Desire in Chromatic Harmony: A Psychodynamic Exploration of Fin de Siècle Tonality (Oxford Studies in Music Theory) 0190923423, 9780190923426

Citation preview

Desire in Chromatic Harmony

OXFORD STUDIES IN MUSIC THEORY Series Editor Steven Rings Studies in Music with Text, David Lewin Music as Discourse: Semiotic Adventures in Romantic Music, Kofi Agawu Metric Manipulations in Haydn and Mozart: Chamber Music for Strings, 1787–​1791, Danuta Mirka Songs in Motion: Rhythm and Meter in the German Lied, Yonatan Malin A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice, Dmitri Tymoczko In the Process of Becoming: Analytic and Philosophical Perspectives on Form in Early Nineteenth-​Century Music, Janet Schmalfeldt Tonality and Transformation, Steven Rings Audacious Euphony: Chromaticism and the Triad’s Second Nature, Richard Cohn Mahler’s Symphonic Sonatas, Seth Monahan Beating Time and Measuring Music in the Early Modern Era, Roger Mathew Grant Pieces of Tradition: An Analysis of Contemporary Tonal Music, Daniel Harrison Music at Hand: Instruments, Bodies, and Cognition, Jonathan De Souza Foundations of Musical Grammar, Lawrence M. Zbikowski Organized Time: Rhythm, Tonality, and Form, Jason Yust Flow: The Rhythmic Voice in Rap Music, Mitchell Ohriner Enacting Musical Time: The Bodily Experience of New Music, Mariusz Kozak Performing Knowledge: Twentieth-​Century Music in Analysis and Performance, Daphne Leong A Blaze of Light in Every Word: Analyzing the Popular Singing Voice, Victoria Malawey Sweet Thing: The History and Musical Structure of a Shared American Vernacular Form, Nicholas Stoia Hearing Homophony: Tonal Expectation at the Turn of the Seventeenth Century, Megan Kaes Long Form as Harmony in Rock Music, Drew Nobile Desire in Chromatic Harmony: A Psychodynamic Exploration of Fin de Siècle Tonality, Kenneth M. Smith

Desire in Chromatic Harmony A Psychodynamic Exploration of Fin de Siècle Tonality Ken ne t h M . Sm it h

1

1 Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America. © Oxford University Press 2020 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. Library of Congress Cataloging-​in-​Publication Data Names: Smith, Kenneth M., author. Title: Desire in chromatic harmony : a psychodynamic exploration of fin de siècle tonality /​Kenneth M. Smith. Description: New York : Oxford University Press, 2020. | Series: Oxford studies in music theory | Includes bibliographical references and index. Identifiers: LCCN 2019048925 (print) | LCCN 2019048926 (ebook) | ISBN 9780190923426 (hardback) | ISBN 9780190923440 (epub) | ISBN 9780190923457 (online) Subjects: LCSH: Music—​20th century—​A nalysis, appreciation. | Desire in music. | Music—​Psychological aspects. | Harmony. Classification: LCC MT90 .S63 2020 (print) | LCC MT90 (ebook) | DDC 781.2/​50904—​dc23 LC record available at https://​lccn.loc.gov/​2019048925 LC ebook record available at https://​lccn.loc.gov/​2019048926 1 3 5 7 9 8 6 4 2 Printed by Integrated Books International, United States of America

C ON T E N T S

Preface Acknowledgments

1. A Linguistic Theory of Chromatic Harmonic Substitution and Progression in the Diatonic Unconscious 2. Romantic Provenance 3. Transcending Root Motion: Productive Death Drives and Cybernetic Cycles in Charles Ives and Aaron Copland 4. Karol Szymanowski’s Dominant Drive Model and the Excess of the Cycle 5. Tragedy and the Gaze of the Living Dead: Functional Harmonic Rotation in Strauss’s Elektra 6. The Thanatotic and the Tonnetz: Repetition, Mourning, and “Mother” in Suk’s Asrael 7. When Octatonic and Hexatonic Collide: Skryabin’s Accelerationist Last Piano Sonata Epilogue: The Way Forward (and Backward) Bibliography Index

vii xvii

1 53 90 141 182 234 270 321 325 337

PR E FAC E

Dialogues between music and what we might call psychodynamics—​ psychoanalysis in the Freudian tradition and the philosophy that supports it—​ can be held on many different levels. One of the most inspired contributions came from Richard Wagner, whose musical response to the philosophies of Arthur Schopenhauer and Friedrich Nietzsche was both direct and pragmatic, foreshadowing the developments of the fin de siècle Viennese writers and composers. Of the many composers in the Western classical tradition who celebrated the marriage between psyche and sound, those explored in this book followed the lines diverging from Wagner that philosophized the nature of desire in music. In this sense, desire is located not merely in the lusty world of steamy sexual encounters but in the hard, literal sense of human subjects wanting objects or sensations, often unconsciously.1 That this wanting can play a musical role is obvious; we listen to music because we desire something from it. And yet the people who write music, and perhaps music itself, also desire something from us. Sometimes, as in Wagner’s case, a composer’s philosophical resources are well documented, and one might profitably aim to match their ideas about life to the details of their music. But a fundamental premise of critical theory is that artists’ intentions can only go so far toward interpreting their artworks.2 Perhaps more than a century later, those who analyze the music and philosophy with the benefit of radical philosophical and musico-​theoretical advancements in the intervening years are well placed to posit new readings of the way music and philosophy interweave, even if this sometimes is driven by an ahistorical power. Such readings purport only to be additional interpretations that can work with (or against) existing ones, perhaps to offer a richer level of detail and a new depth or, at the very least, a new and interesting angle from which to listen. But how we listen is another matter. This book uses psychodynamics and music theory to explore ways of processing a particularly complex type of music—​the chromatic music that is so expressive of decentered fin de siècle subjectivity. To match twentieth-​and twenty-​first-​century progress in music theory, we benefit from a century of philosophical enlightenment in the psychodynamic field since the time of Sigmund Freud. The book exposes century-​ old repertoire and core philosophy to something fresh and vital from both music analysis and psychoanalysis, opening our ears up to new experiences in the process.

viii  T  Preface

Psychodynamics The term psychodynamics is closely related to psychology and psychoanalysis. It is usually associated with early Freudians and their mechanistic attempt to map the psyche as a thermodynamic system. The term applies to this book better than does psychoanalysis, which has its basis in clinical situations and does not squarely cover the fields of philosophy, thermodynamics, and even cybernetics, which psychodynamic theories cover and which are vital to this musical study. The more flexible term covers the rich work of Gilles Deleuze and post-​Deleuzians (even Slavoj Žižek) who aren’t psychoanalysts but who rebuild, critique, and expand their basis in it into other social sciences. Psychodynamics can also be applied retrospectively to help us see what Schopenhauer and Nietzsche—​clearly not psychoanalysts—​were attempting. While centering at first on the figure of Jacques Lacan, a highly experienced psychoanalyst, I  tackle some of the more esoteric connections between Freud, Lacan, and Deleuze that explore the sheer dynamic energy of the human psyche. And it is this energy that we find running through the music we explore. Because the book follows a stream of ideas that flows through Wagner, particularly the libidinal concept of desire and its fundamental role in our unconscious minds, I begin with Schopenhauer, who taught Wagner that desire is an unstoppable force he called Will. This became Nietzsche’s der Wille zur Macht, which became Freud’s libidinal Trieb (drive). We already knew from Friedrich Schelling that we are driven by an unconscious force and that we act out its goals while alienated from knowing it.3 Freud, for all that his theories were contentious, was perhaps only the conduit for these ideas on their way toward empirical psychology. Freud’s rigor was continued in the seminars of Lacan, who reanimated him, proposing that our desiring unconscious was not a blind force of nature but, rather, was animated by means of our accession into language, grammar, and syntax, which unconsciously work through us, recalibrating and reorienting our most intimate drives and desires.4 Our question might then be: Could this linguistic conduit for the libido be music? Lacan’s theories—​as well as his pseudoscientific, egocentric grandeur—​were condemned by Deleuze and by Jean-​François Lyotard, who, in different ways, tried to posit an even deeper return to Freud, whose unconscious desiring libido presented the mind as a machine made of purely material parts, an aspect that had been forgotten in the intervening years. These writers, most of them on the political left, have been critiqued and developed most recently by a former philosopher of right-​w ing cybernetics, the controversial Nick Land, who read Freudian desire not as a complex dialectical linguistic system like Lacan’s, based on a network of imaginary and symbolic signifiers, but as a system of feedback loops in which desire is a self-​regulating and self-​propelling force. This whole discourse is propitious in part because it emphasizes a contrast between psychological materialism and idealism that had occupied the composers under my microscope, though perhaps in different philosophical terms. With the benefit of the twenty-​first century’s innovative new directions, it would be

Preface  T  ix academically naïve to limit the study of music of the post-​Wagnerian avant-​garde to a purely historical Schopenhauer, Nietzsche, and Freud, who, like the composers themselves, were writing “in Plato’s cave.” In applying the theories of key figures in psychodynamics (who can be radically divergent), I make no claim about which psychodynamic theorist was right and work, instead, with a genealogy of desire theory that follows a broadly dialectical arch—​ from materialism to idealism and back—​a llowing us to trace a clear and coherent line through the seemingly opposed theories encountered. One can see psychodynamics as an amorphous body of thought, stretching over the course of a century, making noises that reverberate backward, through the philosophically charged Freudian fin de siècle, to Schopenhauerian pessimism. This book does, however, loosely follow a narrative thread in its philosophical application, moving from the Lacanian Freudianism of Strauss’s “Elektra complex” to the most recent theories of post-​Deleuzian psychodynamic desire, called “accelerationism,” in a cybernetic reading of Skryabin’s dark, esoteric mysticism.

Music Theory Many of the insights presented in this book come from Austro-​German theory, at the core of which lie Hugo Riemann and his contemporaries. A reappraisal of this theory has recently fueled the “neo-​Riemannian” school and theorists of tonal transformation, located mainly in North America. From my position in the UK, a  transatlantic approach is crucial to this project, not because it follows the journey of our compositional interest (from Wagner to Ives and Copland) but because current American theory offers profound new concepts that attempt to critically inform our experience of certain types of music. Rather than adopt music theory as it stands, however, which is impossible in any case because its threads are too diffuse, I adapt it to suit the needs of the repertoire and, I hope, contribute something new to the discipline. While not in the slightest rejecting other rich approaches to this music, the book limits itself to exploring harmonic progression. Moreover, it follows the precept that our experience of fin ​de ​siècle harmony, however chromatic, is fundamentally diatonic—​though the balance between diatonicism and chromaticism is a running concern throughout the book. Two contrasting approaches are therefore taken. First, I  explore “neo-​ Riemannian” and “paleo-​Riemannian” theory to try to understand how we can—​ not necessarily that we have to or that we already do—​experience diatonic tonal grammar and syntax in this chromatic music. This Funktionstheorie is a reductive project, reducing matter (sounds) to ideas (diatonic tonal function), which is a useful if faulty Kantian project in which the listening subject synthesizes the material and the ideal. Second, I try to let the object speak for itself by proposing an alternative theory that reclaims a greater level of objectivity, which locates the diatonic drives (that exist on some level, at least, even if only as mental categories) in extended chromatic harmony. I then alter the course of the book so that this “drive analysis” attempts to expand its theoretical limits. The first view (discussed

x  T  Preface in the first three chapters) is neo-​Schenkerian, and might assume that a diatonic background is obfuscated by a chromatic foreground. If we substitute chromatic notes for diatonic ones, the relation approaches what Leonard Meyer (1956, 217) famously described: “Chromaticism is almost by definition an alteration of, an interpolation in or deviation from this basic diatonic organization.” The second view (explored in Chapter 4), however, might well see chromaticism as a more chaotic background, with diatonic “drives” leaping out at the foreground in different directions. These two distinct views can synthesize and productively serve to antagonize each other. Although it does not evince a casual “take it or leave it” attitude, the work discussed in the first part of the book is theoretical, and its conclusions are cautiously speculative; the reader must decide how far to follow the system laid out. The second part is more “objective” in that it attempts to record items found in sound-​space, the conclusions drawn from these data being where the theoretical work is done. Throughout the book, while diatonicism will be bent and broken, I propose that it is still hard-​w ired—​to varying degrees—​in those who listen to Western tonal music. As Richard Cohn (2012b, 48) says: “A triad is sounded, and the acculturated ear takes it as a metonym for a [complete] tonal system.” The fundamental premise of the book is that this acculturation is an intricate part of our anthropocentric (subjective) desiring apparatus and needs to be theorized as such. In the course of my analyses, certain theoretical tools will be accorded new prominence. One such tool is the theory of tonal functions—​ reducing all chromatic chords to just three primary functions:  tonic (T), subdominant (S), and dominant (D)—​which is inherently too flexible, even in Riemann. As Daniel Harrison claims, “the perception in North America is that function theory is something brittle and useless” (1994, 307). Harrison calls for “an opening up of attitudes” (322), which is what I attempt, albeit in a way that will construct different borders. I try to rein in the waywardness of Funktionstheorie by examining the root motion of chords, finding in this reductive technique a perfect example of what Deleuze would propose as a triangular “Oedipal” structure: a triune of what he mockingly calls “daddy–​mommy–​me,” by which he means any repressive structure that becomes unconsciously imprinted or hard-​ w ired. Although Deleuze lambastes Freud and Lacan’s proposal that we unconsciously reduce phenomena as part of the desiring process, Deleuze never doubts that we do it nonetheless. In certain ways, I suggest that Western listeners probably do this, too, and that composers at the long fin de siècle worked to break down this familial triangle of T, S, and D, though they had to keep it just about alive enough to continue to meaningfully break it down. The connection between Hugo Riemann and Sigmund Freud is actually quite striking, notwithstanding the obvious differences in objective, outlook, and framework. Brian Hyer (2011, 126–​27) claims that “on occasion the tonal function in Riemann verges on full-​blown psychologism,”5 and Riemann’s Die Natur der Harmonik gives the dominant chord clearly psychological properties; as Benjamin Steege claims, “Riemann participates in the ‘libidinal charge’ of modernity” (Steege 2011, 56). Riemann’s response to the material (sonic) research of Hermann

Preface  T  xi von Helmholtz pushed him toward the processing, parsing, and categorizing of chords as part of his Idealist project. However, given Riemann’s protective attitude toward those who creatively use his work, I am under no delusions about whether he would have liked my psychodynamic approach. In my defense, however, I throw his own words back at him, from the famous final page of Die Natur der Harmonik:  “the theory of harmony will become a true exercise in musical thought for it moves from the simplest itself to the more complicated and induces one to attempt something new, to venture, rather than, as hitherto, to seek something new” (Steege 2011, 86).

Historical Objects Why follow a changing philosophical-​psychodynamic landscape and a lineage of music theory but fixate on a single historical moment? Because the fin de siècle, though anything but a static period, forced a collision between chromaticism and diatonicism, in turn forcing composers to reassess the relation in working practice. It would be grossly misleading to imply a smooth historical shift from diatonicism to chromaticism. The music I  theorize may appear to mark such a linear move that ties in with theory from Lacan to Deleuze, but this would be deceiving:  Both systems were alive at the same time in different amalgams within the early twentieth century, brought out using the tools and theories that I propose. For this reason, I also test the historical period under focus by stretching it geographically and temporally. In exploring Ives in the 1920s, for example, we find a corollary to what Copland was doing in the 1950s that is close to the harmonic language of the fin de siècle but adds fresh twists to the dividing line between diatonicism and chromaticism. Here, beyond the upper limits of the period under consideration, chromatic chord progressions operate beneath a seemingly diatonic surface, while the reverse is true in Ives, in whose music the diatonic background was later “spoiled” by an atonal (or chromatic) foreground. This fifty-​year upper margin, treated in part of Chapter 3, is balanced by a fifty-​year lower margin, discussed in Chapter  2, as I  tackle Wagner and Wolf (and even some predecessors as I  develop the necessary harmonic tools). This historical latitude tests the earlier and later applications of the model before I  focus in the remainder of Chapters  3, and all subsequent Chapters, on the true fin de siècle. The composers whose works and ideas are closely scrutinized here all have some level of conscious philosophical engagement, but philosophy works through them on a deeper-​t han-​conscious level. My contention is, for example, that the philosophically naïve Aaron Copland reflects the changing face of desire theory in his humble songs on poems by Emily Dickinson, not only by foreshadowing developments in philosophy and music that were to come, nor by making himself a psychological medium for the more conventionally profound Dickinson to speak through, but by shining a new light on philosophical concepts inherent in her poems and by opening up his art to our scrutiny. All of the composers and

xii  T  Preface works studied in this book speak to us about something deep—​often deeper than they likely intended—​in both musical and philosophical terms. In Chapter 1, I (re)construct an energetic model of harmonic progression in which tense chords are signifiers of tonal functions (Riemann’s T, S, and D functions). The paradigm adopts the linguistic axes that Lacan mapped as metaphor and metonymy, which were so crucial to the formation of a human subject at whose center lies désir—​the sliding of signifiers under the signified. I  demonstrate metaphor to be primarily experienced as octatonic minor-​third transactions, whereas metonymy is most forcefully experienced as a discharge of tension along the circle of fifths or hexatonic major-​t hird root progressions that rotate the functions T→S→D as a paradigm of shifting desire. The theoretical claims of the opening chapter build on the recent work of David Lewin (2007), Richard Cohn (2012), Steven Rings (2011a), Dmitri Tymoczko (2011a), Brian Hyer (2011), and others but also re-​evaluate the earlier work of Ernest Kurth (1920), Hugo Riemann, and Ernö Lendvai (1993). This chapter seeks to account for voice leading, modulation, and tonal diversity in a broad range of works. Although examples come from Debussy, Bartók, Strauss, Skryabin, and others, the model is built demonstrably on the Romantic tradition of Schubert, Beethoven, and Chopin for which I show tonal “charge” and “discharge” to be at work in archetypal cadential progressions involving both minor-​ t hird substitution and major-​t hird combination. Chapter 2 considers how seventh chords, half-​diminished chords, and diminished chords might fit into my root-​t heoretical framework, illustrated through a full functional analysis of the Vorspiel and Liebestod from Tristan und Isolde, following Kurth (1920) in hearing the piece as the locus romanticus of desire and psychological harmonic progression. The phantasy involved in Isolde’s transfiguration is explored from a Lacanian perspective, leading to reflections on how phantasy works to support tonal function. An addition to the canon of analyses of Hugo Wolf’s “An den Schlaf” covers the theme of death, sleep, and the land of limbo in between, offering a corollary to Isolde’s desire for death. These themes weave their way into the outlined theory of harmonic function and offer a precursor to the psychodynamics to come. The third chapter studies the third movement (“The Alcotts”) of Charles Ives’s Piano Sonata No. 2 (Concord, Mass., 1840–​1860) and demonstrates the simplest form of chromatic desire showing through Ives’s loose-​k nit diatonic thread. I examine Bronson Alcott’s Transcendentalist writings from The Dial as well as the aesthetic of others from the New England school to situate us in Ives’s contemporary context. But I ultimately appeal to the Transcendental Empiricism of Deleuze as much as to the Transcendental Idealism of Kant to demonstrate how Ives’s harmony short-​circuits the New England school, anticipating post-​ Lacanian psychological complexity. This chapter explores Lacan’s attempt to engage with the psychodynamics of cybernetics, a body of theory coming from MIT in the 1950s, that explores self-​organizing systems. Lacan likened language to such a cybernetic system, and his theory of the symbolic is the theory of how our psyche engages with this self-​contained, autopoietic world. And this can also speak to our engagement with tonal function. Before focusing on Ives’s

Preface  T  xiii transcendental project, I look to Copland’s Emily Dickinson songs, which use a cybernetic form of desire as a “feedback loop” to allow the composer’s repeated harmonic progressions to explore new territory and change shape incrementally. I then examine the expansion in scale of the dialectic between static octatonic minor-​t hird cycles and mobile major-​t hird cycles, as exhibited in two key scenes from Copland’s opera, The Tender Land. The expanding harmonic rotation portrays the sexual awakening of the naïve young subject of the opera, Laurie Moss. In their broader function the cycles speak of the regeneration of the American landscape and the families who settle on it. They can also create a sense of nostalgia, a theme central to Ives’s vision of desire. In Chapter 4 we move to Poland, where several songs by Karol Szymanowski demonstrate the explicit rotation of the T→S→D substitution model in relatively strict terms. These songs also reflect on the theme of desire as a circular driving force. From the Op. 41 settings of Rabindranath Tagore’s The Garden (Nos. 1 and 4), I examine the gulf between two lovers: first, with love as a reflection of the self in the other’s eyes that takes a line of flight like a “bird in the wilderness,” and second, with the “heart” in Des Letzte Leid as a metaphor of love, exposed as the nothingness of the night that the lover rejects. Then I  look at Szymanowski’s symphonic music, specifically the Third Symphony, Song of the Night Op.  29, whose sonorities spread their tensions out in many directions at once. This excess of the model is examined in a Lacanian-​Marxist light as surplus enjoyment (“plus-​de-​jouir”), following on from my preliminary discussion of Ives’s piano work. The sense of yearning for darkness is likened to Lyotard’s variation of the Freudian death drive. In order to better visually re-​create the drives that are simultaneously active in the mysterious atmosphere, I  employ a method I  call “drive analysis,” which represents triads as triangles and tetrads as squares, each with tapered corners to represent the raising or lowering of pitches. When placed on a graph whose y-​a xis unfolds the circle of descending fifths and whose x-​a xis represents the flow of time, various patterns emerge that unlock new hearings of a work whose harmonic movement we might otherwise consider static. Desiring cycles flow strongly in the music of Richard Strauss, as explored in Chapter 5 and demonstrable in the opening scene of Elektra, the harmonies of which surge in an ever-​tonicward direction. This chapter further reexamines the concept of hysteria, refuting its applicability to Strauss’s opera and opting for a more detailed Lacanian reading, with the concept of perversion. I also explore the “zone between two deaths” as a space in which characters of beauty are located (Lacan 1960). This plays itself out in a particular scene—​often cut from performance—​in which Elektra tortures her mother and behaves almost exactly as the Marquis de Sade in the famous scene from Justine—​from which Lacan takes his concept of perversion. Strauss’s harmonic progressions support my psychodynamic reading. The up-​front octatonic cyclical rotation of this scene is undercut musically by an equally transparent circle of fifths in the bass, which notably plays the role of Agamemnon, whose “glare”—​Lacan’s “gaze”—​draws Elektra onward to death and destruction. This offers an analysis of how one octatonic cycle can begin to control another, separate cycle. I also examine this from an ethical position, following Lacan’s model of Aristotelean catharsis (in

xiv  T  Preface The Ethics of Psychoanalysis), and hear how these functional cycles come to a head in the final dance of death that—​like Wagner’s Isolde—​shuttles to and fro between the cycles as they are completely dismantled. The Andante from Josef Suk’s Asrael symphony—​t he focus of Chapter 6—​is a funeral march in all but name. It celebrates, on one hand, the life of Suk’s teacher Dvořák, and, on the other, his wife, Otilie, whose death during the work’s composition famously changed the projected optimistic tone. The various moods of this movement hang together because of a heavily asserted inner pedal of d ♭ , heard prominently in various instruments throughout. This pitch is never dissonant, and chords are constructed around it in such a way as to replicate a perfect hexagon on the common neo-​R iemannian graphical Tonnetz (a Riemannian “net of tones”), broken only by the use of a seventh chord (B ♭). Although a closed network of pitches—​unlike the octatonic and hexatonic scales formed by minor-​ third and major-​t hird cycles—​t his constellation contains the subdominant and tonic of the pitch at the center, and thus fuses a very limited diatonic tension with chromatic chords. The associations of death with limited harmonic progression are aligned with Freud’s essay “Mourning and Melancholia.” The Freudian plot thickens when Suk aligns this “death music” with the theme of a “maternal” return. The same compositional technique occurs in each of the five pieces from About Mother, Op. 28. Each supports a different inner pedal that acts as a core for the harmonic progressions. However, the core starts to shift in these five programmatic pieces and produces diverse patterns on Riemann’s Tonnetz. This movement away from the inner chromatic core (although ostensibly a diatonic pitch) highlights a form of modulation that maps the outward movement of the developing subject, who becomes separated from the maternal body. The dual association held by this technique between maternal warmth and death leads to a critique of the basic Freudian death drive inspired by Lacan, Deleuze, and Lyotard with further refinements to the tension–release model at the heart of these pieces. Following the rise of Deleuze from the closing thoughts of Chapter 5 through to Chapter 6, Chapter 7 passes through famous remarks by Deleuze concerning cybernetics and acceleration, focusing on the futuristic projects of Alexander Skryabin, who wanted to speed up time through his music—​in particular, his harmonic developments. Whereas other works set the hexatonic and the octatonic in a diatonic flux—​hexatonics as an energy-​discharging mechanism, octatonics as a storage capacity—​Skryabin’s Sonata No. 10, Op.  70, recently explored by Vasilis Kallis (2015), is unique in juxtaposing hexatonic composition with the octatonically rotating model as clearly segregated areas. The final chapter asks: To what extent can the flow between these cycles carry our tonal desire? To what extent does our diatonic engagement fluctuate between distinct sections? How can drive analysis meaningfully be integrated with Funktionstheorie? The answers to these questions are resolved in part by appeals to Formenlehre and Skryabin’s “accelerationist” approach to form as well as harmony. After the predominantly Lacanian exegesis of the previous chapters, this conclusion takes hold of Lacanian critiques from Deleuze and Guattari, positing “desire-​machines” as mechanisms that constantly seek to make new connections. This approaches a

Preface  T  xv reading of the harmonic tempo, finding that one of Skryabin’s principal devices for increasing tension is the mechanical increase in rate of change. This invariably attaches itself to an exponentially increasing pace, bearing out Skryabin’s patterns of evolution through the “root races” of theosophy, famously mapped onto his Prometheus, Op.  60. His philosophical and musical thought here converge on something that is usually interpreted as ridiculous but actually is philosophically very astute according to a recent trend in philosophy, namely accelerationism, in which a unification of human with machine moves toward an exponentially increased rate of production. Although this whole philosophical school is drawn from comments made by Karl Marx, whom Skryabin admired—​and therefore is historical—​t he composer is, in this sense, futuristic. In sketching this connection, I conclude by drawing closely together, but not entirely combining, the book’s two strands (harmonic progression [Funktionstheorie] and harmonic possibility [drive analysis]), using these and the work of previous chapters to consider finally what it means, in psychodynamic terms, to be chromatic in a diatonic universe, or diatonic in a chromatic universe.

Notes 1. For example, more than once has the Freudian libido been shown to be directly linked to the exchange of financial capital. The most famous examples are Deleuze and Guattari’s ’s Anti-​Oedipus (1988) and A Thousand Plateaus (2004), and Lyotard’s Libidinal Economy (2004). 2. See Barthes (1977). 3. See Schelling’s words: “The unground of eternity lies this close in every person, and they are horrified by it if it is brought to their consciousness” (quoted in Bowie 1993, 107). 4. The difference between drive and desire is a rather knotty question. It will be unpacked in Chapter 4 but will remain a running concern of the book. 5. Hyer has reservations about this claim, though, writing:  “Riemann, that is, does not appear to regard the tonic, dominant, and subdominant as psychological constructs, as objects in consciousness. His use of the tonal function is, if anything, anti-​psychological in nature” (2011, 127).

AC K NOW L E D G M E N T S

There are various people who have supported me throughout the six years of work on this book and whom it is my privilege to thank. In particular, Dr. Annika Forkert-​Smith, for whom every silver lining has a cloud, managed to keep my buoyant spirits in check whenever I became overly optimistic. Annika has also helped me raise two Chilean degus, Castor and Pollux, who have both provided much-​needed diversion. I  also extend great thanks to Ciro Scotto, Richard Worth, Ross Edwards, and Paul Harper-​Scott for reading through various drafts. A profound debt of gratitude is also owed to Josh Rutner for his tireless work in copyediting the text. Josh was particularly helpful in offering American equivalents to my British idioms. (I hope we meet in person sometime, Josh—​I’ll stand you a beer.) I  also thank, in advance, my infant nephews and nieces—​ Eva, Eddie, Jonah and Emily—​who will, I hope, one day become faithful readers. Steve Rings needs acknowledgment, for without him and Suzanne Ryan of Oxford University Press, this book would have appeared in Silhouette Publishing’s Desire series. For his great service to erotic literature, this book is dedicated to Steve.

C HA P T E R

One

A Linguistic Theory of Chromatic Harmonic Substitution and Progression in the Diatonic Unconscious There are only three kinds of tonal functions (significance within the key), namely, tonic, dominant, and subdominant. In the change of these functions lies the essence of modulation. Hugo Riemann

Metaphor and Metonymy “Desire is a metonymy.” Thus spoke Jacques Lacan (2006, 439). Just as desire had been at the core of fin ​de ​siècle Viennese psychoanalysis, it was now the fundamental concept behind Lacan’s topology of the human psyche. But unlike the materialist hydraulics of Sigmund Freud’s drive theory, Lacan’s desire energy is processed by operators of the unconscious mind that are deeply linguistic. Desire is no longer an agent of the raw, uncoordinated id; it is a culturally constructed (and constructing) phenomenon that bears the imprint of the linguistic systems that structure it. We might wonder what role music can play in the unconscious programming of desire in listening subjects, and we might further wonder how desire can materialize in the acoustic signals we call music. Looking for answers to these questions in Lacan’s seminars—​w ith their deconstructive Freudian torsions, Hegelian dialectics, and Xenoian paradoxes—​is as problematic as it is fascinating. Lacan had as much idea about music as Freud did—​which is to say, none whatsoever. And yet, in his famous seminar of 1957, published as “The Insistence of the Letter in the Unconscious or Reason Since Freud,” in which Lacan elucidates his hypothesis that the unconscious is structured like a language, he borrows heavily from musical terminologies, throwing words like “polyphony,” “discord,” “harmony,” and “transposition” into the pot.1 After claiming that “it is the whole structure of language that psychoanalytic experience discovers in the unconscious,” he elaborates:  “It suffices to listen to poetry, which Saussure was certainly in the habit of doing, for a polyphony to be heard and for it to become clear that all discourse is aligned along the several staves of a musical score” (413, 419). Lacan had an idiosyncratic view of what constitutes a language. His theories of langage (an abstract concept of language in general) and langue (any particular tongue) were developed from Desire in Chromatic Harmony. Kenneth M. Smith, © Oxford University Press (2020). © Oxford University Press. DOI: 10.1093/​oso/​9780190923426.001.0001

2  T  Desire in Chromatic Harmony his early doctoral study of psychotic language, and it is therefore unsurprising that the concepts are closely integrated into his studies of the psychic unconscious structures of humankind. But is music a language? For the Frankfurt school, it categorically was not: Music is similar to language. Expressions like musical idiom or musical accent are not metaphors. But music is not language. Its similarity to language points to its innermost nature, but also toward something vague. The person who takes music literally as language will be led astray by it. Music is similar to language in that it is a temporal succession of articulated sounds that are more than just sound. They say something, often something humane. The higher the species of music, the more forcefully they say it. The succession of sounds is related to logic; there is a right and a wrong. But what is said cannot be abstracted from the music; it does not form a system of signs. (Adorno 1993 [1956], 401)

Lacan would probably not disagree, actually—​except with Adorno’s inference that language is in any case a “system of signs.” Lacan rejected the Saussurean primacy of the sign, claiming language to be, rather, a schema of signifiers. A language that was not a site of ambiguities would be a simple code. As opposed to the sign, which “represents something for someone,” Lacan defines a signifier as “that which represents a subject for another signifier” (1998a, 207), meaning that, rather than connoting any specific concept or object, a signifying unit tells us that there is a subject present, which is added to the network of other signifying units.2 A linguistic system of signifiers (without fixed signifieds) could easily be music, the art form that we attempt to subjectivize beyond all others, rich as it is with internally cohesive signification networks. If anything, music’s proud semantic slippage of the signified under the signifier—​because, like any signifier, musical signifiers can never fully articulate what they try to signify, instead drawing in more signifiers to help them—​would bring it somewhere near to what Schoenberg called the “language of the unconscious” (Schoenberg 1984, 192).3 Can harmonic language be imprinted on the unconscious? Few would argue that it cannot, after we consider that we unconsciously expect implications—​ harmonic, rhythmic, melodic—​to be realized based on previous exposure to the signifying system. But can this music be profitably mapped onto the infrastructure of the unconscious and shown to be homologous to it? That it can is the hypothesis of this book and its various test cases. The theory tried here is that fin ​de ​siècle composers, taking a cue from Wagner, expanded diatonic harmony to remove the master signifier—​t he tonic chord that was the intractable, controlling center. Such composers, however, maintained a libidinal stream in which harmonic bodies, full of tension, flowed into others equally tense, being incessantly channeled through a linguistic mechanism that nonetheless relied on the evacuated tonic chord as an imaginary—​in the strictly Lacanian sense that we will soon explore—​absent “object-​cause” (Lacan designated this object-​cause as his famous objet petit a).4 Lawrence Kramer (among others) has investigated Tristan apropos of the fluid Freudian libido (Kramer 1990, 135–​75), but we must remember that Freud’s image was only partly aquatic: Freud was interested by

 

A Linguistic Theory  T  3

hydraulics—​water, yes, but water in the context of a heated libidinal engine that routed and rerouted its liquid through its corridors. The libido’s material conduits, I claim, can be musically conceived as certain rich chord progressions, present throughout common-​practice tonal music, but which reach a particular intensity in early twentieth-​century chromatic music. These channels need evaluating in the light of recent music theory. In order to test the capacity of music–​t heoretical canals to carry harmonic signifying content, I intend to open them up and follow them until we run aground at their logical conclusions.5 We test the strength of metal by breaking it. This has been done to some degree with “desire theory,” which passed from Freud (and Arthur Schopenhauer before him) around the deconstructive bends of Lacan, Jean-​François Lyotard, and Gilles Deleuze. In music theory, too, desire—​a lbeit repressed at times—​has run through the various realizations of the Riemannian vision by David Lewin, Brian Hyer, Richard Cohn, and others. It behooves a theorist of the twenty-first century to seek support from other disciplines—​ particularly philosophy and psychodynamics—​ because of the heated psychological atmosphere in which composers expounded their ideas at the turn of the twentieth century, from Wagner and his Schopenhauerian philosophy through the heavy Freudian aesthetics of the second Viennese school—​think particularly of Erwartung (Brodsky 2016)  or Pierrot Lunaire, Wozzeck, or Lulu—​and beyond. As post-​Wagnerian music from this period increased in complexity, so, too, did the psychodynamic theory we must appeal to in order to do full justice to the musical mechanisms of desire employed. Although Lacan mentions harmony in his seminar, he has little concrete to say about this parameter of music, and applications of his theories of language and the unconscious working of desire—​desire being, after all, his main topic—​could lead us in countless directions. This study explores but one of these courses and attempts to carve a new path through harmonic theory as it pertains to the post-​ Tristanesque strain of libidinally charged music that so preoccupied composers at the long fin de siècle. The theory propounded accounts for chord relationships that are placed between the two axes of harmonic discourse:  the substitutive axis that Lacan (following Roman Jakobson) called “metaphor” (which I find in the phenomenon of chord substitution) and the combinatorial axis that Lacan dubbed “metonymy” (which I find in the concept of chord progression). These linguistic functions are based on Freud’s “condensation” (the collapse of several ideas into one) and “displacement” (the release from a source of repression into another idea). Like our Freudian dreams, the Lacanian mutual interdependency of one axis with the other makes linear abstraction of x and y axes impossible and, although I will discuss metaphor (qua chord substitution) first and metonymy (qua chord progression) second, the two weave intricately together, each requiring the other to operate both psychically and musically. Just as a discussion of time without a concept of space would be near impossible, so does my consideration of metaphor need a small amount of metonymic logic to demonstrate its value, and vice versa. By the time I  have conducted my “litmus tests” for metaphoric substitution—​ cadence points and common neo-​R iemannian transformations—​we will already

4  T  Desire in Chromatic Harmony be well prepared, through microdiscussion of these small progressions of just two chords, for the full unfolding of metonymic chains of chords across the temporal harmonic axis.

Metaphor and Funktionstheorie: Chord-​Level Substitution For some reason, it is difficult for us to imagine the relation between the dominant and the tonic in other-​t han-​metaphorical terms. I have referred to this relation, for instance, using both sexual and rhetorical language. Brian Hyer For Lacan, the function of metaphor—​ t he substitution of one signifier for another—​is fully congruent with the crossing of what Ferdinand de Saussure calls the “bar.” This bar exists as an obstruction that prevents a signifier from completely reaching a signified, and meaning is always lost in the attempt to cross it. For example, we might choose a word (signifier) to try to describe how we are feeling (the signified), but the signifier can never express it completely. We can try harder to pinpoint what we mean with a network of more and more signifiers, but there is still a fundamental impossibility—​represented by this bar. The formula for metaphor in Lacan’s essay “The Insistence of the Letter in the Unconscious” registers that it is in “the substitution of signifier for signifier” that a “signification effect is produced that is poetic or creative” (2006, 429). In opting for one word rather than its alternatives (which is Lacan’s formula for metaphor), we attempt to reach out—​hopelessly, of course—​and cross the bar. In choosing a “rose” with which to compare his “luve,” Robert Burns chose one image from a host of alternatives in an attempt to give us a little more semantic meaning. But this always falls short, leaving us to work out whether his love is simply beautiful, prickly, high-​maintenance, seasonal, or in need of pruning. Lacan contends that metaphor involves the substitution of signifiers in a positive attempt to cross the bar, and though the attempt at fixed meaning always fails, the attempt marks a positive step in the right direction. Like words in poetry, chords are substituted all the time in Western tonal music. But are these always metaphorical exchanges? How do they attempt to cross the bar? To see how chords can substitute for each other and attempt to mean something, we need to consider the concept of tonal function, which, like metaphor in Lacan’s topology of the psyche, is one of the main carriers of musical meaning (limited though it always is). Theorists from Jean-​Phillipe Rameau through Hugo Riemann (from his 1872 Musikalische Logik through to the mature Funktionstheorie of the 1893 Vereinfachte Harmonielehre) and up to Daniel Harrison and his contemporaries a century later have tried to unravel this term. David Kopp has demonstrated just how pitifully we have actually been able to cross the bar in Funktionstheorie by illustrating the diverse interpretations of the word Funktion itself over the years.6 Words like “value” (Hyer 1989, 100),

 

A Linguistic Theory  T  5

“signification,” “action,” and “meaning” crop up; as Kopp notes:  “Loosely put, function signifies harmonic meaning or action” (1995, ¶1). John Gabriel Miller surveyed this issue anew and divided the term into four aspects:  (1) behavior, (2) kinship, (3) province, and (4) quality (2008, 11). Chiming with Miller’s concept of behavior, Kopp proves that, while we modern analysts conceive of Funktion as a syntactically oriented phenomenon—​what is the function of this chord in relation to the next?—​this was not the case with Rameau, Riemann, or even Gottfried Weber: What we are looking for in these older theories, I  think, is a reflection of our belief that one of the important things chords do is imply other chords, and furthermore that they do so because of their function, whatever we understand that to be. All three of the theories discussed above [Riemann’s, Rameau’s, and Weber’s] fall short in this regard, each in its own way. . . . It has become natural for us to expect the ideal harmonic theory to explain how chord progressions are determined and goal-​directed. Some of the responsibility for this, ironically, can be laid at Riemann’s feet, for he was the one to introduce the term function in the first place. In his own work he explicitly associated Funktion with Bedeutung [meaning]. But the word naturally evokes more dynamic associations. After all, in everyday usage, the function of any object or concept has to do with what it does more than with what it is. (1995, 13–​14)

Steven Rings tackles this from a transformational perspective. Reanimating Funktionstheorie in a transformational context, he claims that to call a chord “Subdominant” is to see it as an operation, or to hear its relation to the Tonic rather than an acoustic signal; he calls this animation “tonal intention” (2011, 500–​01). This book proposes a similarly mobilized function of Funktionstheorie but significantly departs from transformational theory in that it proposes a strong directed motion associated with the exchange of functions as a metaphorical (and as a metaphysical) concept, rather than with their transforming (however physical) sound bodies. Riemann famously posited three Hauptfunktionen, or primary functions: tonic (T), subdominant (S), and dominant (D). For Ernst Kurth, chromatic chords are reducible to these: “The tension chords in Wagner’s music in relation to the resolution chords, are almost always dominants or subdominants, or are identical” (1991, 116). These three functions were “die eigentlichen Pfeiler der tonalen Harmonik” (the essential pillars of tonal harmony) (Hyer 2011, 94). They are more than chords. As Hyer reminds us, “[a]‌tonal function . . . seems to have been understood since its inception, as a neutral descriptor for whatever it is that the tonic, dominant, and subdominant all are” (93). In Riemann’s Vereinfachte Lehre chords are designated a single function with whatever modifications he deemed appropriate. Yet the analytical process became subjective in excess of its usefulness:  Harrison claims that “a student of Riemann’s system can analyze virtually any chord into any one of the three functions should the occasion demand,” even while “such analytic freedom seems at odds with his rigid theoretical system” (1994, 284, 292). It is my wish to provide a rigorously thought-​ out framework that can be robust and reliable enough to keep our levels of

6  T  Desire in Chromatic Harmony subjectivity under some control while providing enough room to speculate and play with the tension between alternate hearings. If we appeal to Lacan, we might propose that whenever we hear a chord that has been selected over and above other chords, it suggests to us a certain function or meaning—​it attempts a crossing of the bar and is awarded (provisional and imaginary) T, S, or D status by the listener.7 For this branch of harmonic theory, an entreaty to Lacanian psychosemiotics was first made by Hyer, to whom this book owes a great deal. Hyer examines the harmony of Rameau’s Pygmalion, noting the composer-​ theorist’s frequent use of “signifie” and “signe” in the protosemiotic context of Diderot, Condillac, and Rousseau (Hyer 1994, 21). Hyer employs Riemannian Funktionstheorie, claiming, “I attempt to rationalize the idea that the tonic, dominant and subdominant constitute a ‘musical system’ in which relations between triads have more significance than triads themselves . . . the basic premise of structuralist thought” (16). He concludes that the D and the S are “signifiers” for the T, although this triad “is signified as an idea” (24).8 For Kurth, these signifiers are roles that chords assume: a chord’s “musical effect depends on its relationship to the central tonic harmony, on its ‘tonal function’ ” (1991, 119).9 In Rameau, these signifiers are expressed as desiring: Indeed, musicians often conceptualize the dominant as a chord that “desires” another, the chord longed for being the tonic. Rameau himself writes that after the dominant goes to the tonic in the perfect cadence, “one desires nothing further” (Rameau 1969 [1757], 208)[,]‌meaning that after the dominant, one “lusts” for the tonic. (Hyer 1994, 13)

Further: The dominant seventh’s meaning coincides with its “desire” to melt into the tonic, to fade from hearing: it signifies only in relation to the tonic a perfect fifth below. . . . The tonic, then, is signified in Rameau’s theories not by a presence but by an absence, an absence of supplemental dissonance, of a trace. (23)

The absence noted by Hyer is directly conceived as a Freudian-​Lacanian lack: There is a sense in which both the dominant and subdominant signifiers occasion an insufficience, a lack filled (though not quite) by the signified tonic. In musical terms, this insufficience is felt in the need for resolution; it is this musical desire for which the sign accounts. Indeed, for some post-​structuralists, all desire is rooted in the yearning of the signifier for the signified. (30)

Yet part of this lack is, paradoxically, identified with the trace of excess, which Hyer categorizes as twofold: First, pitches 2̂ and 4̂ serve as the dissonances of the S (2̂ as added sixth) and D ( 4̂ as seventh), and yet together they form a dyad common to both S and D. Second, once achieved, the tonic can become the D for the S: “There is a sense, however, in which the tonic is not quite enough to ‘resolve’ the dominant and subdominant, a sense in which the dominant and subdominant signifiers overflow the signified tonic” (27). With his Derridean hat on, Hyer sees

 

A Linguistic Theory  T  7

these dissonances as the “supplement”—​something added to that which we thought already complete, thereby showing us a fundamental original lack. We might be still more Derridean and refer to Riemann’s theory of Scheinkonsonanz—​a sense of false consonance from the Katechismus, created in secondary triads that replace the perfect fifth of a primary triad with a dissonant sixth: a trace—​t he mark of an absent presence. That is, we can hear a trace of IV in ii without even hearing 1 .̂ In the gap between secondary triads and primary triads, we can catch a sense of the other’s absence.10 Riemann believed that secondary triads bear a trace of the primary triads that would yield a mild dissonance if combined.11 But in the guise of Lacan rather than Derrida, Hyer also claims, “The role of desire in signification is to overcome this unconscious resistance, which deflects the signifier away from the signified and displaces desire onto a different signifier along either the metaphorical or metonymical axis” (1994, 45). The very fact that “function” is a slippery and dynamic label—​ what initially sounds like an S could prove over time to be a D, according to Hyer—​w ill take our harmonic logic even closer to Lacanian thought, as we investigate the slippage of desire through the course of this book. The abundant interchanges of chords ii and IV in classical harmony embody this notion: Both are frequently read as subdominant in function. Rameau’s idea was that the fundamental bass privileges fifth motion—​thus D–​G is stronger than F–​G.12 He explains the strength of the S→D motion by virtue of an imagined d root to the F–​G motion.13 This double emploi means that the S resolves into the D via a fifth progression. The IV may perhaps be the “real” S chord itself, but by virtue of the facts that ii so frequently replaces it and that the two work together in the imagination—​in line with Riemann’s later Tonvorstellung theories—​t he chords can be said to have the same function. This interchange of chords invests the word subdominant with a deeper significance; the S is a more profound category of meaning than the chords that represent it and that metaphorically substitute for each other in representing it. Functional equivalence therefore appears to be associated with chord replacement where there is no possible tension-​resolution between substitutionally alternative chords (such as ii and IV). This leads to slightly more nuanced postulations than those of Eytan Agmon (1995, 196) who, in proposing his model of functional prototypes, cites Stevan Harnad: Categorical perception occurs when the continuous, variable, and confusable stimulation that reaches the sense organs is sorted out by the mind into discrete, distinct categories whose members somehow come to resemble one another more than they resemble members of other categories. (Harnad 1987, ix)

Chord resemblance is not a key issue for me, however much I  approve of the Harnad-​Agmon theoretic apparatus of prototypes. To my mind, a chord can quite easily represent another closely but be different in function; similarly, a chord can bear little resemblance and still have the same function. The qualities of a rose do not resemble those of chocolate, but their functions may be similar for the lover on the basis of the substitutional axis of metaphor.

8  T  Desire in Chromatic Harmony The three functions are not—​at this stage of my argument, at least—​identical, and must be independently defined. These definitions will involve a syntactical parameter and will register the behavior associated with the relative position of a chord unit within a signifying chain that either accrues tension or discharges it. Discharge, Daniel Harrison’s preferred term, refers to the release of stored tension from one function onto another, although Harrison refers to each chord he analyzes as the product of three functionally active scale degrees that discharge tension to more stable ones (1994, 90). These are based on Riemann’s “dualistic” principles, by which major keys are associated with dominantness and rising 7̂–​1̂ voice-leading, whereas minor keys are associated with subdominantness and descending ♭6 ̂–​5̂ motion (Harrison 1994, 93).14 All diatonic pitches and modified chromatic ones are aligned with a primary function, and the chord (usually a triad) adopts the aggregated character of the most forceful function. The chord, then, is an assemblage of charges and discharges whose “constituents work so ‘harmoniously’ together that they become a community able to be given a single name” (43). Harrison’s picture of the triad shows the functional base (root), agent (third), and associate (fifth), which can be prolonged through shifting chord patterns (43). There is no room in this theory, however, for the additional sensitive pitches that would create the secondary chords that mobilize a simple progression of V7→I. In C major, the additional f of G would be an S pitch—​easy enough to accommodate, but the theory is clearly more geared toward triads oriented around a unitary tonic. Harrison downplays the great discharge potential from, say, 4̂–​3̂ that harmonizes so well with 7 ̂–​8.̂ 15 My conception of function differs from Harrison’s. In the spirit of the whole being greater than the sum of its parts, I  suggest that the discharge of his two classes of leading tones is only as significant to functional interaction as is basic root motion (or idealized root motions such as the double emploi). Therefore we need a new term to describe the discharge action of these rooted chords, rather than individual pitches. In my meaning, I  will simply italicize discharge, although this will sometimes be categorized further with directed arrows, indicating a D to T discharge as “→discharge” and S to T discharge as “←discharge”; these may also be rendered D→T and S←T. Such discharges occur between chords that are expressions of functional values. In defining individual functions, my own terms are provisional. They will change and actually break apart (productively, I hope) through the course of the book. But for now: • The T function is constructed as a region of pseudo-​stability; it signifies a discharge of D tension and may accrue tension toward the S. This is the most ideal function. • The D function is the main store of diatonic tension; it also discharges the S and heightens our desire for the T. This is the most potent function. • The S function acts dually as both an “other” region of relative stability (to the T) and an auxiliary store of tension (discharging into the D function); it acts as a halfway house between the D and the T—​less tense than the D and less secure than the T. In a minor key (in dualist theory), it adopts certain

 

A Linguistic Theory  T  9

properties of the D of a major key, wanting to discharge right away to the T. This is the most ambiguous function. While the first clause of each of these redefinitions of Riemann’s Hauptfunktionen regards the absolute behavior of each, the subsequent clause proves this behavior to be purely relative. Funktionstheorie classifies the whole functional edifice as a system of related triads, and though relativity is prominent, our relation to the absolute identity of the chord and function drives the system.16 This delicate balance between the absolute and the relative will be constantly readjusted as this chapter progresses. But in a world of relativity, a working definition of function in its broadest terms could be “three variables—​functions T, S and D, whose potential values stand in metaphorical relation to each other and are generally represented by triads—​t hat charge and discharge energy through their exchanges with each other.” A working definition of a single function could be “a collection of chords that metaphorically interchange with each other without discharge.” By way of example, I  note the fact that minor-​third relations can sound static, whether this is C–​Am, C–​A, or C–​E ♭ .17 For me, this is because no leading tone, ̂ can ever develop in the minor-​third group of chords major or minor (7̂ or ♭6), ♯ ♭ (e.g., in C, A, E , and F the leading notes b, g♯ , d, and e ♯ are excluded). This is famously suited to Russian music—​t he octatonic chord progressions of Rimsky Korsakov, for example—​ and fits Taruskin’s category of nepodvizhnost (immobility) (1996, 954). There are no discharges (in Harrison’s sense) possible, nor any discharges (my sense) available either, because the T7 and T4 root-​related chords are absent. This exchange of abstract symbolic values is acutely Lacanian; for him the real bodily energy is driven by the rotation of its place-​holding values in a search for meaning and expression. As a strand of harmonic theory, Funktionstheorie clearly stems from Riemann but is only tangentially related to the neo-​R iemannian transformational theory of David Lewin, Steven Rings, Richard Cohn, and others. Mine is a theory of tension and release inherent in chords and their functions; transformational theory is about the groups of operations that active listeners apply to chords to transform them into each other. It would be crass to claim that subject-​object relations are inverted in the two approaches, but there is a small sense in which, for transformational theory, the music is the object and the listener the subject, whereas for me, the music is the subject and the listener—​listening through the work—​t he object. Thus, I present a modern theory of what one might call a kind of neofunctionality in harmony whose potentials have not, to my mind, been fully assessed and must now be appraised from a psycholinguistic angle.

Refilling Lendvai’s Bath: The Axis System From the 1960s until his death in 1993, the Hungarian theorist Ernö Lendvai developed his ideas of the “alpha chord,” the Fibonacci series, and the “golden section” in the music of Bartók and innovated computerized analyses of Verdi and Wagner.18 Somewhere in his weird and wonderful theoretical maze lies his

10  T  Desire in Chromatic Harmony “axis system,” a chromatic extension of Riemann’s Funktionstheorie, rarely acknowledging its Riemannian debt. Although Lendvai’s theories were always derived from (and reapplied to) musical scores with great virtuosity, the whys and wherefores of some of his finest hypotheses were left woefully undertheorized. Yet for all of his controversies, Lendvai requires recuperation. The oft-​reported sentiment that Lendvai’s scholarship is, at his best, genius, and at his worst, ludicrous, has led to our throwing an impressive litter of children out with some very grimy bathwater.19 My project, then, in the service of Lacan’s concept of metaphor, is to refill the bath slowly and scrub more thoroughly Lendvai’s erroneously ejected babies. As part of the enterprise of consolidating the axis system with more rigorous theoretical formulations, I also return to Hyer’s (1989) dissertation on Tristan, which helped kick-​start neo-​R iemannian explorations in the 1990s. This ongoing project cannot be achieved in a single paragraph, nor a chapter; the reader will be content at this stage with an ex post facto rationalization of Lendvai’s initially esoteric harmonic scheme, which was derived from close scrutiny of Wagner, Verdi, Bartók, Kodály, and even, at times, Beethoven. The axis system shares foundations with the metaphoric-​metonymic axis of the Lacanian psyche, notwithstanding the entirely different species of axis portrayed. Like Lacan’s, Lendvai’s understanding is that the whole musico-​ linguistic system revolves around a tonal lacuna: The most peculiar feature of the system is that its center is being marked by a “Black Hole.” The center—​t he zero point—​coincides with the point of “atonality.” Up-​and downwards from the RE or SI (D or G ♯), every degree occupies a symmetrical position. (E.g., on the piano keyboard—​related to D or G ♯ each interval has its exact mirror image.) Symbolically speaking, an element that is symmetrical to everything represents a state of “physical death.” The symmetrical division (the repeated bisection) of the circle of fifths—​around the RE symmetry center—​results in the “tension” points of the system. (Lendvai 1993, 66)

This central “black hole” lies at the heart of Lacan’s theory of desire. Lacan calls the “signifier without a signified” the “phallic signifier” (Lacan 1998b, 80), referring to the Egyptian goddess Isis, who built phallic statues along the Nile wherever she failed to find the crucial missing piece of Osiris’s body. These statues served as symbols of the lack that was structuring her desire. Music theory has always associated the center point of desire with the T function. Rings most recently brought Rameau and Riemann (among others) into dialogue. Citing Rameau, he writes: The tonic is “the chord that we find most agreeable, the one to which all of our desires tend, and beyond which we desire nothing more” (Rings 2011, 107; see also Christensen 1993, 189; Rameau 1737, 109). Rings notes further that Riemann uses the word Verlangen (translated as “desire”). Our experience of the central (tonic) object, as for Lacan, is the work of the imaginary realm, which, in Lacan’s famous Borromean knot of the Real, the Imaginary, and the Symbolic, is where our misrecognized view of ourselves and our world is located. The Imaginary is highly subjective and an always distorted compromise between the Real (which, like Kant’s Ding an sich, we can never truly access) and the Symbolic

 

A Linguistic Theory  T  11

(which behaves like a self-​f ulfilling world of language that we access but which is already self-​sustaining).20 As Riemann claims, “the C major triad itself is part of the imagination as that Klang by which the significance of the G major triad is determined as something deviating from it—​t he center of its imagination lies, so to speak, outside of it” (Riemann 1882, 188; see also Rings 2011, 107). Hyer describes an ontology in which the D and the S are “representational constructs. Both the dominant and subdominant represent the tonic, though not, of course, in the same way: the dominant represents the tonic lying a perfect fifth below, while the subdominant represents the tonic lying a perfect fifth above” (2011, 98). He discusses Riemann’s “mental representation [Vorstellung] of tone relation which lives in the musical imagination [Tonphantasie] of the creative artist” (130). Riemann’s famous latter-​ day Tonvorstellung theories pitted themselves against Helmholtz’s sensuous bodily response to base acoustic matter—​Tonempfindungen (the sensation of tone) (Riemann 1992, 69–​79). Rings further shows that this imaginary experience involves the theory of tonal categorizations (i.e., functions): “Such analyses can encourage us to direct our ears to the tonic in specific ways, via the mediation of specific theoretical categories” (2011, 106). These categories, while happening in the Imaginary realm, are also Symbolic, because our imaginations (and our very unconscious minds) are symbolically driven once we have accepted language deep into our psyche. Rings expounds on Riemann, who attempted to show that through the intervention of these categories, “a listener relates every harmony back to the tonic—​‘the middle point of our harmonic imagination’—​v ia a system of harmonic functions” (2011, 109). Although Rings chiefly considers the T as a present object (with support from phenomenology), he also contemplates its absence. An “acoustic absence”—​ what Lacan might call a “phallic signifier”—​ can still function as the driving agent of an entire system (106). In 1994, Hyer was also clear on this point: The dominant acts as a “signifier” that brings to mind all the relations that make up the mode, doing so even though the tonic, for the time being, is silent. Like the Statue [in Rameau’s Pygmalion], the tonic is mute in this music, an “indifferent witness” to the dominant’s musical yearning. (21)

Hyer’s conversation about Rameau’s Pygmalion—​a statue—​is significant. Recall the phallus statues erected by Isis that served as symbolic avatars for the real bodily organ of Osiris, which she forever sought. These harmonic pillars, just like Isis’s statues, then adopt a Symbolic function, serving as covers for a central lack, which we fill with our overproductive imaginations. But crucially, Lendvai does not merely observe the T as an absent center: the T that for Rameau was the goal of our desires is for Lendvai just another cog in the machine. Trimming back the layers of solmization and symmetry in Lendvai’s work, its roots are the relative major/​minor key relationships, which essentially stand for the same function. This was acutely Riemannian, reminiscent of the theorist who referred to the relative minor or major of the T function as Tp.21 The same applies not only to the

12  T  Desire in Chromatic Harmony T function but to the S and the D, the S being by far the most common and clearest harmonic substitution (between ii and IV). Lendvai claims that because the parallel major/​minor chords or keys are also too intricately related to have different meanings, “it virtually passes unnoticed if we close Bach’s minor fugues with a major triad” (1993, 80). The relative major and minor of the parallel relation are also functionally synonymous (see figure 1.1a). This logic enjoys a long lineage—​here Kopp cites Gottfried Weber: “Similarity [between parallel modes] is . . . so great, that it almost ceases to be a mere identity, and well-​nigh passes into an absolute identity” (2002, 42; Weber 1871–​72, 309). This absolute identity is monist in music-​t heoretical terms, where modal change leaves function intact. While Am is a relative of C, E ♭ is equally allied with Cm, these chords being functionally related through parallel and relative relationships. Thus Lendvai indicates that P and R are synonymous with the primary triad, and this leads to the joining of three triads in figure 1.1b—​two secondary triads, by relating to the modally androgynous center. The final piece of Lendvai’s puzzle is that the axis system “is none other than the recognition of the fact that the tonic A  and E ♭ not only have C as a common relative, but also the F♯ or G ♭ degree” (Lendvai 1993, 7). This rather shocking claim would lead to the completion of the axis system (figure 1.1c). But here Lendvai offers a large pill to swallow, suggesting that C is practically identical to its diabolus in musica—​t he F♯ tritone “counterpole” (as Lendvai dubs it). And yet in much of the literature that Lendvai examines, this makes wonderful sense. When such chords are imbued with their driving seventh qualities (which they usually are in post-​Wagnerian libidinal works) they contain the same tritone pitch-​class. Plus, as any devotee of Alexander Skryabin’s music will attest, the V7♭5 chord (“French-​sixth” configuration) so ubiquitous at the turn of the century is identical (in pitch-​class content if not in orthography) to its own

Figure 1.1.  (a) Substitution between primary and secondary triads; (b) substitution between primary and secondary triads in both directions; (c) full axis system (as yet unconnected modules)

 

A Linguistic Theory  T  13

Figure 1.2.  Shared pc content of the “tritone link”—​C7♭5 and F♯7♭5 tritone transposition (figure 1.2), being named the “tritone link” (Guenther 1979, 89). This link, exploited by many of the composers considered in this work, played a special part in cementing a relationship that was becoming more than common currency in any case. Even if these chords were conventional dominant sevenths—​C7 and F♯7—​ discharge/​discharge would still not be possible between them; the potent tritone would still be preserved, forming the sevenths and thirds of both chords, and neither chord possesses the leading tones (7̂ or ♭6)̂ of the other. For this latter reason, is it neither possible for C7 to discharge/​discharge to any of its other “octatonic” companions—​A7 or E ♭7. A nugget of empirical research is found in Carol Krumhansl’s seminal text, which demonstrated that the octatonic (8-​28) sets desire to move not to any specific chords within the set but to chords from the 8-​28 set related at T5: Various analyses of these data suggested that the octatonic scale, in isolation, functioned somewhat like a dominant seventh chord requiring resolution to the tonic; the probe tone ratings following the octatonic scale beginning on C [OCT0,1] resembled those for F major, and the probe tone ratings following the octatonic scale beginning on F♯ [OCT0,1] resembled those for B major. This may be interesting in light of Van den Toorn’s partition (1983) of the octatonic collection of dominant sevenths. (1990, 237)

This adds a further dimension to what Fred Lerdahl describes as “space shifting” between octatonic space and other tonal spaces. It seems that we might actually desire to move diatonically through one octatonic space to the next.22 In discussing such chord-​to-​chord “progressions” we may be jumping the gun:  Chord discharge involves metonymy (chord-​to-​chord connection, rather than substitution). But while I  wish to stay at the metaphorical level for the present, the litmus test of this metaphorical chord substitution system is the unfolding of cadences. In cadences we can hear how one chord can, with some success, substitute for another, as in Lacan’s definition of metaphor.

Litmus Tests Riemann worked primarily on phrase movement, based on Rameau’s Génération harmonique (1737), which called harmonic successions “cadences” (Hyer 2011, 95). As Lendvai also implies, the litmus test of his theory of substitution is the moment of cadential discharge. If four minor-​t hird-​related chords can represent the same function, then it follows that the D functions of a D→T cadence are replaceable, while still feeling like a discharge into the T. Discharge of functional

14  T  Desire in Chromatic Harmony tension is the crux. Lendvai explores the three alternative cadences from the repertoire: the modal cadence, the Phrygian dominant cadence, and the Romantic dominant cadence. My task is to examine each of these in a hypothetical cadence to a C major triad, occasionally revisiting Lendvai’s illustrations but also extending his repertoire. Balancing Lendvai’s monist indifference to modal quality, we inspect both major and minor versions. In the cadences listed below, the tritone discharges of each employ stepwise contrary motion, either by a semitone or a whole-​tone depending on the modal qualities of each chord.23 Authentic cadence 1 being the paradigmatic G7–​C cadence, we concern ourselves only with its variations:  authentic cadences 2–​4. These cadences, naturally, are paler, less persuasive versions of the paradigm (what Harrison, comparing the chords of a functional hierarchy to the genetic resemblances in a family tree, calls “weakenings of the function-​triad” [1994, 39]).

Authentic Cadence 2: The Modal Dominant Cadence (D↑→T) As the relative (upper, hence ↑) of V, ♭VII behaves as D even without the 7̂ leading tone, which is now modally inflected as ♭7̂ (figure 1.3). Regardless of this inflection, Harrison asserts that the chord is D-​functioned (1994, 53). In root terms, the cadence is theorized most thoroughly in modern rock music, where it is called the “backdoor cadence” (Coker 1991, 82). In C this means B ♭–​C. Acting as V7 of E ♭ (the key for which C minor would be the lower relative, T↓), B ♭ pivots between the two keys. (E ♭ would be the “front door” for B ♭ to enter through.) The progression is not always regarded as a substitute. Allan Moore’s ears “refuse to hear [♭]VII as merely a substitute V” (1995, 187): “Clearly, the [♭]VII–​I cadence does not have the finality of the traditional V–​I, although it is articulated as a full close. . . . In terms of poetics, it seems to me to qualify the certainty of V–​I with ‘nevertheless’ ” (193). As it pertains to rock music, Moore rightly places the chord as a modal alteration of the leading tone, and in this capacity it behaves in a substitutional way (just not “merely”). The ♭VII7 notably has two elements of the S-​f unction: (1) ♭6̂ (a ♭) comfortably discharges to 5̂ (g) as in the Phrygian cadence while (2)  the 4̂ (f ) descends to 3̂ (e) as in G7–​C. The former discharge would equally suit B ♭7–​E ♭ , so the D impulses would work in parallel with an S impulse. It is worth also considering that a compromise formation of B ♭ and G7 as D-​f unctioned chords would be Gm7.24 The minor seventh more neatly functions as ii7 and would therefore be S in its role as DP (“dominant preparation”), D of

Figure 1.3.  The modal dominant (“backdoor”) cadence

 

A Linguistic Theory  T  15

the D (i.e., a local, modally altered dominant of the dominant), or D D as it appears in Riemann’s Klangschlüssel (1893, 101).25 In a moment from Bartók’s Duke Bluebeard’s Castle (figure. 1.4), a certain B ♭–​C resolution is fudged by the orchestral melodic rise from b ♭ to d ♯ . The latter can be heard as enharmonic 3̂ of Cm and behaves as though the melodic progression is complementing its more normalized B ♭→E ♭ discharge. (The reason for the d ♯ spelling is that the pitch eventually rises further to e ♮ , though in a different register.) In his own examples Lendvai maintains that because we expect e ♭ after the B ♭7 in a modal dominant cadence, an e ♮ is “surprising” and sounds “elevated” (1993, 88). In this Bartók example, we wait two measures for this elevation to e ♮ . Like Bartók, Szymanowski was fond of this maneuver. His imposing opera Król Roger closes on the most flagrant modal dominant cadence when the broken king greets the new dawn, albeit with the B ♭ spelled as a German-​sixth chord (figure. 1.5). But throughout his oeuvre, in subtler phrases such as in his Romance for Violin and Piano, Op. 23 (figure. 1.6), the expected E goal of B7 is replaced by C ♯ (in major rather than the more usual interrupted minor form that would facilitate the leading tone to tonic d ♯ –​e). The sidestep to the major, notwithstanding the weakened ♭7→1 tonic motion, startles me, while still discharging tension, producing what Lendvai, using psychodynamic language, calls a “sublimated” effect, altogether “brighter” (69). Taking one of Lendvai’s own examples, a passage from Act I of Verdi’s Otello (figure 1.7) strikes him as curious because the ascending whole-​tone progression adds this elevating startle on every half-​note beat, leading toward the closing modal dominant cadence. Lendvai further directs us to the poetic message behind these stepwise iterations: the ascension through military ranks. One elephant in Lendvai’s very wet bathroom is that, as in my example from Szymanowski’s Romance, the final T (C) is replete with its seventh and thus mobile beyond itself.

Figure 1.4.  Bartók, Duke Bluebeard’s Castle, §128-​5

16  T  Desire in Chromatic Harmony

Figure 1.5.  Szymanowski, Król Roger, closing measures

Figure 1.6.  Szymanowski, Romance for Violin and Piano, Op. 23, mm. 6–​7

Figure 1.7.  Verdi, Otello, example from Lendvai This reminds us that the T has the dual role, acting both as a T for itself and as a D for another T—​reminiscent, perhaps, of the Lacanian sliding signifiers.26 In Lendvai’s example, the established cyclic maneuver passes from G ♭ to its counterpole C, via S↑→D↑→T—​a whole-​tone progression that ends on a cliffhanger. The modal cadence’s minor form—​B ♭m–​C, also notated D↑→T—​was theorized in Riemann’s Vereinfachte Harmonielehre. It was elaborated by Justin Hoffmann: “In A major, a G minor triad thus replaces an E major triad. Riemann thus argues that the subdominant-​of-​t he-​subdominant and dominant-​of-​t he-​dominant

 

A Linguistic Theory  T  17

Figure 1.8.  Wagner, Die Walküre, final cadence

Figure 1.9.  The Phrygian dominant cadence harmonies can be understood as altered forms of the dominant and subdominant harmonies” (2011, 77–​78). Perhaps the finest illustration of this distinct cadence, from the celebratory close of Die Walküre, uses the modal dominant’s minor form in E (figure 1.8). Establishing the D→T currency, direct discharge (i.e., without substitution) has already occurred via B7→E progressions (as well as B’s tritone substitute, F), but the final Dm–​E is heard in full Wagnerian glory several ̂ the d (as ♭7̂–​8)̂ rises to e. An times. The f falls to e as ♭2̂–​1;̂ the a falls to g♯ as 4̂–​3); added seventh (c ♮) would have likewise chromatically fallen to b. Relatively speaking, the rising whole-​tone aspect of the D↑→T progression, if the D↑ is in the minor mode, is reminiscent of the Phrygian S→D motion of iv→V, which has both discharge value (♭6̂→5 ̂) and discharge value through its root motion (S→D).

Authentic Cadence 3: The Phrygian Dominant Cadence (D✦→T) Tritone substitution is ubiquitous in jazz but also in Romantic harmony. The Phrygian dominant cadence (figure 1.9) utilizes the tritone substitute for the true dominant chord (thus D✦). Because of the bass semitone resolution, the cadence is referred to as Phrygian, despite the voice-​leading embellishing ♭2 ̂→1̂ rather than ♭6̂→5̂ (the latter could provide double impetus for discharge were it not for the resulting perfect parallel fifths). This D ♭→C cadence has a clear Neapolitan role. We generally hear the Neapolitan chord as S-​f unctioned: The Subdominant meaning of ♭2̂ is traditionally expressed in the Neapolitan chord, where it is functionally attached to 6.̂ This link is especially clear in late nineteenth-​ century music, where the Neapolitan and other ♭2̂-​t ype chords discharge as frequently to Tonic as they do to Dominant, their traditional destination. (Harrison 1994, 116)

18  T  Desire in Chromatic Harmony The chord, as Harrison confirms, moves to T just as frequently, suggesting a behavior as tritone substitute for the D. With added seventh it shares the tritone pitches with the chord it stands in for. This demonstrates the significance of a root that can mobilize the inner pitches. From his second book of preludes, Debussy’s La terrasse des audiences du clair de lune uses the cadential progression G→F♯ (figure 1.10), but with subtleties. First, once G is stabilized across the measure, the octave c ♯ s in the upper register remind us of the G’s tritone relative; this reminder, quite distinct from the main articulation of the chord, remains as a binding note while G →discharges into F♯ in the cadential gesture. Second, note how the new F♯ immediately switches to C (open fifths at least), moving upward in whole-​tone pianissimo sixteenth notes before returning to F♯ . Had the initial G triad been given a seventh or an augmented sixth (e ♯), it could have formed a German sixth, discharging fully into F♯ as S→D.27 The difference is contextual: a German sixth would more likely associate with the S-​f unction (as DP [dominant preparation]). As Charles Smith claims, “it is in fact these [augmented-​sixth] chords that so clearly proclaim the dominant function of their successors, since this particular succession of sonorities directly defines the second chord as a dominant” (1986, 97). S is to D as D is to T. A syntax of rhythm, meter, and phrasing defines and fixes function for us.

Figure 1.10.  Debussy, La terrasse des audiences du clair de lune, Preludes, Book II

 

A Linguistic Theory  T  19

Tritone substitution is common in Bartók. Another example from Duke Bluebeard’s Castle acts as a fine twentieth-​century parody of Rameau’s favored ii7–​V7–​I progression, with the final I posited via a D→T✦ cadence (see figure 1.11). The unusual configuration of the Dm7 chord—​Rameau’s sixte ajoutée—​resolves to a viio, which functions ostensibly as D in C. Chord viio’s robust octave bass bs resolve downward by a fourth to F♯ , retroactively inviting interpretation of the viio rather as D in F♯ , the tritone resolution of the b-​f pitches acting as C ♯7 rather than the initially more predictable G7. This progression is weakened by the overriding melodic action, which repeats the characteristically Bluebeardian open-​fifth (d/​a) sigh that forcefully locks us into the broader tonality of D, however much these other harmonic discharge possibilities bubble beneath the surface. In the same scene, a G ♭ triad (with a suspended c descending to b ♭ in the upper line of the orchestral reduction) moves to Dm before climaxing on a C ♯m (figure 1.12). The C ♯m with major-​seventh possesses a b ♯ , which serves as a Tristanesque, nonresolving appoggiatura until Judith resolves her c ♮ upward to the minor third (e) of C ♯ two measures later. Although Bartók moves with parallel bass fifths, the D✦→T cadence in C ♯ utilizes the seventh (c) of the D✦ to spill over

Figure 1.11.  Bartók, Duke Bluebeard’s Castle, §4

Figure 1.12.  Bartók, Duke Bluebeard’s Castle, §17+2

20  T  Desire in Chromatic Harmony from the previous measure to retain the dissonant appoggiatura and “Romanticize” the voice leading.28 Tritone substitution undoubtedly works best when (1)  the D function is presented with its seventh to divulge the tritone of two keys and (2) the fifth of the chord is diminished to produce a symmetrical French-​ sixth chord, which replicates its pc content at T6. Note how this progression from Berg’s Vier Lieder, Op.  2 No. 2 (figure 1.13) contains a descending semitone sequence of French-​ sixth chords that produces a hidden circle of fifths owing to the identical pc content of each chord with its tritone-​ related partner.29 Obviously the interpretation of each chord hinges mainly on the bass pitches that give direction—​as we find with the →discharging E ♭–​A ♭–​D ♭–​G ♭ progression. But the fact that the tritone pitches of each chord discharge their tensions in textbook fashion allows us to hear each chord as a potential local D function. Through substitution, descending chromatic lines lend themselves effectively to diatonic discharge, especially when the line is undergirded with chords that bend our ears toward diatonic linchpins. Riemann claimed that “the ear always inclines toward understanding diatonic progression in the place of chromatic progression” (1890, 38; trans. Kopp 2002, 81–​82). A  simple progression from Riemann’s Systematik der Harmonieschritte, C–​B7–​G7–​C, can be regarded as

Figure 1.13.  Berg, Vier Lieder, Op. 2 No. 2, mm. 14–​18

 

A Linguistic Theory  T  21

T→S→D→T if the tritone substitute S✦ from F operates as B (Riemann 2011, 374). Similarly, at the opening of figure 1.14, from Die Walküre, while Wotan describes the deep sleep that Brünnhilde will fall into, a substitutionally descending diatonic functional rotation preempts the lulling to sleep, first moving from local C as T through S✦and D↑.30 Sustained melodic pitches can lead to imaginative “metaphorical” reharmonization, which is where substitutes come alive, particularly D✦ substitutes. Kurth (1991, 102) cites a passage from Tristan, Act 1, scene 2 (figure 1.15), with C’s “subdominant excursion” into A ♭ rather than F. The excursion from C then swings around to its own D✦, D ♭. The D ♭ then, rather than discharging, refocuses on G7 as a French sixth. We may be inclined to interpret the D ♭7–​G7–​C ̂ 5̂ discharge occurs between D ♭ and G7 before as S→D→T, but the fact that no ♭6–​ they move to C would incline me instead toward a single D✦→T interpretation. Whether we are discussing ♭II→I or ♭VI→V we are talking about the same relative distance between chords, and at some level they can be conceived as functionally relative. In the case of the latter, Harrison comments that “the idea that augmented-​ sixth chords progress to dominants and not to tonics is deeply entrenched” (1995, 178). The augmented-​sixth chords (which Kopp functionally characterizes as ♭VI triads) have, since Gottfried Weber, been regarded as S (tritone substitutes for the double emploi). Chords with an augmented sixth, for Harrison, certainly have

Figure 1.14.  Wagner, Die Walküre, Act 3, scene 3

Figure 1.15.  Wagner, Tristan und Isolde, Act I, scene 2

22  T  Desire in Chromatic Harmony “raw tonal energies” (172), and there is an effective tritone substitution in operation, either at the level of the S✦ or the D✦.

Authentic Cadence 4: The Romantic Dominant Cadence (D↓→T) Earning its sobriquet simply because Lendvai reads the major-​t hird descent as a Romantic topic, the Romantic dominant cadence relies on the relationship between parallel tonics and offers a minor deceptive cadence: Where one might expect Am to follow E7, a surprising C major appears. Commentators on this discharge progression are quick to mention its power as a D→T substitute. Riemann’s own Methode der Harmonielehre (1880) refers to his schlichter Terzschritt, which “has cadential force if it occurs going back to the tonic (i.e. C–​E–​C)” (Riemann 2011, 368). This may be justified by the double leading tone discharge (S and D) of ♭6̂–​5̂ and 7̂–​8.̂ 31 David Kopp is more explicit still: This type of chromatic mediant relation by descending major third is arguably the strongest, most natural-​sounding of the four chromatic mediant types, since it alone contains a leading-​tone progression to the goal chord. It also preserves the tonic of the first chord as common tone into the second. These two attributes, which it shares with the dominant-​tonic relation, give this mediant progression its particular cadential quality. (2011, 403)

The idea of common-​tone progression is significant to the present theory: In G–​ C, the root becomes the fifth; in E–​C the root becomes the third (figure 1.16). This particular progression originates in Riemann’s own work, with Riemann claiming in Systematik Der Harmonieschritte—​section 38 of his Skizze—​t hat the Gegenterzschritt “is likewise directly intelligible and has cadential force when occurring in reverse (a plagal cadence, like the fall back from the Gegenquintklang to tonic.” Thus A ♭–​C is plagal (S←T), while E–​C is authentic (D→T) (2011, 368). These chords are presented in the curious example from which Cohn’s Audacious Euphony (2012) derives its name (figure. 1.17). Avo Sõmer, exploring Debussy,

Figure 1.16.  Romantic dominant cadence

Figure 1.17.  Riemann’s audaciously euphonious progression

 

A Linguistic Theory  T  23

cites this same passage of the “Tonalität” entry from Riemann’s Musik-​Lexikon of 1882, observing: It provides an important late-​nineteenth-​century admission that a tonic preceded or surrounded only by chromatic mediant or submediant chords may still create a coherent tonal structure. In effect, Riemann claims that the elaboration of a tonal focus through chromatic third-​relations is a viable premise within “the compositional logic” of “the new theory of harmony” of his day. (1995, 218)

Although Sõmer finds it “bizarre for omitting the dominant” (218), we might still hear the dominant (G)  substitute by its T3-​relative (E), the leading tone b containing the most potent drive upward. The consonant bass leap of a fifth is replaced by the other function-​confirming jump: the third. The leading tone b rises to c smoothly enough, but the surprise of this cadence is that the g♯ comes close to what Cohn would call a “double-​agent” (2012, 72), resolving downward, disclosing its real identity to be a ♭ . Of course, the previous A ♭ triad would also substitute for the S function (almost in the same way an augmented-​sixth chord would), the lower a ♭ propelling a pseudo-​ Phrygian progression—​ t hus this sequence reads: T→S↑ (→T)→D↓→T. This is not so very different from Alexander Rehding’s interpretation as T→oSP→T→(D)[TP]→T (2011b, 112), an analysis that teases out the implications of Riemann’s own text. Hyer reminds us that “T–​S –​T–​ D–​T ” was called “die groβe Cadenz” (the great cadence) because it offers two cadences in one—​ a plagal and an authentic—​ t hough Riemann tended to eliminate the central zone, making a simple T→S→D→T, which became Riemann’s privileged syntax (Hyer 2011, 99). It is obvious that, though this theory proposes functional substitution, substitutes cannot hold the strength of the primary function, except in particular circumstances (ii⁶₄–​V–​I, for example). A simple ditty that ended on T✦ could not be considered as satisfying as T. However, with the definitions of function outlined above, the same discharge of functional tension can still occur; the tritone pitches b/​f still discharge in a cadential G7–​F♯ , but substitution is never the same as the original.

A New Monism? Metaphoric Functions and Neo-​Riemannian Discourse: A Theory of Chromatic Root Motion Riemann would have disliked many aspects of my project (except perhaps insofar as his ego may have been appeased to know that he was lionized after more than a century) principally because he would not approve of the flexible way I approach his dualistic predisposition, collapsing his dualism into a new type of monism. While minor harmony was symmetrical in his understanding (C, inverted about c, gives Fm), based on 5̂ in minor being regarded as the center of the mode32, my view of Funktionstheorie replaces this with a parallel symbiosis (C major /​C minor). I maintain, however, certain of his sharply defined tendencies. Dualistic, Riemann himself fudged monistic parsing into his Funktionstheorie, to the

24  T  Desire in Chromatic Harmony chagrin of the Dutch theorist Ary Belifante, by maintaining T, S, D parallel variants in the minor as oT, oS and oD (e.g., if C major is T, then C minor is oT).33 When Johannes Schreyer produced a monistic version of Riemann’s Klangschlüssel, Riemann claimed to hold “no esteem for attempts at mediation such as” his (Holtmeier 2011, 4). Other monist versions of Riemannian theory from Belifante and Hermann Grabner suffered similar fates. Despite Riemann’s protestations, Ludwig Holtmeier has claimed that “[w]‌ith the introduction of function symbols, the entire system of dualistic progressions and, alongside it, the dualistic understanding of cadential progressions became defunct, even during Riemann’s lifetime” (7). This paved the way for renewed monist thinking. My monist approach may seem all the more clunky at this stage for being based on a root theory that, at present, reduces triads, seventh chords, and all chromatic varieties into a theory of a primary triadic scale degree. Even with standard seventh chords, this can be problematic, as Harrison explains: “Many theorists acknowledge problems in ascribing roots to both the diminished-​ seventh chord and the augmented-​sixth chords” (1995, 171). My rationale at this stage is that theories of the neo-​R iemannian geometries do not integrate triads and tetrads happily into the same system,34 and the first stage of attempting this is to examine the flow of roots. This follows the practice of Riemann, who saw G7–​C and G–​C as D→T (although G–​C could obviously also imply T→S if beginning a phrase). Extended chord complexes will be reintegrated more subtly into the system in subsequent chapters, where I will show both on the same grid, with different coding. My roots are also distinct from Harrison’s “bases,” which relate to the root of a function—​say, c, f, or g—​pertaining to an established T. Despite the first page of Riemann’s introduction to Vereinfachte Harmonielehre, stating, “Chord successions arise from simultaneous melodic motion of several parts” (1893, 1), for me the chromatic fluctuations cannot be felt tonally unless we impute a fundamental bass to the mutable chordal implications. Where ambiguity arises, my Funktionstheorie makes analytical decisions but tries to be true to the ambiguous moment, particularly with my drive theory of Chapter 4. For example, in the fifth movement of Mahler’s second symphony (§46–​47), Harrison (1994, 203) interprets an upper d of a C9 chord after the E ♭ tonic arrival as a D-​f unctioned pitch (which it is), but the root of the whole chord—​c—​sounds much stronger to me, so I  might interpret it as part of a T↓ chord (R-​transformation), while acknowledging the D implications of the individual pitch at a different level.35 Harrison’s justification might be that “the relationship of aurally salient scale degree to Tonic overrides its relationship to the individual chords of the passage” (47), but this still plays into a pseudo-​Schenkerian theory of levels, which will eventually enter my system—​a system that, while unashamedly monist, benefits from the subtle excursions into the great insights into dualism made by others. This kind of thinking marks one of the rudimentary differences between harmonic theory and philosophical thinking, in which latter monism-​dualism refers to the matter-​spirit (material-​ideal) dichotomy. The Freudian unconscious would be a monist machine, as would the Deleuzian ontology, but Lacanian logic would be dualist, capturing the linguistic reductive grammar of harmonic

 

A Linguistic Theory  T  25

progression in a dialogue between the Real and the Imaginary (or perhaps the Symbolic). In this philosophical sense, our present theory of functions is dualist, as is the forthcoming project of Chapter 4, which attempts to capture the material drives beneath these ideal functions.

“Metaphoric” Function and Transformation: Riemann versus Riemann We soon move toward a consideration of the other Lacanian axis—​metonymy—​ but we must acknowledge that it is already here: It is needed in order to create the space in which metaphor can be articulated (and vice versa). Moving closer to the temporal axis of metonymy, in which chords are connected in a chain, we should take a moment to consider the changes of metaphoric function that occur within the common transformational operations of “neo-​R iemannian” theory and its extensions, assessing their compatibility with the present theory of root functions and their articulation through discharge. Henry Klumpenhouwer is one who has objected to the integration of Riemannian Funktionstheorie and neo-​R iemannian transformational theory. As Engebretsen reminds us, Klumpenhouwer specifically objected to Lewin’s and Hyer’s mixture of dual transformations, such as the parallel, relative and Leittonwechsel transformations (transformations whose effect depends upon the quality of the triad to which they are applied), with transformations based on nondualist, fundamental-​ bass relationships, such as the dominant and subdominant transformations (transformations whose effect remains constant regardless of triad quality), noting that their combinations often yield somewhat counterintuitive results. (2011, 353)

The functional aspect of T, S, and D works on a different plane than the common group of transformations found by Cohn, Hyer, and others, but this is not to say that one supersedes the other. The difference resembles the difference between the neo-​R iemannian RL progression (which, when applied to a major triad, would take C to F) and the “non-​R iemannian” (Hook 2002, 60) D transformation (which also takes C to F): They both may arrive at the same chords, but the former arrives by parsimonious voice leading (affecting two mode changes en route), the latter by straightforward root motion.36 The coexistence of the two ways of thinking is crucial as I  survey common neo-​ R iemannian progressions, establishing their working relationship with my Funktionstheorie.37 First Principles. Of the various transformations that neo-​R iemannian theory has yielded, the P, R, and L are the most deeply engrained. Of these, P registers the emergence of a qualitative parallel modal change (i.e., C major to C minor or vice versa) without any change in function (and note the difference here from Riemann’s “Parallele,” which referred to what we now call “relative”); R similarly transforms a chord into its closest relative without functional compromise (i.e., C to A minor or vice versa). Combinations of R and P can transform C into A, E ♭ ,

26  T  Desire in Chromatic Harmony

and F♯ , thus registering their functional synonymy to produce a static octatonic collection arrayed as individual triads. Each major chord changes into its parallel minor (P), and each minor chord becomes its relative major (R). The PR series wends its way back to the point of origin in eight moves (figure 1.18). While P, like L, is very parsimonious and requires a single semitone adjustment, R requires two chromatic alterations. However, in the libidinally charged, dominant-​ seventh-​based repertoire of the present book, we might remember that ii7 contains both ii and IV, making them capable of functional fusion:  This is the double emploi that Rameau heard even in bare triadic progressions such as IV–​V. In Lendvai’s construction, because all these chords are tied together by a parallel or relative relationship, they have the same function. Thus, it is not the quantity of transformational operations that determines functionality, but their quality. The relatively static P and R preserve and produce this single octatonic family of pitches no matter how many times we apply these procedures (figure 1.19). That an octatonic family should store up functional energy (as Krumhansl suggests above) is supported by the realization that the V–​I →discharge is not possible in a single octatonic collection. This is because, although scale degrees 5̂ and 1̂ are common to any collection, the 2̂ and 7̂ needed for V–​I are absent: The leading tones (major and minor) of all common chords in an octatonic collection are missing. Diatonic discharge is not possible. Referring to my earlier definition of function (as a collection of chords that metaphorically interchange with each other without discharge), an octatonic collection is a closed functional unit. By contrast, L (Leittonwechsel), a crucial component of the hexatonic system, alters function, perhaps in the simplest way possible. This was not necessarily so for Riemann, for whom Leittonwechselklänge (notated T