative split-second jolt becomes a full-fledged interruption;31 3. The meter is suspended temporarily or indefinitely.

We should note in caution, however, that the radical alternative cited above is apt not to represent a response in the same way that the conservative one does. In Ex. 9 and 10, the conservative notation exposes the metrical displacement of the horn fragment just before Rehearsal no. 68; conservatively, listeners respond to the displacement accordingly. In the event of a disruption of the meter, however, the radical response to the displacement of this fragment is far less likely to consist retrospectively of an interpretation of the repeat as metrically parallel to the original alignment. (When Stravinsky’s radical and conservative barrings are viewed as a whole, they appear to have little bearing on how listeners actually respond to a given displacement, radically or conservatively.) While, in theory, listeners would react radically in the manner indicated above by response number 2, the reality would presumably be a good deal messier, perhaps something along the lines of response number 3.32 The difficulties associated with response number 2 involve not only tempo and metrical location, as we suggest directly below, but also the reflexive behavior of listeners where meter is concerned, a matter to which we will be turning in the following section. Whether, in the face of a displacement, the listener’s metrical bearings are merely threatened (in a conservative vein) or disrupted altogether (in a radical one) hinges on a great many factors, tempo and metrical location perhaps above all. Indeed, it is the middle, moderato range of the metrical hierarchy that is most salient to 31The

distinction between conservative and radical responses—between allowing the meter to be sustained and allowing it to be interrupted—was first made in Imbrie (1973, 46–66). The distinction was then introduced in Lerdahl and Jackendoff (1983, 23–25) as a way of classifying alternative readings of hypermeter at the opening of Mozart’s G-Minor Symphony, K. 550. It has been applied to various responses to Stravinsky’s music; see van den Toorn (1987, 67), Horlacher (1995, 285–310), and van den Toorn and McGinness (2012, 20–28). 32This conclusion is somewhat at odds with the analyses of the radical response in van den Toorn and McGinnis (2012). The latter analyses tend to stress the ability of the listener to respond radically to a metrical interruption by hearing the displacement in a metrically parallel fashion. The question is perhaps ultimately one of degree; see Ex. 13(a) in connection with our later discussion of the radical barring that opens the “Evocation of the Ancestors.”

Stravinsky, Adorno, and the Art of Displacement

the listener, where levels of pulsation range from about 80 to 100 beats per minute.33 It follows, therefore, that the displacement of a fragment or chord on and off either the tactus or possibly the level of pulsation just above is potentially the most disruptive in its effect. In Ex. 10, as we have indicated, repeats of the horn fragment fall off and on the half-note beat, with the tactus at 83 beats per minute.

V

Triggered by the metrical displacement of repeated fragments and chords in The Rite, disruptions of the meter affect the listener physically through the mechanism of entrainment, the psychological means by which meter is internalized. Entrainment speaks directly to the impact of The Rite on our senses. Meter penetrates the mind and body, of course, by way of the eardrum, which, in response to the impulses of sonic vibrations, moves back and forth sympathetically. The impulses are converted into neural signals traveling first to the brainstem and then to the brain. Expectations of the sort mentioned above (those of metrical parallelism) are raised, confirmed or frustrated in the prefrontal cortex. Music floods the brain, quite literally, engaging nearly all regions as well as all neural subsystems.34 Crucially, however, it is not just that music echoes and is constrained by our physical selves, our “biological clock mechanisms.”35 More dramatic and consequential still is something like the reverse of this equation, namely, that our internal clocks echo and become synchronized with metrical pulsation. These clocks are oscillations or back-and-forth motions; meter consists not of pulsation alone, but rather of at least two levels of pulsation, with the slower one marking off the faster one into equal spans of two or three beats. The result is the familiar back-and-forth, strong-weak or down-up alternation. (Even with a series of ticks or taps that are phenomenally identical, listeners will tend automatically to “group” them into twos, threes, and fours. Such reflexive behavior, studied for well over a century, has been termed “subjective rhythmicization.”)36 33London

(2004, 31). (2006, 85–86). 35Epstein (1995, 138). 36Fraisse (1982, 55–56). 34Levitin

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Yet the more specific seat of this remarkable capacity to internalize meter may be our brains. The process may have to do with neural networks, as Robert Gjerdingen has proposed,37 networks that oscillate as a matter of course. In Gjerdingen’s computer model set up in 1989, the ebb and flow of excitation and inhibition between two neural populations is made to enter into an up-and-down oscillation, the “tick-tock of a neural metronome.”38 If the rate of excitation and inhibition between populations is doubled, the metronome will beat a 34 waltz time. Quarter-note and dotted half-note periodicities will combine to form a composite, ternary output. Greater metrical complexity is achieved by adding additional neural populations. How any of this might work in the real world still remains something of a mystery. However, it is evident that, in one way or another, listeners entrain to meter, which in turn becomes physically a part of us. Entrainment is automatic (reflexive) as well as subconscious (or preconscious). Like walking, running, dancing, and breathing, meter is a kind of motor behavior, as Justin London has described it.39 Once entrained, it is abandoned by the listener only in the face of “strong contradictory evidence.”40 Hence, with special reference to The Rite of Spring, the explosive potential of an actual disruption of the meter, the physical effect a disturbance of this kind can have on the listener. The physical character of The Rite arises therefore, from entrainment and from the challenges to and disturbances of an attuned metrical grid. This physicality may account to some degree for the immediacy of The Rite’s effect on a great many listeners, the ability of these listeners to become readily engaged with the raw, relentless character of the dissonance.

VI

Stratifications of the kind illustrated in Ex. 1, 3, 4, 9, and 10 are without precedent in the art music of Russia and the West. Yet they can bring to mind the music of other cultures all the same, 37Gjerdingen

(1989, 67–92). 70. 39London (2004, 5–6). 40Lerdahl and Jackendoff (1983, 27). 38Ibid.,

Stravinsky, Adorno, and the Art of Displacement

and perhaps most spectacularly in this respect, they recall the polyrhythmic textures of African dances and drum ensembles. The thought of such a correspondence to African polyrhythm must surely have occurred to any number of enthusiasts of Stravinsky’s music familiar to a degree with African music through recordings and the transcriptions of numerous scholars. The thought is unlikely to have escaped the composer Steve Reich, in any case, as familiar as he appears to have been some years ago with the repetitive methods of Stravinsky and those in turn of various percussion ensembles in Ghana.41 The correspondence is worth pursuing briefly here not only for the additional light it can shed on Stravinsky’s notated bar lines and on the nature of meter. The completely ahistorical nature of the relationship carries with it a certain fascination of its own. At least, there is currently no evidence linking Stravinsky at the time (or any other time, for that matter) to a studied or even casual awareness of African polyrhythm. On separate continents and in isolation from one another, Stravinsky and percussion ensembles in Africa cultivated a polyrhythmic principle in which, against a metrical backdrop, two or more motives or rhythmic patterns of varying length are repeated as ostinatos.42 Example 11 shows David Locke’s transcription of a Southern Ewe dance, Gahu,43 which was subsequently reproduced in Kofi Agawu’s Representing African Music.44 Another transcription of this dance appears in Steve Reich’s memoirs, Writings on Music,45 but it is modeled after the “polymetric” approach favored by earlier scholars 41See

Reich (2002, 55–56). Reich’s biography is well known in this regard. The composer began studying African drumming while a student at Columbia University in 1967. He made an extended visit to Ghana in 1970, enrolling in The Institute of African Studies at the University of Ghana. While there, he made several transcriptions of African dances, although in the “polymetric” mode inherited from A. M. Jones (1959). 42Some definitions of polyrhythm are more elaborate than others. See, for example, the Preface to Arom (1991). The New Harvard Dictionary of Music (1986, 648) reads as follows: “Polyrhythm is the simultaneous use of two or more conflicting rhythms, that are not readily perceived as deriving from one another, or as simple manifestations of the same meter.” 43Locke (1987, 78). 44Agawu (2003, 81). 45Reich (2002, 60).

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such as A. M. Jones.46 The reiterating patterns that are beamed and that enter in staggered fashion in Ex. 11 effectively served as starting points for the staggered bar lines in the earlier “polymetric” transcriptions.

Example 11  Polyrhythmic texture of Gahu, a Southern Ewe dance, as transcribed by David Locke (1987, 78)

As with Stravinsky’s stratifications generally, the six different layers in Gahu represent different instruments as well as distinct rhythmic patterns; reading from high to low or top to bottom in Ex. 11, the ensemble includes a bell, a rattle, and four differently sized drums, the largest of which is the lead drum. Like most of the reiterating fragments in Stravinsky’s layered structures, the 46Jones

(1959). See Burns (2010, 13–16) for a detailed account of developments in the transcription of African drumming since the time of Jones’s publication.

Stravinsky, Adorno, and the Art of Displacement

patterns in Gahu are ostinatos, cycled again and again with little if any modification. (The lead drum may introduce variation, but mostly in keeping with the length and shape of the pattern.)47 Agawu defines bell patterns such as the one transcribed in Ex. 11 (see the top layer, Gankogui) as consisting of “short, distinct, and often memorable rhythmic figure(s) of modest duration ... usually played by the bell or high-pitch instrument in the ensemble”; each pattern serves as “a point of temporal reference” and is repeated as an ostinato throughout.48 Notwithstanding the distinctions in pitch and instrumentation, Agawu’s definition of an African time line fits many of the reiterating fragments of the stratifications shown in Ex. 1, 3, 4, 9, and 10. Many of these latter fragments and patterns from The Rite of Spring are true ostinatos, while others are irregular from the standpoint of the spans defined between repeats. From the vantage point of the meter, many are also supporting “references.” This includes the tuba fragment traced in Ex. 9 and 10, whose spans, although initially irregular, are all multiples of four. Each repeat of the tuba fragment is placed identically in relation to the bar line. In polyphony generally, attention is drawn to the individual character of the fragments or motives, as each of these relates to the others and to the meter in a distinct way. More so than with the idioms of the Classical style, perhaps, the meter lies in the background of Gahu, overshadowed by an abundance of phenomenal accentuation in the foreground. Although the downbeat of each 44 measure carries “power” and a sense of “resolution,” the quarter-note beats receive equal stress. To follow Locke, the 44 meter of Gahu is an “African 44”: the downbeat of each measure “functions physically—in the body and mind—rather than sonically.”49 As we have seen, however, the physical incorporation of meter, to the point where metrical beats are felt by the listener, is a reflexive form of behavior common to listeners in general, not to African listeners in particular. The reflex may be tens of thousands of years old, in fact, with a long evolutionary history, as many scientists now believe.50 47Locke

(1987, 79–123). (2003, 73). 49Locke (1987, 19). Metrical stress in the performance of Ewe music is also discussed in Burns (2010, 8). 50See Merker (2000, 320) and Patel (2008, 402–4). 48Agawu

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What ultimately distinguishes Stravinsky’s stratification in Ex. 9 and 10 are the varying lengths of the reiterating fragments (most of which extend beyond a measure), the irregular spans between repeats of the horn and tuba fragments, and the displacements of the horn fragment in relation to the 44 bar line. (Notice, in Ex. 9, that the two patterns in the bass drum and tamtam are hemiolas or grouping dissonances as they relate to the 44 bar line and the hypermetrical count of four measures; each pattern, three quarter-note beats in length, returns to its initial alignment after three measures.) A real sense of conflict prevails in Ex. 9 and 10, as if each layer were in competition with the others. Compared to Gahu, indeed, parts of the stratification condensed in these two examples can sound like a war zone. To be sure, Gahu is immobile soundwise (“harmonically”), and its reiterating patterns, confined to within a measure, are of varying length. The patterns are also fixed in register and instrumentation, just as they are in Stravinsky’s stratifications. In Gahu, however, they are fixed in their alignment as well; from one measure-repetition to the next, there are no displacements either among the patterns or as each pattern relates to the quarter-note, half-note, and whole-note beats (44 bar line). And so the listener’s perception of a superimposition of varying or conflicting lengths is apt to be less pronounced; Gahu lacks the range of pitch, register, and instrumentation that had been available to Stravinsky. Indeed, many of the fragments and patterns in Ex. 9 are defined as much by pitch as by rhythmic figuration. In the oboes and lower strings, the spans bracketed in this example are entirely a matter of pitch. The six patterns of Gahu fit together as intricate clockwork, creating something like a musical mobile; the repetition does not change, but the listener’s perception may. There are upbeatdownbeat reversals or “Gestalt flips” (as Locke has described them);51 the stressed offbeats of the patterns of the first and third layers (see Ex. 11) might suddenly be perceived as onbeats, while, 51Locke

(1987, 22). Burns takes issue with Locke’s ideas about changing or “multiple reference points” in southern Ewe drumming, suggesting that the experience of these “alternate frameworks” by “enculturated listeners” has not been tested; see Burns (2010, 16).

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subtly, the perceived grouping may change as well. These shifts can be magical in their effect. Both The Rite of Spring and Gahu are tied to the dance, although in very different ways. Gahu’s ties in this regard are more “inseparable” than the Rite’s.52 Performed by men and women, Gahu is a circle dance; in accord with the four quarter-note beats of the meter, small, gliding steps are taken first counter-clockwise and then clockwise while, from the shoulders down, arms are swung gently in the opposite direction.53 The dance is “conservative” in character, given the emphasis it places on the 44 meter, the means by which the exposed upbeats of the first and third patterns of Locke’s transcription (see Ex. 11) are heard and understood as such. Many of Nijinsky’s choreographic designs for The Rite are conservative as well, including the celebrated opening block of the “Augurs of Spring” and its subsequent restatements (see the excerpts at the outset of Ex. 1). On the evening of the premiere, the audience was confronted at Rehearsal no. 13 with what Stravinsky later described (mockingly) as “a circle of knock-kneed and longbraided Lolitas jumping up and down”;54 the jumping would have been accompanied by the hammer-like action of the repeated eighth notes, interrupted by the heavy, irregularly spaced accents in the horns.53 Although the dance obscured the quarter- and half-note beats of Stravinsky’s conservative notation (a 42 meter is applied), the attentive listener might have extracted these from the parallelism of the ostinato pattern, sounded five times against a sustained chord just before Rehearsal no. 13. Internalized in this way, the meter would have allowed the initial irregularly spaced accents to be heard as written, that is, as syncopations falling off the quarter-note beat as the tactus. Further along at Rehearsal no. 13 + 4, however, as the accents are displaced from off to on the quarter-note beat, the 42 meter is likely to have been disturbed. The remaining three measures of this block may well have been heard as meterless, with the meter itself reduced to pulsation (the pulsating eighth-note beats). 52See

Reich (2002, 56–57) and Locke (1987, 8). Locke (1987, 8). 54Stravinsky (1962b). 53See

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Locke treats Gahu as “an autonomous aesthetic force,” an “artifact” or “work” performed the world over for the past several decades by amateur and professional groups with little reference to the original meanings of the song texts, drum rhythms, and dance movements.55 Gahu is now seen and listened to for its own sake, in other words, irrespective of the historical, geographic, and cultural circumstances of its creation. No doubt, as Locke assures us, something of the “African mind and soul” remains, allowing Gahu to stand as a generalized symbol of a traditional culture.56 Such may be the case with recordings and concert performances of The Rite of Spring as well. Dim images of pagan rites and pre-historic Russia, as originally conceived by Stravinsky and Nicolas Roerich, may yet inflect the listener’s experience.

VII

In fact, there are many other ways in which, revealingly, rhythmicmetric phenomena in The Rite of Spring may be compared to various rhythmic practices in African music. In her book, The Music of Central Africa, Rose Brandel struggles with the transcription of a number of songs from the Republic of Congo (formerly Zaire) and other regions in Central Africa.57 In her attempts to bar a Mangbetu song, she finds herself up against a dilemma familiar enough to scholars of African music: whether, “conservatively,” to apply a steady meter (34 here; see Ex. 12[a]), or, “radically,” to shift the bar line “additively” in accord with the irregular accents (Ex. 12[b]). She opts for the second of these alternatives, the rapidly changing bar lines, explaining that the syncopation implied by the first alternative— the irregular accents within a metrical framework—is foreign to the “Mangbetu conception” and to African rhythm more generally. “The subsuming of an independent, asymmetric line under a ‘counter’ line of regularity,” she asserts, “would be a falsification of the rhythmic intent of the music.”58 55Locke

(1987, 6). 6. 57Brandel (1961, 73–76). 58Ibid., 74. 56Ibid.,

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More recently, however, Kofi Agawu, examining the same song, has come to a very different conclusion.59 Opting for Brandel’s “conservative” alternative (Ex. 12[a]), Agawu argues that the notion of syncopation is indeed valid in the context of African music and that irregular accents are regularly heard as stressed offbeats against the background of “a recurring metrical cycle.” Brandel relied too heavily on recordings, according to Agawu. She overlooked the “choreographic component” that would have exposed the meter to a greater extent.60

Example 12  Rose Brandel’s demonstration of “two ways of notating the same [Mangbetu song]” (1961, 74)

As for the present observer, he would have sided with Agawu in this disagreement, not out of any special knowledge of the repertory in question, but rather because of entrainment and what Bruno Repp and other psychologists have called sensorimotor synchronization,61 the ability of spectators, performers, and dancers to respond to the stimulus of a periodic beat by reflexively internalizing and moving in synchrony with it. Quite apart from the musical issues raised by Brandel and Agawu, in other words, the metered version of the Mangbetu song favored by Agawu (Ex. 12[a]) presumes an 59Agawu

(2003, 86–90). 2003, 90). 61Repp (2005, 2009, 27–28). Repp’s experiments with synchronization are for the most part finger-tapping exercises; participants are asked to tap in synchrony with a sequence of evenly spaced beat tones. In some of these experiments, a beat tone is shifted forward (delayed) and the unconscious “correction response” of the participants is tested. As a rule, the tap immediately following the delayed beat tone is delayed somewhat. Circumstances of this kind are not all that distant from those in which the repeat of a motive would be displaced metrically and the listener’s conservative or radical response would be gauged. 60Agawu

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engagement with the cognitive and biological processes discussed above. For the songs, dances, and rhythmic patterns characteristic of much African music to have been conceived and performed without the coordinating support of a meter and its entrainment would have been odd indeed. (The great advantage of entrainment and synchronization involves anticipation and timing, the ability of listeners and performers to predict with certainty and precision.) But the larger point here concerns the correspondence mentioned above, the underlying rationale that links Brandel’s alternate barrings of a Mangbetu song to the conservative and radical notation in Stravinsky’s music. Stravinsky’s stratifications are usually barred conservatively, that is, with a steady meter. Apart from the perceptual implications, there is an obvious practical need in performance for a steady beat and meter to coordinate the irregularly spaced spans defined by the repetition in the various layers. On the other hand, the block juxtapositions examined at length by Gretchen Horlacher and others appear generally to have invited a radical approach on Stravinsky’s part.62 Here, the bar line shifts in order to accommodate the irregular accents and spans. In Stravinsky’s music, as we have indicated, the irregularity of these accents and spans often coincides with a fragment and its subsequent repeats. Irrespective of the irregular spans, in other words, the fragment and its repeats are barred identically, and exhibit in this way a form of metrical parallelism.

Example 13  The Rite of Spring, “Evocation of the Ancestors,” opening block

62Horlacher

(2011).

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Stravinsky can also be inconsistent in his conservative and radical barrings. Example 13(a) shows a reduction of the opening block of the “Evocation of the Ancestors” in Part II of The Rite. An initial fragment, spanning seven quarter-note beats (see the bracket), is immediately followed by its shortened re-peat.63 The notation is radical; Stravinsky imagines the listener as interrupting her metrical bearings (should there be any) in order to hear and understand the fragment and its shortened repeat as metrically parallel; both segments fall on the downbeats of the measures in question. (To adopt Harald Krebs’s terminology: the “pulse”—the quarter-note beat—may continue unimpeded in the listener’s mind, but its “interpretation” by the half-note beat is never firmly established.)64 However, the radical barring of this passage is at odds with the experience of the present listener. Extracting and entraining to a 22 (or possibly 44) meter, he hears the shortened repeat of the fragment as a displacement. The fragment falls first on and then off the halfnote beat, the likely tactus with a marking of 120 beats per minute (see the conservative rebarring in Ex. 13[b]). In effect, the repeat is heard as a syncopated version of the original. The accents in the third measure of Ex. 13(b), while re-enforcing the second half-note beat and downbeat of the third and fourth measures of the radical barring of Ex. 13(a), respectively, are here heard as giant syncopations off the half-note beat. This conservative response is not entirely free of complication. As experienced by the present listener, the response is heard as running counter to the metrical parallelism of the fragment and its shortened repeat. There is the distinct sense of a radical threat to the conservative interpretation, in other words, which, however 63See

Horlacher (2011) for a motivic analysis of the whole of the “Evocation,” and van den Toorn (2017) for a rhythmic-metric analysis of this dance movement. Here, however, we focus entirely on the initial four measures of the opening statement, doing so primarily as a way of engaging David Huron (2006) on the anti-metrical or “contrametric” nature of Stravinsky’s irregular barrings and accents, Hans Keller (1994) on the downbeating effect of those barrings, and Fred Lehrdal (1988) on the “natural” (rather than “artificial”) character of the meter so often concealed by Stravinsky’s shifting bar lines. Van den Toorn (2017) and this present analysis overlap to a degree, although the emphasis here is on the purely disruptive effect of displacement on an entrained meter; see note 32. 64Krebs (1999, 23).

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shadowy in experience, is of sufficient weight to render that response a precarious one. And how could this not be the case? The radical notation forces the performer to hear, understand, and play the fragment’s repeat as a replica of the original, and the shifting bar lines force him to count out the quarter-note beats. Conscious counting of this kind not only prevents the performer from extracting a meter, it also prevents the reflexive triggering of an expressive rubato. From what we have imagined Stravinsky’s metrical concerns to have been at the time of The Rite, much is thus gained from the radical notation of this music. The shifting bar lines in Ex. 13(a) guarantee a clean and punctual performance, one capable of sharpening the articulation of the various forces underlying both conservative and radical barrings. Example 13(c) traces a likely point of departure for the conservative and radical barrings of this passage. The fragment’s span of seven quarter-note beats is extended to eight beats, with the complications surveyed above converted into a veritable metrical comfort zone; the 22 meter is immediately confirmed by the true parallelism of the repeat of the fragment. Then, returning from this point of departure (Ex. 13[c]) to the conservative and radical barrings of Ex. 13(b) and (a), respectively, a single quarter-note beat is subtracted from the stereotypical eight beats of Ex. 13(c), causing, conservatively, the shortened repeat of the fragment to fall on the fourth quarter-note beat rather than the first (Ex. 13[b]), and, radically, the bar lines to be shifted in order to preserve a form of parallelism (Ex. 13[a]). In each case, the shortened repeat arrives a quarter-note beat “too soon,” with the encompassed measures likely to acquire, as a result, a rushed, breathless quality. Perversely, then, Stravinsky’s radical barring at the outset of the “Evocation” (Ex. 13[a]) can seem to have been conceived in opposition to the conservative reaction outlined in Ex. 13(b). Rather than merely non-metrical, the radical conception is anti-metrical. Or, to use David Huron’s term, the irregular accents and spans in Ex. 13(a) and (b) are “contrametric” in their effect. In Huron’s view, too, the contra-metric character of the irregular accentuation in Stravinsky’s music is indicative of a larger “contrarian aesthetic” in Modernist music. Early in the past century, to follow Huron, such a psychology guided the music of a number of composers, including Schoenberg. Huron calculates the pitch sequences in Schoenberg’s

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twelve-tone rows to be “less tonal than random tone rows, which is consistent with a compositional intent to create contratonal organizations.”65 Schoenberg’s “contratonal” twelve-tone rows, then, are analogous to Stravinsky’s contra-metric passages. The expressive quality of Schoenberg’s twelve-tone music lies at least in part with its systematic circumvention of tonal implications.

Example 14  Renard, Pribaoutka, five-note segment, displacement

The passage shown in Ex. 14 is, at this point, breath-takingly convenient. It reproduces the opening two lines of a Russian verse called a Pribaoutka, a kind of limerick designed for children and consisting in large part of riddles and counting games.66 The one quoted in Ex. 14 is from Renard and is accompanied by the first music to be composed for that work. It is also the only passage in all of Stravinsky’s published music that is barred both conservatively and radically. Thus, a 24 meter is accompanied by shifting bar lines 65Huron

(2006, 346–51). Huron does not mention metrical displacement in Stravinsky’s music, that which often underlies the irregular accentuation. But his discussion of the “contrametric” effect of that accentuation matches that here of the metrically disruptive effect of displacement and its irregular accents and spans. 66For further discussion of Stravinsky’s use of Pribaoutki, see Taruskin (1996) and van den Toorn and McGinness (2012, 77–79).

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notated in parentheses. The bar line shifts in accord with the accented syllables, the rationale that underlies Brandel’s “radical” barring in Ex. 12(b). Just as with the opening block of the “Evocation of the Ancestors,” too, an initial fragment is immediately repeated and displaced (see the boxed-off areas in Ex. 14). Relative to the 24 meter, a five-note segment falls on and then off the half-note beat, the likely tactus here at 76 beats per minute. Representing beats, the dots below the two staves in Ex. 14 are arranged according to the LerdahlJackendoff model of metrical hierarchy.67 Above the two staves, the 1–2 count in brackets encompasses the half-note beat or bar line and its interpretation by the whole-note beat. Typical of Stravinsky’s methods of “cutting and pasting” is the addition and subtraction of syllables, beats, and measures when a fragment or phrase is repeated. Here, the second measure of the four-measure phrase is subtracted when the phrase is repeated (second stave in Ex. 14). Listeners, conservative or radical in orientation, are likely to experience a splitsecond jolt when the second measure fails to appear as expected. Following this, they are likely to attempt a match between the third and fourth measures of the original phrase and the second and third measures of the repetition.

VIII

In a related description of an African highlife, Kofi Agawu underscores the 44 meter that is typical of this music, along with the syncopated, offbeat pattern that typically “enlivens” it.68 Other features discussed by Agawu involve the highlife’s structure, instrumentations, and dance potential, concerns more or less universal rather than specifically African, and capable of surfacing in connection with any number of Western art and popular traditions. Even the close ties of The Rite of Spring and other Stravinsky works to choreography and the dance— to the extent that these ties can be viewed as an outgrowth of the 67Lerdahl

and Jackendoff (1983, 12–17). (2003, 129). Highlife is a popular genre that originated in Ghana at the turn of the twentieth century and incorporated melodic and rhythmic formulae in traditional Akan music, marrying the latter with Western instruments.

68Agawu

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metrical and rhythmic dynamics discussed above—could be cited in connection with many of Agawu’s remarks. “Like all beats,” Agawu argues, the beat of the highlife harbors “an irresistible invitation to dance, to move the body in response to a rhythmic pattern.” The listener may respond to this “invitation” by dancing overtly or by realizing the dance “silently or imaginatively without any loss of aesthetic pleasure.”69 Here again, however, although Agawu overlooks the psychology underlying these impulses, it is the psychology that can offer a partial explanation of their nature. For the “invitation to dance,” as extended by the metrical beat, is felt “irresistibly” by the listener because of entrainment, and because of the listener’s desire to make known or act out what has become physically a part of him, the metrical beat that lies implanted within, as it were. The impulse to relate to others by moving or dancing in synchrony with an entrained beat is surely universal in scope. Very few societies or cultures are without some form of metered (or measured) music, and all metered music is—or was originally— allied to a form of collective activity, usually the dance. (In Africa, music that is not metered and is not danced to is not usually considered music at all.)70 In sport, in verbal communication, and in the expression of emotion, humans relate to one another through coordinated rhythmic movement. Moving in step with others as well as their internal selves, they reveal something of who they are.71 Music may well have begun here, in fact, with pulsation, entrainment, and the play of moving with and against an “embodied rhythm.”72 As Bruno Repp has remarked in a preface to one of his many studies of entrainment and synchronized motion (finger-tapping experiments, for the most part), sensorimotor synchronization at a wide range of tempos may be unique to humans.73 “It may come as 69Ibid.,

130. Arom (2000, 28) and Patel (2008, 402). 71See the discussion of ritual, social bonding, and “the euphoria of joint, synchronized movement” in Margulis (2014, 57). 72Repp (2007, 14). 73Repp (2009, 969). 70See

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a surprise,” writes A. D. Patel, but “humans are the only species to spontaneously synchronize to the beat of music.”74 In Representing African Music, Agawu is at pains to clarify the role of meter in the African music with which he is most familiar, that of Ghana and West Africa generally. Closely tied to the dance (“the movement of feet,” in Agawu’s words),75 meter serves as a regulating, “enabling structure,” a role overlooked in much of the “polymetric” transcription and commentary of the previous century.76 To follow Agawu, the familiar bell patterns and polyrhythms of African music are heard, performed, and danced in coordination with a metrical background. Concepts of polymeter, additive rhythm, and cross rhythm are therefore dismissed as colorful “romance terms,” Western inventions that have had the effect of “overcomplicating” and distancing African music.77 Agawu’s aim would seem to be to stake out a more direct path to African music by stressing commonality rather than difference or uniqueness, dynamic contingency rather than piety and preciousness, and the voices of African experts and performers rather than the second-hand ones of Western specialists. “African music shares with European music (and indeed much other music) a conceptual space describable in terms of a hidden background and 74Patel

(2008, 100). To be sure, many animals synchronize with each other in producing periodic signals; in their courtship rituals, for example, crickets, frogs, and fireflies engage in “rhythmic chorusing.” But closer examination reveals this behavior to be fundamentally different from that of human synchronization. Thus, the mechanism used by male crickets “to adjust the rhythm of their calls ... does not involve matching their call period to a periodic model, but rather is a cycle-by-cycle phase adjustment in response to the calls of other males. When multiple males all use this strategy, episodes of synchrony emerge as an unintended byproduct.” It is a “remarkable fact,” Patel concludes, “that despite decades of research in psychology and neuroscience in which animals have been trained to do elaborate tasks, there is not a single report of an animal being trained to tap, peck, or move in synchrony with an auditory beat”; Patel (2008, 40809). Patel has had to reverse himself on this claim, however, as it now appears that a male Eleonora cockatoo (parrot species) is also capable of “beat induction” and synchronized movement with an “auditory beat” at various tempos; see Patel (2009, 827–30). 75Agawu (2003, 73). 76Ibid., 78. 77Ibid., 74, 79–80. Cross rhythm usually implies a more extended or systematic form of polyrhythm.

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a manifest foreground.”78 Like David Temperley before him,79 Agawu subscribes to the sharp distinction Lerdahl and Jackendoff draw between meter and grouping?80 The two phenomena are separate and independent. While meter involves a hierarchical nesting of levels of pulsation, with each level consisting of equally spaced beats and each beat defined as an idealized (durationless) point in time, grouping also involves hierarchical levels, but with groups (phrases, motives, and so forth) rather than beats, and with durations which may or may not be in phase with the meter. The rationale underlying the separation of meter from grouping, derived initially by Lerdahl and Jackendoff from the Classical era of Western art music,81 can seem relevant wherever meter manifests itself in the music of the twentieth century, including, compellingly, in Stravinsky s. Its application to African music is no less appropriate, as Agawu is keen to demonstrate, as it captures the central idea of a ground against which a rhythmic figure or grouping is located in time and brought into focus.82 The continuing support this divorce of meter from rhythm has received from science is pertinent here as well. Studies of patients suffering from certain types of brain injury suggest that the two sides of this symbiotic relationship inhabit different areas of the brain. Meter and grouping are neurally unrelated and appear to be processed in the right and left hemispheres, respectively.83

IX

“Meter does all the dirty work, while melody is able to enjoy itself.”84 With its emphasis on meter as an “enabling structure,” the preceding quotation could easily be mistaken as another attempt on Agawu’s part to describe the meter-rhythm separation in the conception and perception of African music. Instead, however, its author is Hans Keller, the Austro-British critic and theorist, attempting to 78Ibid.,

79.

81Ibid.,

4.

79Temperley 80Lerhdahl 82Agawu

(2000). and Jackendoff (1983, 12–35).

(2003, 84). (2006, 173). 84Keller (1994, 207). 83Levitin

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characterize a pervasive temporal condition of Western art music from the seventeenth through much of the twentieth centuries. A disciple of Hugo Riemann, evidently, Keller believed in auftatigkeit (“upbeatness”), the upbeat tendency of the Austro-German tradition. Against the backdrop of “a square metrical dance scheme,” Keller heard iambic patterns as developmental in character, igniting anticipation and, over the bar line, a sense of forward motion.85 Keller’s thesis—with which this observer is in partial agreement—is that Stravinsky countered this upbeating, developmental flow with “unmitigated, unprepared, and unresolved downbeats.” Stravinsky swam against the current of the upbeat,86 according to Keller, which, by the time of his arrival on the scene at the start of the past century, had become something like a tidal wave. A quick glance at the opening fragment of the “Evocation of the Ancestors” in Ex. 13(a) can serve to illuminate Keller’s perspective. The shifting bar lines in this example allow both the fragment and its immediate, shortened repeat to enter on the downbeats of the first and third measures. The shortened repeat that would have conservatively (Ex. 13[b]) entered on the fourth quarter-note beat (upbeat) of the second measure of a 22 (or 44) meter enters instead on the downbeat. Reinforced by accents, the conversion from upbeat to downbeat (from displacement to a form of metrical parallelism, as we have described it) is one of the many ways in which this and other passages in The Rite and in Stravinsky’s music generally can seem to acquire the “downbeating” effect described by Keller. Nevertheless, just as with the conservative response that is undermined by the radical forces of parallelism, so, too, with the reverse of this exchange. Even in a truly radical interpretation of this passage (Ex. 13[a]), the downbeat of the third measure of Stravinsky’s barring is likely to retain some sense not only of the upbeat which it displaces, but also of the concealed 22 meter on which that sense of an upbeat depends. Here again, in other words, the downbeat of this third measure of Ex. 13(a) is likely to assume an anti-metrical or contrametric character, the sense of being directed against the upbeat and the parallelism of which that upbeat is a part. Indeed, to the extent that Stravinsky’s suggestion of a 22 meter in the opening block of the “Evocation of the Ancestors” engages 85Ibid., 86Ibid.

208.

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the listener’s reflexive (and hence “natural”) ability to entrain to and move in synchrony with a periodic mold, the same downbeat of the third measure of Ex. 13(a) could be heard and understood as an imposition, something forced and supported “artificially” by the heavy phenomenal accents and, for the reader-performer of the score, the radically shifting bar lines. Consistent with Lerdahl’s arguments about the “cognitive constraints” of music and the listener,87 in other words, the 22 meter could be viewed as something that came “naturally” to the listener, and Stravinsky’s rapidly changing bar lines in Ex. 13(a) as something that was “artificial.” To be sure, the conflicting forces of displacement and parallelism, conservative and radical, are irreconcilable and incapable of being attended to simultaneously by the listener. Yet the suggestion here has been that these forces are still apt to be felt in relation to one another, that one interpretation is unlikely to be entirely free of the other. The one presupposes the other, in other words, as part of a dialectic. Indeed, the meaning or expressive force of the opening fragment in Ex. 13(a) would seem to rest accordingly, that is, with a negation, with the fact that its span of seven quarter-note beats misses the metrical span of eight beats in Ex. 13(c) by a single quarter-note beat (the fragment’s repeat arrives “too”). The former becomes a deformation of the latter. Stravinsky’s adventures as a counter-puncher (a downbeating spoiler of the optimistic, forward-moving upbeat) were entirely oppositional, Keller insists, in that the composer never failed to leave traces in his music of the upbeat against which he directed himself. “Stravinsky never forgets to define, by overt or hidden implications, the flow ... against which he moves,” Keller argued.88 In a giant form of displacement, upbeat figures identified with development and 87Lerhdahl

(1988, 235).

88Keller (1994, 208). The composer’s inclusion of the “flow ... against which he moves”

extends to intensely radical conceptions such as the opening block of the “Augurs of Spring” at Rehearsal no. 13. In his analysis of this passage, David Huron judges its accentual pattern to be “not just improbable, [but] less predictable than a random pattern of accents”; Huron (2006, 346). However, Huron overlooks the five-fold repetition of the ostinato pattern just prior to Rehearsal no. 13. As we have noted above, listeners may carry something of the parallelism of this repetition into the opening measures of this passage, hearing the first two accents off the quarter-note beat as syncopations. Disruption is apt to set in when these accents are shifted to the beat, however.

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forward movement were shifted to the downbeat. Hence, here again, the explosive nature of displacement. But what are we to make of the psychology of metrical displacement and of the disruption to which it can often lead in The Rite? Meter, entrainment, and synchronized movement are feel-good conditions, no doubt, as they allow for a close physical engagement on the part of listeners, performers, and dancers. Daniel Levitin’s description of these processes runs as follows: Whether it is the first few hits of a cowbell ... or the first few notes of Sheherazade, computational systems in the brain synchronize neural oscillators with the pulse of the music, and begin to predict when the next strong beat will occur. As the music unfolds, the brain constantly updates its estimates of when new beats will occur, and takes satisfaction in matching a mental beat with a real-in-the-world one, taking delight when a skilled musician violates that expectation in an interesting way—a sort of musical joke that we’re all in on.89

All well and good, one might conclude, but Levitin overlooks the possibility of a disruption or cancellation of his “mental beat,” the mechanism by which his ideas about satisfying and violating expectation are realized. What he has in mind here is playfulness, the pulling and tugging of a grouping dissonance against the meter, for example, the delay of a cadence, or, in jazz, improvisations that constantly slide away from an alignment with the strictly held beat. In the ears and eyes of this observer, the metrically disruptive forces unleashed by The Rite of Spring are of a different order. Moreover, at issue here is not just hypermeter, the cancellation of which is common enough in the music of the Classical era, but the more salient middle range of the metrical hierarchy, the tactus and the bar line. Why should listeners of The Rite and Stravinsky’s music be attracted aesthetically to rhythmic-metrical maneuvers that challenge and disrupt their metrical bearings? This may be the million-dollar question of this inquiry, although it is unfortunately one for which the author has no convincing answer. It may be that further speculation in aesthetics will have to await further discovery in the overlapping fields of evolutionary biology, cognitive psychology, and neuro-science. The point at which aesthetics is overcome by the deliveries of science is another 89Levitin

(2006, 191).

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question worth pondering in this context. The guess here is that it will take about a century before this “dreariest” of pursuits (as aesthetics was once called) exhausts itself. The hope, however, is that, for a short while longer, the individual or “single instance” (“the devolution point of all musical thought, for whose sake alone the class generality—all the way out to the term music itself—is reified”)90 may be spared the general dissolution.

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Rhythm by Neil P. McAngus Todd, Rosanna Cousins, and Christopher S. Lee.” Empirical Musicology Review 2 (1): 14–16.

Repp, Bruno H. and Haitham Jendoubi. 2009. “Flexibility of Temporal Expectations for Triple Subdivision of a Beat.” Advances in Cognitive Psychology 5 (5): 27–41. Schoenberg, Arnold. 1965. Arnold Schoenberg Letters. Ed. Edward Stein. Trans. Eithne Wilkins and Ernst Kaiser. New York: St. Martin’s Press.

———. 1967. Fundamentals of Musical Composition. Ed. Gerald Strang and Leonard Stein. London: Faber and Faber.

Straus, Joseph. 2014. “Harmony and Voice Leading in the Music of Stravinsky.” Music Theory Spectrum 36 (1): 1–33.

Stravinsky, Igor. 1962a. An Autobiography. New York: W. W. Norton.

———. 1962b. Expositions and Developments. Garden City, NY: Doubleday.

Taruskin, Richard. 1996. Stravinsky and the Russian Traditions: A Biography of the Works through Mavra. Berkeley: University of California Press.

———. 2011. “Catching Up with Rimsky-Korsakov.” Music Theory Spectrum 33 (2): 169–85.

———. 2017. “Resisting The Rite.” In The Rite of Spring at 100. 417–48. Ed. Severine Neff, Maureen Carr, and Gretchen Horlacher. Bloomington: Indiana University Press. Temperley, David. 2000. “Meter and Grouping in African Music: A View from Music Theory.” Ethnomusicology 44 (1): 65–96. Tymoczko, Dmitri. 2002. “Stravinsky and the Octatonic: A Reconsideration.” Music Theory Spectrum 24 (1): 68–102.

———. 2011. “Round Three.” Music Theory Spectrum 33 (2): 211–15.

van den Toorn, Pieter C. 1987. Stravinsky and “The Rite of Spring”: The Beginnings of a Musical Language. Berkeley: University of California Press.

———. 2017. “The Physicality of The Rite: Remarks on the Forces of Meter and Their Disruption.” In The Rite of Spring at 100. 285–303. Ed. Severine Neff, Maureen Carr, and Gretchen Horlacher. Bloomington: Indiana University Press.

van den Toorn, Pieter C. and John McGinness. 2012. Stravinsky and the Russian Period: Sound and Legacy of a Musical Idiom. Cambridge: Cambridge University Press. Walton, Kendall L. 1993. “Understanding Humor and Understanding Music.” Journal of Musicology 11 (1): 32–44. Webster, James. 2004. Haydn’s “Farewell” Symphony and the Idea of the Classical Style. Cambridge: Cambridge University Press.

Chapter 10

Individual and “Class Generality”: Reflections on the Postwar Years of Babbitt, Schoenberg, and Stravinsky

The point of departure for scholars of Western art music of the past several centuries has typically been an aesthetic one ignited by the unique qualities of individual art works. Some years ago, Benjamin Boretz drew a distinction with the physical and social sciences on this basis. In science, he argued, the individual is valued to the extent that it can confirm a theory or hypothesis, while, in the study of music, art, and poetry, the opposite prevails. Common practices, systems, and theories are pursued for the illumination or “richness of identity” they afford the individual context. “The qualification of the individual is the devolution point of all musical thought,” Boretz concluded, and it is for the sake of that qualification alone that theorists and musicologists concern themselves with the “class generality.”1

1Boretz (1977, 122–32). Or see Boretz (1995, 86): “Individuals in the physical world … are interesting to students of physical structure just insofar as they instantiate, confirm, articulate, suggest, or demonstrate ‘lawlike’ conditions for the world as a whole. However various, the physical and social sciences … regard the single instance as the least significant aspect of their concern, while the student of musical, poetic, pictorial, and perhaps even philosophical structures must regard those instances as the most important such aspect.”

The Music of Stravinsky: Collected Essays Pieter C. van den Toorn Copyright © 2023 Jenny Stanford Publishing Pte. Ltd. ISBN 978-981-4968-62-1 (Hardcover), 978-1-003-35916-6 (eBook) www.jennystanford.com

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Thoughts of this kind, reflective of American music theory and analysis during the 1950s, 60s, and 70s, can be traced more specifically to Milton Babbitt and what Joseph Kerman used to call the Princeton School.2 Babbitt’s pursuit of the systematic or “class generality” could be ferocious, as is well known, mathematical at times (“scientistic,” as his critics alleged), but always as a means of angling the particular. As a composer and theorist extraordinaire of twelve-tone music, he worried about the foundation of this music, the little that held it together pitch-wise as a distinct class or body of works. Bound only by an ordering and a set of operations, not a common structure, twelve-tone works were superabundantly individual, self-defined or “contextual,” to use one of Babbitt’s favorite terms.3 Composed nearly from scratch, each work represented something of an island unto itself. And the implications of this for the listener were scary. Little if anything could be assumed when commuting between twelve-tone works, extracting from one the means of hearing and understanding another.4 2Boretz’s

celebrated Meta-Variations, his PhD dissertation at Princeton (1969), is as much a critical reaction to Babbitt’s music-intellectual world as it is a reflection thereof. What has tended to set Boretz apart over the years is his “relativism,” pursued as a matter of perspective rather than ideology; his belief in “the primacy of the relative-personal”; that the relevant content and subject matter “of serious musical thinking” should be determined by “person-relative intuitions and values.” His “split” with Babbitt may be traced to concerns of this type. See, in his most recent collection of perspectives and retrospectives, Boretz (2020, 187); “A Talk with Ben: Marion A. Guck and Fred E. Maus Interviewing Benjamin Boretz” (1989). That a concern for the individual context as “devolution point of all musical thought” should be paired with a parallel concern for the personal experiences of individual listener-thinkers is a theme to which we will be turning briefly here, although in a somewhat different vein from that indicated by Boretz. 3Terms such as “self-referential,” “self-contained,” and “contextual” were used moreor-less interchangeably by Babbitt. They refer to the extent to which the structural elements of a piece are specific to it, rather than being “communal” or shared with other pieces. The atonal works of Schoenberg, Berg, and Webern were said to represent the most extreme cases of contextuality: “They are to as large an extent possible self-referential, and what I am going to call contextual.” See Babbitt (1987, 167). Twelve-tone works were less severely contextual, but not by much. 4“You could say the trouble with any twelve-tone work … is that it’s too contextual. The communal aspect shared by a twelve-tone work, and therefore what you can bring from one twelve-tone work to another or even from one piece of the same composer to another, is really not enough.” See Babbitt (1987, 170).

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And there were difficulties of an even more fundamental nature. In his polemical skirmishes with critics and naysayers, Babbitt tended to take the twelve pitch classes for granted, overlooking the formidable hurdle they posed for general listeners, the vast majority of whom lacked the refined sense of pitch that was his to a very high degree. Pressed on these issues of perception, he would respond that what mattered were not the pitches themselves, but how the listener “conceptualized” or conceived of them, how he “thought it through conceptually with [his] musical mind.”5 Typically, no doubt, the ability to make sense of a musical context entails a form of conceptualization. Listeners react to a piece of music by segmenting and grouping the materials (“chunking”),6 doing so hierarchically if possible, with the smaller groups subsumed by the increasingly larger ones. Sought more ambitiously might be the suggestion of a governing premise, a way in which the groups are tied to the unfolding of a larger design. Assisting the listener in these efforts are likely to be 1) repetitive features in the materials, and 2) descriptive terms and concepts pursued informally or with reference to a theoretical framework. Even here, however, with assumptions about the way we listen to music as basic and unassuming as these, questions are apt to arise. Can it truly be the case, as Babbitt insists, that perception is merely “a matter of conception”? As the listener comes to grips with a musical context, doing so reflectively during as well as after audition,7 is the

5Babbitt (1987,23). When addressing the listener’s ability to hear hexachords and relations between them, Babbitt felt compelled to answer the complaints of the skeptics: “it’s not a matter of hearing,” he insisted, … it’s a matter of how you conceptualize it, how you conceive it.” 6The source of much of Babbitt’s early understanding of cognitive psychology as it applies to the listening experience may be traced to George A. Miller, “The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information,” Psychological Review 63, no. 2 (1965): 81–97. The mental process of chunking or “recoding” bits of information, crucial to memory and the ability to recall, was reimagined in terms of the musical context and the listener’s ability to segment that text. “Competent crunching” was underscored as a “teachable skill” by Babbitt and others, available to all listeners, not just to those with special aptitudes in this regard. See Bernstein (2021, 47–52). 7For an account of aesthetic immediacy and the role of reflection in the listening experience, see Dahlhaus (1982, 84–100).

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role of “hearing in any physiological or discriminatory sense” so entirely inconsequential?8 After all, the uses of conceptualization in and out of analysis are hardly without their risk or difficulty. Concepts vary in the degrees of their abstraction; not all are equally accessible. Many of the sets and arrays referenced in Babbitt’s analysis of twelve-tone music may be manageable conceptually, but perhaps not perceptually, given the heightened sense of pitch these conceptualizations would seem to require if they are indeed to be heard and understood appropriately. At the same time, much Modernist music, including Babbitt’s, lacks the redundancy or clear-cut repetition that would allow for the extraction of a reasonably unambiguous grouping structure.9 When addressing the special problems of twelve-tone works, the precarious nature of their existence, Babbitt preferred to stress the high degree of self-reference exhibited, the little that was shared structurally by members of the twelve-tone population as a whole. Individual composers might cultivate their own approaches, to be sure, expanding on the communal aspect of their twelve-tone works. In Schoenberg’s case, such an expansion was served by a method of combining row-forms. But there was no mistaking the enormity of the changes that had taken place. The precompositional foundation that had stretched across centuries of music had given way to an individualization that was truly unprecedented. And what earlier composers and listeners had been able to take more or less for granted had become dependent on the composer, her willingness to supply the missing pieces, as it were, something of the infrastructure of a work that had been built very nearly anew from the ground up. Guidance was required, a way of ushering listeners through the assumptions and particularities of the single twelve-tone artwork.

8Babbitt (1987, 44): “Perception is a matter of conceptualization. I still encounter people who say, ‘But can you hear this?’ Well obviously that’s not the right question. Obviously you can hear these things—you hear the notes. The question is how you conceive them, how you can conceptualize them, how you relate them. It’s not a matter of hearing in any physiological or discriminatory sense.” 9For further discussion of these difficulties, see Bernstein (2021, 50–52). Or see Lerdahl (2020, 89–90), where the point of departure is even more insistently the “competent” listener rather than the composer. In much music by Boulez, Carter, and Babbitt, according to Lerdahl, “events” relate to one another by degrees of association rather than hierarchically. The surface of this music, although lively and “intricate” at times, is nonredundant and hence shallow or “flat.” A revealing account of Babbitt’s music from the vantage point of the listener is Straus (1986, 10–25).

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It was almost by necessity, then, that composers at the time became theorists or at least composer-theorists, explainers of their music and the systems that underlay it. Rarely have the two disciplines been as closely allied. Yet the lectures, articles, and notes of explanation would be aimed for the most part at colleagues rather than the general public, as Babbitt himself stuck to the technology of twelve-tone music, shying away from descriptive or “persuasive” comment, the critical and historical discourse he believed too often uninformed and designed merely to prejudice the listener.10 Left unaddressed was thus the underlying disconnect, the fact that, contrary to the specialists and their claims of a radically new contextuality, twelve-tone works sounded pretty much alike to everyday listeners. Composers and theorists of twelve-tone music might stress the revolutionary character of Schoenberg’s methods and the necessity of approaching this music on its own terms. Yet general listeners tended to hear and understand as they always had, which was by relating the new to the music to which they were accustomed. Such a course could never work to the advantage of the new medium, however, since it led not to an appreciation of that medium for what it was, but only to a vague awareness of what it lacked, namely, tonality, the implications of which, even if occasionally in evidence, were subject to the negating effect of the twelve-tone rows and “aggregates.”11 Curiously, however, a way would eventually be found to reconcile the two sides of this impasse, listeners who were versed in the methods of twelve-tone composition, and the far greater number who were not. A form of expression would be located in the relationship of twelve-tone music to the tonal processes from which its composers, and especially Schoenberg and Babbitt, had sought a complete break. (Babbitt’s allegiance to the music of Schoenberg should be acknowledged here, music he believed to be of greater depth or “richness” than that of Berg or Webern.12 He was drawn more specifically to Schoenberg’s methods of combining row-forms to create aggregates (“combinatoriality”), methods he codified 10Babbitt

was acutely sensitive to the harmful effect critical or descriptive terms might have on the reception of a new work, even before a note had been struck. See Bernstein (2021, 59–60). 11An aggregate is an (unordered) collection of the twelve pitch classes. 12Babbitt (1987, 19).

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and then extended in his own music.13 Comparing Schoenberg’s application of a row to Webern’s, he judged the latter’s “too literal.”)14 To follow David Huron on the psychology of these issues, the pitch sequences in Schoenberg’s twelve-tone rows were “less tonal than random tone rows.” And this was consistent, Huron argued, with this composer’s intent to create not just non-tonal but rather anti-tonal or “contratonal” structures.15 The deliberate avoidance of tonal tendencies in Schoenberg’s twelve-tone music could be felt as expressive by the listener. So, too, Babbitt’s serialization of duration (the “time-point” system), when applied to a piece such as his Semi-Simple Variations for piano (1956), could be interpreted along similar lines.16 The edgy, off-balance quality of this work, its 13By

“combinatoriality” is meant the ability of a collection of pitches to combine with a transformation of itself (or its complement) to form an aggregate. For example, two successive aggregates are formed when, between the corresponding hexachords of two row-forms, no pitches are held in common. For a revealing account of Babbitt’s extension of Schoenberg’s methods of combinatoriality, see Dubiel (1990), Mead (1994, 5–25), and the analysis of Babbitt’s Glosses (1988) in Bernstein (2021, 16– 19). As one such extension, four rather than two row-forms (“lines”) are combined in Babbitt’s works, each of these derived from one of the disjoint trichords of an initial row. The hexachords employed in these arrays are invariably Babbitt’s allcombinatorial “source sets”; such a set may be combined with set-forms from all four of the standard row-orderings to create aggregates. The result of the manipulation is the “trichordal array” featured in many of Babbitt’s works; aggregates are formed with trichords as well as hexachords. As one array succeeds another, the last hexachord of one row-form may unite with the first of the following form to create another aggregate, a “secondary set.” By such means, aggregate-formation was increased markedly. 14See Babbitt (1987, 23). 15Huron (2006, 350). 16Underlying Babbitt’s Semi-Simple Variations are trichordal arrays of the type summarized briefly in note 13. For a highly detailed analysis of the Semi-Simple Variations, see Wintle (1976, 111–54). An aesthetic view of Babbitt’s music is pursued intermittently in Dubiel (1992, 88–131), and Bernstein (2021, 1–35, 231– 70). See also Boretz (2020, 122); “Where have we met before? Milton at 90” (2006). “Redeeming soft edges and sensuous indulgences” are evidently not to be found in Babbitt’s music; “impermeability, toughness, in-your-face challenging complexities, stubbornly sticks in my musicworld as a fundamental aesthetic surface of the music of Milton’s that means the most to me.” Or see Boretz (2020, 205–08); “What did Milton mean by his music?” (2012). Babbitt’s music can seem “opaque in surface and interior, psychically impenetrable.” Yet it would “radically wrong to convict Milton’s music as not having any sensibility, any soul …; it lives in an alternative universe not a counter-normal universe; it’s as indifferent to ‘ugly’ as it is to ‘beautiful’. That is its inner sensibility. Expressive predicates simply don’t live on this planet of Milton. Nor are they always at the center of every familiar act or concern of significant human

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quick, jerky motions, can bring to mind a form of jazz improvisation in which a coincidence with the metrical beat (one not intended by the composer of Semi-Simple Variations, but inferred and imposed sporadically by the listener all the same), is constantly and expressively being withheld.17 And in Stravinsky’s music, the metrical displacement of repeated motives can challenge and even upend the listener’s metrical bearings in ways that could likewise be sensed as expressive. In Huron’s view, the “contratonal” or “contrametric” impulses of this music were part and parcel of the “contrarian” spirit of Modernism.18

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In due course, however, serialism and the total chromatic would indeed be challenged on psychological grounds. To follow Fred Lerdahl on the “constraints” to which “compositional systems” are subject, it is the heavy reliance of human cognition on hierarchical structuring that has put atonal and twelve-tone music at a disadvantage. “Competent” listeners everywhere are at the mercy of that reliance, regardless of the perfection or imperfection of their sense of pitch in the abstract.19 consciousness.” Boretz’s remarks are not unlike Milan Kundera’s when responding to complaints about the hardened surface of Stravinsky’s music, the strict metrics and the absence of expressive affect. Stravinsky’s “refusal to see subjective confession as music’s raison d’etre” had spawned a quality of its own, according to Kundera, one “mercifully” free of a “human subjectivity” that had grown oppressive and “burdensome.” Kundera (1994, 71). 17The jazz-like quality Babbitt’s music can sometimes assume has been noted by others. See Boretz (2020, 122); “Where have we met before? Milton at 90” (2006). “A music of intense local-internal action, something more like the plosive energies of latter-day ‘advanced’ jazz (as in Coltrane, Coleman, …).” 18Huron (2006, 346–51). 19See Lerdahl and Jackendoff (1983, 12–17) and Lerdahl (1988, 231–59). In general outline, Babbitt’s view of the relationship between musical structure and cognitive processes overlaps Lerdahl’s. Babbitt, too, saw the need for a nested hierarchy in music, with each level subsumed by deeper levels of structure. And he traced that need to processes of human cognition, especially where memory was concerned; the way the mind conceptualizes or “chunks” the materials of music. See Babbitt (1987, 145), Bernstein (2016, 241–42), and note 6 above. Lerdahl’s misgivings about twelve-tone music and its apprehension stem from a more detailed, comprehensive conception of the requirements and limits of cognition.

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True enough, Babbitt and Schoenberg organized combinations and sequences of row-forms in a hierarchical fashion. Yet these “higher-level hierarchies are extremely difficult to cognize hierarchically.”20 In twelve-tone music, change is made possible through permutations of the row; segments of different row-forms relate to one another loosely by “association,”21 not by “elaboration,” a process that is inherently hierarchical and that, as such, allows for a more immediate, effortless comprehension of the materials. In addition, little if any allowance is made for the distinction between consonance and dissonance, a distinction that would seem to prevail regardless as to whether, in twelve-tone music, it is forfeited and “defined out of existence.” Contexts that ignore “sensory” distinctions of this kind are difficult if not impossible to process effectively.22 In the end, Lerdahl concludes, too much of a “gap” separates “compositional method from heard result,”23 the strategies of twelve-tone composition from those that come “naturally” to the listener.24 Whether as a consequence of these psychological constraints or not, atonal and twelve-tone music during the 1950s, 60s, and 70s 20Lerdahl

(1988, 253).

21See Babbitt (2003, 409); “Stravinsky’s Verticals and Schoenberg’s Diagonals: A Twist

of Fate” (1987). Not much was meant by “associative harmony.” To be so designated, a harmony had to be “contextually coherent.” 22Lerdahl (1988, 253). In Lerdahl (2020, 67–68), the distinction between “sensory” and “musical” consonance and dissonance is drawn in the following terms: the sensory perspective, “a product of the interaction of the acoustic signal with the auditory system,” does not vary from one culture or history to the next, while the transition from consonance to dissonance is “gradual.” By contrast, musical consonance and dissonance is “a result of a given musical idiom and varies within limits from culture to culture.” For a perspective from neuroscience on these issues, see Koelsch (2013, 9–11). The sensory conception may have been at the heart of Babbitt’s dismissal of consonance and dissonance as “absolutes,” his contention that the matter was “purely contextual.” Babbitt (1987, 12). Or see Babbitt (2003, 198–99); “The Structure and Function of Music Theory” (1965). Too many contradictions, including the minor triad, marred the tonal approach to consonance and dissonance and its ties to “the overtone follies.” This was because “consonance and dissonance are context dependent tonal concepts; it is impossible to assert that an interval is consonant aurally, since it always can be notated as dissonant, and this notation reflects a possible context.” 23Lerdahl (2020, 78). The argument about “cognitive constraints” is clarified somewhat in this recent publication, as are the objections of several of Lerdahl’s critics, mainly where the issue of hierarchy is concerned. The argument itself is left intact, however. 24Lerdahl (1988, 231, 235–37).

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hastened the flight to the universities, widened the gulf between the listening public and “the Composer as Specialist,”25 and increased immeasurably the fragmentation of serious music. The prospect of a runaway pluralism frightened Babbitt, most likely because of what the absence of a sense of community, of a referential base linking members of a musical population, seemed to imply, namely, music that was shallow or lacking in structural depth.26 No such difficulty beset the tonal realm, of course, the lost paradise, and the lens through which Babbitt, Boretz, and other American composers and theorists had sought to assess the means and promise of their own chosen repertories.27 Tonal works shared a structure, a vocabulary of triads and a musical syntax or “functionality.” The depth of the transparency could sometimes seem to rival that of language itself. Even to listeners only modestly informed, individuality could indeed be heard and understood as permeating the cracks and crevices of the single artwork. In Schenkerian analysis, the model of tonality is always weighed against the demands of the individual. Compliance is not really the point, even if it may well have been for Schenker himself. What 25See

Babbitt (2003, 48–54); “The Composer as Specialist” (1958). Famously, Babbitt’s article was first published in High Fidelity 8, no. 2, under the title of “Who Cares if You Listen?.” Discouraged by the indifferent and often hostile reception of atonal and serial music, Babbitt urged that composers “do themselves and their music an immediate and eventual service by total, resolute, and voluntary withdrawal from the public world to one of private performance and electronic media.” The survival of their music would have to depend on their ability to situate themselves in a university setting; see Babbitt (2003, 53). Babbitt held no illusions about the difficulties posed by such a withdrawal, the serious misconceptions that prevailed among scholars and scientists about music and musical composition. His conclusion, however, was that the college or university offered “the best of all available worlds.” Babbitt (2003, 261); “The Composer in Academia: Reflections on a Theme of Stravinsky” (1970). 26See Babbitt (1987, 169–72). The “musical core of our crisis” can be traced to the “contextual situation,” the fragmentation of music and its consequent isolation from the academy and the general public. The “physical materials” of music may remain familiar, but not the splintered repertories, which have introduced “a complexity that is unequal in the history of music.” 27Babbitt was much taken by the idea of a close parallel between Schenker’s theory of tonality and twelve-tone composition. Common to both was “the idea that a piece develops outward in hierarchical, self-similar stages”; see Bernstein (2021, 197). “Just as Schenker’s genealogy of a tonal composition originates with the Ursatz and unfolds therefrom, so Babbitt’s genealogy of a twelve-tone composition begins with the series. Later developments in a piece are shaped by the possibilities inherent within the chosen series” (14).

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matters is the response of a given context to an application of the model, how one such response to an application may differ from that to another. The conceptual framework of structural levels and linear progressions is recast on each occasion, made to fit the individual. And the comparisons that are pursued in the course of this recasting serve a single purpose, that of further individualizing the context at hand. Given the role assumed by that context as an object of aesthetic attraction, it follows that its individualization is very much in the interests of the analyst. One of her objectives would surely be to relive and if possible intensify her experience of that object of attraction. The tonal piece or pieces under scrutiny are kept in full view throughout, maintained as a constant presence. And it could not be otherwise, given that the truly individual or unique is something sensed and felt by the listener—a quality captured in experience, held in memory, and capable of being invoked in a moment’s time. Resistant to analysis, uniqueness is ordinarily identified with something other than a mere sum, to borrow from the cliché of Gestalt psychology. In an attuned environment, all is magically one, all is individual.28 And the greater the attraction on the listener’s part, the greater the sensed individuality, and the more tightly knit are the variables of yet another cliché likely to be, that of the whole that both defines and is defined by its parts.29 And so the theory or class generality and all it may presuppose by way of its applications is put to use as a kind of foil, a way of drawing the listener into a work’s particular detail. The value of that detail lies not with its ability to verify a theory or instantiate a class. Its aesthetic worth is not determined by its ability to stand 28To

experience each part as integral to the context; to do so for the purpose of experiencing that much more of the context, that much more of what it is that attracts—such would seem to be the ultimate goal of analysis and theory, at least from an aesthetic standpoint. 29It is not as if the individuality of a context could be confined to a mere part, in other words, even a motivic part or character trait of one kind or another. It is not as if, sensed and felt, the individual context could be judged here but not there, a part of this but not of that. In the most rewarding of circumstances, if with varying degrees of intensity, all parts partake of the quality of the whole; they resonate accordingly, are cast anew in this fashion, made contextual, individual. Such a view of the “unified totality” differs little from Babbitt’s; that a piece of music be made whole in the listener’s mind, “entified as a unified totality, an all-of-a-piece of music.” Babbitt (1987, 167).

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as a “statistical sample from a musical population,” to quote from one of Babbitt’s published lectures.30 The reverse is true, as we have argued, that the theory is valued in so far as it can shed light on the particular. Few in music are interested in creating, performing, or analyzing entities that merely duplicate existing ones, “and to learn to hear a unique thing as a categorical thing is a net loss for musical experience.”31

II

Which is how it is likely to be with our personal relationships as well. In matters of human interaction, the loss is no less when, too routinely, the individual subject is made a function of the larger categories or groups to which he belongs or might be assigned. When we engage with others on a personal basis, we do so in principle as individuals, not for what we could, should, or might possibly represent categorically; we do so free of the vulgar taint of utility. In Wagner’s opera, the woman sought by Lohengrin “would not ask who he was or whence he came, but would cherish him as he was because he was what he appeared to her to be.”32 Is there in fact anything in the above discussion of the individual musical work and our study thereof that does not apply to the single human being and our attempts to come to terms with that singularity through general concepts of human behavior?33 What we know in our analysis of that being we know only as he relates to other beings, which is the dynamic that applies to no less an extent to our analysis of the individual musical work. We use what we know as a way of highlighting or setting the particular in relief. And so it has been until fairly recently with the study of literature, art, history, and philosophy. As an idea whose origins in antiquity lay with the cultivation of the individual, with virtue acquired through the study of literature and poetry, Humanitas embraced 30Babbitt

(1987, 4). (1977, 130). 32Richard Wagner, “A Communication to My Friends” (1851). Cited in Meyer (1991, 248). 33See Boretz (1969, 86): “The study of musical structure is quite unlike that of the structure of the physical world, and rather more like that of poetry or human personality.” 31Boretz

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benevolence, an early kind of “humanitarianism.” When this initial conception of the humanities was rediscovered in the early years of the Italian Renaissance, it was so as a kind of curriculum in schools and universities, one that underscored Greek, history, poetry, and moral philosophy. The liberties that, centuries later, would become identified with the individual and enshrined in documents such as the US Constitution and its amendments would become so by way of the Renaissance, the Reformation, the scientific revolutions of the seventeenth century, the religious tolerance as practiced in the Dutch Republic, and the Enlightenment in England and Scotland as well as France.34 In modern literature, the novel is distinguished from earlier forms of fiction, including Greek tragedy and French Classical drama, by the attention it lavishes on the “individualization of its characters,” to quote from Ian Watt35 and, more recently, Stefan Collini.36 Such literature is distinguished by the focus it places on the environment of its characters, the collective constraints that curb individual excess and the social norms that inform those constraints. Here, too, we could begin with the Renaissance and the Protestant Reformation, but then end with the Puritans, not with their work ethic or piety, necessarily, but with their tradition of self-inspection, the encouragement that was lent an individual’s interior life. In the history of Western art music, the “polyglot diversity” that troubled Babbitt in the second half of the past century excited others,37 not least the American minimalists and their near total rejection of the disciplinary rigors of twelve-tone composition. 34In

recent years, no doubt, study in the humanities has tended to abandon the traditional view of these large-scale socio-political forces, along with the individual subject in whose interests those forces were thought to have been set in motion. Replacing the individual and the forces enveloping him/her has been a narrative more akin to the social sciences, according to which the familiar equation is reversed, with the individual now placed at the service of the general, the meaning and significance of that individual—her “identity” or personhood—determined almost entirely by the immutable circumstances of her birth, her gender, sex, race, ethnicity, and even class. This would not be to question these overlapping categories as class generalities, the role they unavoidably play in the makeup of who we are. But the collective forms of shame, guilt, or aggrievement currently being assigned to one or the other of these groups are at odds with the values and purposes that have long been associated with the humanities and liberalism more genuinely. 35Watt (1957, 15). 36Stefan Collini, “Unreasoning Vigour,” London Review of Books, May 9, 2019. 37Babbitt (1987, 164).

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Paradoxically, those rigors had come in the form of a doubling-back, an attempt to capture a common framework for the “emancipated” pitch classes of atonality, a structural determination that could add depth to the single work while allowing for a more fastened, tangible sense of individuality.38 On a larger scale, these efforts had come in response to a musical meltdown, a tonality that, formulaic at first, had picked up steam through the extraordinary products of genre and style in the seventeenth and eighteenth centuries, before entering the second half of the nineteenth inflamed with concepts of individual self-expression, aesthetic autonomy, and originality, much of this a reflection of the growth in political and religious freedom chronicled briefly above. A point seems to have been reached at which tonality, exhausted and stretched to the bone, could no longer deliver, as it were, be individualized, except possibly from the outside looking in, selfconsciously with the bits and pieces of a style or convention, which seems to have been the case with Stravinsky and many other neoclassicists of the past century. Or else, as Boretz has argued, the “motivic language” that had taken root within the tonal structures of the eighteenth and nineteenth centuries (“the style of developing variation,” as Schoenberg called it),39 began to assert itself independently of those 38See

Babbitt (1987, 9–10). In the twelve-tone idea Schoenberg had found “a new communality,” a way of linking members of a new class of works. Members would be bound not by a common structure, to be sure, but by procedures or operations performed on an ordering of the twelve pitch classes. The hope, certainly, had been that this shared foundation would enrich each atonal or non-tonal work, while rendering each more readily intelligible to the listener. Much later, critics would contend that serialism had come at the expense of the liberation that atonality had represented; Schoenberg had found it necessary to exert a measure of “control” over the new medium; see McClary (1989, 57–81). A somewhat similar view is expressed in Adorno (2006, 57–59), although from a different perspective. 39Schoenberg (1969, 8); “Homophonic music can be called the style of developing variation. This means that in the succession of motive-forms produced through variation of the basic motive, there is something that can be compared to development, to growth.” Or see the description of “developing variation” in Schoenberg (1985, 129–31); “Criteria for the Evaluation of Music”; or in Schoenberg (2006, 247–48). Ideas encompassed by this term are examined in Dahlhaus (1987, 128–34), Frisch (1983), Boss (1992, 125–49), and Haimo (1997, 349–65). See also van den Toorn (1995, 101–42). Schoenberg’s motivic analyses are well known, but see his study of Brahms’s String Quartet in A Minor, Opus 51/2, in Schoenberg (1985, 429–31); “Brahms the Progressive” (1947).

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structures.40 Toward the close of the nineteenth century, in the music of composers such as Mahler and Schoenberg, that “language”—a motivic logic—had begun to move expressively against the tonal edifice, doing so in pursuit of the individualization that had seemed no longer possible within the edifice itself. Soon enough, the tonality on which the expressive character of this motivicism was at least partly dependent, began to recede altogether. The end result was atonality, music that Boretz called “motivic,”41 Babbitt, “contextual,” and Huron—although much later— “contratonal.” Even with all explicit ties to tonality extinguished, atonality could still seem to exist as a form of transgression or even negation. And it can seem to do so even today, aesthetically as well as conceptually or historically. No doubt, motives taken by themselves are nondescript and inconsequential. But such is entirely the point. Meaning and significance are acquired as the motive is elaborated upon, subjected to processes of developing variation that are inherently contextual and “defined within the piece itself,” as Babbitt would have it. “Composing with the tones of the motive”42—Babbitt’s description of Schoenberg’s methods during his “middle” or atonal period— represents “the ultimate contextual idea with regard to musical structure.”43 And there could be little doubt, Babbitt continued, “that, genetically, many of the operations of the [twelve-tone] system were suggested by the local motivic ideas in the music of the past.”44 And so the motive seems to have functioned as a kind of frontier, at the very least in the “extended-tonal,” atonal, and twelve-tone music 40Boretz

(1995, 343). Boretz (1995, 247); “My suggestion that ‘motivic’ is a conceptually preferable term for this [atonal] literature derives from the notion that the basis of the compositional approach involved is to be found in the interstitial, non-triadic counterpoint in ‘extended-tonal’ music, where the elaborations between triadic references are so extensive that an ‘inner’ referential basis is essential if one is to account for the structures with a degree of specificity.” 42Babbitt (1987, 171). “Composing with the tones of the motive” is an elaboration of Schoenberg’s own description of his method of composition at the time, which was “composing with tones.” See Schoenberg (1985, 89); “My Evolution” (1947). 43Babbitt (1987, 171). 44Babbitt (1987,16). 41See

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of the Second Viennese School.45 A piece defined itself individually by way of the motive and its transpositions and transformations, its successions and verticalizations. And such were the means by which atonality or anti-tonality (“motivic” or “contextual” music) succeeded tonality and its “extended” forms, and by which twelvetone serialism succeeded atonality. The successive and sometimes overlapping stages in this development of the motive, as set forth by Babbitt, Boretz, and, as we shall see, Theodor Adorno, is entirely consistent with Schoenberg’s own reflections on the subject: that the thematic construction in Verklarte Nacht (1899) was based in part on “Brahms’s technique of the developing variation”; that “a more rapid advance in the direction of extended tonality” was achieved with Pelleas und Melisande, (1903) where “many of the melodies contain extratonal intervals that demand extravagant movement of the harmony”; that “the transition to my second [atonal] period” was secured in the first and second movements of the Second String Quartet (1908), where, in many sections, “the individual parts proceed regardless of whether or not their meeting results in codified harmonies”; and so forth.46

III

Which brings us to the second of the two symbiotically related topics prefacing this inquiry, the formation of what Boretz called a class generality. The idea would be to isolate something of the shared basis of a class of works, doing so as a means of focusing more specifically 45For

a study of “motivic saturation” in the atonal music of Schoenberg, Webern, and Berg, see Straus (1990, 24–27). In an analysis of the first of Schoenberg’s Three Pieces for Piano, Opus 11, Straus underscores the “motivic orientation” of this music, its “motivic density,” indeed, the “dense web of motivic associations that defines the pitch structure of ‘freely atonal’ music.” Where pitch is concerned, the “density” of motivic relations is naturally increased when motives are represented as pitch-class sets and vice-a-versa (reduced to their interval-class content, for the most part, except for the Z-related pairs). See the discussion of this in van den Toorn (1995, 108–15). 46Schoenberg (1985, 80–86); “My Evolution” (1947).

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on the individuality that may be sensed on the part of each member.47 Or, to rephrase the project: how is it that features held in common as “communal” are made whole and distinct, individual and organically so?48 The musical population seeking definition here is that of a single, individual composer, an old-fashioned, musicological way of devising a class or literature, to be sure, but one very much in keeping with our present concerns.49 47Intuition

may play a role in the determination as to what might constitute a viable class generality. In several linguistically sumptuous passages in Meta-Variations (not always easy to follow), Boretz addresses the adaptable character of the line separating individual from class, the contextual from the communal. Permissiveness in the standards of admission to a given class will obviously tend to undermine “the defining capacities of the system.” “Sub-categories” under an umbrella such as “tonal music” are possible, such as the “intertriadic linear-structural characteristics” that might distinguish the music of Brahms from that of Wagner. See Boretz (1995, 241, 320). In the twentieth century, however, neoclassicism is too broad and indefinite a concept to be able to serve as a super category in the manner of “tonal music” or tonality. Classes with adequate “defining capacities” might include each of the three “stylistic” periods of Stravinsky’s music; the complete oeuvre poses difficulties in this regard. 48The parts of an organic structure are sensed as adhering naturally rather than artificially. See Korsyn (1993, 91). Early organicist thought was associated with the instinct and unconscious (“instinctive necessity”), above all with what was natural rather than willed or mechanical. “Organicism must also be seen in relation to mechanistic and materialistic trends, as a response to everything that threatened to reduce human beings to mere mechanisms.” For a brief survey of the extensive use of the metaphor of organic life in music criticism and analysis, see Bernstein (2021, 5–10). 49The normalization implied by terms such as class, system, and model is disparaged as a “tyranny” in Straus (2021, 341). However, listeners regularly reduce and standardize as a way of making sense of groups of musical contexts and ultimately of the world at large. Strategies of class normalization relieve them of the necessity of having to begin anew with each work, treating each as a blank slate. Norms may not be the issue, in other words, only their appropriateness. In the phrase that opens Mozart’s Piano Sonata in A major, K.331, dissonant (0 3 5) simultaneities, mostly in terms of (B D E), are composed of harmonic and non-harmonic tones. In his examples 3 and 4, Straus has sought to rescue this dissonance from what he views as an oppressive “traditional music theory,” one which, allied to “a medical model of disability,” has “stigmatized” dissonant elements as a form of “abnormality,” “a deficit or defect located within an individual body, and requiring remediation or cure.” (The metaphors of tonal analysis can sometimes seem to have been stretched beyond what might originally have been intended.) If only locally for the passages in question, Straus normalizes the (0 3 5) trichord: recurring (0 3 5)s are noted, and a transpositional path is traced by way of the (0 2 5)/(0 3 5) Tonnetz. Traditionally, of course, the E in the (B D E) trichord at m.4 in K.331 is a dissonant neighbor, or possibly suspended, note. Tonally speaking, E in the top voice clashes with the harmonic

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When Milton Babbitt turned to Stravinsky’s music in 1964, he turned to the serial and twelve-tone music of the 1950s and 60s,50 and then to what he used to call “set structure,” by which he meant a study of the content and ordering of a hexachord, along with the transformations to which it might be subject. He confined himself in large part to the operations of the system, in other words, that sliver of a foundation upon which rested the claims of a repertory. By contrast, the American minimalists, especially Steve Reich and John Adams later in the century, were attracted to the repetitive, ritualistic features of Stravinsky’s earlier Russian-period music, the ostinato patterns and the polyrhythmic textures of which those patterns were often a part. Here, however, we turn to a few passages from Stravinsky’s late neoclassical works of the 1940s and 50s, the other side of the vast divide at the time that separated Schoenberg and the serialists from the neoclassicists or “quasi-tonalists.”51 It tone D, its expressive character stemming from its non-membership of ii6. First a consonance and then a dissonance, the E is obliged to resolve into the D, emitting a sense of motion in the process. Although subsidiary, the E is hardly so on aesthetic grounds. Far from “disabled” or underpriviledged, the E is likely to stand out at m.4 and, retrospectively, earlier as well. Why would listeners forfeit this nuanced, richly structured sense of (B D E) for the relatively static, flattened out sound favored by Straus? Schenker’s “bristling normative” (Babbitt’s term) may leave many questions about tonal music unanswered, of course, and the theory is not equally applicable to all sub-categories of this vast terrain. Yet the conceptual framework can light up a phrase such as the one discussed here with a transparency that is nothing short of magical. That same framework can stretch and bend in accord with the demands of the individual, its high degree of determinacy ideal as a foil in this regard. 50See Babbitt (2003, 147–71); “Remarks on the Recent Stravinsky” (1964). 51This was Schoenberg’s term. See the Forward to his Drei Satiren, Opus 28 (1925), where he takes aim at the “half measures” of the “quasi-tonalists” and “folklorists.” In the third of the Satiren, Stravinsky the neoclassisist was mocked as “Der Kleine Modernsky.” Schoenberg’s mini-manifesto may have come in response to Stravinsky’s earlier complaints about twelve-tone composition, to the effect that its practitioners worked with “formulas instead of ideas”; see Messing (1988, 141). Neither Schoenberg nor Stravinsky appears to have known much first-hand about the other’s music, however. In conversation with Babbitt in 1962, Stravinsky confided that, following a performance of Pierrot Lunaire in Berlin in 1912 and another a bit later in Paris, he had heard not “another note” of Schoenberg’s music until the Prelude to the Genesis Suite, which was first performed on November 18, 1945, in Los Angeles. Babbitt (2003, 265); “Stravinsky (1882–1971): A Composer’s Memorial” (1971). During the 1920s and 30s, Stravinsky and Schoenberg took account of the reviews and interviews in the press, and then weighed in accordingly; see van den Toorn (1995, 149–51). Schoenberg’s Forward is translated and quoted in full in Messing (1988, 144).

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was the serialists who tended to hold sway through the 1960s and even into the 70s, the accepted wisdom having been that theirs was indeed the music of the future. Above all, the serialists were “progressive,” to quote from Theodor Adorno’s notorious Philosophy of New Music (1947), the opposite of “regressive” or merely reactionary and backwardlooking, which is how this critic-philosopher viewed Stravinsky’s music. Adorno was not alone in dividing the music world into these opposing camps,52 but he did so on the basis of a single factor, namely, the developmental style of the eighteenth and nineteenth centuries, the style of developing variation and its continuation in the music of Schoenberg, its absence in Stravinsky’s.53 Nearly all of his concrete objections to Stravinsky’s music may be traced to this single delinquency. They include the static quality of Stravinsky’s music, the irregular accents and spans (which can seem the result of an arbitrary “game of chance”),54 and the apparent need for a “rigidly maintained meter,” one that lacked “subjective, expressive flexibility.”55 For Adorno, healthy, developmental music took account of the reality of the human predicament in modern times. Mirroring the individual subject and his self-reflecting quest for fulfillment in a world conditioned by alienation, the musical subject or theme and its “motive-forms” underwent a parallel development, emerging 52To

the two “disjoint domains” of Stravinsky followers and Schoenberg followers, Babbitt added a third: “those whose loyalty was to neither.” Babbitt (2003, 264); “Stravinsky (1882–1971): A Composer’s Memorial” (1971). Babbitt felt not the least discomfort with these widely recognized categories, for they underscored “differences” that were specific and “crucial” (265). 53Adorno, Schoenberg, Babbitt, and Boretz may have approached the motivic process from different angles, but all were convinced of its significance in the music not only of Schoenberg, Berg, and Webern, but also of the many who were allied in one way or another. The same cannot be said for Adorno’s Philosophy of New Music, however. Babbitt thought Adorno’s writing “unintelligible or unbelievable.” Babbitt (2003, 431); “On Having Been and Still Being an American Composer” (1989). In a letter to Hans Stuckenschmidt, January 7, 1949, Schoenberg pronounced Adorno’s treatment of Stravinsky’s music “disgusting … I am certainly no admirer of Stravinsky, although I like a piece of his here and there very much.” See Walsh (2006, 238). Adorno’s perspective on contemporary music and analysis—Schoenbergian very nearly in its entirety—may well have come by way of Berg, his composition teacher for a time during the 1920s. 54Adorno (2006, 115–17). 55Adorno (2006, 116).

Individual and “Class Generality”

from these trials recognizably the same subject, yet transformed in some fashion.56 Twelve-tone methods intensified these processes. Transformations of the row were variations, according to Adorno, with “the principle of variation elevated to a totality.” “Once everything is equally absorbed in variation, a ‘theme’ no longer remains, and every musical phenomenon is indifferently determined as a permutation of the row.”57 Such dynamics were nowhere to be found or sensed in Stravinsky’s music, needless to say, whatever the stylistic orientation. Indeed, the neoclassical music to which we will be turning was valued at next to nothing by Adorno and the serious compositional crowd of this period, ridiculed on both sides of the Atlantic.58 By way of illustration: the first movement of Stravinsky’s “Basle” Concerto in D ((1946); see Ex. 3a and 5) and Schoenberg’s twelvetone works of the late 1930s and 40s, were composed in the same city (Los Angeles) and more-or-less concurrently. Where pitch, rhythm, and expression are concerned, however, the two sides of this dividing line can seem light years apart. Both sides draw heavily on the tonal past, but they do so in markedly different ways.

IV

At the same time, there is today nothing to prevent those sympathetic to Stravinsky’s music from setting aside Adorno’s verdict and profiting from his descriptions of the music, many of which are insightful, notwithstanding the incendiary language. In fact, in seeking to assemble features that would have to be included in a profile of this composer’s music, we could begin where Adorno left off, that is, with the literal nature of the repetition in Stravinsky’s music. And we could attribute the frequent lack of a traditional way of varying or elaborating that repetition to certain of his rhythmic practices. 56See

Subotnik (1991, 20). Echoing Theodor Adorno’s account of the Classical style, Subotnik defines developing variation as that process “whereby a musical element subjects itself to logical dynamic change while simultaneously retaining its original identity.” 57Adorno (2006, 80). 58See Walsh (2006, 236–38).

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Often enough in Stravinsky’s music, when a motive is repeated, its alignment relative to the meter is changed. Typically, Stravinsky repeats not to vary or to develop in the manner of the Classical style, but to displace metrically. This single rhythmic maneuver can account for many of the features of melody, articulation, notation, and performance practice we tend readily to identify with his musical style. Consider, in Ex. 1, the opening two measures of the Triple Pas-deQuatre in the ballet score, Agon (1953–57). Here, a repeated triplet figure in the flutes, trumpet, and strings pizzicato falls first off and then on the eighth-note beat of a 4/8 meter. As the brackets show, the time spans between successive repeats of this figure shrink from four to three sixteenth-note beats. In effect, the displaced repeat arrives a sixteenth-note beat “too soon,” and is apt to acquire a rushed, breathless quality as a result.

Example 1  Agon, Triple Pas-de-Quatre, opening bars

Or see, in Ex. 2a, the opening measures of the Allegretto movement of the Symphony in C (1940). A repeated motive in the lower strings falls first on and then off the quarter-note beat of a 4/8 measure. The spans between these repeats grow from four to an irregular five eighth-note beats. What can seem to take precedence in these passages is the rhythmic-metric scheme, with the rationale underlying much else falling into place accordingly. The two repeated motives in Ex. 1

Individual and “Class Generality”

and 2a are fragments rather than melodies or themes; short and open-ended, they invite the immediate repetition to which they are subject. And that repetition lacks elaboration. In Ex. 1, the string pizzicato that percussively punctuates the initial appearance of the triplet figure does so at subsequent appearances as well. And the articulation remains in place, starting with the forte and continuing with the two slurs in the flute parts.

Example 2  Symphony in C, III, opening bars

In this way, the repetition in Ex. 1 and 2a is fixed registrally as well as instrumentally. There are no transpositions or imitative exchanges. The two motives are not tossed about from one instrumental part to another, mirroring that sympathetic sense of a dialogue that can often seem to epitomize the development of motives in Classical settings. These static, unchanging conditions in Ex. 1 and 2a serve a purpose, for they allow the metrical placement and displacement of the two motives to stand in relief. The literal repetition acts as a foil

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for what does change, namely, metrical alignment and the spans that separate the motivic repeats.59 Moreover, where the performance of this music is concerned, the conventions of expressive timing or rubato must be kept in check. If the metrical displacement of the two repeated motives is to have its effect on the listener, then the beat must be maintained strictly in performance.60 And so begins the composer’s lifelong battle with interpretation and nuance, not with the formalist aesthetics, necessarily, but rather with these practical matters of performance. The need for a strictly held beat springs from the rhythmic invention as a necessary condition thereof. A summary of these rhythmic-metric features and their wider implications for Stravinsky’s music as a whole (Russian, neoclassical, or early serial in origin) can take the form of a directive:

1. That a profile of Stravinsky’s music would have to include the metrical displacement of a repeated motive; 2. That, for the reasons cited above, the repetition of the motive would have to be literal, apart from the metrical 59In

his criticism of Stravinsky’s methods, Schoenberg seems not to have understood or appreciated (not to have felt?) the rhythmic invention underlying the literally repeated motives, the expressive character of metrical displacement and its melodic, harmonic, and articulative implications. In an unpublished document dating from 1922 (“Ostinato”), he decried the nakedness of the repetition in Stravinsky’s music, the lack of elaboration. In still another document, “Polytonalists” (1923), Stravinsky’s themes and motives, “in their germinal state,” are judged incapable of inviting a proper continuation; the materials are stitched together mechanically rather than organically. The missing ingredient in Stravinsky’s music can now seem rather obviously to have been the style of developing variation. The typescripts “Ostinato” and “Polytonalists” are identified as T34.05 and T34.07, respectively, at the Arnold Schoenberg Center in Vienna. Both are cited and discussed in Neff (2017, 310). 60See, in this connection, Neff (2017, 312–24). The author discusses the forms of expressive timing introduced by Rene Leibowitz in his recording (1960) of The Rite of Spring. Leibowitz’s performance was not “unmusical,” of course, but it sidelined the pronounced effect the rhythmic invention can have when the beat and the articulation are strictly enforced. As an enthusiast of Schoenberg and twelve-tone composition, Leibowitz was predictably critical of Stravinsky’s music, and in what can now seem to have been a predictable fashion: the music lacked an “organic way” of linking “segments, themes, and sections”; the latter were “juxtaposed rather than being developed organically.” Missing once again, evidently, was a form of developing variation. See Leibowitz (1948, 361–65); as cited in Neff (2017, 314).

Individual and “Class Generality”

realignment itself; it would have to remain fixed in register and instrumentation; 3. That the repetition might be highlighted in the manner indicated in Ex. 1, punctuated with a string pizzicato; 4. That the motive, repeated irregularly or as an ostinato, might be joined polyrhythmically by the repetition of other motives, with its alignment shifting in relation not only to the meter but also to the other reiterating motives; 5. That the ideal location of the metrical displacement would be the salient middle range of the metrical hierarchy, with the motive falling on and off the tactus (see the eighth-note beat in Ex. 1), or possibly the beat immediately above or below the tactus61; 6. That the ideal tempo would be within the moderato range, 80–100 beats per minute for the tactus being “maximally salient”62; 7. That, for the reasons cited above, the beat would have to be maintained strictly in performance; and 8. That the notation might be conservative, with the meter sustained (conserved) and the metrical displacement exposed to the eye, or radical, with the meter interrupted as a means of preserving a form of metrical parallelism.63 By such means, a standard practice might be devised, a profile that, in useful and concrete ways, could act to illuminate features that distinguish one member of this particular class of works from another. If the motive and its developing variation can seem to dominate the landscape of much of Schoenberg’s music, then the motive and its metrical displacement can seem to do so in much of Stravinsky’s. 61The metrical location of Stravinsky’s repeated and displaced motives is discussed in

van den Toorn and McGinness (2012, 28–30). (2004, 31–33). 63The distinction between conservative and radical responses—between allowing the meter to be sustained and allowing it to be interrupted—was first made in Imbrie (1973, 46–66). The distinction was then introduced in Lerdahl and Jackendoff (1983, 23–25) as a way of classifying alternative readings of hypermeter. It has since been applied to various responses to Stravinsky’s rhythmic maneuvers; see van den Toorn (1987, 67), Horlacher (1995, 285–310), and van den Toorn and McGinness (2012, 20–28). 62London

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V In Ex. 1 from the Triple Pas-de-Quatre in Agon, the initial repeat of the triplet figure in the second measure falls off both the eighth- and quarter-note beats of the 4/8 meter, locations that are metrically parallel to those of the figure’s original appearance.64 In the listener’s mind, the parallelism of this initial repeat helps to establish and confirm the meter, while at the same time raising expectations that subsequent repeats will be aligned similarly. When these expectations are thwarted by the metrical displacement of the triplet figure and the creation of an irregular, nonparallel span of three sixteenth-note beats, the listener’s sense of the meter is apt to be threatened or possibly disrupted altogether. Meter and parallelism no longer coincide, but are split apart, and although the listener may yet succumb to one of these two forces, she is unlikely to do so without a degree of resistance manifesting itself on the part of the other. The evidence may not be sufficient for a clean, undisturbed interpretation, in other words, and the meter may be interrupted temporarily. Yet the notation in Ex. 1 and 2a is unequivocally conservative. The assumption here is that the meter will be sustained (conserved), and that the displacement of the two repeated motives will be felt as such. Alternatively, however, the listener might attempt to align the displaced motives as before, that is, at a metrically parallel location, one that would require the 4/8 meter to be interrupted. In Ex. 2b, the opening measures of the Allegretto are rebarred analytically in accord with this radical alternative. To allow the third repetition of 64For

a definition of metrical parallelism, see Lerdahl and Jackendoff (1983, 75). See also Temperley and Bartlette (2002, 117–49). As introduced here, metrical displacement is a form of nonparallelism that differs from Harald Krebs’s idea of a “displacement dissonance”; see Krebs (1999, 25–33). Displacement dissonances are the products of recurring offbeat patterns. A recurring motive, equal in length to the measure, may begin off the beat or bar line. In the current view, however, such a motive is not metrically displaced because its alignment relative to the bar line never changes; all repetitions of the motive are metrically parallel. By contrast, Krebs’s “grouping dissonances” frequently involve the metrical displacement of a recurring motive, although there are important distinctions here as well. In the Pasde-Quatre in Agon (Ex. 1) and other Stravinsky works, the repetition of a motive that is metrically displaced is often literal in other ways, and the spans separating motivic repetitions are irregular. For additional comment, see van den Toorn and McGinness (2012, 36–41).

Individual and “Class Generality”

the motive to enter at a metrically parallel location, an eighth-note beat is added to the second measure. And, frequently enough, the composer bars accordingly, that is, irregularly as a means of exposing a form of parallelism. In the opening eight measures of the “Basle” String Concerto in D (1946), shown in Ex. 3a, an extra beat at rehearsal no. 1 (see the irregular 9/8 measure) allows the (F A) chord in the next measure to fall on the second dotted quarter-note beat. This alignment is metrically parallel to the chord’s initial appearance in the third measure.

Example 3a  “Basle” Concerto in D, opening bars, notated, radical

Conservatively, however, the listener might persist with the 6/8 meter at rehearsal no. 1, which would mean that the repeated chord would be felt as displaced. And such is by far the more likely of the two courses of action, given the metrical squareness of the opening five or six measures. The eight-bar phrase is rebarred in Ex.  3b,

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with the hypermetrical spans exposed and the agogic accents of the punctuating F♯s and the (F F♯ A) major-minor third chord of the third measure coinciding with the downbeats of the 6/8 measures. Here, the regularity of several levels of meter and hypermeter, together with the fixed articulation, serve as a backdrop for the metrical displacement of the major-minor third chord. In the eighth measure of Ex. 3b, the repetition of the chord (with its F♯ missing, although sustained in the violins) falls on the second rather than the first dotted quarter-note beat of the 6/8 measure, on the upbeat rather than the downbeat.

Example 3b  Rebarred, conservative

VI The analytical chart attached to the musical illustration in Ex. 3a seeks to capture something of the melodic and harmonic life of the introductory section of the “Basle” Concerto—in effect, its first five rehearsal numbers. As can be seen at levels 5 and 6 in the diagram, the total pitch-class content of this section, D, E♯/F, F♯, A, and B, is as octatonic as it is accountable to the D-major scale. It is the latter, however, only by virtue of an interpretation of the E♯/F as a chromatic tendency tone to the F♯, the major third of the tonic triad, (D F♯ A). In fact, much of the play of this music would seem to rest with the duel, pivoting behavior of this E♯/F: conceived octatonically as a cohesive member of the symmetrically defined (D F F♯) (F F♯ A) major-minor third units, it is also a chromatic tendency tone on the D-major side of the dotted vertical line in Ex. 3a. As an expressive inflection, it can be traced to the Classical style of Haydn, Mozart, and Beethoven. So, too, the (F F♯ A) chord in the third measure of Ex. 3a is a majorminor third unit. On the Classical side of the bargain, however, E♯/F

Individual and “Class Generality”

clashes with the tone to which it tends, the F♯, a typically Stravinskian form of superimposition. The clash, static in its implications, flattens out the harmony and allows the rhythm-metric scheme to come to the fore. And so the neoclassical idiom manifests itself here in the form of an interaction between the octatonic and the D-major scales. And although there are no harmonic progressions or definitions of key in this music, only conventions or the surface gesture of the Classical style, it is still the D-major scale that can seem to prevail, in relation to which elements of the octatonic scale assume a subversive role. The two scales are placed in juxtaposition in Ex. 4. Held in common and bracketed in each is the tonic triad, (D F♯ A). The chromatic tendency tones E♯ and G♯ along with the major-minor third units of which they are a part are shown intruding on the diatonic, major-scale framework. These intrusions are among the “impurities” of old, the “wrong notes” with which, for much of the past century, Stravinsky’s neoclassical music was said to be afflicted.

Example 4  Octatonic and D-major scales

Transposed in various ways, the relations and techniques depicted in Ex. 3a and 4 may not be present in all of Stravinsky’s neoclassical works, or even in the majority of them. Yet they are so consistently enough in the later ones as to qualify as characteristic. Were a stem to be drawn representing octatonic-diatonic interaction from the Firebird (1910) through the Russian, neoclassical, and early serial periods, these relations and techniques would figure prominently as an offshoot. For an additional illustration of these scalar interactions so typical of Stravinsky’s late neoclassical works, see, as reproduced in Ex. 5, the configuration later at rehearsal no. 55 in the first movement of the “Basle” Concerto; the pitches E♯ and G♯ tend chromatically to

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F♯ and A, respectively, the third and fifth of the tonic triad, (D F♯ A). Or see, in Ex. 6, the Danses Concertantes (1942) at rehearsal nos. 30–34, where, in pitch-specific terms, the thematic outline is very nearly identical to that of the “Basle” Concerto in Ex. 3a and 5. Or see the opening pages of Babel (1944) and then later at rehearsal nos. 16–24; the second movement of the Symphony in Three Movements (1945) at rehearsal nos. 125–30; or sections of Orpheus (1947), including the “Air de danse” at rehearsal nos. 5–29, and the “Pas des furies,” beginning at rehearsal no. 58.

Example 5  “Basle” Concerto in D, I

To be sure, the illustrations listed above are sectional in nature, reflecting in this way the fractured appearance of much music following the breakdown of tonality. Held in common by all is an actual structure, however, one consisting of a form of pitch-centricity, interacting octatonic and diatonic major scales, and a shared vocabulary. In effect, what might earlier have prevailed continuously through an entire work, oeuvre, or even literature, is here available only episodically.

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Example 6  Danses Concertantes, II

Reproduced in Ex. 7, the opening phrase of the second movement of the “Basle” Concerto is a case in point. The B-flat major scale (or even key, bV1) that may be inferred lacks the octatonic interaction of the first movement. Instead, triads progress stereotypically from a tonal standpoint, in a fashion that is very nearly unimpaired by the familiar “impurities” of neoclassicism. Among the latter is the clash and consequent blurring of dominant and tonic functions at m.5, a typically Stravinskian device that may be traced back to the cadencies in the Overture to Pulcinella (1920). In the first violins, the Bb is sustained much like a tonic pedal. And were we to delete the extra quarter-note beat at m.3 while shifting the melody from the third to the first beat of the 4/4 measure, the model itself (the four–measure prototype) would emerge unscathed. Even as it is, however, the opening phrase comes about as close to the genuine article as it can without forfeiting altogether the composer’s “rare form of kleptomania,”65 his instinct to “recompose” or “repeat in my own accent.”66 In the spirit of Tchaikovsky, a tonality is made to unfold in the Classical manner of a theme and its accompaniment. The leading tone-to-tonic or A-Bb reiteration at the start of the melody, a “stutter” motive, as Stravinsky once described 65Stravinsky 66Stravinsky

and Craft (1960, 104). and Craft (1962, 126).

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reiterations of this kind in his music,67 mirrors the semitonal inflections of the chromatic tendency tones in the first movement. The highly expressive character of these semitones in the second movement is owing in part to their replacement by the stretch of a minor ninth in the cellos and a major seventh in the first violins. These “octave displacements” add weight to what is in essence a form of embellishment.

Example 7  “Basle” Concerto in D, II, opening bars

VII The melodic and harmonic vocabulary cited in Ex. 3a and 5 is further encapsulated by the Tonnetz in Ex. 8 and 9, the greater abstraction here allowing for a view of the larger octatonic world from which this vocabulary may imagined as having sprung. Running along the 67See

Stravinsky and Craft (1966, 58). “Two reiterated notes are a melodic-rhythmic stutter characteristic of my speech from Les Noces to the ‘Basle’ Concerto in D, a lifelong affliction, in fact.” Stravinsky’s “stutter” motives are examined at greater length in Horlacher (2011, 71–129). See also van den Toorn (1995, 177–78, 182–87).

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horizontal and vertical axes of the Tonnetz are the major- and minorthird cycles, respectively. The circle of fourths appears along the northwest-to-southeast diagonal. Transpositions of the minor-third cycle yield the three overlapping transpositions of the octatonic set, which are labeled Collections I, II, and III.

Example 8 Tonnetz, major-minor third units; with a view toward Stravinsky’s late neoclassical works

As can be seen by the graphs prefacing Ex. 8 and 9, while the squares represent the (0 3 4 7) tetrachord,68 the triangles within the squares represent the (0 3 4) (3 4 7) major-minor third units in Ex. 8 and the (0 4 7) (0 3 7) major and minor triads in Ex. 9. Ideally, the octatonic side of the interactions traced in these examples would be fortified by a transposition along the minor-third cycle, one that would extend relations beyond a single square. 68(0

3 4 7) is not a unit of vocabulary, as are the major and minor thirds and triads cited in Ex. 3a and 5. Instead, (0 3 4 7) is a segment of the total pitch-class content shown at level 5 in these examples, a segment in turn of the sets and scalar orderings of reference, the octatonic (Collection II) and D-major scales. Similarly, the minorthird cycle is the transpositional path of the just-noted vocabulary. It is not a unit of vocabulary as a diminished-seventh chord.

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Example 9  Tonnetz, major and minor triads; with a view toward Stravinsky’s late neoclassical works

In point of fact, most of the above-noted examples include, on the Classical side of the interaction, the chromatic tendency tone to the fifth as well as the major third of the tonic triad. From an octatonic perspective, this inclusion would entail the addition of a third majorminor third unit to the two already cited in connection with Ex. 3a: (0 3 4), (3 4 7), and (3 6 7). Were we to translate the numbers in these units to the pitch letters associated with Ex. 3a, 4, 5, and 6, the series of interlocking major-minor third units would read as follows: (D F F♯), (F F♯ A), and (F G♯ A). The three units cited just above are represented graphically by the three shaded triangles along the Collection II column in Ex. 8, reading from top to bottom. Transposed one way or the other, the three units are the norm where octatonic-diatonic relations are

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defined along the neoclassical lines set forth in Ex. 3a and 5. The total count of six pitches includes, as before, the B as pitch number 9. So, too, the content remains as octatonic as it is diatonic in terms of the D-major scale. And the chromaticism may yet be attributed to the convention of the tendency tone. Crucially, the third of the three major-minor third units, (F G♯ A), is also the first in a transposition along the D-F-G♯-B minorthird cycle, from the first to the second square in Ex. 8. As can be seen in Ex. 10, (F G♯ A) pivots between the “home base” area and the transposition. And the implications of this pivot for octatonicdiatonic relations are as follows: a fourth or possibly even a fifth unit will be needed to balance or tip the two interacting scales in favor of the octatonic. In the present case, the two added units might be (G♯ A C) and (G♯ B C). They complete the transposition outlined in Ex. 9, adding a seventh pitch to the total count, the C as pitch number 10. Example 10  Major-minor third units; transposition along the D-F-G♯-B minorthird cycle, Collection II

VIII Just as with the major-minor third units in Ex. 8, so, too, with the triads in Ex. 9. Using the same tonnetz, but with the squares—the (0 3 4 7)s—sliced differently, the three shaded triangles are now triads. They appear along the Collection II column in Ex. 9, a tonic triad (D F♯ A) flanked by its parallel and relative minor triads. And although the parallel triad (D F A) casts but a shadow on the first movement of the “Basle” Concerto (the F of the minor third functioning almost entirely as a chromatic tendency tone to the F♯), the relative minor (B D F♯) surfaces conspicuously later on. And to no less an extent than the major and minor thirds in Ex. 8, the three triads of Ex. 9 form a nucleus. Tipping the scales of this nucleus in favor of the octatonic side of the equation would require a fourth triad, possibly (B D♯ F♯). And such are the means by which, as a rule in Stravinsky’s music, more thoroughly ocatatonic settings are secured. Three transpositions of triads along the 0-3-6-9 minor-third cycle may be needed to solidify a context as decisively octatonic.

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An early manifestation of this octatonic-diatonic nucleus of three triads may be found in a celebrated passage in Stravinsky’s opera/oratorio, Oedipus Rex (1927). As can be seen from the excerpt in Ex. 11, the passage is a stratification. Five strata or layers of reiterating fragments or chords are superimposed, the repetition consisting of the following triads or triadic parts: (D F A), (D F♯), B-F♯, (D F), and (F♯ B D). The latter reduce to the same set of three triads, (D F A), (D F♯ A), and (B D F♯).

Example 11  Oedipus Rex, stratification

There is a difference, however. In Oedipus, the central triad or point of departure is (D F A) rather than (D F♯ A). And the implication is that, instead of the pitch E♯/F tending chromatically to F♯, the latter is likely to be heard and understood as a tierce de Picardie in relation to (D F A). Apart from the three related triads, inflection and surface gesture account for the Baroque or Classical side of Stravinsky’s neoclassical bargain. And the three triads, instead of progressing regularly, are superimposed. Observe, however, that the stratification lacks polyrhythm. In Ex.  11, the repetition in all five layers is fixed in metrical alignment as well as register and instrumentation. The spans separating the repetition total three or six quarter-note beats, all very much in synchrony with the 3/4 meter. So, too, there are no metrical displacements. These conditions differ markedly from those in Russian-period works such as The Rite of Spring (1913), Renard (1915), and Les Noces (1917–23), where the stratifications are invariably polyrhythmic, and where, as a consequence, the reiterating motives and chords are displaced relative to one another and the meter.

Individual and “Class Generality”

The vast immobility of this music carries a dramatic purpose. Indeed, we have arrived at the high point of the opera/oratorio: following the departure of the Messenger and Shepherd, nos. 167– 69 coincide with Oedipus’s recognition of guilt, no. 169 with his final resignation. Musically as well as dramatically, the pause represents a period of reflection and anticipation. Coupled with conventional scale patterns and accompaniment figures, however, the forms borrowed from Baroque opera in Oedipus are no less contributing factors to the stasis. At least initially during the 1920s, Stravinsky’s preoccupation with Baroque and Classical practice had the effect of reining in much of the rhythmic-metric invention of the earlier period.

IX

Mention should also be made here of the mother of all major-minor third units, the tetrachord defined by the first four pitch numbers of the octatonic scale, (0 1 3 4). In one of his later books of “conversation” with Robert Craft, Stravinsky identified this tetrachord as the “root idea” of the Symphony of Psalms (1930), describing it further as consisting of “two minor thirds joined by a major third.”69 Both the label and the description appear already in 1931, however, not in an interview or publication of Stravinsky’s, but rather in the lectures Nadia Boulanger was in the habit of delivering to her students at Ecole Nationale de Musique and the American Conservatory at Fountainebleu.70 (By the early 1930s she and Stravinsky had become 69Stravinsky

and Craft (1963, 45). Francis (2015, 56–63). Francis implies that Boulanger was fully aware of the octatonic scale in her lectures on the Symphony of Psalms beginning in 1931, especially where the first movement was concerned, the tritone-related (0 1 3 4)s, F-Ab-E-G and B-D-A♯-C♯, that appear superimposed at rehearsal no. 7. Francis’s assumption is reasonable, even if there is little hard evidence to support it. (For what it may be worth, the present writer studied with Boulanger for a few years during the 1960s, closely examining many of Stravinsky’s works. No mention was made of the octatonic scale.) Stravinsky was aware of the scale, of course, at the very least since his years of tutelage with Rimsky-Korsakov (1905–08), when the scale was known as the tonesemitone scale or the “Rimsky-Korsakov scale.” Not a single mention of the scale can be found in his publications, however. This includes the Autobiography (1935), the Poetics of Music (1947), the six books of “conversation” with Robert Craft (1959–70), and the published interviews that stretch over a half century. Stravinsky may have guarded the octatonic scale like a trade secret, a key too revealing of his compositional detail to risk disclosure. 70See

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close friends and associates, so that the terminology may yet have originated with the composer.) Boulanger’s analytical notes stress the form or “architecture” of the three movements of Psalms, small-scale and in the large; unity is pursued in spiritual as well as musically technical terms. But whether her discussion embraced an awareness of the cohesive and coordinating role of the octatonic scale is another matter. Octatonic configurations appear to have been regarded as a form of chromatic inflection.

Example 12  Symphony of Psalms, I, octatonic stratifications

Of the three movements of Psalms, the first is the most heavily octatonic. Like the excerpt from Oedipus in Ex. 11, the passages quoted in Ex. 12 are stratifications lacking polyrhythm. In the Tonnetz of Ex. 13, the tritone-related (0 1 3 4)s at rehearsal no. 7, B-D-A♯-C♯ and F-Ab-E-G, are represented by the shaded squares along the Collection I column. Semitones traverse the horizontal axis of this Tonnetz, while major thirds are located along the northwest-tosoutheast diagonal. The three octatonic scales are again represented by overlapping transpositions of the minor-third cycle. In the second movement of Psalms, the subject of the initial fugue is C-Eb-B-D, with the tetrachord located within a quasi C-minor context. Still earlier articulations of the (0 1 3 4) tetrachord

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include the variation theme of the Octet (1923), second movement, as shown in Ex. 14. A variant of the Classical model of a theme and its accompaniment, an octatonic theme outlining (A Bb C C♯) and (A C♯ E), the latter as a kind of dominant, is superimposed over an accompaniment that implies D minor. The transposition by a minor third at rehearsal no. 25 allows the theme to remain confined throughout to the same octatonic scale, that of Collection III. In the concluding measures at rehearsal no. 25 and later as well, the theme’s closing F♯ neatly unites the octatonic scale with the D-minor accompaniment by way of a tierce de Picardie.

Example 13  Tonnetz, (0134) tetrachords; with a view toward Stravinsky’s neoclassical works

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Example 14  Octet, II, octatonic theme, D-minor accompaniment

X The “hyper-octatonic network” pictured in Ex. 15 incorporates features of Richard Cohn’s “hyper-hexatonic systems,” published over twenty years ago in Music Analysis.71 Included here on the outside of the three circles, however, are not only the roots of the triads, as represented by the upper-case pitch letters, but also the three transpositions of the octatonic scale. In Fred Lerdhal’s Tonal Pitch Space, a diagram of “triadic/octatonic space” is drawn similarly72; just as in Ex. 15, Lerdahl’s circles connect the roots of the triads at the “chordal level,” while the larger triangle connects the three circles or transpositions as separate “regions.” Analogous to a key area in tonal music, a region represents, roughly in Stravinsky’s music, a section or “block” of material. (There are lengthy passages 71Cohn

(1996, 9–40). (2001, 257–58).

72Lerdahl

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in Les Noces that feature an interaction between two transpositions of the octatonic scale, but such interactions are exceptional when the literature is taken as a whole.)

Example 15  Hyper-octatonic network, with a view toward Stravinsky’s neoclassical works

In transposing (or modulating) from Collection I to Collection II in Ex. 15, the lower-case pitch letters of the first circle become the upper-case pitch letters of the second, a maneuver that is duplicated when transposing from the second circle to the third, and from the third back to the first. In sum, each circle or collection shares a minor-third cycle with the other two circles or transpositions. Holding the pitch numbers on the inside of each circle constant, we can rotate the pitch letters at fifteen, thirty, and forty-five degree angles. Doing so will allow all four of the upper-case pitch letters on the outside of the circles to serve as pitch number 0, representing a localized or regional form of pitch-centricity or priority. More importantly, the minor-third cycle defined by the uppercase pitch letters is the transpositional path not only of the major and minor triads, but also of the major-minor third units and the (0 1 3 4)s, as discussed above. In the circle implicated by the first movement of the “Basle” Concerto, that of Collection II, the transpositional path of all three forms of vocabulary is D-F-G♯-B. And all three forms implicate the semitone-tone ordering of the octatonic

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scale, the numbering of which is shown on the inside of each of the three circles: 0 1 3 4 6 7 9 10 (0), reading clockwise. Were these numbers to be read in reverse, however, counterclockwise, with the identical pitch serving as pitch number 0 (the D), the result would be a descending scale beginning with a tone rather than a semitone: 0 2 3 5 6 8 9 11 (0). The two numberings of the octatonic scale, with each realized in terms of Collection II, are shown in Ex. 16a and b. The overlapping brackets in these examples outline successive transpositions of the two tetrachords, (0 1 3 4) in Ex. 16a, and (0 2 3 5) in Ex. 16b.

Example 16  Octatonic scale, alternative numberings

The (0 2 3 5)s in Ex. 16b open up a new octatonic universe, one linked to the countless (0 2 3 5)s—or minor tetrachords—that may be found reiterated in Stravinsky’s Russian-period works, from The Firebird (1910) to Les Noces (1917–23).73 Often gapped by a minor third, with the four pitches reduced to three as (0 2 5) or (0 3 5) trichords, these (0 2 3 5)s are invariably open-ended, repeated, and confined to a perfect fourth; constrained in this way, they assume a folk-like character. Crucially, they link the octatonic scale to the modal diatonicism that underlies many of Stravinsky’s Russianperiod pieces. The octatonic-diatonic interaction resulting from this 73For

an analytic-theoretical account of the (0 2 3 5) tetrachord in Stravinsky’s Russian-period music, its affiliation with the octatonic and diatonic (modal) scales, see van den Toorn and McGinness (2012, 114–72), and van den Toorn (2017, 158– 71). The tonnetze in these two studies feature the (0 2 3 5) tetrachord and its (0 2 5) (0 3 5) trichordal subsets.

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linkage initiates the stem alluded to earlier, the one that extends through the neoclassical era to include, as an offshoot, the later neoclassical works of the 1940s and 50s.

XI

Stravinsky’s use of the octatonic scale in works composed during the war and postwar years followed a near ten-year hiatus during the 1930s. His renewed interest in the scale coincides with his arrival in Los Angeles in February of 1941. Cut off from wartime Europe and in need of cash, he began to teach. His student, Earnest Andersson, a wealthy retired inventor, brought with him the beginnings of a four-movement symphony which he wished to complete under the composer’s supervision. For a year or so, from early 1941 to late February in 1942, Stravinsky appears to have taught his student what he himself had been taught by Rimsky-Korsakov decades earlier in St. Petersburg; orchestration and octatonic harmony. And it may well have been these lessons with Andersson that served as the catalyst, stirring the composer in the direction of some further exploration of the ways in which the octatonic could be combined with the major and minor scales of tonality.74 Also in Los Angeles at the time of Stravinsky’s arrival there was Schoenberg, of course, who had settled in seven years earlier. For the next ten or so years the two composers would inhabit the same city without ever communicating with one another. It was as if the ParisVienna split, sparked and fueled during the 1920s by followers and adherents as much as by the protagonists themselves, had crossed the Atlantic and shrunk to within a ten-mile radius of no-man’s land separating Hollywood from Brentwood. Musicians from all over the world would visit them, but without mentioning to one their meetings with the other. As might be expected, however, the two composers had mutual friends, and would sometimes attend the same functions. They were present at Franz Werfel’s funeral in August of 1945. And they were present again at the Wilshire Ebell Theater in Los Angeles when, on 74See

Slim (2019, 214–33) and van den Toorn (2020, 145). The Danses Concertantes (see Ex. 6) was composed during the period of Andersson’s lessons, while the first movement of the Symphony in Three Movements (1945), one of the most extensively octatonic of Stravinsky’s works, was begun later in 1942.

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November 18, 1945, Stravinsky’s Babel and Schoenberg’s Prelude to the Genesis Suite were first performed.75 From what we know of the circumstances, however, there were no handshakes or greetings of one kind or another. At rehearsals and performances of the Genesis Suite, the two sat on opposite sides of the theater. A glance or two may have been the extent of their interaction. That these exiled composers, approaching or in the twilight years of their respective careers, should so stubbornly have kept their distance speaks to the special trauma of twentieth-century music. The artistic divide that separated the two may have become too entrenched, too much a part of a settled landscape, to risk overturning. Already in the 1920s the gulf had become personal, making the prospect of a rapprochement all the more remote.

XII

Stravinsky’s “cataclysmic,” if finally gradual,76 adoption of serial methods during the 1950s could not have occurred without Robert Craft,77 the confidant and sounding board who, even before meeting up with the composer in 1947, had been an enthusiastic conductor of the atonal and serial music of the Viennese School. Nor could it have transpired without Schoenberg’s death on July 13, 1951, the effect of which was to bracket serialism with a kind of historical legitimacy, a sense of tradition which it could not have had with its founding father still alive. His death removed, simultaneously, the potentially crippling handicap of an all-too-knowing, watchful ear Yet it would not be to Schoenberg’s music that Stravinsky would turn for a model as to how to proceed. With the exception of Pierrot Lunaire (1912) and the Serenade (1924), the “pathos” of this music was thought overwrought and dated, too much a part of the late 75Organized

and commissioned by Nathaniel Shilkret, a composer and music publisher, the Genesis Suite was a collective undertaking. Participants were invited to set to music passages from the early chapters of Genesis. In addition to Schoenberg and Stravinsky, the composers included Alexandre Tansman, Darius Milhaud, Mario Castelnuovo-Tedesco, and Shilkret himself. Bela Bartok, Paul Hindemith, and Serge Prokofiev were also asked to take part, but they declined for various reasons. 76Babbitt (2003, 266); “Stravinsky (1882–1971): A Composer’s Memorial” (1971). 77When asked in 1998 whether, without him, Stravinsky would have found a path to serialism and twelve-tone music, Craft answered unequivocally: “I am certain he would not have.” See Craft (2006, 171).

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nineteenth century.78 Nor would he be turning to what he called the “radically alien emotional climate” of much of Berg’s music.79 Instead, like the younger generation at the time, he was attracted to Webern’s music, that member of the Viennese trio who had so completely divested himself of the rhetoric which neoclassicism had sought to reclaim, and who, by so doing, had bequeathed twelvetone serialism a new sense of musical timing and space. And the source of Webern’s appeal may have been the imagined persona almost as much as the music. The simple, pure, and direct manner that had emerged from Webern’s published letters appealed to Stravinsky; Webern the non-theorist and non-teacher, the composer who, severely tried by the necessity of explanation, was sometimes “tortured by teaching”; a “village priest,” in effect, seeking not to explain but merely to behold.80 The characterization resonates with the ideal that Stravinsky had coveted since the earliest days of neoclassicism in the 1920s, the image of a humble artisan dutifully pursuing his craft as “honest labor,” all in the ears and eyes of God—A la gloire de DIEU, as this sentiment is expressed on the dedication page of the Symphony of Psalms.81 At the same time, Stravinsky’s limited experiences as a teacher appear not to have been the least anguished. On the contrary, he regarded these experiences as by nature ironic, even comic to a degree.82 78Craft

(1957, 7). and Craft (1959, 79). 80Stravinsky and Craft (1960, 97–98). 81See Francis (2015, 49). The publication of the Symphony of Psalms by Edition Russe was edited by Nadia Boulanger. The composer insisted that all appearances of the word DOMINUM in the text (or DIEU on the dedication page) be fully capitalized. 82In Stravinsky and Craft (1960, 93), Stravinsky makes reference to a single pupil (Earnest Andersson) or, as he puts it sarcastically, “a composer who visited me twice a week to have his works recomposed.” Stravinsky fancied himself a natural or “instinctual” composer, a “doer” rather than a thinker or explainer, one who learned “chiefly through my mistakes and pursuits of false assumptions, not by my exposures to founts of wisdom and knowledge.” Stravinsky and Craft (1966, 7). When, in Stravinsky and Craft (1959, 12), he began dismissing theory as mere “hindsight,” a by-product of composition that was “powerless to create,” and then, in Stravinsky and Craft (1969, 44), recommending that students of composition forego the universities and “go directly underground,” Babbitt, who maintained cordial and even friendly relations with Stravinsky, responded with considerable irritation. See Babbitt (2003, 259–62); “The Composer in Academia: Reflections on a Theme of Stravinsky” (1970). And see note 25. Babbitt’s defense of “the serious occupation of empirical theory-construction” may be found in Babbitt (2003, 164); “Remarks on the Recent Stravinsky” (1964). 79Stravinsky

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We may grant the cool, detached manner of Webern’s musical intensity, the leanness and transparency of texture that in any event would have met with a sympathetic ear. More specifically, however, Stravinsky was drawn to the row-segments of Webern’s twelve-tone compositions, especially those of his derived sets, as Babbitt called them, rows that were drawn in their entirety from the transposition/ transformation of a single trichordal type. In the row of Webern’s Concerto for Nine Instruments (1934; see Ex. 17), the (0 1 4)s are major-minor third units, even if detached utterly from the octatonic-major scale interactions that mark their appearance in Stravinsky’s late neoclassical works. Stravinsky found in the segmentation of the Concerto and other Webern works familiar grounds from which to depart.

Example 17  Early row forms

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In the row of Webern’s Variations for Orchestra (1940; see Ex. 17), successions of major and minor thirds abound, with the row so deployed as to afford these groupings a quite unmistakable measure of articulative cohesion. The row’s division is more readily tripartite, with the initial tetrachord in terms of A-Bb-Db-C having as its retrograde inversion the concluding segment, F-E-G-Ab. These latter are (0 1 3 4)s. Transposed or transformed, (0 1 3 4)s dominate the serial application not only in Stravinsky’s In Memoriam Dylan Thomas (1954), but several sections of Agon as well. Agon’s “Pas-dedeux “ at m.441, surely the most gloriously beautiful of Stravinsky’s musical miniatures, is built serially on the (0 1 3 4) tetrachord, initially, Bb-B-D-Db. Remarkable, too, in Ex. 17, is the overlapping of successive (0 1 3 4)s later in the “Pas-de-deux,” Coda, and “Four Trios,” with the last pitch of one becoming the first of the next. This, too, is a borrowing from the row of Webern’s Variations. Of Stravinsky’s twelve-tone works, Babbitt was drawn to the Movements for Piano and Orchestra (1959), where the row contains a three-fold, ordered repetition of the chromatic trichord; see the brackets in Ex. 18. These ordered repetitions guarantee a high degree of “internal set organization,” and they play a role not only “in unifying the highly differentiated rhythmic, timbral, and registral constituents” in Movements, but also in serving “as a proxy for the ostinato, the dissolution of which is now complete.”83 In fact, the row of Stravinsky’s Movements is very nearly derived in terms of the chromatic trichord, and would have been so had the sixth pitch, the D, appeared as the third. All the same, in intervalclass content, the row’s hexachord is the fourth of Babbitt’s allcombinatorial “source sets,” capable of yielding aggregates at two transposition levels of the standard four orderings of the row. In a lengthy discussion of Movements with Stravinsky in early January, 1960, Babbitt, “in a spontaneous burst of détente,” revealed to the composer that the hexachord of Movements “was the same as 83Babbitt

(2003, 164–65); “Remarks on the Recent Stravinsky” (1964). Babbitt spoke too soon. Swept aside in Movements, ostinatos reappear in various guises in subsequent works. In Stravinsky’s Variations (1964), a polyrhythmic section of “12part polyphony” (Stravinsky’s term) is repeated twice. While the instrumentation and the row forms of the twelve parts change in these restatements, their durational patterns remain intact, ostinato-like. Curiously, in Variations, the rotation scheme is applied to the entire row, not to the hexachords independently of each other.

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that of Schoenberg’s De Profundis” (1950).84 What this piece of information might have meant technically to Stravinsky at the time is difficult to say. Like Schoenberg, Stravinsky composed his rows “thematically” (or “rhythmically”) and pretty much from scratch, without recourse, in any case, to the sort of codification to which, by 1960, Babbitt had been devoting his theoretical energies for well over a decade.85 More importantly, little if any advantage is taken of the combinatorial potential of the hexachord of Movements, as Stravinsky turned instead to the hexachordal rotation scheme that he would subsequently be applying in all his major works. The complete twelve-tone row of Movements, as introduced in the opening two measures, is shown in Ex. 18. To the left in this example, the row’s initial hexachord is followed by five rotations or “alternates,” as Stravinsky sometimes called them.86 Subject to rotation is the hexachord’s interval series: starting with a common set-factor, the Eb here, the first rotation begins with the hexachord’s second interval, completing its cycle by reaching the first; the second rotation then begins with the third interval; and so forth. Stravinsky’s usual practice was to plunge through the entirety of an array of 84Babbitt

(2003, 405); “Stravinsky’s Verticals and Schoenberg’s Diagonals: A Twist of Fate ” (1987). Prior to a still earlier discussion of Movements, this time at the Gladstone Hotel in New York in January of 1958, Stravinsky emerged from his hotel room “waving a sheet of manuscript paper” and shouting remarks that, to Babbitt, carried “lovely resonances”: “I found a mistake,” Stravinsky declared, “and the right note sounds so much better!” The ear had a mind after all, evidently, and Stravinsky’s reliance on his row-charts could be cited as evidence thereof. Earlier, in an interview with the New York Review of Books, Stravinsky had expressed himself a good deal more equivocally on the issue. Although “our calculations and our feelings obviously overlap, I will persist … and say that I trust my musical glands above the foolproofing of my musical flight charts. The flight charts are formed in part by the same glands, … but I prefer to exercise the ‘free’ option of my ear, rather than submit to a punch-card master plan.” Stravinsky and Craft (1969, 13–14). 85When asked about his compositional process in Stravinsky and Craft (1959, 11–12), Stravinsky replied that “long before ideas are born I begin work by relating intervals rhythmically. This exploration is always conducted at the piano. Only after I have established my melodic or harmonic relationships do I pass to composition.” He was a bit more specific when it came to serial composition, adding that “when my main theme has been decided I know on general lines what kind of musical material it will require. I start to look for this material, sometimes playing old masters, sometimes starting directly to improvise rhythmic units on a provisional row of notes (which can become a final row).” 86Stravinsky and Craft (1960, 90–100).

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this kind (the formula is applied to the remaining hexachords of the four standard row-orderings),87 successively and from top to bottom or vice versa. Sometimes he employed a zig-zag pattern, traversing the rotational array by alternating from right-to-left and left-to-right. The vertical columns (“verticals”) in Ex. 18 are ignored in Movements, but they would be deployed in subsequent works as chords or “simultaneities.”88

Example 18  Movements, row: hexachordal rotations

From the earliest days of Stravinsky’s serial conversion, Babbitt took an interest in his methods, however much they may have differed from his own. The belated embrace of serialism served to confirm the path that he and other “progressives” had taken earlier in the century. Babbitt kept abreast of the Stravinsky-Craft “conversation” books as well, even as he must have suspected that, however reflective of Stravinsky’s words and deeds, they were very much a product of Craft’s literary imagination. In the late 1950s and 60s, Stravinsky would sometimes type out Craft’s drafts, “deleting what he did not like, and amplifying what he did.”89 For the most part, however, the materials attributed to him in these volumes were 87To the traditional four row-orderings in twelve-tone music, Stravinsky added a fifth,

the inversion of the retrograde or IR. He seems to have preferred the latter to the RI form. 88For a detailed account of the serial mechanism in Stravinsky’s late works, see van den Toorn (1983, 427–55) and Straus (2004). 89Craft (2006, 189).

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ghostwritten. To rely on their authenticity obviously requires that a certain trust be placed in Craft’s stewardship.

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Stravinsky lived long enough to be able to reflect and comment upon what he called the “neoclassical” aspects of Schoenberg’s twelvetone works,90 possible areas of intersection between the great divide, as it were, literatures that in many other ways could not have been more distant from one another. What he had in mind were not only the large-scale forms of tonality, but also the phrases and thematic types of Schoenberg’s music. As is well known, Babbitt objected to this line of thought, insistent as he was on the incommensurability of tonality and the twelve-tone system, the absence of any “conceivable principle of correspondence” between the two “formal systems.” Since the tonal motivation for the forms being transferred was lost in the process, the most that could be achieved by any such transfer was a kind of “thematic formalism.”91 To follow Babbitt, the rationale behind the divisions and articulations of Schoenberg’s twelve-tone works could be heard and understood in terms of the system itself and the particulars of its application. Those particulars were defined above all by the formation and completion of aggregates.92 In the opening measures of Schoenberg’s Fourth String Quartet (1940), the Classical routine of a theme and its accompaniment is unmistakable. So, too, is the subsequent development of rhythmic figures drawn directly from the theme. Yet the registral location 90Stravinsky

and Craft (1959, 144–45).

91Babbitt (2003, 46); “Some Aspects of Twelve-Tone Composition” (1955). “If one were

seeking mere formalisms, there are certainly more ingenious ones than ‘sonata form’, ‘rondo form’, etc., for all that they might not possess this purely verbal identification with the hollowed past.” Pierre Boulez went much farther, as is well known, urging that the baby be thrown out with the bath water. The tonal forms, themes, and accompaniments in Schoenberg’s twelve-tone music were too obviously incongruent with the serial apparatus. And the difficulties were such that the music could not be salvaged; Schoenberg’s music was pronounced “dead”; see Boulez (1991). 92See, for example, the analysis of Schoenberg’s Piano Concerto (1942) in Mead (1989). Mead underscores the formation and completion of aggregates as the chief means by which the phrases and larger divisions of this music are defined. See also Mead (1987, 67–92).

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of the two hexachords outlined by the theme, which consists of a presentation of the row, clarifies the inversional relationship between the two. And the hexachord formed by the first three pitches of the viola and cello parts is kept registrally and instrumentally separate from the one formed by the first three pitches of the two violin parts. The separation exposes the relationship between the two hexachords, with the lower one being the transposed inversion of the upper one. Not only are the registers and other forms of articulation at the outset of this quartet reflective of the row and certain principles of transposition and hexachordal relations. There is in addition an intimation of what lies ahead, according to Babbitt, a forecasting of coming events, all in the manner of a “directed motion.”93 But what are we to make of the fugal exposition of the Gigue in Schoenberg’s Suite, Opus 29 (1925), the opening three measures of which are reproduced in Ex. 19? This is music from which the early model and its role in perception as well as composition is not so easily dismissed. And it is music with which Stravinsky was intimately familiar during the early 1950s, the years of his apprenticeship in serialism and twelve-tone composition.94 The subject’s initial entry 93Babbitt

(1987, 23). And see Berry (1976, 187–99); “Apostrophe: A Letter From Ann Arbor.” Berry’s contribution to a double issue of Perspectives of New Music featuring “A Critical Celebration of Milton Babbitt at 60” was the only (mildly) critical account in the collection. Berry voiced his growing frustration with the lack of a sense of direction in the new, advanced music: “Of music lying beyond the historical prevalence of modality and tonality, how does it establish a basis for, and express, directedness— i.e., to-ness, from-ness, nearness/distance, here-ness/there-ness—within elements of structure in ways that are empirically plausible and appreciable? If it does not do so, does it follow that such music is, in effect and often in its professed nature, purely adventitious in its stream of events”? In his response to Berry’s critique, Babbitt seems not have grasped its highly critical, subversive nature; see Babbitt (2003, 358– 9). Babbitt’s use of the term “directed motion,” normally associated with Schenker’s theory of tonality, may have come in response to Berry’s critique. On the other hand, Babbitt favored analyses that did in fact proceed on the basis of events predicting later ones and later ones recalling earlier ones; see Straus (2012, 16). 94See van den Toorn (2020, 152–53). Following performances of The Rake’s Progress in 1951, Stravinsky and Craft turned in earnest to Schoenberg, Webern, and Berg, studying the music and listening to the recordings. In January and February, 1952, Stravinsky attended all twenty rehearsals of Robert Craft conducting Schoenberg’s Suite, Opus 29, at the University of Southern California. Later that year, with score in hand, he attended at least as many rehearsals and studio sessions when Craft recorded the Suite. His choice of a Gigue in his Septet (1953) was undoubtedly influenced by the Gigue in Schoenberg’s Suite.

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in the clarinet states the row in its entirety, a statement that is subsequently broken up and repeated as an accompaniment to the subject’s second entry, a transposed inversion of the prime form.

Example 19 Schoenberg, Suite, Op. 29, Gigue, opening

The two row-forms being combined in the second measure of the Gigue, P3 and I8, are so in a manner consistent with Schoenberg’s Golden Rule: that a row be constructed in such a way that, between the first and second heaxchords of a prime form and those of its inversion at the interval of 5, no pitch-classes are held in common. Two successive aggregates are formed by such means, unordered totalities of the twelve pitch classes.95 It is at this point, however, that an oddity in the serial apparatus of the Suite makes itself felt. Although, as with nearly all his twelve-tone pieces, Schoenberg confined himself to the inversional combinatorial relationship described above, the unordered hexachord of the Suite 95See,

as quoted in Hyde (1982,99), the letter from Schoenberg to Josef Rufer, 8 April, 1950: “Personally, I endeavor to keep the series such that the inversion of the first six tones a fifth lower gives the remaining six tones. The consequent, the seventh through the twelfth tone, is a different sequence of the second six tones. This has the advantage that one can accompany melodic phrases made from the first six tones with harmonies made from the second six tones, without getting doublings.” While Schoenberg stressed the avoidance of doublings in combinatorial relationships, Babbitt stressed the formation of aggregates.

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is the hexatonic set 6–20, the fifth of Babbitt’s “source sets,” and one capable of yielding multiple combinatorialities: P3 may be combined in the prescribed manner with two other prime forms, three inversions (including I8), three retrogrades, and three retrograde inversions. As a reflection of the kind and degree of its symmetry, 6–20 lacks two classes of intervals, whole tones and tritones. Likely to have appealed to Stravinsky, however, is Schoenberg’s ordering, which is nearly derived in terms of the (0 1 4) trichord; see the brackets attached to the row in Ex. 19. Although all four of the row’s disjoint trichords are (0 1 4)s, the ordering of the first and last differs from that of the second and third. Yet the result is another series of major-minor third units, even if again in the form of a twelve-tone row rather than in that of a major triad embellished by chromatic tendency tones; or in that of the conjoint, interlocking thirds that, as we have seen, prevailed octatonically in many of Stravinsky’s late neoclassical works. The reader will note, however, that the (0 3 4 7) s on each side of Schoenberg’s row allow for a partial replication of the octatonic conception. All of which is not to imply that Schoenberg was unaware of the vast combinatorial potential of 6–20. The wealth of tables and charts of row-forms and segments produced precompositionally or in the act, so to speak, leaves little doubt as to his close familiarity with the materials lying to the background of the Suite. One such table includes, in transposed form, the set of twelve row-forms mentioned above, all combinatorially related, with three forms from each of the standard row-orderings.96 At the same time, Schoenberg may have acquired his familiarity with these relationships in the manner indicated by Babbitt, that is, not with guiding “general principles” or theories, but informally with a good deal of trial and error.97 With the composition of each twelve-tone work, he may have begun almost anew, as it were, seeking and testing out the combinatorial potential of a row with on-the-spot strategies of his own making. In nearly all other ways, however, the world of the Bach/Baroque Gigue is invoked to the letter. The second fugal entry in the exposition of Schoenberg’s Gigue is a contour as well as a transposed inversion, 96See 97See

Hyde (1982). Babbitt (1987, 14–16).

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doubtless in imitation of the loose suggestions of such that may be found on the other side of the double bar in many of Bach’s Gigues. And the third entry returns to P3, just as the third entry in a Bach fugue might return to the tonic. And there is the 12/8 meter along with the staccato dots and slurs that accompany the fugal subject. With the dotted quarter note as the tactus, Schoenberg begins with a staccato dot over the second and third eighth-note beats followed by a slur over the first and second beats. This articulation is common enough in performances of Bach’s Gigues, notwithstanding the aged Schirmer edition of Bach’s French Suites referenced in Ex. 20 (still popular and inexpensive), where the editor, Carl Czerny, with a fast tempo intended, has drawn a sweeping phrase marking over half of the G-major subject.

Example 20  Bach, French Suite in G major, Gigue, opening subject

No less familiar in Schoenberg’s subject is the slur that subsequently straddles the second and third dotted quarternote beats. The change in location reflects the subject’s shape: accompanying each of the two hexachords are two dots followed by two slurs; the contour is repeated as well. As with nearly all of Bach’s fugal subjects, Schoenberg begins off the beat, the sense of the upbeat being one not of movement alone, but also and more sympathetically one of joining in on a process that has already gotten underway. On the matter of Schoenberg’s use of Baroque and Classical forms and thematic types, the verdict among scholars has tended to conflict with Babbitt’s.98 The consensus has been that the aesthetic attraction of a piece such as Schoenberg’s Gigue is apt to hinge at least in part on the listener’s familiarity with the earlier model. Especially with fairly knowledgeable listeners of Schoenberg’s fugal exposition, an image of the Bach/Barooque model may intervene early on in the listening experience. And although initially shadowy in appearance, the model may gain in specificity through reflection and 98See,

for example, Straus (1990), Hyde (1996), and Burkholder (1999).

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repeated hearings. As it does so, its role as a backdrop is enhanced. Identifications and differences are sensed, as the listener, by way of the model, is able to focus that much more intently on Schoenberg’s variant. The model becomes a means of such focus, a way of setting the variant in relief. No mere formality, then, something purely “external,” as Babbitt would have it, the fugal subject and its succession of entries are rediscovered as a vehicle of transmission, a way of organizing the row and its aggregate-forming transposed inversions. What is communal or held in common between the original model and its variant acts as a foil for that which differs. The dynamics are not altogether different from those that apply when a theme or motive is followed by a variation. The nature of the aesthetic charge, what it is that attracts in this music, may be located accordingly: recognizably the same in its appearances in Bach’s Suites and in Schoenberg’s Suite, Opus 29, the Gigue is transformed nonetheless. It retains its original identity while simultaneously being subjected “to logical dynamic change.”99

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The “external forms” of tonality may pose less of a problem in Stravinsky’s neoclassical works than they do in Schoenberg’s. Routinely present in the former are the major and minor scales along with the stylistic veneer of Baroque and Classical music. Both the scales and the veneer come with “impurities” and in bits and pieces, no doubt, which is true of the functional relations of tonality as well. Nevertheless, questions are apt to arise here, too, about the listener’s reliance not only on the “forms” and articulative surface of Baroque and Classical music, but also on the scales and functional relations of tonality. The reader will recall, in connection with Ex. 3a and 11, the absence of such relations in the opening section of the “Basle” Concerto in D and in the passage quoted from Oedipus. In the analytical portion of Ex. 3a and 5, the right side of the dotted vertical line was designed to represent the Classical foundation of this music, with the chromatic pitches E♯/F and G♯ interpreted as tendency tones to the major third and fifth of the tonic triad. The clashing of 99See

note 55.

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the former with the latter was represented as a form of “impurity.” To the left of the dotted line in these examples, the tendency tones were grouped with the chord tones to form a succession of interlocking major-minor third units. Together with the tonic triad and its parallel and relative minor triads, these symmetrically defined units implicated an interacting octatonic scale. But to what exactly do we owe the aesthetic appeal of this music? Does the attraction of the “Basle” Concerto, first movement, hinge on “impurity,” that is, on its conception as an expressive deviation from traditional practices? Or do the “impurities” unite with the practices in the creation of “a new reality,” as Stravinsky once phrased it,100 something that might include the interacting octatonic and diatonic scales portrayed in Ex. 3a, 4, and 5? The contention here has been that both interpretations may play a role in the listening experience, with the emphasis on one or the other possibly fluctuating between sections or movements.101 In his celebrated account of “Pitch Organization in Stravinsky,” Arthur Berger expressed the hope that, in the case of Stravinsky’s neoclassical works, a “new branch of theory” might someday be able to circumvent the models, conventions, and tonality of the Baroque and Classical eras.102 The purpose of that circumvention was to accord this music a greater sense of autonomy and, presumably, integrity. Doing justice to this music would mean treating its individual members not as hybrids or forms of adulteration, but as integrated wholes (“unified totalities”). Whether from the standpoint of the individual context or the larger populations of which it was a part, each detail could be dealt with from within rather than from without. 100Stravinsky

and Craft (1962, 115). an alternative view of the eighteenth-century model in Stravinsky’s neoclassical works, see Straus (1990, 16, 72). At odds in these neoclassical works are two simultaneous and distinct “layers of structure,” according to Straus, two “fully developed conceptions of musical structure” that represent the old and the new, the tonal and post-tonal. The first of these “layers” is based on “traditional tonal relations,” the second on “the logic of recurring motives.” The latter, transposed and/or inverted, are generalized as pitch-class sets. And the result is a “clash” in which the two sides are “not reconciled or synthesized but locked together in conflict.” 102Berger (1972, 123–24). A “Self-contained” theory would start “from what [Stravinsky’s] music itself is, rather than dwelling upon its deviation from what music was previously.” 101For

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Such a “theory” has not been forthcoming, however, and its failure to materialize may be attributed to the stubborn refusal of the Baroque or Classical side of Stravinsky’s neoclassical bargain to relent, as it were, to dim and disappear altogether. The aesthetic ideals underlying Berger’s search for a “self-contained” theory are the system-building ones of the 1950s and 60s, the preoccupation at the time with impeccably closed formulae. Milton Babbitt’s quest for a “completely autonomous conception of the twelve-tone system” may be reckoned as an embodiment of these ideals103 Yet the lens through which they passed was once again that of tonality, conceived in terms of a “formal system.” For many listeners today, however, the pursuit of autonomy, quixotic even for the music for which it was intended, can seem downright unreasonable on the other side of the divide, with the neoclassical or “quasi-tonal” music of composers like Stravinsky. Even if the models and conventions underlying a piece such as the first movement of the “Basle” Concerto stem from the distant rather than the immediate past, they are no less consequential as a form of communality. And if the whole of Stravinsky’s music is made less cohesive, integral, or coherent as a result these analytic-theoretical determinations, then so be it. For these listeners, the nature of the beast is defined by its extraordinary reach in this regard, with each of the three orientations or “stylistic” periods representing something of a negation (even a betrayal) of the one preceding it.

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Like the musical biographies of many composers of the past century, Stravinsky’s resembles a batch of stems, uneven and broken apart in places. While many of the stems overlap the Russian and neoclassical periods, fewer continue on through the early serial works, and still fewer through the twelve-tone works of the 1960s. The ties to the late works are not insignificant, however. They may be incidental where pitch is concerned, but the rhythmic articulation and the patterns of repetition are quite capable of bringing earlier contexts to mind. 103Babbitt

(2003, 40); “Some Aspects of Twelve-Tone Composition” (1955).

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This is especially true of the repetition at mm.73–85 in Stravinsky’s Variations and sections of the Requiem Canticles (1965). Two or more “blocks” of contrasting material, sometimes no longer than a measure or even a chord, are placed in an abrupt juxtaposition with one another. When repeated, the order and length of the blocks may be varied somewhat, but the content, instrumentation, and dynamics remain fixed. All four dance movements in Les Noces (1917–23) were composed in this fashion,104 as was, famously, the first movement of the Symphony of Psalms (1930), and, as noted already, a section in Variations (1964). The latter represent all three “stylistic” periods, and are but a few of the many examples of this type of construction that may be found in the oeuvre as a whole. But to juxtapose in the manner of Stravinsky was not to compose at all, according to Pierre Boulez, given the sense of a continuous development that was “annulled.”105 Since then, however, this process of juxtaposition has been treated much more sympathetically by Nickolas Nabokov apropos of Orpheus (1947),106 by Edward Cone,107 Jonathan Cross,108 and in still greater detail by Gretchen Horlacher.109 Richard Taruskin has traced juxtaposition to drobnost’, the Russian quality of being a “sum-of-parts” rather than a “unified totality” governed by a continuous development,110 a motion that is directed from start to finish. The scale of Stravinsky’s juxtaposed blocks can sometimes seem quite different from that implied by the term drobnost’, yet the connection between the two may have been real enough. True, the juxtaposition of distinct blocks of material may not be present in all or even the majority of Stravinsky’s works. Like the interaction between orderings of the octatonic and diatonic sets, however, along with the melodic and harmonic vocabulary accompanying that interaction, juxtaposition overlaps the three 104For a discussion of “block” juxtaposition in Les Noces and other works of Stravinsky’s

Russian period, see van den Toorn and McGinness (2012, 82–113, 225–35). 105Boulez (1991, 49). 106Nabokov (1949, 152). 107Cone (1972, 155–64). 108Cross (1998). 109Horlacher (2011). 110Taruskin (1996, 955–56).

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“stylistic” periods. As does stratification,111 in which, polyrhythmically, two or more motives or chords may repeat according to cycles that vary independently of each other. As do the “bi-quintal” structures that, according to Joseph Straus, lie to the background of many of Stravinsky’s works.112 As does the metrical displacement of repeated motives or chords, along with the literal nature of the repetition that follows as a consequence of displacement. To which might be added the need for a strictly maintained beat, a demand that follows no less consequentially when motives, repeated, are displaced relative to the meter. “My music can survive almost anything,” Stravinsky mused in one of his “conversation” books, “but wrong or uncertain tempo.”113 When accompanied by a sagging beat, the point of a displacement is indeed apt to be lost. Such, in brief summation, may be the extent to which a profile can be drawn of the musical materials when viewed in their entirety. As a definition of that which is shared communally by a significant number of Stravinsky’s works, the account is full of gaps. For the reasons cited already, the definition is informal and incomplete. Entire pieces or sections thereof may relate only marginally to the aspects of pitch, rhythm, and articulation examined in these pages. Yet the expectation is that, when pressed with questions about the sound, sense, and feel of Stravinsky’s music, enthusiasts are more than likely to gravitate in the direction of these identifying features. A single feature may be insufficient as an identifying mark, to be sure. 111The term stratification first appeared in Cone (1972) as a way of describing the “block” structures in three Stravinsky works, one from each of the “stylistic” periods. Cone used the term to describe the vertical slicing up of the materials into discrete blocks which, repeated, are placed in juxtaposition with one another. Here, however, stratification refers to the horizonal, polyrhythmic layering of fragments and chords that repeat according to varying spans or cycles. The latter use appears in Cross (1998, 18–104), van den Toorn and McGinness (2012, 4), and Straus (2014, 5). 112Straus (2014, 1–33). Straus identifies six “Models” on the basis of the interval separating a pair of fifths (or fourths). The idea of such a “bi-quintal” structure underlying many of Stravinsky’s works incorporates that in turn of a superimposition of the “opposing” fifths—melody and harmony, in Straus’s view. When pieced together, the fifths of Models 3 and 6, related by a minor third and a tritone, respectively, yield the familiar 0-3-6-9 transpositional path of the octatonic vocabulary discussed above. In some instances, the vocabulary may be regarded as an elaboration of the underlying fifths. 113Stravinsky and Craft (1959, 135).

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Yet when all traits are taken together and their interaction is fully appreciated, their source is likely to be revealed with little complication.

Works Cited

Adorno, Theodor W. 2006. Philosophy of New Music. Trans. and ed. Robert Hullot-Kentor. Minneapolis: University of Minnesota Press.

Babbitt, Milton. 1987. Words about Music. Ed. Stephen Demski and Joseph N. Straus. Madison: University of Wisconsin Press. __________. 2003. The Collected Essays of Milton Babbitt. Ed. Stephen Peles. Princeton: Princeton University Press. Bernstein, Zachary. 2016. “The Problem of Completeness in Milton Babbitt’s Music and Thought.” Music Theory Spectrum 38, no. 2: 241–64.

__________. 2021. Thinking In and About Music: Analytical Reflections on Milton Babbitt’s Music and Thought. Oxford: Oxford University Press.

Berry, Wallace. 1976. “Apostrophe: A Letter from Ann Arbor.” Perspectives of New Music 14, no. 1: 187–99.

Boretz, Benjamin. 1977. “Musical Cosmology.” Perspectives of New Music 15, no. 1: 122–32 __________. 1995. Meta-Variations: Studies in the Foundations of Musical Thought. Red Hook: Open Space.

_________. 2020. Inside in … outside out…. Ed. Tildy Bayar. Red Hook: Open Space Boss, Jack. 1992. “Schoenberg’s Op. 22 Radio Talk, and Developing Variation in Atonal Music.” Music Theory Spectrum 14, no. 2: 125–49.

__________. 2014. Schoenberg’s Twelve-Tone Music: Symmetry and the Musical Idea. Cambridge: Cambridge University Press. Boulez, Pierre. 1991. Stocktakings from an Apprenticeship. Trans. Stephen Walsh. New York: Oxford University Press.

Burkholder, J. Peter. 1999. “Schoenberg the Reactionary.” In Schoenberg and His World. Ed. Walter Frisch, 162–94. Princeton: Princeton University Press. Cohn, Richard. 1996. “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions.” Music Analysis 15, no. 1: 9–40.

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Cone, Edward T. 1972. “Stravinsky: The Progress of a Method.” In Perspectives on Schoenberg and Stravinsky. Ed. Benjamin Boretz and Edward T. Cone. 155–64. New York: W.W. Norton.

Craft, Robert. 1957. “A Personal Preface.” Score, no. 20. __________. 2006. Down a Path of Wonder. Naxos Books.

Cross, Jonathan. 1998. The Stravinsky Legacy. Cambridge: Cambridge University Press. Dahlhaus, Carl. 1982. Esthetics of Music. Trans. William W. Austin. Cambridge: Cambridge University Press. Dubiel, Joseph. 1990–92. “Three Essays on Milton Babbitt.” Perspectives of New Music 28, no. 2 (1990): 216–61; 29, no. 1 (1991): 90–122; 30, no. 1 (1992); 82–131.

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Index

accents 96, 126, 131, 141–142, 157, 174, 222, 338–339, 341–343, 356, 417, 420–421, 428–429 displaced 236, 238, 343, 375 irregular 385, 409, 418–420, 422–423, 452 accentuation, irregular 422–423 accompaniment 177, 184–185, 222, 251, 333, 463, 471, 482, 484 Adorno, Theodor W. 9, 129, 210–211, 213, 221, 223–226, 236–240, 242, 337–383, 387, 389, 391, 393, 395, 397, 399, 401, 403, 405, 407, 409, 411, 413, 415, 417, 419, 421, 423, 425, 427, 429, 431, 433, 447, 449, 452–453 anti-humanism 212, 219, 221, 226, 352 art music European 85, 165 Western 427–428, 435, 446 atonality 192, 285, 447–449 Augurs of Spring 6, 252, 262–263, 289, 291, 294, 302–303, 305, 387, 391, 396–397, 402–403, 417, 429 Babbitt, Milton 1, 166, 396, 431, 435–449, 451–452, 476–487, 489 analysis of twelve-tone music 438 music 438, 440 background partitioning 30–32, 36–37, 39, 42

ballet 14, 22, 24, 110, 209, 246, 248, 250, 266, 312, 314, 405 baroque 3, 96–97, 159, 165, 184, 468–469, 486–489 barring 127, 132–133, 136, 141, 146, 149, 229, 233, 420–421 alternative 201–203, 357 radical 410, 421–422, 424 Basle Concerto 7, 453, 459–464, 467, 473, 487–489 beats auditory 426 crotchet 133, 146–148, 150, 152, 154 extra 356, 365, 459 first 46, 129, 139, 144, 201, 228, 463 mental 430 second 144, 377–378, 486 spaced 230, 355, 409, 427 steady 9, 420 strict 9–12 strong 127, 152–153, 430 Beethoven 96–97, 118, 121, 126, 150, 157, 163, 173, 229, 351, 356, 432, 460 music 12, 229, 356 bitonality 265, 276, 285, 287, 336 black notes 267–268 block juxtaposition 13, 36, 42–43, 79, 93–94, 296, 420, 490 block structures 200, 398, 491 blocks periodicity of 144 repeats of 145–146 Brahms 7, 95, 106, 108, 121, 163, 173–176, 377–378, 398, 447, 449–450

498

Index

music 106, 378 brain 234, 363, 411–412, 427, 430, 432–433

C-major tonality 6, 181–183 C-major triad 183, 265, 267, 277 cadence 11–12, 34, 234, 430 chromatic tendency tones 172, 396, 460–461, 464, 466–467, 485 chromatic trichord 479 chromaticism, vertical 38, 52, 55–56, 393 class generality 431, 435–491 collection hexachordal 46–47, 73, 75, 80, 85–86, 89, 91 octatonlc 117 consonance 442 Craft, Robert 10, 14, 95, 112, 117, 131, 133, 137, 148, 191, 193, 196–198, 222, 235, 337, 397, 469, 476, 483 Danses Concertantes 8, 312, 462–463, 475 Danses des adolescentes 22–23, 39, 56, 59, 70 Debussy 207–208, 244, 248, 250, 259, 287, 304, 313, 315, 321, 331–333, 335, 380 music 207, 247, 288, 303 diatonic 2, 19–20, 35–36, 41–42, 44, 59, 67, 69–70, 75, 93, 110, 162, 180, 185–186, 245–247, 261, 263, 271–273, 278, 280–281, 283–284, 290, 303, 314, 320–322, 326, 328, 331, 388, 393, 461–462, 467, 474 diatonic C-scale 185, 188 diatonic components 261, 313, 319 diatonic context 69, 99

diatonic elements 262–263, 277, 279–280, 320, 322, 328 diatonic framework 59, 69, 74, 78, 83, 85–86 diatonic hexachordal segment 43, 67 diatonic pitch collection 19, 39 diatonic scale-fragments 261 diatonic scale passages 185 diatonic sets 111, 184, 188, 294–295, 393, 490 diatonic transposition 321, 323 diatonicism, modal 2–3, 474 dissonance 56, 239, 364–365, 392, 397, 412, 416, 442, 450–451 dorian tetrachords 97, 223, 291, 294, 296–297, 299, 305, 386–387, 391, 393–394, 397, 406 tritone-related 296 half-note beat 6, 199, 201, 204, 345, 355–356, 358, 365, 367–370, 407, 411, 417, 421, 424 harmonic complexion 93 harmonic sorcery 195 harmonic stasis 32, 49–50, 79, 82–83 Jazz musicians 252, 303, 314–315, 333

Liszt 96–99, 114, 119, 121, 174, 397 octatonic passages 388

Mangbetu song 418–420 melody and harmony 1, 387, 393, 491 metric accentuation 29, 31, 47, 55, 79

Index

metrical alignment 7, 9–10, 199, 204, 233–236, 337, 354, 359–360, 372, 378, 456, 468 metrical beats 223, 225, 415, 425, 441 metrical displacement 7–9, 13, 224–225, 229, 236, 238, 342, 352, 354–355, 367, 372, 375–376, 379, 382–383, 407, 410–411, 423, 430, 441, 456–458, 460, 468, 491 metrical parallelism 8, 228, 230–232, 354–355, 359–360, 364, 376, 409, 411, 420–421, 428, 457–458 motivic identity 137, 142 motivic order 148–149 motivic paths 173, 180, 182 motivic repetition 142, 151, 157, 458 motivic succession 177, 349 music African 413, 418–420, 426–427, 431–432, 434 art 386, 412 atonal 119–120 chamber 234, 350 classical 3, 96, 487 contemporary 123, 223, 342, 344, 452 homophonic 7, 164–165, 174, 340, 398, 447 metered 425 Modernist 422, 438 neoclassical 161–162, 166, 453 nineteenth-century 160, 193, 195, 350, 399 post-tonal 175 serial 120, 443, 476 tonal 11, 120, 126–127, 131, 150, 153, 157, 175, 229–230, 285, 354, 433, 450–451, 472 triadic 166

twelve-tone 439 twentieth-century 5, 134, 161, 333, 335, 381, 476 whole-tone 331–332 musical biographies 198 musical consonance 442 musical idiom 355 musicologists 122, 194, 219, 435 musicology 194, 198, 214, 382

neoclassical works 2–3, 159, 161, 166, 289, 291, 475, 488 neoclassicism 6, 95–96, 115, 159–189, 193, 209, 450, 463, 477 non-diatonic 243–244, 258, 261, 277, 280, 286, 291, 303, 313–315, 319–321, 328 non-diatonic scales, assignments of 319 non-diatonic triadic tetrachords 273 non-harmonic 253, 256, 320 non-octatonic 37, 267, 280, 296, 307–308, 314, 319, 391, 407 octatonic, music 118, 262, 280, 298 octatonic collection 3, 20, 33, 35, 43, 53, 65, 96–99, 185–186, 188, 247, 261, 266–267, 272, 274, 301, 327, 330 content-distinguishable 53, 63, 78 interpenetrating 41 nearly complete 330 single 65, 265 octatonic context 2, 69, 296, 308 octatonic-diatonic approach 2, 4–5, 15, 112, 289, 307, 312 octatonic-diatonic frameworks 44, 71

499

500

Index

octatonic-diatonic interaction 20, 34, 36, 44, 51, 53, 56, 63, 65, 69–70, 244, 259, 276, 302, 316, 333, 348, 387, 461, 474 octatonic-diatonic perspectives 111 octatonic-diatonic relations 466–467 octatonic-flavored tetrachord 272 octatonic framework 53–54, 73, 184 octatonic imagination 75, 312 octatonic interpretation 180, 265 octatonic partitioning 29, 41, 67, 387 octatonic penetration 36, 69 octatonic perspective 41, 466 octatonic pitch collection 20 octatonic pitch elements 91 octatonic scale 2–3, 7, 26, 29, 38–39, 50–51, 53, 63, 80, 92, 118, 243–245, 262–263, 265–266, 268, 270, 272, 274–275, 277, 280, 284, 286, 294, 296, 306, 313, 320, 327–328, 330, 387, 393, 461, 469–475 octatonic transposition 298, 399 octatonic triads 392, 402 octatonic vocabulary 397, 405, 491 octatonicism 15, 94–95, 98, 118, 223, 243, 266–267, 270, 274–275, 280, 286, 297, 307, 313, 331, 348, 399, 403 ostinato bass 316

pagan rites 209, 418 partitioning 20–21, 27–29, 32, 34–36, 38–41, 43, 47, 49–51, 53–57, 59, 61–63, 66, 69, 79–80, 84, 89, 92, 97, 307, 388, 394 registral 256–257, 300

tetrachordal 28–29, 31, 40, 61–62, 65, 67, 92 triadic 28, 46 tritone 29–32, 42 partitioning elements 31–32, 63 accented 62 symmetrically defined 29, 32, 35, 40, 61–63, 74, 310 passages, melodic-minor 257, 316 Petroushka/Petrouchka/Petrushka 2–5, 18, 21–23, 31–32, 34, 43–44, 46, 52–55, 59, 69, 78, 80, 83, 85, 88, 99, 106, 109, 117, 119, 195, 200, 246–251, 258, 266–268, 273, 284, 288–291, 303–304, 306, 308–310, 314–316, 319, 331–333, 336, 380, 388, 396–397 chord 244, 264–271, 286, 306–312, 314, 319, 326–327 pitch-class 27–31, 40, 47, 59, 111, 119, 121, 185, 268, 289–290, 294, 437, 439, 447, 484 nonoctatonic 184 pitch-class priority 19, 30–31, 47, 50–51, 62, 79, 81–82, 85–86, 93, 111–112, 319 pitch-class sets 111, 119, 162, 164, 271, 391, 449, 488 abstract 161, 175 unordered 110, 177 pitch organization 41, 93, 112 poetry 435, 445–446 polarity 30, 32–35, 50, 176, 306, 327, 331, 381, 387 polychord 177–178, 184, 395 polyrhythm 413, 426, 431, 468, 470 polyscalarity 264–266, 276 polytonality 264–266, 276, 306, 312–313, 326–327, 333 principal articulative betweenreference 55–56

Index

pulsation 230, 345, 355–356, 364–365, 373, 409, 411, 417, 425, 427

Rimsky 97–99, 114, 119, 197, 199, 207–208, 218 music 198 Rimsky-Stravinsky link 198 Rite of Spring, The 332, 385–386, 388, 390, 392, 394, 396, 398, 400, 402, 404, 406, 408, 410, 412, 414, 416, 418, 420, 422, 424, 426, 428, 430, 432, 434 Russian music 191, 220

Schoenberg, Arnold 1–2, 7, 110, 121, 159–161, 164–167, 173–174, 176–177, 183, 188, 191–192, 225–226, 245, 336, 338–340, 343–344, 372, 382, 395, 397–398, 422–423, 434–436, 438–440, 442, 447–449, 451–453, 456, 475–476, 480, 482–487 atonal music 111, 449 Gigue 485–486 methods 439–440, 448 music 165, 167, 188, 439, 451–452, 457, 476, 482 Schoenberg-Stravinsky divide 342, 382 Schoenbergian model 341, 344 Schoenberg’s atonal and twelvetone music 342 Schumann 96, 114, 237, 375, 377 music 239, 377 Scriabin 110, 117–118, 120, 194 Straus 161, 174–175, 243, 288, 387, 391, 393, 395, 398, 431, 434, 438, 449–451, 481, 483, 486, 488, 491 models 391, 393 Stravinskian chords 278

Stravinskian superimposition 278, 461 Stravinsky, Igor 1, 4, 10, 14, 21, 30, 38, 42, 112–113, 118, 125–126, 130–131, 148, 156, 164–165, 174, 180–181, 186, 191, 193, 197–198, 217, 222–223, 235, 244, 262, 272, 286–288, 291, 310, 312, 315, 332, 336–337, 348, 352, 380–381, 387, 395, 413 contra-metric passages 423 diatonic 42, 58, 94 diatonic music 1–2, 17–94 displacements 374, 379 harmony 223, 345, 393 methods 6, 123, 199, 392, 424, 456 music 4, 7–10, 12, 17–18, 34, 36, 96–98, 110–112, 161, 174–176, 188, 199–200, 223–227, 229, 231, 234–245, 284–286, 289–290, 306–307, 311–313, 327–328, 330, 333, 335, 337–338, 340–345, 348–357, 359–360, 374–376, 379, 381–383, 410, 420, 422–423, 428, 430, 432, 434, 441, 450–454, 456, 489, 491 displacement in 341–342, 344, 369, 373, 381–382 Russian origins of 97 neoclassical music 461 neoclassical works 159, 163, 166, 183, 188, 461, 471, 473, 487–488 neoclassicism 3, 182, 186, 380 octatonic 31–32, 83, 290, 391 octatonic-centered readings of 259, 265 octatonic contexts 29 octatonic perspective 94

501

502

Index



octatonicism 98, 118, 333 oeuvre 1, 309 pitch organization 280 processes of displacement 340 recollections, octogenarian 113 scales 245, 313, 320 stratifications 385, 414, 416, 420 style 263, 381 superimposition procedures 279 superimposition technique 327 superimpositions 277, 327–328, 397 vocabulary 244, 276 works 18, 20, 244, 262, 271, 312, 469, 475, 490–491 stutter motives 241, 463–464 superimposed pitch-centers 327 superimpositions 3, 32–35, 43, 50, 52, 79, 83, 119, 168, 184, 186, 188, 223, 244–245, 256, 258, 263–264, 266–271, 273, 276–281, 284–285, 300–301, 306, 310, 322, 326–328, 330–331, 345, 385, 391–392, 394–397, 399, 402, 405, 416, 461, 491 octatonic-diatonic 322 polyscalar 275, 285–286, 313 triadic 99, 244–245, 270–271, 392 Symphonies of Wind Instruments 21–22, 130, 370–371, 378 Symphony of Psalms 1, 4, 20–23, 29, 33, 36–37, 92, 110, 182, 250, 272–277, 281, 284, 289, 291, 330, 379, 469–470, 477, 490 collections in 279 taintedness 211, 213–216

Taruskin, Richard 3–5, 9–11, 13–14, 95–122, 130, 141, 164, 175, 191–198, 207–215, 217–220, 222, 243–245, 247, 259, 265, 268, 270, 284, 288–289, 291, 302, 311–312, 326, 331, 336, 386–388, 392–393, 405, 423, 434, 490 tetrachordal melodies 386–387 tetrachordal ostinato 59, 62 total pitch-class content 26–27, 48, 291, 460, 465 triadic articulation 73, 99 triadic tetrachords 271–273 major 272 minor 272 triads 2–4, 7, 31, 33–34, 36–37, 39–41, 46, 48–49, 52, 54, 62–63, 73–75, 78–80, 82–83, 85–86, 88, 97, 111–112, 170, 266, 269–271, 273, 278, 281–283, 291, 294–295, 297, 305, 307, 309, 386–388, 391, 394, 396–397, 399, 401–402, 404–405, 465, 467–468, 472 incomplete 7, 173, 175 tonic 17, 186, 278, 460–462, 466–467, 487–488 trichord 2, 6, 227, 271–272, 278, 281, 386, 404, 440, 450, 474, 485 trichordal arrays 440 tritone-related tetrachords 38, 393 tritone-related triads 3, 168, 178, 392, 394, 396 tritone relationship 6–7, 173, 304–305, 403 twelve-tone composition 166, 439, 442–443, 446, 451, 456, 478, 482–483, 489 whole-tone scale 247–250, 277, 288, 304–305, 331–332, 403