Musical Motives. A Theory and method for Analysing shape in music 2020025132, 2020025133, 9780197526026, 9780197526057, 9780197526033, 9780197526040

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Musical Motives

Musical Motives A Theory and Method for Analyzing Shape in Music B R E N T AU E R BAC H

1

3 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 2021 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: Auerbach, Brent, author. Title: Musical motives : a theory and method for analyzing shape in music / Brent Auerbach. Description: [1.] | New York : Oxford University Press, 2021. | Includes bibliographical references and index. Identifiers: LCCN 2020025132 (print) | LCCN 2020025133 (ebook) | ISBN 9780197526026 (hardback) | ISBN 9780197526057 (oso) | ISBN 9780197526033 (updf) | ISBN 9780197526040 (epub) Subjects: LCSH: Musical analysis. Classification: LCC MT90.A87 2020 (print) | LCC MT90 (ebook) | DDC 781.2—dc23 LC record available at https://lccn.loc.gov/2020025132 LC ebook record available at https://lccn.loc.gov/2020025133 DOI: 10.1093/​oso/​9780197526026/​001.0001 1 3 5 7 9 8 6 4 2 Printed by Integrated Books International, United States of America

To my wife, Meli, and my daughters, Isabel and Natalie, for their boundless love and support.

Contents Acknowledgments  About the Companion Website 

ix xi

PA RT I :   T H E G R O U N D S F O R A D I S C I P L I N E O F M O T I V IC A NA LYSI S  1. Introduction to Motives  Motives Play a Central Role in Music  How Motives Move and Move Us  “Musical Motives” 

3 3 10 20

2. A Brief History of Motives—​Composition  Motive as a Style Element of Music  Early Developments  Motives in Ascendance: Compositional Practice, c. 1750–​1900  More Recent Developments  Further Thoughts on Surveying Motives in Composition 

25 25 30 39 50 53

3. A History of Motives—​Theory and Analysis  Origins of the Musical Motive Concept, 1600–​1750  The Rise of Melodielehre, 1750–​1890  Schoenberg’s Conservative and Radical Conceptions of Motive  Unintended Legacy: A New Concept of Motive Develops in the Twentieth Century  An Account of Present-​Day Motivic Analytical Techniques  Summary: The Bridge to Part II, Methods of Motivic Analysis 

55 56 61 69 80 87 100

PA RT I I :   M E T HO D S O F M O T I V IC A NA LYSI S  4. A Universal Nomenclature for Pitch and Rhythm Motives  Rules for Labeling Pitch and Pitch-​Class Motives  Rules for Labeling Rhythmic Motives 

105 108 119

5. Basic Motivic Analysis  Principles of Reduction  Principles for Linking Motives  Assembling Analysis: Preliminary Narrative Strategies 

129 130 150 161

viii Contents

Interlude 1:  BMA Narrative Archetypes   The Role of Narrative in Motivic Analysis in General and Its Role in BMA in Particular  Theoretical Justification for Framing Motivic Analyses as Narratives  The Four BMA Narrative Archetypes 

165

6. Exemplars of Basic Motivic Analysis  A Pitch and Pitch-​Class BMA of Beethoven’s Op. 2, No. 1, Movement I  A Rhythmic BMA of Beethoven’s Op. 10, No. 1, Movement III 

183

Interlude 2:  CMA Narrative Archetypes  New Freedoms on the Focal Point’s Content and Location  Summary of BMA and CMA Narratives 

205 205 216

7. Complex Motivic Analysis  Introduction: A Rationale for CMA  Formalizing Complex Motives  Complex Motive Assembly  The Paired End Products of CMA: Organic Map and Narrative  Conclusion to the Methodology Area 

219 219 221 235 238 261

165 165 169

183 195

PA RT I I I :   A NA LYSE S A N D C O N C LU SIO N  8. Analysis of Three Works in Contrasting Styles  “L’Ondine,” Op. 101, by Cécile Chaminade  “Paranoid Android,” by Radiohead  “At the Ballet,” by Marvin Hamlisch 

267 267 276 296

9. Conclusion  Motivic Theory in Context  What Motives May and May Not Be  The Persistent Limitations and Future Promise of Motivic Analysis 

311 311 314 324

Notes  Bibliography  Index 

329 355 367

Acknowledgments I would like to first to acknowledge my dear friends and colleagues at the University of Massachusetts Amherst. This project could never have come to fruition without their support. To Gary Karpinski, Jason Hooper, and Chris White: thank you for all of your advice generously given about how to improve this work. I owe a special debt to Jason Hooper for his adept co-​mentoring and for sharing his impeccable research on nineteenth-​century conceptions of form and motive. I would like to thank Erinn Knyt and Roberta M. Marvin for their advice on navigating the publication and post submission process, and Chair Salvatore Macchia for graciously protecting my time in the critical last months leading up to manuscript submission. Laura Quilter, the Copyright and Information Policy Librarian on campus, deserves recognition for helping me to fully understand and to negotiate my publishing contract. Thanks go, last, to the graduate students in the Department of Music and Dance, who bravely volunteered to serve as test subjects for Musical Motives. Their feedback, both in and out of the classroom, proved invaluable for improving the book’s style and content. My sincere thanks go also to the Society for Music Theory for its generous assistance in the form of a subvention grant helping to cover permissions and indexing fees. I offer my gratitude as well to the Massachusetts Society of Professors and UMass’s College of Humanities and Fine Arts for their sustained and generous professional support in the form of travel grants and computer replacement funds. Further afield, I benefited greatly from the help of colleagues who saw and commented on early versions of this book. Thanks go to Rob Haskins, my good friend dating back to my Eastman days, for aid proofing the manuscript, and to Scott Murphy at the University of Kansas for his insights and ideas for correcting inconsistencies in the chapter on complex motivic analysis. Sincere thanks go as well to René Rusch and Brad Osborn for their helpful suggestions for carrying out research on Radiohead. In particular, I am grateful to Alan Street at the University of Kansas for his suggestions on broadening and strengthening the portions of the method concerning narrative. His expertise and research have not only impacted this project, but also will serve in perpetuity as resources in my research and pedagogy. My deep thanks go as well to Suzanne Ryan, former Editor in Chief in Humanities at Oxford University Press, for believing in this project and for expertly shepherding it through all but the very last stages of the publication

x Acknowledgments process. Her feedback and suggestions, simultaneously pithy and kind, provided the clearest guidelines imaginable for taking the next step forward through draft revisions. Thanks go, as well, to the capable, supportive staff at OUP—​to Sean Decker, in particular—​for their quick, informative, and good natured responses to every minute query I sent their way. Finally, I would like to acknowledge my loving, supportive family, for—​how else to put it?—​everything! To my parents, Lisa and Richard: thank you for setting me on the path for a life in music and for encouraging me at every step to continue its pursuit. To my other parents, Ada and José Matos: thank you for all you do to help keep my household happy and well fed, from emergency school bus service to regular, world-​class dining served at your home and delivered as take-​out. Last, I  thank my precious wife, Melissa, and children, Isabel and Natalie, for their love, good humor, and occasional interest in my work. Each of them amazes me, daily, for who they are and for their willingness to share this life with me.

About the Companion Website www.oup.com/​us/​musicalmotives Oxford has created a website to accompany Musical Motives:  A Theory and Method for Analyzing Shape in Music by Brent Auerbach. Supplementary musical examples are provided here. The reader is encouraged to consult this resource in conjunction with the chapters. Examples available online are indicated in the text with Oxford’s symbol  .

PART I

T HE GROU N DS F OR  A DISC IPL INE OF  MOT IV IC A NA LYSI S

1

Introduction to Motives Motives Play a Central Role in Music There are not many absolute truths that can be asserted about music, but here is one: all music moves.1 The physical embodiment of music, sound waves, causes particles in the air to vibrate. This in turn causes listeners’ eardrums and then their basilar membranes, brains, and bodies to do the same. That’s all well and good, most musicians might think, except that this first attempt at describing musical “motion” falls far short of capturing what music truly is. Music is not mere sound waves, although it may be best enjoyed when it actually hitches a ride on these invisible sails. (Even when it sounds purely in the realm of imagination, the inner ear, music remains essentially music.) It is a sound-​based art that communicates sensation, emotion, and energy; it impels us to feel, to dance, and to think. This awareness of what music is gives us cause to revise our original assertion. It is not just that all music moves, but that music moves us. We take this first point about music and movement as axiomatic. We next extend it with a claim that will ground this book: through exploring the mechanisms by which music moves and moves us, we stand to gain understanding about art and ourselves. Above, I summarized the path by which musical waves manifest in the body, but how does music pervade our senses and our consciousness? The answer is suggested by laws of perception known as Gestalt principles that describe how our brains involuntarily process stimuli, sonic and otherwise. For example, humans tend to group together pitches that share attributes such as frequency, timbre, and volume. (The well-​known “law of common fate” in the visual domain offers an example: a swarm of dots all moving together gives the impression of a larger, single entity in motion.) If we lacked this ability, the concept of melody would likely never have developed in any culture. In musical settings, we would be wholly unable to untangle the mass of sound waves arriving at our eardrums into coherent strands. There would be no way to distinguish between “more important” (solo) and “less important” (supporting) material. In listening to a rock band play, it would be impossible to tell which sounds were coming from the singer and which from the drums, bass, and guitars. Although scientists who study the brain hardly ever take for granted our reliance on the processes that render human-​intentioned sounds in the air into music, the rest of us usually do. Anyone who enjoys, plays, or simply “gets” music Musical Motives. Brent Auerbach, Oxford University Press. © Oxford University Press 2021. DOI: 10.1093/oso/9780197526026.003.0001.

4  Grounds for Motivic Analysis does so by grace of a grand illusion that transforms streams of particulate sensory data into coherent wholes. In the case of music, the standard bit of data is a note, which by itself does not communicate a whole lot of musical meaning. To confirm this, imagine the sound of a single, brief E4 played in the central register of the piano, as shown in Example 1.1.2 Now imagine your reaction to my declaration that you’ve just heard a whole piece of music. Pretend that this “Sonata in E” is being offered to the public with no ironic or metaphysical wink. You can assume that this pseudo-​micro-​ masterpiece is meant as music and not as some highfalutin’, aesthetic statement about music. In other words, it is not supposed to provoke any “big” questions like “What is the essence of a ‘piece’ of music?” Even so, you’d find this piece fatuous. A single note hardly constitutes even the barest musical idea. The piece is now newly expanded. In Example 1.2, the E4 is connected to a D and then a C, with all of the notes played briefly and in close register. This second effort is also not much of a piece, but it is at least recognizable as something. Something wonderful has happened in that three separate notes are forged into a coherent, descending, moving line.3 We have generated a recognizable musical shape in motion, our first example of a musical motive. Having broached the topic that will occupy our attention for the duration of this study, we are not yet ready to address the bigger question, “What is a motive?” We will postpone that activity to c­ hapters 2 and 3, where paired historical surveys of the concept will prepare and inform a comprehensive method for identifying, linking, and interpreting these shapes. A working definition will have to do for now. Our starting point will be the conception of motive put forward by Arnold Schoenberg (1874–​1951), the composer-​theorist whose writings and teachings were instrumental in establishing motivic analysis as a modern-​ day discipline. As Schoenberg worked on the manuscript meant to enshrine his Example 1.1  A single note, E4.

Example 1.2  The one-​note piece is extended to three notes.

Introduction to Motives  5 fully realized theory of music, he defined motive as “the smallest part of a piece or section of a piece that, despite change and repetition, is recognizable as present throughout” (1995, 169).4 The open-​ended character of Schoenberg’s definition, meant to render the term “motive” flexible and intuitive, may also be seen as impractically vague. Consulting his many writings, however, affords us with a set of more useful particulars. For instance, it is clear that for Schoenberg a motive is a small entity, typically shorter than a four-​measure phrase in common or triple time. A  motive’s identity may derive from any musical domain, including articulation, timbre, or harmony. Inclusion of this last area means that, for Schoenberg, a chord progression may serve as a motive, although that occurs less often in practice. In the vast majority of published analyses, including those by Schoenberg, motives are generally assumed to be melodic, monophonic, entities. To facilitate the present introduction to the concept, we will initially fall back on that assumption. In later chapters, this view will be broadened to allow for more complex, polyphonic motives that are more analytically rich. In a separate treatise, The Fundamentals of Musical Composition, Schoenberg explains that a melodic motive is encoded primarily by its “intervals and rhythms, combined to produce a memorable shape or contour which usually implies an inherent harmony” (1967, 8). Rhythmically, a gesture as small as a two-​note pickup figure may qualify. Similarly pitch-​wise, a bare two-​note configuration (a basic intervallic second, third, fourth, etc.) can serve as a motive in analysis. Often the domains of pitch and rhythm work together: the profile of the three note shape from Example 1.2 would be sharpened if, in a larger work, it always appeared in a characteristic rhythm such as q q h. But this does not always happen. In many instances, analysts will equate one set of pitches with another in the same piece, even when the gestures have no rhythm in common. The adagio excerpt by Mozart shown in Example 1.3 illustrates a case in which pitch motives act independently of rhythm. The first melodic gesture shown in brackets is a “neighbor” figure, C5–​D♭–​C, set in a dotted, siciliana rhythm. The shape is imitated in pitch and rhythm in the alto and tenor voices in mm. 2–​3. The pattern of descending entries suggests the bass should eventually have it, too, and so it does in mm. 5–​7. The characteristic rhythm disappears; however, the neighbor shape’s pitch-​intervallic connection remains strong and audible.5 By virtue of being set in more ponderous, dotted half notes, the neighbor motive figure seems to gain stature and importance. Even in cases where this kind of patterning is absent, an open interval can sound striking enough to suggest itself as an important span to be explored. In Haydn’s Piano Sonata 31 in E, Hob. XVI: 31 I, shown in Example 1.4, the first melodic gesture heard is given by the left hand. It is the intervallic fifth, E4-​B.

6  Grounds for Motivic Analysis Example 1.3  Neighbor (N) motives in Mozart’s Piano Sonata in F, K. 280 (II), mm.  1–​8.

Example 1.4  Opening of Haydn’s Piano Sonata in E, Hob.XVI: 31 (I).

The melody takes longer to move from its first high B5, but as it does it traverses the same letter-​note span in reverse, B down to E. The two zones of activity, both fifths, echo each other. It is worthwhile to mine Schoenberg’s writings for technical guidance in how to treat motives. That task will in fact be the focus of major portions of a later chapter. Yet at the same time that we strive to read between the lines of Schoenberg’s definition to discern more and less “correct” methods, we should keep another approach in mind. To wit, we should embrace the notion that Schoenberg’s imprecise mode of communication, in its own ideal way, conveys valuable information. It may not directly answer the question “What does a motive look like?”; however, it squarely addresses an equally important concern, “What is the essence

Introduction to Motives  7 of motive?” Here we may expressly link the words “recognizable” and “memorable” from our previous Schoenberg quotations. The two terms are functionally equivalent. Memorability emerges as the essential measure of music’s “unity, relationship, coherence, logic, comprehensibility, and fluency” (Schoenberg 1967, 8). Memorability, it turns out, is everything for Schoenberg. It is easy to test whether a motive within a piece is memorable. The process is personal, intuitive, and efficient, and even today remains the primary means for determining which figures in a work qualify as motivic. As a practical matter, the memorability requirement allows us to derive a working set of subrequirements. A motive must •​ be short enough to fit in memory •​ be distinct enough from its surroundings to be perceived as a whole, and •​ exhibit sufficient character to compel listeners’ attention. There is a further advantage in acknowledging the role of memory. Doing so prioritizes subjectivity and musicianship in analysis, accurately reflecting the fact that all listeners will hear or remember a piece in different ways. Schoenberg’s conception of motive has proved itself sufficiently sturdy, having remained largely in effect for almost a century now. Nonetheless, it could do with some fortification; an update is well past due. Though academics and performers of all stripes to this day routinely work with motives, these entities often serve an auxiliary function in their analyses. Few scholars at present seek to analyze the motivic content of a piece, in and of itself. Instead their primary goal is usually to examine a work’s form, harmony, counterpoint, and/​or narrative. Motivic connections, when noted at all, usually are mentioned in asides or footnotes. Where motives play this kind of supporting role in analysis, authors have two reasons for pointing them out. One is to bolster evidence for conclusions already reached by other means. Often, it seems that the more complicated and technical the primary method is, the more pressing the need to defend it in terms of an audible motivic connection. Another reason authors turn to motivic analysis is to demonstrate their cleverness. Even where a motivic relationship is not central to the primary analytic argument, an author will usually mention it anyway. The temptation to exhibit her credentials as an analyst possessed of deep musicality and ingenuity is too strong to pass up. As we shall soon see, music is oversaturated by motives. This condition is a boon, artistically. Most composers think in motivic terms as they write. Consciously or not, they begin by designing a set of shapes and then take inspiration in deciding how to deploy them from one passage to the next. When listeners later partake of their creations, the underlying unity of motivic content within registers as coherence, with all ideas seeming to connect logically.

8  Grounds for Motivic Analysis Concurrently, the overabundance of motives in music causes problems, analytically. This condition, together with the flexibility of Schoenberg’s “memorability” clause, means it is usually possible to assert some kind of motivic connection between any two events in a work, no matter how dissimilar. It also means that motivic analysis can yield irrelevant, nonsensical results when carried out without sufficient training or care. Example 1.5 from Sharpe 1983, shows how one could begin with the E♭ minor theme from Beethoven’s Sonata in C minor (Pathétique), movement I, and gradually transform it into the theme from the Colonel Bogey March.6 Sharpe’s demonstration is designed to produce a laughable result; therefore, both it and its accompanying claim that “there is something wrong with a theory that allows” for such shenanigans may be set aside (Sharpe 1983, 279–​280). The goal of motivic analysis is not to impose far-​fetched readings on works. It is to clarify the nature of already-​intuited connections. As in all things musical, this requires a fair amount of analytic know-​how. Convincingly establishing a motivic connection between dissimilar shapes is difficult. An analyst must sense the underlying unity, seek an explanation for the similarity—​hidden correspondences in pitch, rhythm, contour, and so forth—​and effectively communicate the finding to the audience. The musical community has long regarded motivic analysis with ambivalence. Analysts have generally been unwilling to give up on a practice that yields rich and rewarding results, but at the same time they cannot help viewing it skeptically. One barrier to motivic analysis’s acceptance is the long-​standing awareness that few rules exist for identifying and associating motive forms, which amounts to saying that no proper theory of motivic analysis exists. The solution to this problem entails advancing a consistent set of rules for working with motives. Other barriers to acceptance are cultural in nature. In addition to the distrust held by many scholars and specialists about the viability of motivic analysis, there is the matter of the general low regard held for it by musicians of all types. One might guess that the problem stems from musicians not having had enough experience in working with motives. The situation is quite the opposite, in that motives and motivic analysis have become overexposed. Most performers and academics are aware that little shapes and rhythms recur throughout pieces, having sat before a score with an instructor or a colleague watching him draw circles around scads of seemingly insignificant pitch configurations. Charles Rosen, in a staged moment of doubt, fills two pages of an essay with a host of trite analytical findings to show “how easy motivic analysis can be.” He asserts that it can “be taught in five minutes to any student, [who] can produce term papers on motivic analysis while watching television or doing anything else that engages his mind while leaving his hands free” (Rosen 1994, 95). These are harsh words from Rosen, but his agenda is, fortunately, constructive. His aim is to rescue motives by reframing the questions we ask of them, namely: “What has the composer done to make us responsible for hearing these

Example 1.5  Abuse of analytic transformation technique (Sharpe 1983, 279–280). The numbers that appear in line (a), which indicate “order position,” track specific note shifts that occur in subsequent lines.

10  Grounds for Motivic Analysis relationships?” and “How else do these invariances enter into the experience of the work?” (1994, 97). Questions such as these take motives seriously by acknowledging their role in musical structure and by weaving them into the listening experience. The spirit of this book endeavor is closely aligned with Rosen’s. Instead of suggesting a single avenue toward elevating the status of motives, I will propose and proceed down many. I start with the premise that the concept of motive can be strengthened as new attributes are grafted on to it. The chapters and interludes that follow will carry out this task by introducing increasingly stringent definitions and rules. The first and perhaps most important step will occur in the philosophical realm, as Schoenberg’s classical definition is extended. My formulation, which embodies the musical truth declared at the outset, is as follows: Proposition 1: For a musical figure to earn motivic status it must not only be memorable, but must move and move us.

The two new requirements “to move” and “to move us” overlap to a large extent; however, as a thought experiment, it is useful to try and tease them apart. Let us think for a moment what it would mean to develop a comprehensive theory for explaining how musical particles are able first, to instantiate motion, and second, to provoke listeners’ emotions. Were that endeavor to succeed, it would not only cement the importance of motives; it would also establish them as the smallest possible elements that can be music. For anyone who wishes to truly understand music, it is hard to imagine a worthier set of structures to examine than the ones constituting its very essence.

How Motives Move and Move Us Our original E4-​D-​C shape from Example 1.2 will serve us one last time as we further explore how motives embody motion and musical meaning. The three pitch events occur successively and thus take time to traverse a distance: this fulfills the basic definition of motion. The shape, furthermore, stands in direct opposition to any single-​note utterance—​for example: just the E alone—​that by itself implies no continuation or direction. By extension, no piece can proceed forward except through the activity of motives.7 With regard to moving us, this is where the aforementioned Gestalt principles come into play. If listeners consciously engage the shape as it forms, then at the moment the final C sounds there will be a real sense that they have moved along with it. Physiologically speaking, each note heard is a note recreated, or “re-​performed” in the brain, immediately and internally.8

Introduction to Motives  11 Each listener traverses the same journey that the notes do and in the same time. That experience is universal. What remains individualized is the manner in which different listeners feel and conceptualize their journeys. Listener TM, a trained musician, might imagine herself inside the musical texture, thus experiencing a downward glide through space. Listener NM, a nonmusician less familiar with the up/​down metaphor of pitch, might regard the notes externally as moving toward or pulling away from him.9 If the E4-​D-​C gesture is played more rapidly, it becomes more likely that the two listeners will hear the tones fitting within one beat. The shape will still be experienced as motion, but perhaps in different ways. Listener TM now might feel the shape as a footfall in a purposeful stride forward, while NM may only be able to perceive it as a kind of energy that coils up and then is released. The mechanism just described can be represented by the following graphic: motive

motion

The arrow is double-​headed, allowing for implication to flow in both directions. The heads are of different sizes, though, to reflect the unequal logical status of the two claims. All motives suggest motion; however, motion in music is not created purely though motivic activity. The next link in the chain in the experience of hearing music is that connecting the sensation of motion with the experience of emotion. This slightly more complicated mechanism can be represented as follows: motive

motion

emotion

The close linguistic correspondence between the latter terms, “motion” and “emotion,” is hardly coincidental. One of English’s main words for denoting state of mind, “emotion,” derives its meaning from a reference to literal motion. The Oxford English Dictionary dates this usage to as early as 1330, when if something “moved the blood” it meant that it excited or stirred a passion. This connection invites us to speculate on a mechanism by which musical motives produce emotion. The motives of a piece, consciously attended to or not, are perceived as figures in motion. The listener’s mind hears these shapes while simultaneously re-​creating them. This produces a cascade of novel thoughts. The brain’s self-​awareness that it is thinking new things and traveling through virtual space—​and all this quite without effort!—​causes pleasurable sensations:  feelings of inspiration, joy, excitement, and so forth. This mental activity engenders secondary physiologic responses in the brain, where neurotransmitters are triggered and neurochemicals released, and in the body, where heart rate and vasodilation are impacted by hormonal signals.10 In the

12  Grounds for Motivic Analysis end it seems there is something to the Old English notion of “moving the blood” after all. This informal proof of the causative link between motive and emotion is perhaps unnecessary, but it remains valuable. Taking the time to consider the mechanism that links sound, mind, and body helps us to appreciate the primary role motives play in the musical experience. This, again, helps establish their legitimacy as objects of inquiry. We can only advance our argument so far, though, by speaking in terms of a single, abstract third-​motive (E-​D-​C) and idealized listeners. In the next stage of our philosophical excursion into the role of motives, we open the frame to include some concrete, real-​world examples. The discussion will move beyond the issue of what motives look like to consider how they interact. The typical textbook account of motives’ behavior conveys some accurate and useful information. Readers who consult introductory texts on musical form learn that motives may recur dozens or even hundreds of times throughout a piece, aiding the sense of flow in the music. Before all that repetition happens, motives typically combine early on to generate a piece’s larger primary melodies, otherwise known as its themes. This process is illustrated in Example 1.6, where an early theme from Sousa’s Liberty Bell march is shown to be made up of four motives. To facilitate analysis, each unique motive is given a label. For this purpose, analysts traditionally have used neutral symbols such as “Motive X” or “Motive alpha” or loosely descriptive names such as “Neighbor figure.” The analysis in Example 1.6 strives for greater precision in labeling by referring wherever possible to pitch interval content, namely 3rds (see pickup figure and mm. 3–​4), 4ths (mm. 3–​4), and 2nds/​stepwise motion (the neighbor shape in m. 1). By means of the brackets above and below the staff, the graphic further indicates how multiple motivic interpretations may arise. The clinical accounts given in musical dictionaries offer the bare and true facts about motives but illuminate little about their inner life. Our response will be to step back and take motives in with a fresh perspective. This endeavor has already begun, in fact, with our earlier etymological study of the word “motive.” It continues now with an illustration of additional roles played by motives that Example 1.6  Motives combine to form a theme in Sousa’s Liberty Bell, mm. 5–​8.

Example 1.7  The primary motive as a texture element in Beethoven’s Symphony No. 5 (I).

14  Grounds for Motivic Analysis is better demonstrated in a musical context. The setting will be an early passage from Beethoven’s Fifth Symphony, mm. 25–​48 (see Example 1.7). One important function that motives achieve through repetition is the forging of a coherent texture. The passage given in Example 1.7 is twenty-​four measures long, which means that, at Beethoven’s indicated tempo of Allegro con brio (m.m. h = 108), it will occupy a little more than thirteen seconds. In the context of the full movement lasting seven or so minutes, this amounts to a modest swath of canvas. Yet if we take time to fully contemplate it, playing it through in tempo in the mind, thirteen seconds comes to feel like a significant span of time. This sonic space is saturated by motive (see arrows). The original, iconic form of this motive shown in Example 1.8 is constituted in rhythm as three eighth notes followed by an elongated half note and in pitch as spanning a descending diatonic third.11 For the purposes of this discussion, the motive will be defined loosely, as a shape with the rhythmic profile of three-​ shorts-​ then-​ long (S-​ S-​ S-​ L), oriented as a pickup gesture with the contour profile of repeated-pitch-then-leap. Formulating the motive in this looser, generalized manner is tantamount to arguing that all of the shapes identified in Example 1.7 register as equivalent, even those that leap upward at the end. Counting up the incidences of the motive reveals that it occurs about twenty-​two times: that averages out to about once per measure and twice per second. More occurrences could be included in the tally if we relax the contour requirements further. A space that once was empty is now motivically embroidered, as in the manner of cloth tapestry or wallpaper.12 This is not an analogy made lightly: a vast body of evidence from art history attests to humans’ near-​universal desire to enliven blank expanses of visual space with patterns of small, repeating figures. Such figures, known as motifs—​the Example 1.8  The opening four-​measure idea of movement I consists of a single motive characterized by its pitch interval, rhythm, and contour.

Introduction to Motives  15 Example 1.9  (a) Inner court of the Mausoleum of Mulay Isma’il, Morocco (c. 1727). From Degeorge and Porter 2002, 79.

16  Grounds for Motivic Analysis Example 1.9 Continued (b) Pottery from Susa, Iran, c. 4000–​5000 b.c.e. (Janson’s History of Art 2007, 91).

cognate with our motive can hardly be missed—​appear in tile work from tenth-​ century mosques and tapestries from Europe’s Middle Ages (see Example 1.9(a)).13 They also frequently appear in the buildings, furniture, and fabrics associated with more ornate design styles, such as Beaux-​Arts and Art Deco. Example 1.9(b) shows a piece of early Iranian art dating from more than 5,000  years ago. The work is beautiful—​timelessly so. It points up a critical function of motive as a tool that connects two spheres of existence. The concrete world is invoked by the container’s subject matter, the animals it depicts. The plane of the abstract manifests by means of the decorative, highly artificial patterning. The vertical lines ringing the top segment are birds’ necks, and the thick curved and straight lines in the bottom half derive from the ram’s horns, legs, and body. The horizontal divider between them takes the form of a parade of hounds, whose elongated bodies create the impression of a gentle spiral. The stylized animals bind together the real and the abstract in a breathtaking synthesis that makes them seem both utterly familiar and impossibly alien.14

Introduction to Motives  17 Artists of all kinds have known since time immemorial that the zone lying between reality and abstract thought is where a kind of magic resides. The shapes that play about in this realm freely associate. Causality and connections may be strongly implied—​as when one object in a painting resonates with another—​but cannot be proven. Whole other levels of interaction are possible, too, as when shapes associate loosely with meanings. A set of lines or curves in a painting may assemble in viewers’ minds so as to remind them of an object or a human figure, especially if a title is given to nudge their perceptions. But even if viewers do not recognize a form from their daily lives, they will still assemble the smaller images into conglomerations that have their own local meanings and directed energies. A potent description of this instinctive, energetic process is given by Christopher Alexander in his treatise on visual patterning, The Nature of Order (2002). In the series of graphics shown in Example 1.10, for example, he shows how every individual element added to a sheet of blank paper generates a field of Example 1.10  Five-​stage illustration of the visual fields created when a single dot is placed on a piece of paper (from Alexander 2002, 81–​82; numbers and arrows mine).

18  Grounds for Motivic Analysis Example 1.11  Beethoven Symphony No. 5 (I). A singable melody emerges from the motivic interplay among voices at the surface.

energy and how, taken together, these fields merge in the mind to create a larger sense of wholeness. Alexander’s diagram models unconscious perception as a set of stepwise processes.15 The six images in the series describe the effects of placing a single dot on a piece of paper. It acquires power as soon as it appears, dividing the visual field into zones and radiating energy as a focal point. To apply this notion to music, we will delve further into the phenomenon of motives joining to assemble themes. Example 1.11 centers on mm. 6–​10 of the same Beethoven symphony movement from before. The surface of the music, shown in the lower staff, acts as the source for the motives. In the upper staff, which “reduces” the busy surface by concentrating only on changes in pitch, we see how these separate four-​note shapes (dotted circles) assemble into an emergent, singable line. But wait: we can now be more precise. In this example, it is more accurate to say that the close succession of motives at the surface can be heard joining together to create the broader, singable line. This shift in wording, which assigns the listener an active role in perception, expands our conception of how motives work. Very quickly, even the most run-​of-​the-​mill motives such as the trivial E-​ D-​C introduced earlier, acquire new life. They remind us less of dull, nondescript puzzle pieces and more of ceramic shards inscribed with glowing symbols. We move beyond the view that motives are simple building blocks; it is more proper to regard them as elements of expression, artifacts of musical thought. As for assigning a specific meaning to these motives, that is a complicated task. It is certainly true that a musical shape can accommodate literal, texted meaning, as in the case of song. In Schubert’s song “Erlkonig,” a recurring, high-​pitched semitone gesture conveys urgency, fear, and alarm by literally evoking the cry of a sick child calling out for help (Father! Father!). Similarly powerful text/​music associations are routinely explored in opera and film music, to the extent that certain note configurations can come to stand for characters or ideas even when they are not literally present onstage or onscreen.16 Importantly, for our purposes of studying Western music, we must

Introduction to Motives  19 clarify that emotional and dramatic meaning is also quite possible in music in the absence of any text.17 It may seem we have stumbled onto a conundrum: does musical meaning depend on the presence of a text or not? To avoid confusion, we will sidestep that minefield of intentions and instead assert a second proposition for motives that concerns meaning: Proposition 2: At the same time that motives are capable of communicating many kinds of meaning, at their base level they communicate essentially musical meaning.

I am claiming here that an inalienable purpose of motives is to communicate intentional musical relationships such as, “these notes follow from those” or “this pattern resonates with the one adjacent to it.” This is not to deny that motives carry a host of other meanings intended by the composer and inferred by listeners.18 We have to start somewhere, though, and so here we temporarily strip motives of subjective associations so as to concentrate on this more objective quality.19 The analyses created in the initial methodology chapters, specifically ­chapters 5 and 6, will manifest as networks of almost purely musical association (to the extent that is possible!). Only after the procedure for building these networks is established will we consider how to ​layer other associations, meanings, and stories back onto them. Proposition 2 may seem radical, but a short thought experiment will help to illustrate that it is not. I invite you to imagine hearing the start of a piece by Mozart in which one phrase presents a set of small, melodic shapes and the next repeats them. The first movement of any of his symphonies or overtures will do. Now, imagine further that you are an amateur listener who does not notice that there is any correspondence between the phrases. You may be enjoying this music vastly; I hope you are! If you are, though, you are doing so in a manner differently from how trained Classical musicians (Mozart included) do. Perhaps you appreciate the sheen of the violins in the recording, or the sweet harmonies of the chords. All this is wonderful, but does not change the fact that you are not understanding the language of this music. Anyone who is unaware of the tonal, formal, and gestural structure of such music, by definition, does not “speak” the language of the High Classical style. This extreme declaration is softened by some mitigating factors. First, the hypothetical “you” being addressed is not really meant to apply to you, the reader, or really anyone. All humans possess the ability to process musical shapes at least to some extent by virtue of the Gestalt principles mentioned earlier. Composers who consciously plant motives in their music, moreover, are not doing it to hide their musical intentions, but to make them clear. One reason of many that

20  Grounds for Motivic Analysis Beethoven repeats the same rhythm of three-​shorts-​and-​a-​long so often in his Fifth Symphony is that he wants the motive to accrue meaning and be memorable. Whenever Franz Liszt, Radiohead, and George Crumb write music, they employ repetition to achieve the same end. Second, there is no “right way” to prove that you are hearing motives in the music. You can demonstrate your motivic literacy by successfully singing a verse of a song from memory. You are entitled to full credit even if you forget some of the words at times and lapse into half-​singing on nonsense syllables. The point is that if there are motives in the music and you can accurately reproduce them by whatever means, that signals that you are aware of them. All this is to say that a person’s knowledge of motivic content need not be explicit. Most people who know instinctively what motives are can’t define them even informally or identify them. Surely that is a technicality that means little. Think about all the fluent speakers of English who, despite consistently demonstrating the ability to construct a proper noun clause, would be unable to identify the one that I am just now insinuating into this sentence. Passing grammar exams does not make one a good speaker. Likewise, the ability to define and list motives does not make one a good listener and/​or musician. It is one’s primary, unthinking ability to speak a language that defines competence and fluency in it. And yet, schools continue to require their students to study grammar. They do so because upper-​level skills in reading and analyzing a language serve as important tools for raising one’s level of expertise. No matter what a person’s current level of fluency with a language is, an increased knowledge of its grammar will make them more qualified to describe, teach, and control it.

“Musical Motives” This book’s title is a play on words. At the most basic level, the term “motive” has a mundane, technical meaning. It refers to literal note configurations that recur in pieces. As this introduction has indicated, the goal of this study is to further both our technical proficiency with and philosophical understanding of these elemental musical objects. On the former front, this will require a lot of theoretical groundwork. New definitions will be developed to account for the many kinds of content motives may contain: intervallic, rhythmic, harmonic, and so forth. As part of that process, I will propose a universal nomenclature system for motives. I will offer, in addition, a set of strict procedural rules for extracting motives from a busy musical texture (reduction) and for judging which shapes may be linked in a logical, explanatory chain. Another reading of the book’s title turns on the common-​parlance meaning of “motive,” indicating “a need or desire, that causes a person to act.”20 The term

Introduction to Motives  21 “motive” is familiar to most from criminal court proceedings, where it refers to the reason(s) a defendant might have for committing a crime. In the theater, actors looking to fully inhabit their characters will often ask the director what their characters’ motivations are. The term “motive” readily applies to music making as well. One might assume that only composers, performers, and listeners can harbor musical motives. That viewpoint makes sense in that it reserves the capacity for thought and feeling to humans. How could it be otherwise? Can it ever be said that music itself harbors motives? With a little imagination and a willingness to skirt the metaphysical realm on our part, it turns out that it can. All it requires is projecting our thoughts about a piece of music outward from ourselves and onto it. This behavior may seem complicated, but for most it is as routine as any other act of personifying objects from daily life. We might say a tight lid on a jar is stubborn or that a car with a faulty transmission is complaining. Listeners to music similarly cannot help ascribing human characteristics to it, intention among them.21 The moment we embrace that kind of metaphorical thinking, a host of new players in the musical fabric pop up that all seem capable of emotion and desire. Musicians talking about their art often feel that tones “want” to move in certain ways; for example, a suspension tone that “seeks” downward resolution or the raised seventh step in a major scale that “leads to” tonic. Our impulse to personify phenomena such as music is more than a habit; it is hard-​wired behavior that arises out of our dependence on metaphor for comprehending the world around us.22 Just as we empathize with inanimate objects that are acted on by natural forces, we empathize with motives, the most recognizable objects in music. These entities can be likened to characters that are subject to musical forces such as tonal or registral gravity (e.g., melody’s tendency to descend over time). The changes a motive undergoes in successive appearances in direction, register, and tone will naturally suggest to many its desires and actions. In some cases, it may seem to flow along with the music, content in its setting, and in others it may seem to clash or strain against the elements in the accompanying texture. Following from the assumption that our culture bestows a sense of life to motive, the present study will dedicate considerable effort to investigate how motives convey drama and meaning. The analytic techniques laid out in Part II of the book will, among other things, offer recommendations for selecting both motivic main characters and plot archetypes in which to situate them. Potential storylines include journeys to a far-​off destinations and “struggles” against other motives or musical forces that result in triumph, failure, or synthesis. The extended sample analyses provided in c­ hapters 6–​8 will demonstrate how motivic narrative theory applies to the analysis of complete works.

22  Grounds for Motivic Analysis Just earlier, I called attention to the word “motive” as denoting the human desire to act, which caused the discussion to veer off to entertain the notion of personified music. In doing so, it skipped over another highly relevant type of musical motive, that being the practical impulse that underlies a musician’s decision to make or do music. A near-​infinite variety of motives explain why individuals choose to participate in musical culture. Some of these motives seem purer, such as a composer’s desire to craft something beautiful or a performer’s to communicate with an audience. Some seem more worldly, such as the desire for wealth, fame, or influence in public and/​or academic sectors. I would not presume to speak for anyone as to why they engage in musical activities and thought, but I feel it is appropriate to disclose some of my own musical motives. My primary aim is to revive discussion, and, if possible, faith in the discipline of motivic analysis. This is to be achieved by shoring up definitions and methods of analysis, then applying them to a large set of pieces in a variety of styles. The large-​scale analyses that result will be offered as one argument in the case for motivic analysis’s viability. Another argument for motives appeals to their near universality. Motives appear in most musics, and can thus be used to better understand those musics. Though I wish it could be otherwise, it will have to suffice for now to assert this point instead of proving it. It should also be made clear at the outset that discussion and analysis in this book will center on Western Classical music, the repertoire that originated the notion of motive and the one I know best. Readers, however, should feel free to apply these principles to any music they like, including world music (popular and classical) and jazz. The latter two analyses of ­chapter 8, which center on prominent works from rock and Broadway traditions, are intended as a light primer in this regard. With regard to my motives as an author, I will admit to a further ambition, which is that this work will expand the lay public’s awareness of music analysis. In earlier generations, a significant body of amateur musicians in Europe and America sought to read published analyses. They subscribed to trade journals such as The Musical Quarterly and tuned into radio talks such as those given by Arnold Schoenberg and Hans Keller. As the practice of creating and studying music migrated from the home into the college and conservatory classroom, theory and analysis became increasingly insular. The degree of specialization is so acute at present that most published music analyses are incomprehensible to all but the relative few who have undertaken graduate-​level training in music. The widespread reliance on expert-​level techniques such as Schenkerian and set-​ theory analysis has only accelerated that condition. In contrast to those methods, motivic analysis is more accessible to nonexperts. As such, this book is intended for the general public. Any individual with any amount of musical training can hear and work with motives at least

Introduction to Motives  23 at some level. To reach as many readers as possible, this text has been designed progressively. Early chapters discuss and analyze the simplest types of motive in the simplest environments. In later chapters, the scope of the discussion will expand. More attributes will be grafted on to motives (harmony, contrapuntal and multivoice content, coloristic features, etc.), and more advanced techniques for assembling results will be introduced. The most complex analyses have been written in a manner to ensure that all who can read music should be able to follow their arguments to some extent. This does not mean that novice readers will wish to read this book from cover to cover. There are large swaths of it that concern more purely scholarly issues, such as the entirety of ­chapter 3. Amateurs keen to get started with motivic analysis can skip that chapter, moving directly from the close of ­chapter 2 to the methodology section initiated at ­chapter 4. Academics interested in the history and theory of motive will likely want to engage it. By virtue of the other sections comprising historical and analytic research, Music Motives in its entirety is suited to a professional audience of music theorists, music historians, composers, and performers. The book may be read as a treatise on motivic theory and analytical technique. Owing to the instructional, step-​by-​step tone of many of the analyses, it may alternatively serve as a text for graduate seminars or advanced undergraduate courses in music analysis and/​or Western music history.

2

A Brief History of Motives​—​Composition Motive as a Style Element of Music Chapter 1 established motives as a primary concern of music analysis on the basis of their capacity to project motion, emotion, and unity. The first lines of argument supporting that point were couched in somewhat abstract, philosophical terms. Yet had we opted for a different approach for our first look at motives, for example, a chronologic musical survey, the same conclusion would be borne out. It is this: Proposition 3: Motives constitute one of the several generative forces in music.

The historical account presented in this chapter will support and elucidate this point. In that it spans several centuries, the survey will need to remain extremely general. It will also need to remain sensitive to the fact that artistic styles change. As they do, the sub-​elements that characterize them—​motives numbering among these—​fluctuate in prominence. The first task of this chapter will be to establish a context for discussing how the role of motives has changed over time. We take inspiration from Leonard Meyer, one of the preeminent style critics of the twentieth century. Meyer’s Music, the Arts and Ideas advances a model for understanding the life cycle of a style, musical or otherwise (Meyer 1967, 117–​121). The approximate time span for such a cycle is a generation, or roughly thirty to fifty years. Meyer tracks this evolution in terms of relative levels of “information,” meaning the number and sequence of musically meaningful events in pieces, e.g., melodic, harmonic, and rhythmic schemata.1 In Example 2.1, this trend is represented by the line studded with dots. A style’s early, pre-​classic phase is marked by a preponderance of highly formulaic content. This time period allows artists and audiences to gain familiarity with the few conventions that do exist; these stock formulas repeat extensively, which explains the presence in the example of the inverse curve showing “compositional redundancy.” Nearer toward the end of a style period, artists experiment with new options, introducing a great deal of novel content. The common, basic patterns from the decades before are hardly ever heard; more often, they are alluded to or presented in distorted form. The development of rock and Musical Motives. Brent Auerbach, Oxford University Press. © Oxford University Press 2021. DOI: 10.1093/oso/9780197526026.003.0002.

26  Grounds for Motivic Analysis roll music adheres to Meyer’s style theory. Early rock from the 1940s and 1950s (Rhythm and Blues), for example, is rife with twelve-​bar blues patterns and verse-​refrain structures. Progressive rock, a much later style that prevailed in the 1970s, retains these structures but exhibits far fewer stock harmonic and formal patterns that were standard in rock’s first period. In order to apply Meyer’s model to our own view of history, some adjustments are necessary. To streamline the appearance of his graph, we will strip out the lines showing “Compositional redundancy” and “Perceived information,” leaving only “Compositional information.” The next change is necessitated by our survey’s scope, which causes it to span multiple style periods. Meyer’s model for a single style must be extended beyond its present edges to account at left for a style’s prehistory, when it is nascent, and at right for its final passing, when it becomes obsolete. This change, illustrated in Example 2.2, recasts Meyer’s arctangent-​shaped line as a large, irregular arch. A further adjustment involves dissecting the concept of “style.” Meyer’s graph is monolithic and is meant to apply to style movements such as “Galant” or “post-​ modern composition” in their entirety. Such an examination, however, could

Example 2.1  Diagram of style development in Meyer 1967 tracking the inverse relation between information content and redundancy (118). Time Compositional redundancy: Perceived information Compositional information Preclassic

Classic

Mannerist

Example 2.2  Extension of the style development curve given in Example 2.1. (compositional information line only). Time Meyer’s Style Evolution (center zone)

Nascent

Preclassic

Classic

Mannerist

Obsolete

A Brief History of Motives—Composition  27 focus in on the specific musical traits that contribute to style, such as major/​ minor tonality, orchestral color effects, or “presence of a program.” This adjustment allows for a finer view of style by charting the interplay and fluctuation of these traits over time. In case it is not clear, we will soon characterize each of the familiar Western historical/​style periods—​Renaissance, Baroque, Classical, and so forth—​in terms of these constituent traits. But which ones should we rely on? We do not want any major period to lack too many essential traits, nor would we want it to appear as a caricature, reflecting the effects of a single trait. At the same time that we seek balance, we should not fear to proceed boldly. It is natural to worry that this approach will distort and oversimplify history. For those harboring such concerns, fear not, because it will. One consolation in this regard is to accept that the ship, Simplification, set sail ages ago, when society grew comfortable branding wide swaths of artistic history with “isms.” Another is that, by making a renewed effort to specify the content of each style, we are at least striving to appreciate each historical period in greater detail than a single umbrella term allows. To be relevant for the time span under consideration, the style traits we select should exhibit longevity and a certain kind of universality. The categories to be listed may be thought of as an abridged set of essentially “timeless” domains of Western music that have flourished for ages and are applicable for describing most pieces. (The list is far from comprehensive, of course, as rhythm is missing!) A  quick generalization about one such domain may help illustrate: “Counterpoint is a consciously controlled element of composition for most Western pieces.” Note well that this statement does not indicate that the rules of counterpoint are stable over time. Such regulations have the tendency to shift radically in each era. To accommodate such shifts, I allow for all of the style traits to be technically modified—​or even rejuvenated—​over time. For example, the idea of “Standard Form” is relevant for the years 1100–1400 and for 1730–1830, even though it was ballade and rondeaux forms that were prevalent in the former period and sonata and rondo forms in the latter. The traits contributing to style in this account are as follows:  Standard Form:  Abstract structural models that carry expectations about the number, arrangement, and kinds of subsections in a work. Standard formal schemes typically derive from song and dance traditions in both simple forms such as call and response, folk song, ballad, and verse-​refrain as well as in highly stylized forms such as ternary and sonata form. Harmony: A vocabulary that governs the content and ordering of simultaneous (“vertical”) pitch structures. Harmony is said to be “functional” when a syntax is in place that controls the ordering of sonorities, roughly

28  Grounds for Motivic Analysis akin to the way that a grammar functions in language to coordinate word order and proper sentence construction. Note: because harmony is built of more than one voice, this trait is interdependent with counterpoint. Counterpoint: Coordination of multiple voice lines in terms of (1) their general interaction (relative distance and direction) in pitch space, and (2) how they align at certain points to produce vertical sonorities. Note: following from point (2), counterpoint is interdependent with functional harmony.2 Program: Presence of a storyline or impression from “outside” the music that is realized in the form and/​or by local sonic events in the piece, often mimetic ones (e.g., a cymbal crash representing a lightning strike). Motive: Recurring gestures of pitch and/​or rhythm. This trait may coordinate with harmony and tonality, but is not required to. The diagram in Example 2.3 arranges these traits according to their relative influence on successive styles. The arrangement of style periods along the top line corresponds to the textbook version of music history. The vertical axis charts the relative degree of prominence for the traits. Placement in the lowest group indicates that a trait is present nascently, as a noticeable and localized phenomenon (e.g., motive in the medieval period); placement in the highest group means that a trait generally presents as a primary organizing force or premise of works (e.g., “song forms” for this same era.) Where multiple traits appear together in a group, I have made an attempt to approximate their increasing relative importance by listing them from bottom to top. Despite its appearance, Example 2.3 is not intended as a style chart, per se. It has been developed to allow us to observe the staggered bell-​curves of multiple traits, rising and falling like the curling stripes on a barber pole. For decades, a certain trait may be present as a minor element of music. At some point, it will rise in prominence until it comes to dominate the structure of the music, helping to define the aesthetic (artistic rules) of its age. We may take harmony as an example, which is tracked by the dashed line. This aspect of music was a concern for composers even in the Middle Ages; as such, it appears as a surface trait in the column designating the years 1100–​1400 C.E. It was not until the Classical period that chord progression at the small and large levels became a prime concern in the construction of musical works. In the first half of the twentieth century, harmony’s structural influence waned as composers relaxed rules of dissonance treatment and chordal syntax. Today, rules about chord order continue to exist in the genres of pop and rock music, modern Classical music, and film and TV music; however, they are far more irregular than in the Classical period’s heyday.

Example 2.3  Historical styles viewed in terms of the relative prominence of five basic traits. The arch exhibited by each (three drawn) peaks at a different time. A sixth trait, “process” is noted for two streams in the most recent time period.

30  Grounds for Motivic Analysis In place of offering judgment on the quality of any period’s music, we prefer the more neutral claim that harmony was once ascendant as a structural force in music and now it is not. To reflect this, the harmony designation is placed near the top of the columns spanning the years 1730–​1830 and 1830–​1910. In the twentieth century, harmony’s influence diminishes to the point where, more often than not, it serves more as an important, secondary element in music. Its trend line seems to break off near 1945, but only because it cannot connect to the three separate compositional streams posited for that time period.3 The arch showing the influence of program music (dotted line), is displaced rightward (meaning: chronologically) behind harmony. After centuries of gestation, where it only occasionally influenced the design of Renaissance and Baroque pieces, the idea that a musical work should represent stories, characters, and events gained prominence. The notion of program quickly rose to become a hallmark of Romanticism both in symphonies and character pieces and, indeed, remains a powerful force in many genres today. A similar arch shape traces the influence of motive across style periods; see the solid, bold line. Unlike program, however, motive retained much of its prominence into the twentieth century. The discussion to follow will trace this history in more detail through a series of brief analyses. These have a didactic purpose as well, which is to begin framing motives in more technical terms. The formal introduction of definitions and methods will not occur until ­chapter 4. By working through these preliminary analyses, however, readers will begin gaining exposure to the techniques of labeling, analysis, and interpretation that will occupy us for the duration of this study.

Early Developments The composition-​based historical survey of motives will officially start in the High Baroque era. Situating it here will cause the “prehistory,” as it were, of motive to largely go untreated. What I will say about the roughly 1,000 years leading up to the Baroque period is that motives are necessarily present in all major styles and genres. They play a significant role even in the monophonic genre of Gregorian chant, which dominates the compositional record from 600 to 1000. Listeners familiar with that genre will readily recognize certain recurring melodic patterns, among them linear third figures such as E-​D-​C and D-​E-​F, “neighbor” gestures such as F-​G-​F that decorate a note, and the commonly-​found stepwise “dip” below the final tone that occurs at closing moments. The stock pitch configurations of chant served to aid singers’ memories. They served a structural role, as well: Robert Hatten notes that each mode’s “characteristic motives” serve to “express the . . . distinctive features” of it (2015, 316).

A Brief History of Motives—Composition  31 For example, a signature gesture of chants written in Lydian mode is to initiate phrases with the notes F-​A-​C.4 To modern ears that sounds like arpeggiation of a major triad, where contemporary musicians would simply have heard it as emblematic of Lydian-​ness. That said, it is extremely difficult to speculate on the presence of other kinds of meanings, poetic and/​or emotional, encoded in chant motives. While we cannot rule out the possibility that individual musicians associated certain shapes with certain sentiments, history informs us that the idea of a specific motive encoding a specific emotion or meaning generally lay outside their conception of music. The phenomenon of recurring pitch and/​or rhythm shapes presents in all major genres appearing in Western composition from 1000 to 1600 C.E. They appear in organum pieces by Léonin and Pérotin (ca. 1160–​1240) in the form of two-​, three-​, and four-​beat melodic cells that are repeated and rapidly exchanged among the upper voices. Motives manifest in the song-​form pieces and motets that proliferated between 1200 and 1400 in the form both of “stock” cadences and melodic/​rhythmic patterns favored by individual composers. Motives figure prominently in pieces written during the long period of the Renaissance, as well. The composers of sacred music in this period, for instance, explored new ways of tying together the separate sections of their masses by initiating each with the same brief segment of music called the “motto.” A bit later, in the sixteenth century, Renaissance composers increasingly experimented with “word painting,” a technique of animating words by setting them to pitch shapes that match their sentiment. Common examples of this procedure include writing scalar ascents and descents to set texts about characters “climbing” or “falling” and deploying strident chromatic tones where the words mention physical or emotional pain. Identifying a few instances of motive within a six-​century span cannot support any strong conclusions about its role in the music of those eras. Doing so may nevertheless inform our broad view of how that role evolved. The way that isolated motivic events manifest in early music, like tips of ice jutting out from a broad span of ocean, suggests the presence of more massive structures (icebergs) below. The motivic content that lurks in the music of the medieval and Renaissance periods is worth exploring further. To do so properly, however, would require us to engage the other domains of music that motives are genetically tied up with, such as rhythm, melody, harmony, and counterpoint. (Because motives are literally composed of these elements, they cannot be understood wholly separate from them.) Given that the pace of style evolution in music was as rapid between 1000 and 1650 as it was in later centuries, that is not feasible here. It would necessitate discussing motive in tandem with medieval counterpoint, scratching that relationship to consider motive in tandem with modal harmony and Renaissance counterpoint, and then scratching all of that to consider it in tandem with the harmonic and contrapuntal practices of tonal composition.

32  Grounds for Motivic Analysis Our survey will formally begin in the early Common Practice era, meaning the time between 1600 and 1730. As the corresponding column in Example 2.3 indicates—​and as those familiar with Baroque music will attest—​this is an age in which motives were very much present at the surface of music. This time is marked also by the arrival of a new organizational force in music, known as “functional harmony.”5 In contrast to previous periods, when harmonic practice was concerned more with how the various voices of a texture are arranged vertically, seventeenth-​century harmony was marked by a new concern for how chords should succeed one another.6 The Baroque, in other words, is the first period that accommodates Roman numeral analysis, although some pieces and genres from the time period obviously fit this generalization better than others. Turning now to music, specifically pieces by Bach and Handel, we can observe two principles of motivic activity in the Baroque. Example 2.4. presents a theme from the beginning of a gigue by Bach. The structure of this theme reveals that, even at this time, motives are often designed to project a sense of harmony through chordal leaps. The first melodic gesture in the piece communicates a strong sense of F tonic harmony. Another remarkable feature of motives well established by the Baroque is that their initial form often suggests their later development. The strong sense of upward motion conveyed in m. 1, for instance, hints that more upward-​striving gestures will follow.7 To better engage those later developments, the motive in Example 2.4 will be named descriptively as a “climbing” idea composed of paired two-​note “arpeggiations.”8 It is here labeled Climb4’: the “4” superscript indicates that the motive is built of four tones. (If the C4 pickup were included, it would be Climb5, spanning an octave and a fourth.) The act of establishing parameters for a motive facilitates the search for other instances of it. We shall carry that task out now to determine where and how the music responds to the motive’s original impulse to climb. This occurs as more and more Arp2 fragments (small brackets) are added in a self-​chaining process. In mm. 14–​16, the alternating arpeggiations of F and C chords create a larger

Example 2.4  Upward Climb motive from Bach’s Fourth English Suite, Gigue, m. 1.

A Brief History of Motives—Composition  33 octave-​plus-​fifth span on seven successive beats. This Climb7 motive is shown in Example 2.5(a) by the line connecting F2 up to C4. A grander Climb9 rises in the bass voice in mm. 49–​51 spanning F2-​A4 (or further if the low C2 is included).9 This passage, shown in Example 2.5(b), occurs very near the work’s conclusion. Its presence there is doubly satisfying, as it raises the intensity of the music in the manner of a fireworks finale while also “fulfilling” the implied destiny of the original Climb idea. Our other example of motivic treatment in this period is the first movement of Handel’s Concerto Grosso, Op. 6, No. 1. The intelligibility of this stately instrumental work depends largely on listeners’ familiarity with tonal harmony. The piece would make sense, for example, even if played as a 34-​measure set of block chords. The slow pace here serves yet another artistic purpose. With activity scaled back in the harmonic realm, the music invites listeners to attend to other aspects of the work. I would list among these the dynamic and textural contrast of the full consort alternating with the solo violins and, of course, the development of the pitch and rhythmic motives.

Example 2.5  Extensions to the Gigue’s Climb motive. Brackets indicate Arp2 motives. (a) mm. 14–​16, Climb7 spans one and a half octaves.

(b) mm. 49–​51, Climb9 spans more than two octaves (climactic presentation).

34  Grounds for Motivic Analysis We begin with some preliminary impressions based on the opening passage printed in Example 2.6. In m. 1, the solo violins’ motion from D4 to G3 suggests linear fifth descent as a prominent motive. After repeating twice, the descending shape undergoes a change in m. 4 as it is stretched both in pitch and rhythm. The five-​note running gesture elongates to six tones (B5-​D), and the shape now takes up the full measure.

This well-​meaning account of mm. 1–​4 well encapsulates the analytic instinct to “read into” the audible shifts of content and character that motives routinely undergo. It is, unfortunately, inconsistent with the goal of establishing a rigorous motivic methodology. The two labels, “linear fifth” and “linear sixth” in the example broach the question of motivic identity (i.e., a motive’s essence). Analytically speaking, motives are notoriously slippery creatures. As tradition would have it, a motive may gradually be altered over the course of a piece with regard to its pitch and rhythmic content, its length in numbers of notes, and even its overall contour profile. This process produces a series of closely related motive forms. To effectively fit these forms into a single category, e.g., “Motive Z under all its transformations,” one must take care when establishing rules for inclusion. The requirements should be general enough to accommodate all the forms the analyst wants, but specific enough that the motive retains a distinct identity. Our preliminary view of this movement assumed that the first clear candidate shape in m. 1 would serve as the prototype for a motive category. This solution is workable, but we should be wary of any approach that prioritizes first impulses Example 2.6  An illusory motivic transformation in Handel’s Concerto Grosso, Op. 6, No. 1 (I), mm. 1–​4.

A Brief History of Motives—Composition  35 and heads off other viable interpretations. We need not blindly accept that the six-​note motive in m. 4 must be an enlargement of a central five-​note motive, when the longer one is just as likely to represent the primary shape. Let us think on whether a six-​note shape makes sense in the context of m. 1. I contend not only that it does, but also that adopting this new perspective prompts a new way to understand the music. In m. 1, we may now hear the downbeat G4 in the solo Violin I part connecting across the silence of the rests to the running notes. The next task is to define this motive in such a way that all of its surface variations are accounted for. The solution I propose is a “Cascade” motive (C), constituted as follows: “Cascade” (C) = any note + linear fifth descent

Under this definition, the two component elements must be attack adjacent: no pitch events may intercede. Importantly, no restrictions are made on how much time separates the solitary note from the fifth descent, nor on the size or direction of the pitch interval that separates them. Formatting the Cascade motive in this broad manner enriches the analysis as a multitude of candidate shapes spring into view. Every “C” shape annotated in the full score in Example 2.7 adheres to the stated requirements. This includes the later, more transformed appearances of the shape in the systems near the end of the movement. The C motive appearing in m. 21 is extended by a third (see beam). The forms of C in mm. 29–​30 and 32–​34 are even more obscured, to the extent that some may dispute them entirely. Yet consider the following:  any interpretation of the work’s conclusion attempted without access to Cascade’s late return would almost assuredly fixate on the final, dominant V6/​5 sonority in m. 34. On the harmonic basis alone, it is easy to say the end is “suspenseful.” Awareness of the Cascade shapes, however, enriches this interpretation. The music of mm. 28–​34 need no longer be viewed as a fantasia-​like transition to the second movement. At the same time as it points forward harmonically, the last passage rounds things out, motivically, by restoring the C motives heard at the outset in mm. 1–​6. This discovery of motivic symmetry provides new evidence to suggest that the movement can, to an extent, be regarded as a self-​contained piece. The analysis also charts the progress of an important secondary motive, designated “3rd” because of its characteristic pitch interval span. This smaller shape associates strongly with the two-​beat dotted rhythm of long-​short-​long (L-​S-​L), though it also sometimes occurs independently of it. The migration of this rhythmic gesture, R = L-​S-​L, in m. 6 from the ensemble into the solo Violin I is significant; it provides the first indication that the motives in this piece shift among the voices. The moment one develops the inkling of a musical motivation, meaning an idea that can ground a dramatic analysis, it is

36  Grounds for Motivic Analysis wise to pursue it. In this case, examining the motivic content of the solo lines versus that of the orchestra reveals a progression of events that form a coherent storyline. This narrative, the first of many to be discussed in this book, is structured in terms of a long-​range double migration, or material swap between the solo and group voices. The process, as represented by the graphic below, appears as a kind of invertible counterpoint cast in motivic terms:

Solo voices:

Cascade

Group voices: 3rd motive

3rd motive Cascade

Example 2.7  Score of the full movement of Handel’s Concerto Grosso, Op. 6, No. 1, (I), with annotations indicating the activity of Cascade (C), 3rd, and L-​S-​L rhythm motives.

A Brief History of Motives—Composition  37 Example 2.7 Continued

We next impose a dramatic reading onto the analysis to enhance its emotive content. In m. 6, a new rhythmic element, L-​S-​L, is injected into the previously C-​based solo violin material; this is indicated by the “R” arrow. This disruption causes a ripple in the melody. It derails the solo violins, which soon after abandon all explicit reference to the C motive. Beginning in m. 7, they explore a contrasting, lyrical idea. The purpose of the new, flowing figure is unclear until mm. 10–​11, where it culminates in a longer, upward-​striving version of the 3rd motive (see beamed notes). This motivic event is highlighted by the parallel thirds motion in the violins and the dramatic silence of the continuo. The annotated score shows that from this point, the solo voices increasingly concentrate on the linear third (in both ascending and descending forms) with its attendant L-​S-​L rhythm. The motivic 3rds attain their greatest prominence in mm. 16–​23. The material swap sketched by the crossed arrows above occurs in two parts. The “Solo voice” activity, which abandons C for 3rd motives, is initiated first and completed in mm. 19–​20. A high level of tension is felt there due to the concentration of 3rd motives and the high register. Some of that stress seems to derive from

38  Grounds for Motivic Analysis Example 2.7 Continued

harmony, specifically from a fully diminished viio7 of E minor chord. Remarkably, this chord can be understood to result from melodic motive activity: all of the linear 3rd shapes identified in the score in mm. 19–​20 express motions among D♯, F♯, A, and C, the notes of the viio7. Soon after the upper voices abandon the Cascading motive for the linear 3rd, in m. 21 the orchestra (“Group voices”) seizes on it, completing the exchange. The Cascade motive returns in full in measures 23 and 25. This analysis of the Concerto Grosso movement traced the development of two carefully delineated pitch-​based motives. By invoking basic pathways—​upward versus downward in pitch space, and migration between solo and orchestral forces in texture space—​we were able to generate musical narratives that can direct future intentional hearings of the piece. To this point, these narratives have been framed almost purely in musical terms. A myriad of other plot frameworks are available, however. At the moment that pieces begin supplying analysts with about this level of motivic complexity, a tipping point is reached. By virtue of our

A Brief History of Motives—Composition  39 instincts to project meaning into music, many of us begin to feel the urge to layer extra-​musical interpretations on top of these first-​level findings. Space does not permit a full consideration of how such a narrative could be engineered to fit this concerto movement. We can at least sketch how such a reading might go, taking our cue from the contrast in the C motive’s disposition across the piece.10 In mm. 1–​4, the Cascade motive’s descent manifests as sixteenth notes. By the end, though, the Cascade shape becomes diffuse, comprising longer, quarter-​note values that drift downward. (We earlier interpreted the return of the C shapes here as significant, but only from a formal standpoint). Taking inspiration from David Yearsley’s creative, historically informed reading of a chorale prelude by Handel’s contemporary, Bach, we could propose a metaphysical storyline wherein the initial, “bodily” version of the Cascade motive is in the end “transfigured,” dissolving into a vaguer, more spiritual form (2002, 1–​41). The first portion of this survey has touched on events from a wide swath of history, from the origins of polyphony to the dawn of tonality. In this account, the musical motive reached its first maturity in the Baroque, where it gained the ability to transform and to support large musico-​dramatic processes. Of course, this maturation did not occur everywhere at once. While Handel and Bach lived, many styles and modes of composition coexisted, each drawing on its own melodic, rhythmic, formal, and harmonic conventions. It is true that one may find a number of movements from the interior of Baroque concertos, oratorios, and partitas that exhibit a similar premise as the Handel work above, where a slower harmonic rhythm facilitates freer motivic development. On the whole, though, Baroque pieces like this are rare. This point is borne out when one recalls the vast number of contemporary works that exhibit (1) extremely rapid harmonic shifts, as in the manner of stylized dances, fantasias, and chorales, or (2) relatively little functional harmonic sensibility at all, such as fugues and ricercares drawing on stile antico tradition. It is safer to say that the Baroque era bore the first fruits of motivic composition from seeds that were planted long before. In other words, it would still be several generations before this mode of structuring music would become dominant.

Motives in Ascendance: Compositional Practice, c. 1750–​1900 Following the period in the Baroque in which motives first matured, Classical period composers elevated their profile. This development occurred in tandem with a trend toward increasingly “square” and formulaic composition, as typically found in the expository regions of works. I am referring specifically to balanced phrase structures—e.g., 4 + 4 and 8 + 8 formations anchored by half and full cadence patterns—​found in works by composers such as J.C. Bach, Galuppi, Haydn, and

40  Grounds for Motivic Analysis Example 2.8  Three primary motives from Mozart’s Symphony No. 25, (I).

Mozart.11 Another sign of style change is the new level of surface motivic saturation in Classical pieces, as exemplified in Mozart’s Symphony No. 25 in G minor from 1773. The score of the symphony’s first movement is excerpted in Example 2.9. The analysis of this work will center on the activity of the three motives stated near the work’s outset as given in Example 2.8. First there is the four-​note, zigzag shape that is stated in unison in mm. 1–​4. It is flexibly defined here as a “Leap+Leap” contour motive: the two-​note expressive intervals that constitute this shape are initially a descending fourth and a descending seventh, but they change size and direction in subsequent appearances. Next there is the energetic “five-​note arpeggio joined to ornamented third” motive, which first sounds in m. 5. The label given to this figure, Arp5⊕↓3rd/​turn, employs a special addition sign to indicate that the component shapes overlap by one note, B♭5. The last motive, most likely related to the second one by truncation, is the descending third figure in the horns and Violin I in m. 31 (“↓3rd”). In Example 2.9(a), we observe a trend in the first 24 measures of motive statements being literal and tightly packed. In comparing this to Handel’s from just earlier, one might say that the motivic treatment has grown heavy-​handed. But this comparison is glib. The surface repetition of motives in this later style increasingly serves to stretch out time. Classical phrases are not necessarily longer than Baroque phrases, but they often feel so because they unfold fewer harmonies. The surface motivic repetition creates interest at two levels. At the same time we coast on the longer tension/​resolution arcs in the harmonic sphere, we enjoy the brisk chop of a musical surface rippling with motives. The motives support a wide range of expressive moods. Where the quick succession of “Arp5⊕↓3rd turns” in mm. 5–​9 generates explosive energy, the long stretch of Leap+Leap motives in mm. 13–​24 creates more a feeling of suspense. In c­ hapter 1, I said that motives that repeat frequently at the surface serve to embroider musical space, implying that they act in some respect as “filler.” A bit of false logic might follow from this: have motives suffered a regression in the Classical age?

A Brief History of Motives—Composition  41 Example 2.9  Score of Mozart, Symphony No. 25, (I). (a) Th  e first part of the movement’s exposition, mm. 1–​16.

It is all well and good that they impart continuity and energy to the music, but if that is all they do, then they are functioning more as textural elements—​like the stamped patterns on wallpaper—​than as meaningful shapes that communicate through transformation. Here we should be careful. There is no reason to believe that composers of the late eighteenth century, while forging new musical syntaxes, would disregard advances in melodic technique pioneered by their forerunners.12 For this reason, we should not allow a work’s dizzying array of texture motives to blind us to the possibility that a subtler play of shapes lies beneath the surface. A spotlight examination of three transformations of the Leap+Leap motive in this movement will clarify this point. Over the course of four appearances across

42  Grounds for Motivic Analysis Example 2.9(b)  Measures 29–​44, in the second tonal area (STA).

the exposition and development, the transformations of Leap+Leap steer the music down novel paths of development. The motive appears plainly in mm. 1–​4, fulfilling the role of motto. It returns in mm. 13–​24, where it participates in the transition. Its intervals are fully preserved in mm. 13–​20; a two-​stage presentation of G5-​ D-​E♭-​F♯4 in whole notes prepares listeners for its upcoming transformation in mm. 21–​24. Next, it self-​perpetuates in a move toward the viio7 of D major in preparation for a half-​cadence (not shown). The first of the two Leaps inverts direction and is stretched to the octave, G4-​G5. The original, gestural outline of the motive remains clear, however. In its third incarnation in mm. 29–​36, the Leap+Leap shape is camouflaged. It undergirds the contrasting theme of the exposition by virtue of the large, two-​ measure leaps traded off between high and low voices (see Example 2.9(b)). The first of these leaps is the recently achieved upward octave. The latter leap is a seventh, now inverted upward as well and sounding in the horns. The presence of the Leap+Leap motive here promotes structural unity within the exposition. Even as the foreground of the music in mm. 29–​32 sounds a new theme—​a singable, snappy four-​measure bit in Violin I—​at a slightly higher level it retains the stately whole-​note pacing and large leaping intervals of the motto. In this way Mozart establishes a balance between new and old: the violin theme feels novel, but not so much that it feels at all out of place in this movement.13 In preparation for discussing Leap+Leap’s last appearance in the exposition, it is necessary to view it in terms of its specific intervals. Doing so allows us to

A Brief History of Motives—Composition  43 appreciate the jagged, dissonant-​interval leaps of mm. 1–​4 as the presentation of a musical problem—​or less severely: an issue—​that calls for resolution. The motto’s jaggedness serves as a “hook” designed to attract listeners’ attention. Upon hearing the large spans of pitch space skipped over by the ↓4th (G-​D) and the ↓o7th (E♭-​F♯), listeners wonder whether these gaps will be filled in at some point. A meaningful resolution will not come from filling them quickly or shoddily. Note that the strings in mm. 10–​12 make an attempt at the task (Example 2.9(a)). Starting at m. 10 they rapidly connect all of the needed tones from G5 down to F♯4; the original motto notes are shown in circles. This first “answer” to the question of the gaps, though, fails to satisfy. The lightning bolt-​shaped gesture they trace in mm. 10–​12 merely summarizes what went before. It does not indicate how the four-​note emblem of Leap+Leap will ultimately be absorbed into the fabric of the piece. Much of the activity in the rest of the movement appears dedicated to finding a more satisfying resolution to this motivic issue. Previous discussion noted how most of the music through m. 48 works to sustain the Leap+Leap motive’s presence. All of those occurrences, however, restate the large leaps (particularly of seventh and octave) without filling them. The possibility of filling in the original G-​D and E♭-​F♯ spans is put off once more in mm. 59–​70, where the exposition’s closing theme concentrates on strolling up and down from the local tonic, B♭. The even, stepwise melodic motion introduced here provides a break from hearing Leap+Leap. It does not meaningfully “solve” that motive’s issue, though, because the area of the scale being explored leaves the boundary tones of G-​D and E♭-​F♯ untouched. The movement’s development section is short, taking up less than a minute of time at allegro tempo. Its first portion, lasting fourteen measures (mm. 83–​96), explores the four-​measure cadential tag of the exposition (mm. 81–​83). This represents a brief lull in the overall motivic narrative. The Leap+Leap motive is not taken up again until the close of the development. This occurs in mm. 97–​106, where the music prepares for the moment of recapitulation.14 Example 2.9(c) shows how the transitional “tails” of these two phrases revisit our two note-​spans of interest. In mm. 102–​103, the first tail fills G5-​D, though its E♮ puts it in a mode slightly “foreign” to G minor. The second tail in mm. 107–​109 falls one note short of reaching the F♯4, leaving the o7 interval incomplete. In mm. 109–​113, the G4-​D span is more convincingly resolved by the drawn-​out chromatic descent in the violas.15 The high drama of this area is signaled by the hushed dynamics and the imitative texture forged by the high and low strings. The fact that this “charged” moment can be heard as a filled-​in ↓4th produces a resonance: the moment of retransition can be heard as an elongated restatement of mm. 1–​2. To maintain tension over the course of the recapitulation, the music delays filling in the remaining open ↓7th for as long as possible. The closing theme

44  Grounds for Motivic Analysis Example 2.9(c)  Motivic activity in the development section.

Example 2.9(d)  ↓7th Leap filled in near the end of the recapitulation, mm. 181–​185.

beginning at m.  177, now in the home key of G minor, takes two stepwise-​ descending swipes at this span; see dashed lines below Example 2.9(d). The first attempt in mm. 182–183 does not fall far enough; the second pitch-​class descent completes the task and reaches F♯. This moment of resolution occurs with little fanfare. The event nevertheless has a profound impact on the movement, as evidenced by the last set of developments in the coda. Example 2.9(e) shows the music of the coda, mm. 201–​214. At its start, the Leap+Leap motive returns, but the troublesome diminished ↓7th has vanished. Notably, the descending interval that replaces it remains diminished in quality. The motive sheds tension as the second component leap now mirrors the first

A Brief History of Motives—Composition  45 Example 2.9(e)  In the coda, the original Leap+Leap motive attains a degree of resolution through elimination of the ↓7th.

(↓4th+↓4th). The upper and lower strings sound this new version of Leap-​ then-​Leap in imitation. The high winds then enter at m. 205, guiding it in a new direction. The high E♭ has to this point consistently served as the launch point toward F♯4, but no longer. In m. 207, the E♭5 leaps to the more normative high C6 in preparation for the long-​awaited, gentle descent to the tonic, G.  Having solved the “problem” of the Leap+Leap gesture, the piece quickly concludes with untroubled arpeggiation of the G minor tonic (low strings, mm. 212–​214). Our discussion of motive in the High Classical period concentrated on two innovations as responses to Baroque style: the rise of the texture or filler motive and the use of motives to promote unity and large-​scale drama. Moving forward, it makes sense to similarly conceive the Romantic treatment of motive as a response to Classical models. Romantic composers escalated these shapes’ prominence, increasingly making it seem as if music was “about” motives. This behavior can be regarded as a wholehearted embrace of the motivic techniques they inherited. The Romantics did not necessarily seek out new ways of deploying these shapes. They were more keen to continue exploring the two modes of expression they had observed in their predecessors’ output. Increasingly, their pieces could be viewed as vehicles not just for exploring large-​scale tonal processes, but for working out the ramifications of one or two main shapes, from the surface to the deepest levels.

46  Grounds for Motivic Analysis The strongest influence on this generation was Beethoven, whose musical statements were sufficiently forceful to define the technical and emotional expectations not only of specific genres (symphony, string quartet, etc.), but of a whole age. The common thread running through his output is motivic saturation. Many of Beethoven’s most famous works consist largely of transformed restatements of one or more core gestures:  notable examples include the first movements of the First String Quartet and Fourth Piano Concerto and the entirety of the Appassionata Piano Sonata, Op. 57. Although the new Romantic emphasis on motive is most closely associated with this composer, it is also well represented in works many of his contemporaries, among them Mendelssohn, Chopin, and Schubert. The post-​Beethoven generation of Romantic composers, active approximately from 1830–​1890, maintained a fascination with motivic processes, although of course they strove to put their own stamp on them. By the mid-​nineteenth century, two opposing factions had developed within this group, one more conservative and the other more ostensibly progressive. The schism between them was rooted in a host of aesthetic issues concerning tradition, form, process, and meaning in music. For our purposes, however, it is productive to filter their debate through the prism of motive. The artists of the New German School such as Wagner and Liszt used motives to represent characters and ideas in works that often had a literal, program-​based component. In service of this aim, they desired to make their motivic materials even more distinctive. In many cases this involved lengthening motives, rendering them into full melodies of the type shown in Example Web.1(a) .16 The idée fíxe (Leitmotive) of Berlioz’s Symphonie Fantastique is meant to depict a specific person, the female love interest of the work’s protagonist. Her image or, sonic “calling card” appears in several settings: at a ball, in the countryside, and in the protagonist’s most disturbed fever dreams. This shift in motives’ function necessarily limited the kinds of transformation that could apply to them. Distort a theme too much and listeners might miss the reference to the character it represents. The three versions of Berlioz’s idée fíxe shown in Example Web.1 are taken to be equivalent, because the main pitches, contour, and length remain generally consistent. It is more the character and mood that are altered, or “thematically transformed,” to use the technical term. Hearing the different versions produces an effect similar to seeing an acquaintance’s physical appearance shift in different settings or lighting schemes.17 Running counter to the camp that worked to expand motives’ length and dramatic content was the other that strived to keep them compact. This latter group were the formalists, who prioritized aesthetic unity in music. Their most prominent representative was Brahms, though many others such as Mendelssohn and

A Brief History of Motives—Composition  47 Saint-Saëns may be included among their number. In the minds of these more traditionally minded composers, a well-​built piece of music exudes a sense of steady growth and development all the way toward its end.18 A logical way to engineer this dramatic trajectory is to begin by introducing a short melodic shape. A composer may then subject it to a series of minor alterations, in effect pulling and kneading at its intervallic and rhythmic content.19 There is another compelling reason that explains why short motives proliferated in late Romantic pieces. Carl Dahlhaus identifies a cultural paradigm shift that took place in western Europe during the 1800s, in which audiences and artists demanded that new creative works exude originality to as great an extent as possible. During the course of the nineteenth century, for socio-​historical reasons among others, it became virtually obligatory for themes, or their initial ideas, to be original, because form itself fell into a state of one-​sided dependence on the musical idea. Schematic forms, of the kind predominating in short character pieces for piano, were sustained exclusively by the quality of the initial idea, the individual character of which compensated for the conventionality of the overall outline. . . . In [music] in which every part or detail is supposed to be an original idea or the consequence of an original idea, conventional material is bound to be regarded as superfluous padding, and a work in which platitudes are conspicuous will be condemned aesthetically as derivative hackwork. (Dahlhaus, 1980, 44)

In other words, the repetitive formulas and pat cadential figures of the Classical period fell out of favor. In response, composers turned to exploring the expressive potential of smaller pitch cells, often comprising only a few notes. This manifold change in the conception of the art, of course, did not occur in a vacuum, but went hand in hand with a revision of the view of the composerly persona. The composer was no longer regarded as a mere craftsperson, as had been the case for millennia, but instead came to be seen foremost as an artist. An accompanying tectonic shift took place in the realm of harmony. In contrast to the transition to the High Classical period, the one into the Romantic age was marked by a sharp rise in the use of chromatic techniques. The new emphasis on chromaticism, which necessarily led to an expanded chordal palette, was expressed at all levels of composition. It follows that this development would have a profound effect on motives, too, and indeed there is ample evidence that members of both camps, Wagnerians and Brahmsians alike, adapted their melodic style to accommodate the new chromaticism. On the former front, composers working with Leitmotive—​Liszt, and later Wagner, Mahler, and Strauss—​relied heavily on a technique known as real

48  Grounds for Motivic Analysis sequence, in which an initial melodic/​harmonic gesture is transposed with chromatic intervals intact to start at a higher or lower pitch level.20 This is shown in Example 2.10, which shows an excerpt from Wagner’s prelude to Parsifal. An impressive degree of emotional tension can accumulate in passages employing real sequence. The dizzying array of keys—​three distantly related ones are rapidly juxtaposed—​often produces the sense that the music is wandering, seeking an elusive resolution. The composers in the formalist school incorporated chromaticism in their motivic practice in a whole other way. In the previous two hundred or so years of music, the prominent shapes of pieces were most often tonal elements: leaping and stepwise thirds and fifths as well as neighbor-​note figures tethered to scale degrees. This practice arose out of traditional counterpoint practices that privilege diatonicism. Within that practice, modal, major, and minor note collections are considered to be inherently structural, while chromatic tones are accorded unstable, “outsider” status. This tone hierarchy explains the essential similarities of millions of melodies penned during the Common Practice period and undergirds most theories of melodic structure in tonal music. Under increasing pressure to base pieces on short, distinctive motives, Romantic composers began to assemble them from novel combinations of intervals. In the early stages of this development, motives remained more or less diatonic but began incorporating large, athletic leaps of the type shown in Example 2.11. In Brahms’s Intermezzo in A Minor, Op. 118, No. 1, the first 3rd + ↓leap shape, shown boxed, Example 2.10  Real sequence in Wagner’s Parsifal, Prelude, mm. 45–​53.

Example 2.11  The four-​note motive of Brahms’s Intermezzo, Op. 118, No. 1 contains a large leap that crosses to the other hand.

A Brief History of Motives—Composition  49 closes with a leap of an 11th from A5 to E4; the same holds for its sequenced repetition two measures later. As Charles Rosen has observed, these leaps are a source of emotion in the music. Their inherent awkwardness, subliminally embedded in performance, is sensed by listeners as struggle, anxiety, and a sort of nervous energy (Rosen 2000, 162–​197). Over time, the growing influence of chromaticism accelerated motives’ evolution, allowing them to acquire new forms and behaviors. Just as Romantic harmony acquired new flavors through modal borrowing (“mixture”), so too did melodic shapes that could now incorporate chromatic pitches as structural. These newer romantic motives exhibited both conventionally tonal and unconventionally chromatic elements. Late nineteenth-​century composers seized on melody’s new quasi-tonal potential to exploit a new relationship (and thus, a new source of expression) between a motive and its local environment. In the past, motives were usually treated as malleable, adapting their intervals to accommodate chord changes. Recall the Climb motive from the Bach English Suite, which manifested first as an F major arpeggio but later shifted to accommodate see-​sawing C and F harmonies. During the late Romantic period, motives developed into more rigid entities that sound less or more dissonant depending on how their notes intersect with local tonality. “Uranus” from Holst’s The Planets is based on just such a quasi-​tonal motive. Motive U, shown in Example 2.12(a), consistently appears as a descending third, ascending tritone (TT), and descending large leap. When sounded in monophony at the movement’s opening, there is no context for understanding this shape; it is a mysterious cipher. In pieces such as this, Example 2.12  The four-​note pitch-​cell motive from “Uranus” from Holsts’s The Planets. (a) Main pitch-​cell motive, “U,” from Holst’s “Uranus.”

(b) Motive U in transition to the march and as march accompaniment figure.

50  Grounds for Motivic Analysis Example 2.12 Continued (c) Motive U at the conclusion, mm. 248–​250.

the motivic process involves injecting this shape into a diverse set of harmonic environments. As novel sonic qualities attach to its four tones, listeners can register the motive’s progress on its merry-​go-​round-​like journey. In Part b of the example, the main motive projects the sound of an altered C Dorian scale (the leading tone, B, is raised above its usual B♭). More than one hundred measures later, the motive leads to a final cadence in E minor, in which its final note, B, occurs as the fifth of the harmony (Example 2.12(c)).

More Recent Developments We will briefly consider the role of motives in post-​tonal music of the twentieth century. Most historical accounts of music, upon reaching the tumultuous, transitional years around 1900, concentrate first on the issue of harmony, showing how extreme dissonances resulted as the role of tonic (and the associated collection of supporting tertian sonorities) was weakened and soon after eliminated. It is more accurate to say that Western composition fractured here. A  set of traditionalists interested in maintaining the tonal status quo, Holst among them, went one way, while a set of experimentalists interested in atonality went another.21 The last part of this survey will concentrate on the latter stream that was famously helmed by Schoenberg, Anton Webern (1883–​1945), and Alban Berg (1885–​1935). In many respects, the pieces that emerged from this Second Viennese School sound quite different than anything that had been written before. Yet at the same time that these composers worked to obscure traditional tonal harmony, they remained deeply concerned that their modern compositions remain intelligible. An early strategy to balance out the new post-​tonal complexity was to pen miniatures in standard forms such as gavottes and minuets; this is precisely what Schoenberg does in his Op. 25 Suite for Piano. Another strategy was

A Brief History of Motives—Composition  51 to write songs in which the text could serve as a reference point to gauge the music’s forward progress; this approach undergirds Berg’s Four Songs, Op. 2 (1910) and Schoenberg’s Pierrot Lunaire (1912). Though effective, these two stopgap measures came to be regarded by the composers themselves as inadequate. For one, these techniques offered little means for unifying a work’s total harmonic content. For another, they could not aid in the project of developing lengthy, coherent works that are purely instrumental. To overcome these deficiencies, post-​tonal composers sought to unify their works in the domains of texture and timbre and by working in synthetic note collections that could manifest both in melody and harmony.22 Amid all of this innovation, motivic processes played a conspicuous role in promoting cohesion.23 In the wave of post-​tonal pieces Schoenberg wrote between 1898 and 1920, motives act as the glue tying one phrase to the next. Example 2.13 illustrates a set of passages from Schoenberg’s first Piano Piece from Op. 11. It opens in mm. 1–​3 with the presentation of a “Motto” figure composed of two motives. The first of these is a third leap with a suffix stepwise motion (3rd\); the second is a generic up-​and-​down contour gesture (↑↓) followed by a descending 2nd. The two components are elided at G4 as indicated by the ⊕ symbol. The quasi-​tonal structure of Schoenberg’s Motto = 3rd\ ⊕ ↑↓ 2nd and its role in the music is not wholly dissimilar to Holst’s Motive U. In m. 6 of Schoenberg’s piece, there is a rising five-​note gesture in the tenor voice that analysts might be tempted to label a new motive form. In the analysis, it is regarded as an flipped version of the 3rd shape from mm. 1–​2. Following the opening third, D3–​F♯, its suffix component is doubled so that now it ends with two semitones.24 The Motto motive is restated in mm. 9–​11, although there the last 2nd turns questioningly upward. Further exploration of the 3rd\ motive continues in mm. 13–​16. The intervals labeled in m. 13 are reckoned in pitch-​class rather than pitch space. The linking together of 3rd and stepwise suffix fragments culminates in a full Motto presentation in m. 17. Here, the chordal accompaniment is rewritten to cast the shape in a new light. Instead of a dyad major seventh sliding up a major third, the left hand here is composed as a whole-​tone sonority (G♭, E, and A♭) in which each of its members slides a minor second in letter name, or pitch-class (pc), space (to F, E♭, and A). After 1920, shifting conceptions about the format and role of motives played a significant role in ushering in the next stage of post-​tonal composition. I am speaking here of twelve-​tone serialism, a style wherein an initial “row” consisting of the total chromatic is repeatedly deployed over the course of a work. Reflective of its role to promote unity, a piece’s central row serves as the source for all of its melodic and harmonic structures. The practitioners of serialism were acutely aware that a row is essentially a motivic entity (see Babbitt 1987, 171 and

Example 2.13  Motivic activity in the first of Schoenberg’s Three Piano Pieces, Op. 11.

A Brief History of Motives—Composition  53 Schoenberg 1985, 226). The concept of motive at this relatively late point had changed, to be sure. It elongated and became fully chromatic, contrasting sharply with the four-​to seven-​note shapes that predominated in previous centuries. Motive had also grown distinctly more abstract. Conceived of as a string of pitch-​ classes, a row logically does not exist in any one specific note form. It resides “outside the work,” continually taking on new countenances as its notes appear in varied registers and in novel groupings. Viewed one way, the early twentieth-​century phenomenon of the pitch-​class row appears as a diffuse, watered-​down form of motive. It no longer fulfills the original requirements that motive be memorable and self-​referential. The musical relationships it instantiates are less audible, and there is no longer a guarantee that any short melodic strings in its interior will recur. But note that we can change our perspective to regard a work’s central row as a repository of potential melodic and harmonic relationships. Viewed in this alternate manner, the motive is elevated to a position of aesthetic preeminence. For twelve-​tone works, the row is a primary element that is preconceived. As such it fulfills a role analogous to a fugue’s main subject: every aspect of its shape and every possibility of combination with itself must be understood before composition begins. In other words, the row (central motive) is the germinal seed of the finished work. All melodic and harmonic gestures are directly spawned by it; likely, many of the rhythmic ones are as well. Motives would continue to evolve in form and function over the subsequent decades of the twentieth century. Ironically, some of these later developments, particularly those leading to the development of minimalism, in many ways bring polyphonic music full-​circle back to the motivically rich textures of the early Middle Ages.25 It is necessary to draw this narrative to a close somewhere, however, and the spot where they enjoyed peak influence in twelve-​tone serialism is perhaps a better place than many others.

Further Thoughts on Surveying Motives in Composition In the foregoing chronological survey, we saw motives originally serving a utilitarian function, filling and unifying musical textures at their surface. Over the course of the late Baroque through Romantic periods, they increasingly encapsulated the core material of pieces. In doing so, motives rose to a rank roughly commensurate with the other organizing forces in music. In other words, it increasingly becomes possible to explain the succession of events in these works in terms of motivic development. This adds a new capacity to analyze beyond viewing pieces harmonically as a succession of key areas, formally as adhering to architectural models, and contrapuntally as products of large-​scale voice leading.

54  Grounds for Motivic Analysis The motivic activity of Classical and Romantic music, though important, is always coordinated to an extent by tonality. Readers will recall that the tension inhering in the Brahms and Holst examples cited earlier results from pitting a peculiar pitch shape against shifting tonal contexts. Pieces composed before 1890, moreover, almost universally begin and end in the same key and exhibit strong tonal leanings. The sense of key, both locally and globally, serves as a barrier against which the idiosyncratic, jagged motives strain. For generations, the two independent forces of motive and tonality productively struggled against one another, and the frisson of their clash was felt across the European continent. It should be kept in mind that relatively few composers active in the 1910s, 20s, and 30s pursued free atonality and serialism. Our interest in the few that did stems from the historical impact of their innovations, motivically speaking. With classic tonality temporarily vacated, motives annexed their territory. It became common for highly chromatic pitch or pitch-​class shapes to dictate the large-​scale harmonic trajectory of works. But this outcome is merely a special case of a more important condition. For the first time in history, a work could spring wholly and unilaterally from a single source. The novel style of composition and the novel aesthetic were one and the same: a fully serial piece represents the expression of a central motivic utterance projected across the multiple domains of melody, harmony, rhythm, articulation, and dynamics.26 The history of motives given here has necessarily been highly abridged. It is too narrow, with far too little attention given to developments in France, Italy, eastern Europe, and the Americas. And it ends too early, with no mention given to the role motives play in the most prominent musical styles of the twentieth century, among them jazz, rock, and music for film and television. Some of these lacunae will be filled in by subsequent chapters on analysis, which examine motivic activity in pieces from a variety of genres. With regard to any gaps that persist past this book’s conclusion, it is my hope that they will invite the attention of future theorists, who may continue fitting styles and genres into this historical account.

3

A History of Motives—​Theory and Analysis In this chapter we shift attention away from the compositional history of motives and toward their theoretical history. The aim is to bridge the conceptual chasm between our preliminary, working definitions of motive and the formalized definitions and techniques that will be presented in Part II. This will entail a shift in tone: the relaxed and curious mode of inquiry favored earlier will give way here to a more clinical approach. We assume that no fully formed theory and method of motivic analysis lies dormant in history, waiting to be revived. At the same time, wisdom cautions that we should not try to formulate a new method wholly from scratch. A more prudent strategy is to seek a middle ground between these possibilities. In doing so, we shall take license to innovate. Yet as we forge ahead, it is incumbent on us to examine the past to benefit from practices that have previously proven effective and to jettison those that have proven less so. The chapter is organized in five sections. The first section will cover 1600–​ 1750 c.e., the last period in which motive remained in its conceptual prehistory. At that time, the preeminent musical structure was the “figure,” a passage of music that conveys a single character. The second section covers 1750–​1890, a period in which the influence of figures waned. As this occurred, authors began theorizing about the smaller musical cells that make melodies logical, pleasant, and memorable. Their investigations would produce a new group of theoretical entities such as phrase, Satz, and dessin, all of which to varying degree embody elements that we today think of as motivic. The decade 1890–​1900 will mark the approximate start of the modern era of motive, in which theorists developed more precise terminology for motives and increasingly viewed them as having deterministic forces. The third section of this survey nominally covers the time between 1900 and 1950. In truth, it concentrates on the work of Arnold Schoenberg, the composer-​theorist who worked assiduously to develop and popularize motive-​based views of music. His approach was so influential that most significant motivic developments in the second half of the twentieth century can be considered responses to his work. The fourth section, covering 1950 to 2010, treats these later developments. This late period is marked by stark changes in how motive was conceived and Musical Motives. Brent Auerbach, Oxford University Press. © Oxford University Press 2021. DOI: 10.1093/oso/9780197526026.003.0003.

56  Grounds for Motivic Analysis handled in analysis. Specifically, motives in the late twentieth century underwent intense fragmentation, a “boiling away” of their elements, often leaving behind only bare pitch intervals and/​or rhythms. The survey here will comment on academic cultural factors that led to this development, many of which persist to this day. Upon completion of the historical survey, the fifth section of the chapter will ruminate on past and present conventions of motive and motivic analysis. That closing area will lay the groundwork for the rules and conventions underlying the new motivic theory to follow in Part II of Musical Motives.

Origins of the Musical Motive Concept, 1600–​1750 Within the two-​and-​a-​half millennium span that music theory has existed, the concept of motive is a recent phenomenon, only emerging about four hundred years ago. Although this survey will properly begin at 1600, we will take a two-​ page glance at the preceding centuries to establish the context for motive’s place within music theory. Music theory entered the Middle Ages as a speculative discipline primarily concerned with string ratios and scale systems.1 By the ninth and tenth centuries, the (mostly monastic) scholars writing on music increasingly concentrated on issues more immediately relevant to them. As choir directors and composers, they were concerned with instructing their fellow clergy in reading music and—​ talent permitting—​improvising polyphony from a single line of music. The first three centuries following the year 1000 C.E. thus witnessed the first emergence of musica practica as a new branch of theory. Guido of Arezzo (991–​1033?) is the most famous innovator of this period: he is credited with inventing staff notation as well as a method for singing scale steps on syllables (solfege). Later theorists in the practica tradition responding to new challenges of polyphonic music would, in the thirteenth and fourteenth centuries, begin writing major treatises on rhythm, meter, and counterpoint. The third and last area of classical theory scholarship to coalesce—​the one most relevant to our discussion on motive—​was Poetics.2 Musica poetica, according to one of its founders, Joachim Burmeister (1564–​1629), concerns how melody, harmony, and the “affectations of periods” influence listeners’ minds and hearts to various emotions” (1993 [1606], 16). What is remarkable about this quote from Burmeister is how it signals awareness, even at this early time, of the causative link between composers’ technical decisions and the degree of emotion in their music. Since time immemorial, theorists writing about music have noted its expressive affects. The ancient Greeks were fervent adherents to cosmology, believing that all realms of existence are connected and governed by common forces.

A History of Motives—Theory and analysis  57 According to Greek theorists, the straightforward ratios among the counting numbers (2:1, 3:1, etc.) were reflected in “pleasing” consonances that leapt from vibrating strings of these same proportional lengths. These theorists saw further evidence for their worldview by observing that the different scale systems, or modes, had different emotive effects on listeners’ psyches. One given mode, according to Plato and Aristotle, might provoke people to take up arms; another mode might soothe them, and yet a third might cause them grief (Strunk 1998, 5). Some remarkable similarities in worldview carried over from ancient Greece to western Europe in the Renaissance era. The latter culture, for example, remained heavily invested in cosmology. One of their most powerful metaphors for communicating this belief, appropriately enough, took musical form as the “Divine Monochord.” The monochord was, as its name indicates, a ­commonplace one-​stringed instrument from antiquity used to demonstrate varying pitch intervals. In drawings depicting its mythically “divine” manifestation, the device is overlaid onto the universe, with fanciful arcs showing how various earthly and heavenly realms intersect the tuning board.3 Even as the specific nature of the divine shifted in Renaissance Christian Europe, the conviction that humankind’s emotive and physical states (humors) were impacted by music remained constant. Setting that similarity aside, the cultural environment in western Europe in the second millennium was, of course, markedly different than that of ancient Greece. So although the newly birthed field of Musical Poetics may have taken inspiration from Classic sentiments, it would evolve in radically new ways. One of the strongest forces shaping this development was print technology. The appearance in the late 1400s of a movable-​type printing press for music allowed for sacred and secular pieces to proliferate in standardized forms. Musicians for the first time in history had access to a canon of pieces that could serve as a point of reference for discussing compositional technique.4 New treatises on music increasingly exhibited a common sensibility, that specific techniques of melody and harmony could be cataloged and taught on the basis of examples drawn from the canon. The preferred means for communicating this knowledge to budding composers was also established by this time. Children enrolled in formal education in this society were instructed according to the principles of rhetoric, the ancient art of assembling and delivering arguments. Rhetoric had become highly formalized by the 1500s, such that students would be eminently familiar with its terminology and methods.5 A  signal trapping of this discipline is its extensive meta-​language that catalogs figures of speech.6 Some of these terms pertain to planning an argument, as when students are taught to devise an idea (inventio) and claims to support it (dispositio). Other terms describe techniques

58  Grounds for Motivic Analysis for amplifying an argument, such as immediately restating an utterance for emphasis or interposing a sudden silence to draw in listeners. With this framework for learning in place, it would not be long before someone would adapt it to musical purposes. In 1606, Joachim Burmeister published his Musica poetica, which founded the branch of theory that would eventually house interpretive analysis.7 His work, for our purposes, also lay the groundwork for thinking of music in terms of successions of formal segments and emotive figures, the latter of which can be viewed as precursors to motives.,8 Burmeister defines a figure, also known as an “ornament,” as follows: a passage, in harmony as well as in melody, which is contained within a definite period that begins from a cadence, and ends within a cadence; it departs from the simple method of composition, and with elegance assumes and adopts a more ornate character. (1993, 156–​157)9

This early definition establishes the scope of a figure both as small, occurring within a single phrase, and as extraordinary, standing out from the rest of the composition. The definition further folds in a critical bit of form theory. Burmeister defines the musical period in a way that makes it largely analogous to the modern segment, a locally cohering stretch of music that lasts a few seconds and has a clear beginning and end.10 Following this definition, he continues by enumerating sixteen types (species) of figure, which may manifest in one of three ways, via harmony, melody, or a combination of the two.11 Burmeister’s position in the poetic tradition is early; thus, many of his descriptions of ornaments are general. (At this point in history, we are still more than a century away from the development of more specifically pictorial figures such as the “sigh” and “lament.”) With regard to the Climax figure shown in Example 3.1, he describes the technique of “repeating similar pitch [patterns] on gradations of pitch levels.” The descending gestures that are separated by rests all resemble each other, but do not repeat exactly; Burmeister, it seems, is most concerned with the broad-​stroke notion of restating a compositional idea at a new pitch height. A similar emphasis on procedure over content applies to many of his other figures, particularly those concerning voice disposition. One of these, Example 3.1  Burmeister’s Climax figure. Example 12.7 from Burmeister 1993 [1606].

A History of Motives—Theory and analysis  59 Fuga realis, refers to the standard technique of gradually thickening a texture by bringing in voices one at a time in imitation. Others delineate imitation via contrary motion and composing fugues with multiple subjects (double fugue). Some of Burmeister’s ornaments are couched in more specific terms which, viewed anachronistically, causes them to read as almost motivic. One is Noëma, a “harmonic affection or period that consists of voices combined in equal note values” (1606, 165). This highly general rhythmic notion can apply to multiple passages from different parts of a piece, allowing them to be associated despite exhibiting different durations (e.g., half notes versus whole notes). Another example is Pathopoeia, which “arouses the affections” by introducing “semitones that belong neither to the mode nor to the genus of the piece” (1606, 175). Burmeister does not explain which foreign semitones a composer should use; his examples identify E♭ (local fa) as a likely foreign tone to appear in G Dorian mode. Nevertheless, his recognition of this type of figure calls to mind the idea of a higher-​level type motive, one that recasts a compositional decision or act—​in this case, the choice to insert chromaticism to heighten the emotion in texts—​as motivic. After Burmeister concludes his listing of figures, he applies them in service of one of the first full-​scale musical analyses known to history (Palisca 1972). It is of an Orlando Lassus motet, In me transierunt. In accordance with his definition of Poetics stated at the outset, Burmeister divides Lassus’s work into “periods,” each of which exhibits a unique emotional character stemming from its figural content. As with all truly great advances in theoretical thought, Burmeister’s work constitutes a dual offering: the terminology he innovates is part and parcel of a grander method of analysis . . . that he also innovates. The writings on rhetoric that followed Burmeister’s Musica poetica, notably Joachim Thuringus’s Opusculum bipartitum (1624) and Athanasius Kircher’s Musurgia universalis (1650), differ in scope but not in kind.12 They mostly serve to expand the number of recognized ornaments, although remarkably, Kircher’s text is the first to conceive the composition process in rhetorical terms through the introduction of the topics of inventio, dispositio, and elocution (Bartel 1997, 168).13 The next significant development occurred in the 1660s in the writings of Christoph Bernhard (1628–​1692), a student of the Italian-​trained Heinrich Schütz. The figures Bernhard proposes for even the most adventurous styles of composition are similar to Burmeister’s. Examples include abruptio, a “breaking off a vocal line instead of achieving” and mora: “inverted [upward] resolution of a suspension” (Bartel 1997, 164). Bernhard further recommends text painting, for example ending “questions . . . a step higher than the penultimate syllable” and employing high and low registers, respectively, for texts “wherein Heaven . . . and Hell are mentioned” (Hilse 1973, 111).14 Another major development in Poetics was brought about by Johann Mattheson (1681–​1764), a composer of operas and a close friend of Handel. Mattheson’s many articles, treatises, and letters stand as “valuable standard

60  Grounds for Motivic Analysis sources on music of the Baroque period” (Harriss 1978, 4). More importantly, they represent “the first serious acknowledgement of the central role of melody in the newer musical styles emerging in the 1720s and 1730s” (Lester 1992, 161). Mattheson’s interest in melody is on display throughout his most famous compendium, The Complete Capellmeister, published in 1739. The center of the book, Part II of three total, concerns melodic construction. Mattheson lays the foundations for this study of melody in Chapter  2, where he demands that aspiring composers master all languages they will work in, and in c­ hapter 3, where he rehearses common ornaments of figuration such as trill, tremolo, passing tone, and fill (tirata). Part II, ­chapter  4, frames the topic “Melodic Invention” in terms of rhetoric. True to the spirit of invention, Mattheson suggests eleven general topics, which essentially are sources of inspiration. The first is notation, corresponding to the manipulation of pitch shapes to assemble melody. The term “motive” does not specifically appear there; however, the techniques that show how to assemble melody by experimenting with and recombining small pitch shapes resonate with modern motivic sensibilities. Mattheson lays out several such strategies for spurring invention, three of which are reproduced in Example 3.2. The first technique constrains the composer to work with a single duration or a small set of varying durations. Another technique, shown last in the example, utilizes mirror inversion. A number of passages appearing later in Part II of Capellmeister foreshadow other types of motive. Chapter 6 catalogs a wide variety of rhythms corresponding to the meter and stress patterns of poetry.15 Short musical passages built of spondees, iambs, trochees, and other rhyme schemes are printed with the understanding that each repetition of these constitutes a poetic unit, a repeating rhythmic shape. Mattheson’s monumental role in the development of music criticism and analysis is indisputable; his agency in the development of the concept of motive is similarly important. As Lester notes, Mattheson’s approach “illustrate[s]‌ the role played by rhythmic and motivic activity in creating successful musical continuity—​aspects of musical structure that had gone unnoted by most earlier writers” (1992, 166). His work was widely read, too. It is well known that Beethoven and Haydn owned copies of Capellmeister, and that Haydn worked out all of the exercises in his (Wyn Jones 2010). The first section of this survey has documented two key developments in the history of motivic theory. The first was the onset of the practice of music analysis, which sprung, seemingly fully formed, from the mind of Joachim Burmeister. His analysis of Lassus’s In me transierunt offers a model for segmentation and pioneers the idea that specialized configurations of pitch, harmony, and counterpoint communicate meaning. The second development stemmed from Mattheson in the form of a new school of melody. His approach of breaking

A History of Motives—Theory and analysis  61 Example 3.2  Excerpt of methods for invention from Mattheson 1981 [1739].

down melody into components that can be manipulated and recombined to various effects is today widely recognized as an early instance of “thematic working”(thematische Arbeit), a theoretic concept that would quickly and permanently attach to motivic theory.16

The Rise of Melodielehre, 1750–​1890 The prehistory of motive is tightly interwoven with rhetoric. The rhetorical tradition, however, rapidly began to wane in the mid-​eighteenth century. As Baroque-​style composition matured in German lands, the classically objective, formula-​driven approach to rhetoric was increasingly displaced by a “freer

62  Grounds for Motivic Analysis and subjective concept of musical expression” (Bartel 1997, 157). Composers active between 1730 and 1800, working in newly emerging “Sensitive” (Empfindsamkeit) and Classical styles would radically recast the affective and formal content of their music. This survey will say relatively little about the former, emotive content, assuming that readers possess passing familiarity with the most common figures and tropes of Classical music. (Through acculturation, amateur listeners can reliably distinguish, for example, between the “happiness” of major mode versus the “sadness” of minor, or between the frivolity of a gallop versus the somberness of a funeral march.) The most profound developments in motivic theory in the long nineteenth century did not concern whether figures were present—​they very much were!—​but how they were deployed. Traditional doctrine in the Baroque held that pieces should express a single or perhaps two contrasting affects, as in da capo aria. Classical composers, in contrast, explored far wider ranges of affects in a single work and interposed them more rapidly.17 In contrast to motives’ expressive content, which is difficult to pinpoint in any age, their development in terms of literal structure and function between the years 1750 to 1890 can be tracked with more precision. The composer-​theorist Joseph Riepel (1709–​1782) is recognized today as a pioneer in the study of musical form. He was among the first to codify the modern phrase. In addition, he demonstrated how phrases may be mechanically manipulated to generate longer stretches of material by “changing their endings, their contour, their motives, their meter,” and so forth (Lester 1992, 262). Riepel does not refer to his smallest phrase components as motivic; however, his mechanical manipulations of phrase material as shown in Example 3.3 are suggestive of that idea. Demonstrations of this type signal his recognition of the Example 3.3  Examples 3 and 4 from Moreno 2000 illustrating Riepel’s treatment of figures (1755).

A History of Motives—Theory and analysis  63 role that small pitch-​and-​rhythm shapes play in analysis and model composition. The upper line of the example shows how four figures constitute five measures of melody. Two of the figures return in the cadenza passage presented in the example’s lower line. Remarkably, there the interval content of both Figures 2 and 4 is significantly altered, and the latter shape is extended through repetition. The fact that distinct but related forms of the entries labeled “No. 2” and “No. 4” recur in separate locations signifies that figures, for him, are malleable. Moreno 2000 expressly associates this chain of logic—​in which all of a figure’s varied recurrences are shown stemming from some “simple prototype”—​with the doctrine of thematic working (thematische Arbeit) (131). Riepel, along with his contemporaries, J.N. Forkel (1749–​1818) and J.A. Scheibe (1708–​1776), continued to subscribe to rhetoric as a living practice. Despite this stance, certain aspects of their approach contributed to bringing that tradition to a close. McCreless 2002 singles out Forkel for “detach[ing] the figures completely from texted vocal music,” claiming them to be “fundamental and analogous forms of human expression” (873). He credits Forkel and Scheibe for facilitating music theory’s pivot toward emphasizing secondary over primary rhetoric. In doing so, they elevated the status of musical gesture as the embodiment of inventio, where earlier that term merely denoted a step in the creative process. Music was increasingly viewed not just as an argument, but as an argument with a central issue (status) calling for resolution.18 This late-​Baroque maneuver constitutes a watershed development in the history of both motive and interpretive analysis. Near the turn of 1800, the premotivic concept hopped aboard a new conveyance. After lumbering into the century on a sturdy wagon powered by rhetoric, it coasted through it in a sleeker coupe powered by advances in form theory. Riepel had made important new claims about the constitution and combination of phrases. Heinrich Christian Koch (1749–​1816), building directly on that theory, describes in detail how a phrase divides into lesser, incomplete segments (unvollkommene Einschnitten). This awareness is prerequisite to his description of a process of extending phrases by repeating one of its internal segments “on the same scale degree or a different one” (Lester 1992, 287). Riepel and Koch peered ever closer into the workings of melody, distilling periods and phrases down to the measure-​and submeasure levels. Their writings recognize incomplete segments, yet these segments do not quite qualify as motives because they are nonfunctional. For Koch, when segments repeat, they distort more normative four-​or eight-​measure phrases. This means that any internal repetitions, if present, technically exist out of time. For motive to emerge as a fully autonomous concept, some further theorizing was necessary. Theorists would need to narrow their focus still further on the shapes that make melodies, and they would need to newly characterize those smallest parts as dynamic, living entities.

64  Grounds for Motivic Analysis Jairo Moreno offers a compelling account of these paired developments in his article, “Challenging Views of Sequential Repetition:  From Satzlehre to Melodielehre” (2000). The two German words in his title encapsulate the grand shift in musical thinking that took place between the 1770s and the 1860s. Early in that period, theorists explained melody in terms of static, building blocks akin to sentences and paragraphs; this is Satzlehre. Near the close of that period, theorists regarded the tiniest fragments of melody as almost alive, dictating its destiny; this is Melodielehre, the study of how expert composers create. One of the figures responsible for this shift in thought was Anton Reicha (1770–​1836). He was a Czech theorist that wrote extensively on melody, but did so largely in the context of form. Reicha’s mature formal theory privileges models that exhibit tight symmetry and hierarchy (Hooper 2017, 26). Example 3.4(a) illustrates a set of his formal structures, all nesting one within another. The totality is an eight-​measure period, which corresponds roughly to the modern phrase. This period made up of three rhythmes (members) which in turn are composed of similar and dissimilar dessins (figures). Example 3.4  (a) Example J from Reicha 2000 [1814] (125).

(b) Example J5, 7 from Reicha 2000 [1814] (176).

(c) Example B5, 11 from Reicha 2000 [1814] (169).

A History of Motives—Theory and analysis  65 It is the dessin that is of central importance. Example 3.4(b) illustrates its role in composition; here, a ten-​measure theme is shown to be composed of thirteen dessins. The scope and function of the dessin confirms it as an analog of the modern day pitch-and rhythm-​based motive.19 A further aspect of the ­example worth commenting on is the window it opens onto Reicha’s technique. He does not draw hard and fast boundaries around his shapes. Instead, he allows the bracketed and slurred configurations ​to overlap, a maneuver that resonates with modern motive practice. Reicha’s dessin would be noteworthy on its own. Remarkably, though, Reicha extends his so-​called “decomposition” analysis one more level. In Example 3.4(c), he identifies a smaller entity called petit dessin at work in a melody from Mozart’s “Hunt” Quartet. This element appears in m.1, taking the form of a major 2nd on B♭4-​C5. In a manner foreshadowing Schoenberg, the petit dessin establishes a single, bare interval as the ultimate source of music’s life and energy. On this basis, Jairo Moreno credits Reicha with a revolutionary role in supplanting Satzlehere with Melodielehre. A further aspect of this coup is Reicha’s breathtakingly new approach to analysis: To point out a major second as a melodic unit, and, more importantly, as a potential source for further melodic material, comes as no surprise to us post-​ Schoenbergian analysts of motives. But let us make no mistake: never before Reicha had the analytical scalpel performed such millimetric incisions. (Moreno 2000, 148)

Rapid theoretical developments occurred in the wake of Reicha’s writings. One of his immediate successors was Adolf Bernhard Marx (1795–​1866). Marx’s interest in motive spanned his career; however, he was already theorizing about motives in 1837. Example 3.5(a) reproduces a graphic from his four-​volume Example 3.5  (a) A.B. Marx illustrates a period composed of two phrases. Example 12 from Moreno 2000 (142).

(b) Two-​note motives identified in Marx. Example 13a from Moreno 2000 (143).

66  Grounds for Motivic Analysis treatise, Die Lehre von der musikalischen Komposition, illustrating a period composed of two phrases. Marx quickly narrows his focus to the smaller elements making up each phrase, commenting that “if we know the construction of the first bar, we also know what the others are about, the first being a model for the rest” (1868:1, 32). Moreno informs us that the two-​note(!) entities shown bracketed in Example 3.5(b) are, for Marx, motive (2000, 141). Marx’s procedure of starting with melody and focusing on its smallest elements bears close affinity to Riepel and Koch. But what a difference a few decades make! While all three theorists’ views of motive hinge on recognition of transposed repetition, Marx’s is truly novel. The additive scale formulations he proposes stretch to unprecedented lengths. Also significant, Marx’s repetition occurs at the outset of the phrase instead of internally, suggesting that mechanical repetition could plausibly generate a theme. Marx’s argument that a cell can self-​replicate and chain together advances a radically new view of melody.20 He writes that “Any union of two or more tones can be considered a motive.” These motives, which harbor the germ and root of the forms growing out of them,” provide the basis for all tonal shapes.”21 Marx, positioning himself as inheritor of the theories of Mattheson and Reicha, conclusively states that it is these elements, the motives, that drive music forward. 22 Marx’s early writings on motive concern repetition and small-​scale melody. His later views would engage larger-​scale analytic issues—​in particular, form. In a famous analysis of Beethoven’s Piano Sonata 16 in G, Op. 31, No. 1, I, Marx describes the interplay of two kinds of gesture. The gesture labeled A in Example 3.6 embodies the “will to motion,” the general phenomenon of “going” (Gang) “that arises from the continuation of a motive over some stretch” (Marx 1868, 1:35, quoted in Moreno 2002, 139). The gesture labeled B is emblematic of a more static idea that is suitable for communicating a coherent expository thought (Satz). One notion advanced by Marx that would become especially popular was that of “motivic debt.” This is a framing device for analysis, somewhat in the manner of a status, that animates the relationship between themes with opposed dispositions such as Satz and Gang. Motivic debt is said to accumulate when a piece concentrates on one motive type to the exclusion of another. The longer that occurs, the more the listener comes to expect the return of the absent type.23 Another analytic archetype originating from Marx holds that the pitch and rhythm events occurring at a work’s beginning strive toward a later climactic event or goal (Moreno 2000, 139). These two frameworks for understanding music stand simultaneously as products of and arguments for an “organicist” view of music. Organicism, which holds that all aspects of an artwork are essential and interrelate, has been a dominant force for generations in the West and will significantly impact the methods to be detailed in Part II of Musical Motives.

A History of Motives—Theory and analysis  67 Example 3.6  Example from A.B. Marx illustrating the interplay of static (Satz) and “will-​to-​motion” (Gang) gestures. Image from Moreno 2000 (140).

A last set of advancements in motivic theory stemmed from Johann Christian Lobe (1797–​1881), a German flutist and composer who turned at midcareer to editing journals and writing extensively on composition.24 His Catechism of Composition of 1863 emerged less than fifteen years after Marx’s Manual on composition and shares a close affinity with it. Taken together, the work of these two theorists effected the last great changeover in compositional theory “from one of a phrase structural framework driven by the Baroque theory of affect according to rhetorical strategies, to one of a potentially infinitely expanding structure triggered by an initial motivic inspiration and perpetuated by the laws of organic musical procreation” (Bent 1994, 16). Lobe defines the motive in purely melodic terms, as a “note-​group to be found within one measure” (95–​96). He theorizes that motives exist in “simple” form, consisting of a single, held note (!)  or in “compound” form containing many notes in faster duration. (His insistence that motives last for the duration of one measure can be understood in the context of his views on form, in which the normative, four-​measure phrase is shown to be assembled from four motives combining). He demonstrates how compound motives are often formed through the

68  Grounds for Motivic Analysis joining of several smaller, two-​to four-​note cells called “members”; these correspond to Reicha’s petits dessins. Lobe’s first contribution is fixing motive’s place within a hierarchy of form that, starting with the fragmentary “member,” would reach upward to encompass phrase, period, theme group, and even full piece.25 His theories on motivic working (motivische Arbeit) would prove even more revolutionary. Like Reicha and Marx, Lobe offers extended demonstrations of the role motives play in melodic composition. One such chart, reproduced in Example 3.7 illustrates the logic holding together the primary theme of Haydn’s Symphony 104, I.

Example 3.7  Ex 1.3.11 from Hooper 2017 (30), after Trippett 2013 (122, Ex. 2.5). Lobe illustrates motivic working in Haydn’s Symphony 104 (I).

A History of Motives—Theory and analysis  69 Stage 1 in the chart shows the theme’s basic framework, an eight-​measure idea (Gedanke) built of eight tones. In the stages that follow, this idea is worked out (Ausarbeitung) via a series of rhythmic and pitch transformations. Some, such as Stages 2 and 4, produce poor results that are varied but “rambling” (Herumschweifen). Others, such as Stages 3 and 5, produce better results unified by the close repetition of rhythmic and tonal patterns. Lobe later presents an expanded list of transformations that apply to the first motive of Haydn’s theme (See Example Web.3.1  ). The staves marked Pitch 1, 2, 3, and 4 respectively illustrate transposition, intervallic contraction, intervallic expansion, and mirror inversion. The staves marked Rhythm 1 and 2 illustrate augmentation and diminution, and the lowest two staves illustrate fragmentation, free motivic addition, and figuration. Lobe’s regimented, operational approach to handling motives would come to the fore of motivic theory in the next century, particularly in writings by Arnold Schoenberg, Rudolph Réti, and Allen Forte. The close of this portion of our survey takes us to 1890, the approximate time when motive emerges as self-​standing analytic entity. As evidence for this, one may note the rising trend of contemporary treatises opening with wholly uncontested claims about motive. Writing in 1906, Hubert Parry declares motive simply to be “the shortest complete idea in music,” which under subdivision “will leave only expressionless single notes, as unmeaning as the separate letters of a word” (Dunsby 2002, 907). At this same time, Heinrich Schenker (1868–​1935) was initiating his grand project on common-​practice tonality that would yield volumes on harmony, counterpoint, and free composition. The first technical claim he makes in the first book, Harmony, is as follows: The Motif, and motif alone, creates the possibility of associating ideas, the only one of which music is capable. The motif is a primordial and intrinsic association of ideas. The motif thus substitutes for the ageless and powerful association of ideas from patterns in nature . . . Music became art in the real sense of this word only with the discovery of the motif and its use. (Schenker 1980, 3–​4)

Tellingly, the concept of motive serves as a cornerstone on which Schenker’s entire theory of music was to be built.

Schoenberg’s Conservative and Radical Conceptions of Motive Near the turn of the twentieth century, the musical shapes that once had been known as figures evolved into leaner entities responsible for all musical energy and logic. Yet as radically as the notion of motive had developed, at the turn

70  Grounds for Motivic Analysis of 1900 it remained an idea very much rooted in the previous century. Its analytic applications were largely limited to local melodic-​rhythmic phenomena. No theorists had asked if motives could help explain why a movement explored one set of harmonic areas and not others, or one set of themes but not others. Answering these questions became increasingly pressing in light of a pronounced aesthetic trend: since the late 1700s, musical works had been steadily growing in both length and complexity. The musicians of the age, acutely aware of this shift, set out to offer explanation of how these larger pieces functioned.26 The most prominent theorist active at this time, Hugo Riemann (1849–​1919), contributed a great deal to elevating motive’s significance. In Riemann’s mature theory, the motive is established as the original building block of music; he cites its similarity to word in speech.27 His Catechism of Composition constructs a full theory of form and harmony on the basis of motive, which requires its scope to be broadened in most respects. Under Riemann, the motive acquires a distinctively robust profile that far exceeds one dimension. Its identity is “melodic,” stemming from pitch. Importantly, though, it is also “rhythmic” and “dynamic,” stemming from “absolute and relative tone strength” (1889, 5). Perhaps the only aspect of motives Riemann declines to expand on is their prototypical length, which remains roughly one measure; Example 3.8 illustrates a typical case. Note that Riemann invests this shape with some richness by viewing it as a unity built of smaller subgestures. He opens his analysis of Bach’s Fugue in B​♭ Minor from Book II of the Well-​Tempered Clavier by asking readers to “Consider . . . the initial motive,” which he defines as “a turn, and a step of a second approached from the fourth” (Bent 1994, 114). One might presume that having recourse only to compact motives would weaken their analytic significance. Indeed, Riemann has little interest in pursuing motivic analysis in a piece-​specific, interpretive sense. Motives serve in his theory, rather, as form-​building entities. Part I of Riemann’s Catechism unspools a progression of ever-​ larger melodic/​formal units. This occurs as two-​element motive gestures multiply and combine to form larger structures all exhibiting the same asymmetrical, weak-​ to-​strong, binary energy. (For Riemann, the basic force in all music is the tactus, which manifests first as a two-​beat event and then, recursively, at all higher levels.28) Example 3.8  Riemann identifies the primary motive of Bach’s Prelude in B♭ Minor, WTC II (from Bent 1994, 114).

A History of Motives—Theory and analysis  71 It cannot be stressed enough how ambitious Riemann’s view is that small motivic gestures underlie all music. His steadfast adherence to this principle leads him down some remarkable avenues, including one where he theorizes on how harmonic progressions are motivic. At one point, Riemann establishes two extremely broad categories of harmonic motive, “positive” and “negative,” to represent motions away from tonic harmony and motions returning to it (1889, 51). His idea to construct motive on the basis of shared patterns of harmonic function—​ tonic, dominant, and subdominant—​ foreshadows the creative, cross-​domain approaches to theory that would flourish a century later. The harmonic motives Riemann prescribes in Catechism, in fact, closely resemble the harmonic motives that will be proposed in ­chapter 7 for use in complex motivic analysis. Riemann’s expansive view of motives would greatly influence the next generation of theorists. The twin giants, Schoenberg and Schenker, would both follow Riemann’s lead in privileging motive, but would diverge with respect to the kinds of motives they would recognize. Schenker, for example, would prioritize tonality-grounded intervallic gestures, such as leaps and linear motions linking together triad tones.29 Schoenberg, on the other hand, was more inclined to prioritize idiosyncratic, piece-​specific shapes. Of the two, Schenker’s method is more fully organic, in that the same analytic principles operate at multiple levels. (He has sound reason for declaring the preeminent motives to be fifths, thirds, and octaves: these intervals are the most abundant in tonal music at every span, from less than one measure to three hundred measures.) Reflecting Schenkerian theory’s firm entrenchment in modern American academic musical thought, Part II of Musical Motives will make frequent reference to it. Historically speaking, however, Schenker’s ideas coursed down a narrow stream of influence at first. His theory would not spread widely until after his students in Europe brought his ideas to the United States in the 1930s and 1940s (Berry 2003). Arnold Schoenberg’s (1874–​1951) theories, in contrast, promulgated widely from the start in public lectures, radio broadcasts, and widely read composition manuals. For this and other reasons to be noted later, this survey views Schoenberg as the primary force behind the development of the motivic concept in modern times. In addition to founding a school of composition and serving as a prolific critic of modern music, Schoenberg wrote multiple theoretic treatises. These activities resulted in a prodigious analytical tradition. His views on music in the last century have directly inspired a host of books and essays, including this one. While space constraints prohibit us from discussing Schoenberg’s universal theory of music at length, a brief summary of it is necessary to ground the upcoming set of historical terms that, in turn, pertain to motive’s most recent developments.

72  Grounds for Motivic Analysis Schoenberg’s thoughts concerning music’s organization were not fashioned from whole cloth. His theories are rooted in the Western aesthetic principle of organicism, which likens an art work to a living creature.30 A living being, plant or animal, may present highly differentiated aspects—​ such as a trunk and branches, or fingers, face, and torso—​nevertheless, it spawns from a single cell and remains genetically unified. Organicism dominated the discussion of the “how” and “why” of art in Schoenberg’s time and for many years thereafter. As late as 1966, Alan Walker asserted, “It should be the purpose of analysis to reveal the causes of unity” (43). Present-​day scholarship has changed dramatically in that not all analyses seek to explain unity. Many still do, however, and it remains a viable mode of inquiry, provided that it is applied responsibly. To wit: if one does decide to invoke the doctrine of organicism, one should do so morally, with sensitivity to the long history of its being used as a tool of Western chauvinism.31 With regard to the anatomy of musical works, Schoenberg’s view holds that each piece expresses an Idea (Idee or Gedanke), a certain ineffable content that it was created to express.32 A brief mental exercise may help convey a sense of the “Idea.” Try to conjure up an immediate impression of a song, such as the Beatles’ “Yellow Submarine” or Duke Ellington’s “Take the A Train.” It is better if you are unable to recall individual details about it. The goal here is to attempt to fit the song’s totality in your mind: its sound, its meaning, its groove, what it feels like to listen to it, just the “everything” of it. The totality of that song can be thought of as its Idea that infuses all of its aspects. To accommodate all of those melodies and rhythms and content, the Idea must be expansive. In fact, it must be large enough to have guided every impulse the composer(s) and band members took into consideration when planning, performing, and recording and engineering their pieces.33 The Idea represents the sum total of musical meaning and content in a piece; it therefore crowns the hierarchy of all of the formal musical entities Schoenberg recognizes.34 His full taxonomy of music from large down to small is reproduced in Example 3.9. Proceeding downward through the list, the fully abstract Idea gradually takes form in sounding music structures. These are Shapes, which are brief, two-​to four-​measure complexes containing pitches, rhythms, and harmonies.35 A piece will typically contain several Shapes, each of which serves to spawn the content of its own local section of music. Of these, special consideration is afforded to the Basic Shape (Grundgestalt), the prioritized Shape that Schoenberg conceives as occurring at the outset of a work. This entity represents the first literal reflection of the Idea in Schoenberg’s theory. Patricia Carpenter calls the Basic Shape “the concrete, technical aspect of the Idea,” meaning that it renders composerly inspiration into music incarnate (1983, 15).

A History of Motives—Theory and analysis  73 Example 3.9  Hierarchy of formal terms in Arnold Schoenberg’s theory of music. The quotation concerning the Idea is from Schoenberg 2006 (303–​304); that concerning Grundgestalt is from Carpenter 1983 (15). ABSTRACT Idea (Idee or Gedanke) “The Idea which the composer wanted to present” Totality of work Basic Shape (Grundgestalt) “The concrete technical aspect of the idea” Central utterance built of pitch, harmony, rhythm, etc. Shape Any such utterance, but unmarked

Motive Short but memorable configuration of pitch, interval, rhythm Feature Sub-element of motive, a one-dimensional entity CONCRETE

Moving further down the hierarchy, we observe that the Basic Shape is assembled out of smaller conglomerations of Motives and Features. Writing in June 1934, Schoenberg was careful to define “motive” in two ways, as 1. “the smallest part of a piece that, despite change in variation, is recognizable as present throughout” and 2. a “complex of interconnected features with regard to intervals, rhythm, character, dynamic stress, metric placement, etc.” (129–​130). Schoenberg is more consistent about these points in his theoretical discourse than in the many informal analytical demonstrations he carried out over the years. Consider the analysis of Mozart’s String Quartet in C, K. 465 (I) shown in Example 3.10. In this example and in many others like it, Schoenberg’s analytical brackets are not clearly labeled with regard to content or function. In this case, anything given a letter label serves as a motive. This includes a, a four-​note idea in which the first three stepwise notes proceed by leap or step to a strong-​ beat note. Additional motives noted include b, a descending sixth followed by some other note, and x, any semitonal motion. The primary forms of a appear in

74  Grounds for Motivic Analysis Example 3.10  Schoenberg’s analysis of motivic activity in Mozart’s String Quartet in C, K. 465 (I).

mm. 1–​4; smaller, derivative forms appear in mm. 7–​8; these, too, are specifically referred to in Schoenberg’s accompanying text as motive, despite their size. Motive b, first introduced in m. 6, returns in altered form in m. 16. The situation is less clear in Example 3.11, wherein Schoenberg examines the content of the opening gesture of Beethoven’s Third Piano Sonata in C, Op. 2, No. 3. Schoenberg refers to mm. 1–​2 of Beethoven’s theme as “a gestalt” (shape) that comprises a set of “characteristics” a through h. Characteristic a, shown both in the piano music and the first analytic staff below, is “the main line, rhythmically and harmonically” (2006, 163). Characteristic b is the interval of a second. Other characteristics include the intervallic fourth skip of m. 2 (f), and the I-​V harmonic progression shown in the lowest line (h). Schoenberg’s use of the word “characteristic” again makes it difficult to tell whether both the a and b gestures are motives. The fact that this portion of the treatise specifically deals with “Kinds of Variation,” helps resolve the issue. The discussion that follows gives indication that the smaller b shapes (intervals of a second) are not motives. Their format and behavior is more consistent with the formal entity known as the feature, which Schoenberg defines as “the [mark] of motive . . . pitches (intervals), harmony, contrapuntal combination, stress, and possibly dynamics” 2006, 130). In other words, the identity of a motive depends on the features that comprise it across various domains. One page earlier in The Musical Idea, Schoenberg defines a hypothetical motive, M, in terms of seven component features: M = a + b + c + d + e + f + g

A History of Motives—Theory and analysis  75 Example 3.11  Schoenberg’s view of mm. 1–​2 of Beethoven’s Piano Sonata in C, Op. 2, No. 3 (I) as a gestalt.

A second look at Example 3.11 may help to clarify this terminology.36 We see now that the soprano melody of mm.1–​2 constitutes a full motive, M. (Recall that the full, multivoice complex is a gestalt in Schoenberg’s view). The intervallic entities called b are features. They cannot be motives because they pass by too quickly

76  Grounds for Motivic Analysis to be individually heard and remembered. Upholding the distinction between motive and feature leads to a more nuanced understanding of Example 3.11’s purpose. Schoenberg does not mean to show motives in any of their dynamic aspects; his aim is to illustrate the latent, genetic content of the music. He is endeavoring to show composers and interested amateurs how Beethoven’s music is composed of many features that overlap at the cellular level.37 Schoenberg’s intense interest in music’s smallest elements had both retrospective and prospective ramifications. On the former front, it allies him closely with tradition, specifically the dynamic theories of Marx and Reicha. Schoenberg’s feature and Reicha’s petit dessin are both tasked with illuminating how melodies cohere on the basis of their interval content. This philosophy is laid bare in one of Schoenberg’s most famous analyses, concerning the first theme from Brahms’s String Quartet in A, Op. 51, No. 2, II (Example 3.12). According to Schoenberg, the analysis unveils that “the A major Andante contains exclusively motive forms which can be explained as derivatives of the interval of a second, marked by brackets, a” (1995, 430–​431). It is hard to imagine a humbler element on which to base analysis than the interval of a second. Yet Schoenberg was not content to note the presence of features; he wished to understand the processes by which they operate. His innovations in conceiving and explaining the activity of these microscopic elements would have a tremendous impact on the future of music theory. One such innovation took the form of a quasi-​mathematical notation for illustrating how motives and figures combine. This technique was cited earlier Example 3.12  Schoenberg’s analysis of motives in the melody of Brahms’s String Quartet in A Minor, Op. 51, No. 2 (II). All labels in the staves refer to the Violin 1 part, meaning that the example is not a string quartet score.

A History of Motives—Theory and analysis  77 with respect to a hypothetical motive, M, and its component features, a–​h. Here, in analyzing Brahms’s melody, Schoenberg relies on loose addition to assemble larger and larger melodic elements. His chain of derivation proceeds as follows: c is a + b d is part of c e is b+b, descending seconds, comprising a fourth f is the interval of a fourth, abstracted from e, in inversion (Schoenberg 1995, 431) Analyses supported by this nomenclature helped popularize the idea that lower-​ level musical phenomena behave in mechanistic terms. This insight did more than alter the musical community’s view of motive; it ushered in a new understanding of the art of composition. According to Schoenberg, the Basic Shape (Grundgestalt) of a piece is always present, guaranteeing a work’s coherence. Composers generate new phrases by repeating Grundgestalt material while altering the intervals, rhythms, and other coloristic features. As these elements repeat, they retain a set of critical traces. Marianne Kielian-​Gilbert identifies three categories of trace that operate simultaneously and independently, promoting a sense of continuity even when the motive repetition is imperfect: The repetition of a musical motive can vary or preserve aspects of its material identity (its sounds: notes, contours, rhythms, harmonies, textures); or its functional identity, by which I mean the relational profile of its internal relationships (e.g., scale degree, harmonic-​tonal or gestural functions); or its processive and procedural identity, the broader functions and musical roles that it effects (e.g., processive, recessive, and static; expository, transitional). (Kielian-​ Gilbert 1997, 259–​260)

At the same time that composers are concerned with coherence, they also wish to keep listeners engaged. To achieve this, they continually reshape the main idea to provide novelty. Schoenberg dubbed this practice Developing Variation—​one that paradoxically weds static repetition and dynamic change—​and made it a cornerstone of his theory. He also applied it to his own creative output. In twelve-​ tone composition, a technique Schoenberg pioneered, the Basic Shape manifests as the tone row. This central material is consistently transformed by means of transposition, inversion, retrograde, and rotation operations, which present the tones of the row in novel orders and orientations while preserving its pitch-​class interval content.

78  Grounds for Motivic Analysis Schoenberg’s mechanistic conception of musical process partially resuscitated music theory’s status as a rational discipline. (It had been formally recognized as a science in Ancient Greece and Enlightenment Europe.) As for early critical reception (1900–​1950) of his analyses, it did not seem to matter much that Schoenberg’s equations were inconsistent. The spirit of the demonstrations carried the day. It was enough that Schoenberg’s mathematic “proofs” imparted the air of empiricism to his analyses. Even as many of his readings of specific pieces fell into dispute, the deductive impulse at their core would continue to inspire readers. Decades later, the notion of building a theory and analytical method around strict operations would flower into a wide range of theories, notable among them set theory and transformational theory.38 The few passages and analyses cited so far may give the mistaken impression that Schoenberg engaged in the same “small-​scale” thinking that constrained motives in earlier ages. In fact, Schoenberg also spoke of motives manifesting over extremely wide spans of music. The key to his doing so was a special quality attaching to his grand hierarchy of music depicted back in Example 3.9: fluidity. The difference between upper-​and lower-​level entities in Schoenberg’s theory is one of size, not of kind.39 An awareness that a single set of forces plays out at multiple levels manifests in Schoenberg’s frequent reliance on melodic reduction, the technique by which a denser configuration of notes is pruned to reveal their underlying shape.40 Example 3.13 reprints an image from Schoenberg’s Fundamentals text in which reduction is carried out. Line c) reproduces the first four measures of the melody of Beethoven’s Piano Sonata in C, Op. 2, No. 3, II. The reduction proceeds in two stages, with some notes removed in Line b) and yet more in Line a). The essence of shape a is stepwise content, which Schoenberg posits both when tones are

Example 3.13  Schoenberg’s Example 15 from The Fundamentals of Musical Composition.

(a)

(b)

(c)

A History of Motives—Theory and analysis  79 adjacent and when distant, in durations ranging from eighth note to half note. Shape b is a three-​note gesture composed of step-​then-​third leap. It may seem at first that Line a)’s purpose is to reduce the ornate melody of Line c), illustrating its basic construction out of a single, stepwise interval. In fact, it is best to apprehend these lines together and all at once, with a) appearing as a reduction of c) and c) simultaneously heard as a composing-​out of a). Line b), in contrast, delves further into the total feature content of the melody, seeking out all forms, big and small, of a and b. The second, third, and fourth measures of Line b) are especially noteworthy for two-​level bracketing that shows gesture a embedding within itself. This self-​similar embedding or recursive relation is commonly referred to as a motivic parallelism. Soon after being formally recognized in analytic practice, it became prized by theorists of the early twentieth century. Schenker’s name is the one most commonly associated with parallelism; however, Schoenberg placed considerable emphasis on it as well.41 In an early writing from 1911 discussing Brahms’s Third Symphony, I, Schoenberg argues that the F-​A key structure of the first movement’s exposition is predicated by a small-​scale F-​A♭ motive stated in the piece’s first measure (1978 [1922], 164). If one were to enlist two-​level bracketing to depict this embedded relation, it would be on a much grander scale than in Line b) of Example 3.13; however, the same principle would apply. Through a growing awareness of the activity of motives, analysts gained a means for diagnosing situations in which small-​and large-​scale events resonate with each other. As such, the emergence of the concept of motivic parallelism stands as a critical event in not just the history of motive, but of all Western music making. For centuries, musicians and their audiences increasingly sensed that music “meant something” in its own right, regardless of whether it was texted or not. To support this intuition, they developed various tools for apprehending this phenomenon. In 1854, Eduard Hanslick famously proposed that music’s form serves as the medium by which it dictates its intuited content and meaning (Savage 2010, 59). Over the years, other authors theorized how other domains of music could supply meaning, among them large-​scale harmony (D.F. Tovey), multilevel harmonic syntax (Hugo Riemann) and counterpoint and energetics (Ernst Kurth). No matter which organizational aspect of music was prioritized, the goal of critical analysis remained the same. It was to illustrate the elegant complexity that was presumed to reside in well-made compositions. Complexity on its own was the easy part. It is all but assured in any piece of music containing thousands of notes. For the complexity to appear elegant, however, one must limit the number of explanations for how the notes and ideas coordinate. This logic explains analysts’ persistent desire to winnow down pieces to the fewest possible number of core shapes and forces, while giving those shapes free rein to appear at spans

80  Grounds for Motivic Analysis of all sizes. It is a matter of discerning a workable set of “rules for understanding a piece,” as it were.

Unintended Legacy: A New Concept of Motive Develops in the Twentieth Century The previous section of this survey made the claim that Schoenberg’s conception of low-​level form did not diverge significantly from his nineteenth-​ century forbearers. Motives for him are complex, multivalent gestures, whereas features are the additive fragments that define motives. No evidence exists that Schoenberg ever intended for this terminological dichotomy to collapse, yet that is precisely what happened in American music theory in the decades after his death. The present section of this historical review will investigate this development, which can be symbolized as follows:42 Schoenberg’s feature ⇒ late 20th-​century motive

In searching for a cause for this shift, it is overly simplistic to say that theorists of later generations simply misread Schoenberg. To some extent, yes, they did do that. Historical context is everything, however: what might be ruled a “misreading” by one generation of scholars might be deemed a “reimagining” by the next. In this section, a reevaluation of twentieth century events will yield a new narrative. The momentous theoretic shift symbolized above will be shown as the product of a surprising, unintended collaboration among scholars hailing from many disparate—​and in some cases: presumably opposing—​camps. Exhibit A in this new account is the analysis by Schoenberg reproduced in Example 3.13, discussed earlier. In that account, I resisted calling the fragments in Line b) motives because they are too small and simplistic to accord with Schoenberg’s definition. Mid-​twentieth-​century theorists confronting graphics such as Example 3.13, in contrast, would not have hesitated to call all of the example’s bracketed entities motives. The difference in approach can be understood in part based on what is known about Schoenberg’s theories now versus then. Only two theoretical works by Schoenberg were published in his lifetime, Harmonielehre in 1922 and Models for Beginners in Composition in 1943 (Schoenberg 2006, xii). It was not until the 1970s that Schoenberg’s Musical Idea treatise became widely known through the agency of Alexander Goehr, a son of one of Schoenberg’s Berlin pupils.43 With little or no access to Schoenberg’s writings detailing the structural hierarchy of music from the surface to the crowning Idea, theorists active between 1942 and 1967 could hardly be expected to preserve a distinction between

A History of Motives—Theory and analysis  81 motive and feature. Those who wished to know about Schoenberg’s views on motives mostly made do with a few relevant passages from Harmonielehre and in the essays that would later be collected in Style and Idea. We have noted the profound influence the radio talks/​essays had on motivic theory by virtue of their inspiring, yet loosely systematic, readings. We have not acknowledged the role of Harmonielehre. That book is not concerned with analysis, per se; nonetheless, it offers a remarkable number of technical claims about prominent Classical pieces. One such insight referenced earlier comments on resonating small-​and large-​scale third relations in the exposition of Brahms’s Third Symphony, I.  In addition to exemplifying motivic parallelism, this insight— for good or ill—​established parameters for a motive’s format. A motive, it seems, could manifest in as few as two notes. According to what Schoenberg thought in 1922, it could, moreover, present as a rhythmless intervallic entity capable of reaching across large formal areas. Schoenberg’s early conception of motive does not fully accord with his mature theory. Its pervasiveness came to be so great, though, that even present-​day theorists with access to The Musical Idea are likely to confound feature and motive. In the case of Example 3.13, it is again possible to lay some blame for this on Schoenberg’s commentary. The relevant accompanying text in Fundamentals is, again, maddeningly ambiguous: it never says which bracketed a gesture, the two-​ note form from line (a) or the five note form from line (c), constitutes the actual motive. The midcentury shift in the concept of motive has thus far been attributed to a general lack of awareness of Schoenberg’s mature theory and to the fogginess of his on-​air and in-​print analyses. These two factors make it seem like the feature ⇒ motive shift was an accident of history. That conclusion, critically, overlooks agency. It fails to account for the active role that theorists played in bringing about the evolution of motive. Here we seize on the narrative of motive’s twentieth-​century evolution and reframe it in active terms. A few decades after Schoenberg opened the door a crack to the possibility of a two-​note motive, theorists rushed to pry it open and charge through. Embrace of this new, cellular form of motive entailed a theoretic sacrifice: motive would shed a key aspect of its original identity, its multifacetedness. Theorists, of course, still could require motives to exhibit characteristic rhythms, harmonies, articulations, and so forth. In their excitement to capitalize on musical connections based on pitch-​interval relationships, however, they increasingly neglected to specify those other attributes in their analyses. As a result, a new theoretic entity emerged that should more appropriately be called a “feature motive” (my own term). The feature motive is similar to a motive, but “flatter” in the sense that it exists in fewer dimensions, specifically, often in pitch and rhythm only.

82  Grounds for Motivic Analysis A watershed event in motive’s twentieth-​ century evolution was Allen Forte’s article, “Motivic Design and Structural Levels in the First Movement of Brahms’s String Quartet in C Minor” from 1983. In it, Forte lays out four “guidelines” for motivic analysis that are printed here in their near entirety: 1. The motive is primarily an intervallic event, distinct from any particular pitch manifestation. 2. The original pitch or pitch-​class representation of a motive is of singular importance . . . and we call this referential function of a particular form pitch-​specific which means that the motive designated consists of the same pitches as the original form of the motive; and the term pitch-​class specific means that the motive is recurring, but at some level of octave transposition with respect to the original form. 3. The boundary interval of the motive is its most salient feature. The internal structure is variable or may even be absent in some representation of the motive . . . 4. A motive may be transformed without losing its basic identity. The transformations which Brahms uses are retrograde, inversion, and retrograde inversion. He also uses a transformation which I will call minor to major or major to minor depending on the circumstances. (Forte 1983, 474) The guidelines, which in hindsight read more like tenets, constitute a full revision of the motivic concept. They accord to the motive the properties of a mathematical set, which is a collection “of all the objects of a specified kind—​that is, consisting of all the objects which satisfy a given condition” (Pinter 2014, 10). Set theory, originally pioneered by Howard Hansen and Milton Babbitt in the late 1950s, steadily gained influence in the 1970s as theorists increasingly recognized its capacity for explaining the content and structure of freely atonal works. Near the time that Forte’s article was published, set theory analysis had begun to explode in popularity.44 That bit of context helps explain what is most surprising about the four guidelines, which is that Forte declines to offer a single citation or explanation for any of them. He likely assumed that readers would be comfortable transferring the essential concepts of set theory to motivic analysis. His own recent treatise, The Structure of Atonal Music (1972), on set-​based analysis would presumably have served as the primer in this regard. In Chapter 1 of Structure, he establishes the viability of pitch-​class equivalence, then shows how a set’s content is preserved when it is subjected to uniform transposition, inversion, and retrograde (Forte 1973, 2–​13). He next demonstrates how the identity, sound, and potential behavior of a set is directly predicated on its total intervallic content, as measured among all member pairings (Forte

A History of Motives—Theory and analysis  83 Example 3.14  Excerpt from the Table of Motives given in Forte 1983 (476). Annotation and arrow added by the author.

1973, 13–​18). These set-​theory concepts correspond directly to Guidelines 2, 4, and 1. Two additional features of Forte’s “Motivic Design” would turn out to be similarly influential. The first is its protocol for organizing a motivic analysis. Forte’s analysis opens not with any score excerpts or motivic derivations, but with the summary “Table of Motives” shown in Example 3.14.45 (Though Forte does not provide a score to illustrate the origins of each motive, his prose indicates that they are all derived from events in mm. 1–​8.) Twelve central pitch-​based motives are presented in this table in staff notation and are assigned a Greek letter label; a separate chart lists rhythmic motives. Common variant forms, such as mirror inversions and retrogrades, are indicated with modified labels such as a bar over the letter or a prime (′) marking. This mode of presentation is dry and objective, imparting an air of authority to the analytic process. (An additional, subtle boost in intellectual cachet is afforded by the Greek symbols, which call to mind mathematic and chemical formulas.) Many of the trappings of Forte’s analysis, both organizational and stylistic, would be emulated for decades following this article’s publication.46

84  Grounds for Motivic Analysis A second notable feature of Example 3.14 appears at the start of the fifth row. To account for the viola’s double-​stopped Gs in m. 7, Forte allows the two notes of motive theta to appear simultaneously. To his credit, Allen Forte makes it clear that his decision to allow this vertical form of motive is “unconventional” (477). It is impossible to know, now, exactly why he felt that disclaimer was necessary. Was it meant merely to stave off critiques of this isolated analytical decision? Or did he feel responsible for pointing out the line in the sand demarcating the edge of traditional motive formatting, even as he tiptoed over it? The significance of this appearance of a chordal motive, itself a special case of feature motive, cannot be overemphasized. Forte’s adventurous theorizing is striking. What is far more striking is that no objections to it were voiced at the time. The first substantial critique of this article did not appear until decades later, with the publication of Huron 2001. In its own time, Forte’s essay was greeted by a critical silence as resounding as “the dog that didn’t bark” from the Sherlock Holmes tale, “Silver Blaze.” The theory community’s tacit acceptance of this motive form, along with these four “proto-​set theory” guidelines, indicates that the motive => feature motive shift had by this time all but concluded. The reason that feature motives were wholly uncontroversial in 1983 was because the two dominant analytic methodologies of the time already accommodated them. The shift would have been all but imperceptible within set theory. That entire discipline, concerned with parsing and comparing (mostly) small pitch-​class configurations in atonal music, was essentially born of Schoenberg. The organizational principles he devised and promulgated as composer and teacher in the early 1900s would later serve as a breadcrumb trail for midcentury set theory pioneers to find their way through his work. Schenkerian theorists, on the other main front, would similarly have had little cause to object to Forte’s chordal motive or to feature motives in general. Pitch motives in Schenkerian analysis conform to tonality, the environment they inhabit. Thus, they mostly manifest as thirds, seconds, neighbors, fifth-​spans and the like (Cohn 1992, 154). Furthermore, since these tonal gestures may manifest over long stretches of time, they are typically decoupled from rhythm.47 As tonal intervals with no characteristic rhythms, Schenkerian motives enjoy privileged status based on their traceable links to a piece’s deep-​background contrapuntal content (Ursatz). When viewed in isolation as configurations of notes in voice-​leading graphs, however, such motives are largely indistinguishable from feature motives.48 It is fitting that Schoenbergian and Schenkerian scholars would agree on the viability of feature motives.49 Some concessions would be necessary for this to occur, in the form of selective historical amnesia from the former camp and some methodological slippage from the latter. Both groups seemed willing to make these compromises, though, to promote a common analytic language. It

A History of Motives—Theory and analysis  85 came to pass in the second half of the twentieth century that, no matter which analytical technique one preferred, one could reasonably expect “motive” to refer to a short, arrhythmic shape enfolding melody and harmony. The reason this agreement may be characterized as “fitting” was because it realigned two approaches that—​excepting the occasional attempt to integrate their methodologies (see the fourth section of this chapter)—​for decades had stood quite separate. Here it is important to remember the shared central conceit that underlies both Schoenberg’s and Schenker’s theories, which is that harmonic and linear forces are interdependent. According to Schoenberg, a tone row is a “two-​dimensional” entity that can be realized both horizontally to create melody, or vertically to produce harmonies or chords (Schoenberg 1975, 226). According to Schenker, the Ursatz is a vertical triad that is composed out horizontally over the length of a full piece.50 The cautious re-​knitting of Schoenberg and Schenker that began in the 1980s accelerated in later decades. In the late 1980s, pitch and pitch-​class sets had become standardized to such an extent that it was acceptable to apply them in the study of tonal pieces. Forte wrote another essay, “New Approaches to the Linear Analysis of Music,” to establish a method for this practice (1988). Soon after, a slew of analyses emerged that rationalized the large-​scale key progressions of certain late Romantic works as “composing out” the iconic, dissonant sonorities sounded at their openings, typically an augmented triad or diminished seventh chord (see Todd 1988 and Cinnamon 1992). By 1996, it was not at all controversial for Mark Anson-​Cartwright to attribute motivic significance to a sonority itself, as he does in his “Chord as Motive” essay on Wagner. Of all of the changes motive underwent in four centuries, this most recent shift may well be the most profound. In little more than half a century, the motive was stripped of most attributes excepting pitch and rhythm and allowed to collapse into an instantaneous verticality. The primary force of transformation was the rising influence of set theory, with Allen Forte’s 1983 essay serving as the model for how the concept of set could extend its tendrils toward the concept of motive. By the close of the twentieth century, the notion of the set had become so dominant that it essentially co-​opted motive. An introductory passage from Joseph Straus’s Remaking the Past, for example, conflates the two concepts as follows: “A pitch-​class set is a motive from which many of the identifying characteristics—​ rhythm, register, order—​have been boiled away” (1990, 24). In stating this, Straus implies that there is no longer room nor need for motives to exist in time at all. He continues, illustrating all of the pitch-​class sets in Schoenberg’s Piano Piece, Op. 11, No. 1, mm. 1–​5 that span a major third with semitone attached to either end (Example 3.15). It is specifically the pitch-​class content, he declares, that makes the music “motivically coherent” (Straus 1990, 24).

86  Grounds for Motivic Analysis Example 3.15  Analysis of motives (pitch-​class sets) in Straus 1990 (24). The work under study is Number 1 from Schoenberg’s Three Piano Pieces, Op. 11 (cf. Ex. 2.13).

While Straus does not speak for all theorists, his formulation of motive may be fairly said to represent a presently prevailing view. This is not a condition to be lamented, necessarily; however, since it establishes a starting point for any new theorizing on motive, it must be interrogated. Feature motives rose to prominence for a reason, and they do confer many analytic benefits. Feature motives are relatively easy to work with, apply to a wide range of musics, and are good for demonstrating the interrelation of melody and harmony. As we have seen over the course of this survey, however, there is much they cannot do or no longer do. This section’s account of motive’s evolution in the twentieth century is of course far from comprehensive. By concentrating on Schenkerian and Schoenbergian theory, for instance, it has neglected to consider how motive intersected with other developing theories. In a separate conference paper, I  delve further into the twentieth-​century intellectual environment that promoted the feature motive, giving special consideration to the impact of a newly developing third stream of theorizing, transformational theory (Auerbach 2016).51 The topic of the history of motive is rich enough to sustain a host of further investigations. To continue in this vein, however, would take us too far afield from our more immediate goal of defining motive and motivic analysis anew. For this reason, the final part of this chapter will turn away from issues of history toward those of philosophy and methodology. The section that follows provides a brief overview of motivic analytic techniques developed over the past one hundred years. Certain aspects of this survey activity will be carried out more or less impartially, for example as we identify major treatises and report on schools of thought. Some criticism will come to bear as well, as we evaluate each method, cite published commentaries, and make fresh assessments of it.

A History of Motives—Theory and analysis  87 This active engagement will serve a practical purpose: as the separate aspects of each method are evaluated as weak or strong, they will either be discarded, or adjusted and incorporated into the new formal method to be proposed in Part II of Musical Motives.

An Account of Present-​Day Motivic Analytical Techniques To facilitate discussion of the many analytic approaches to motive explored in the past century, this account groups them into three areas. The ordering of the categories corresponds roughly to their chronology.

Method Category 1: Adherence to Schoenberg The first analytic tradition to be assessed is the one that hews closest to Schoenberg’s theories and methodologies as originally formulated. One group of analysts, most notably Josef Rufer (1893–​1985) and Patricia Carpenter (1923–​ 2000), acquired their techniques from studying directly with Schoenberg. Others, such as Rudolph Réti (1885–​1957), absorbed his teachings from a distance through study of his extensive print and radio output.52 Last, there were a select set of analysts whose views accorded with Schoenberg’s, it seems, mainly through force of Zeitgeist. Hans Keller is one such figure: he wrote and lectured extensively on motivic unity despite claiming that he was largely unfamiliar with Schoenberg’s theories (Garnham 1998, 84). Keller’s student, Alan Walker, continued his work, releasing several book-​length studies that similarly investigated issues of musical unity in Classical and, in a remarkable extension, twentieth-​century post-​tonal  works. The main element common to analyses in this category is a high degree of methodological freedom. This freedom pertains to both how motives are identified and discovered in music and how the various forms are shown to interrelate. In Rufer’s case, this freedom arises from his close adherence to Schoenberg’s notion that motive is rooted in gesture. This view is exemplified in Rufer’s demonstration of how two motives unify the three movements of Beethoven’s Piano Sonata in C minor, Op. 10, No. 1. A portion of his analysis is reprinted in Example 3.16. Motive a, shown in the fifth line of the table (see asterisk), does not refer to any specific interval or rhythm from the piece; instead it represents triadic arpeggiation in general. The essence of motive b (see first line, at star) is descending motion by step.

Example 3.16  Excerpt of Rufer’s analysis of Beethoven’s Piano Sonata in C minor, Op. 10, No. 1 (1966). Annotations added by the author.

A History of Motives—Theory and analysis  89 Rufer’s gesture-​based view of motive helps to explain the sheer number of motivic associations made in his theme table. The bracketed annotations give the illusion of a consistent method; however, the only real justification for linking events is whether one reminds him of another.53 That said, many of the connections he notes, such as those involving recurrences of motive a across the first movement, seem cogent. Others are dubious, such as that involving the two forms of b from the main theme, mm. 9–​10 (again, see asterisked line, end of system). The problem here is Rufer’s unmusical parsing. Although the melody descends in mm. 9–​10, there is nothing particularly 2nd-​like about it. If anything, the linear fifth should be parsed as two elided 3rds, G5-​E♭ and E♭-​C. (The short duration of the F5 makes the two-​note figure marked b2 extremely unlikely.) Réti’s Thematic Process in Music (1967) improves a bit on Rufer’s method. Like Schoenberg and Rufer, Réti favors melody-​only analysis. His work is distinguishable from theirs in how it attempts to formalize analysis. Réti is one of few theorists for whom motivic analysis serves not as an element within a theory, but as a discipline unto itself. He devotes two chapters of The Thematic Process to tracing the history of motives back to Gregorian chant. A third chapter investigates the psychology of motive as it asks whether the thematic process is perceived consciously or subconsciously. Of Réti’s several extensions to motivic analytic method, the most well-​known occurs in Chapter 4, which delineates “Various Categories of Transformation.” The categories, which are presented as section headings in the text, are listed here with glosses given in parentheses:

1. Inversion 2. Reversion (retrograde) 3. Interversion (note reordering) 4. Change of Tempo, Rhythm, Accent 5. Thinning, Filling of Thematic Shapes 6. Cutting of Thematic Parts 7. Thematic Compression 8. Change of Harmony 9. Change of Accidentals (while pitch names are retained)

These transformations are, on the whole conventional and are either retained or have close analogs in modern atonal and tonal theory. Many of the demonstrations Réti offers of these transformations are convincing, as well. The techniques of “thinning and filling in,” for example, are demonstrated through ̂ ​1̂ (sol-​do) motions across the movements of a survey of variously decorated 5​– Beethoven’s First Symphony. The premise of Example 3.17(a) is that a central

90  Grounds for Motivic Analysis shape of G-​B-​C, which appears in movement I at the pickup to the Allegro, is just as likely to appear thinned out as a fourth leap or thickened into the full linear fourth G-​A-​B-​C (images at center and at right). Other demonstrations are less theoretically sound. With regard to Beethoven’s Fifth Symphony, I, for example, he reduces the “Second Allegro Theme” to reveal the four-​note horn call (“Second motto”); see Example 3.17(b). The implication Example 3.17  (a) In Example 129 from Réti 1967, the motive G-B-C from (I) of Beethoven’s First Symphony is thinned in movement II and filled in movement III (86).

(b) In Beethoven’s Fifth Symphony, (I), Réti derives the second allegro theme in mm. 63–​66 from the Second motto event from 59–​62, shown below it (1967, 175). The annotation challenging the status of the E♭5 is newly added.

(c) The Second Allegro theme, mm. 63–​66, in context with string accompaniment.

A History of Motives—Theory and analysis  91 is that the second theme represents a transformed version of the symphony’s Motto:  G4-​E♭-​F-​D. Réti’s point is weakened by the fact that the contour of the Second Allegro theme is completely different from the Second Motto shown under reduction below. The former centers around B♭4, while the latter descends the octave, B♭4-​B♭3. Further doubts on Réti’s derivation arise when the Second Allegro Theme is viewed in a fuller context. Example 3.17(c) reintroduces the lower string parts supporting the melody. In Beethoven’s harmonization, dominant harmony controls all of the second measure. If E♭ is a non-​chord tone, it cannot also be structural; the four-​note shape Réti arrives at through reduction must be invalid. The analyses by Rufer and Réti are sufficient for diagnosing two types of error endemic to this analytic tradition. The first stems from allowing analysts to posit relationships solely on the basis of intuition. To avoid errors resulting from this practice in our own method, we might consider outlawing it entirely. But this would go too far. By removing the personal aspect from analysis, one risks effacing Schoenberg’s spirit entirely. We gain more, I argue, by retaining Schoenberg’s associative practices while also reining them in. This may be achieved by splitting the monolithic act of motivic association into a series of transparent, objective, and concrete decisions. The other questionable practice in this tradition involves analysts making claims out of context. In this case, “context” almost always means “proper harmonic context.” The literature is rife with criticism of melody-​only style analysis. Of the many essays warning of the dangers of misrepresenting music in this way, John Rothgeb’s 1987 review of Walter Frisch’s Brahms and the Principle of Developing Variation stands as authoritative. His critique concerns Schoenberg’s view of Brahms’s Quartet Op. 51, No. 2, II. In an analysis that serves as a core model for Frisch, Schoenberg identifies the first four notes of the melody, C♯4-​D-​E-​D as a motive (see Example Web.3.2 ). Rothgeb believes that shape is invalid, because it cuts off the melody before it can complete a pattern of 10-​10-​10 outer voice counterpoint spanning the downbeats of mm. 1–​3. This error, according to Rothgeb, results not from oversight but willful neglect. “Schoenberg’s examples,” Rothgeb pointedly reminds readers, “do not even sketch the bass,” a practice that contradicts what is definitively known about Brahms’s approach to composition (1987, 215). The danger of applying a stylistically insensitive technique is not that an analysis will fail to explain a piece. It is that the analysis will fail to “understand that it is failing to explain it,” a problem made all the more pernicious as the investigator remains unaware of the deficiency (Rothgeb 1987, 201). Our response to the acknowledged weakness of melody-​only style analysis is unequivocal, which is that this practice must be finally and fully abandoned. Before moving to the next category, I wish to clarify a last point about the decision to outlaw melody-​only style analysis. This stance does not mean that all motives proposed under the new system must be polyphonic (multivoice)

92  Grounds for Motivic Analysis entities. It means that whenever analysts extract a shape from a musical texture, they must take harmonic context into account. Doing so is essential to avoid positing musical shapes that run counter to the composer’s aim.

Method Category 2: Schenkerian-​Schoenbergian Approaches For the past fifty years, many of the sharpest barbs against motivic analysis were lobbed by Schenkerian analysts. The difference in approaches to reduction favored by the dual camps could hardly be more extreme. Where Schoenbergian analysts are more inclined to examine melody only, Schenkerians consider the full texture. Indeed, the foundation for musical structure in their tradition, the Ursatz, is a polyphonic structure that incorporates bassline and harmonic elements. Where Schoenbergians are traditionally given great latitude in how they extract notes from music, Schenkerians abide by stricter rules for determining which notes in a local context are structural and which are ornamental. One might think, given the comparatively thin methodological footing on which Schoenberg’s method rests, that Schenkerian analysts would have come to disfavor motivic analysis. In fact, they consistently give high priority to motives. When reading a commentary written to accompany a Schenker graph, one can expect that at least a few paragraphs will describe the piece’s motivic content. As previously noted, the precedent for this concern with motives comes from Schenker himself. Over time, conventions of Schenkerian analysis gradually shifted so as to emphasize multilevel motivic correspondences. Knowingly or not, Schenkerians began to posit musical shapes in their analyses that, under scrutiny, could be said to violate the formal system’s rules of reduction and hierarchy.54 This secondary hermeneutic impulse precipitates an internal conflict. On the one hand, Schenkerian analysts have always had a keen interest for working with motives. On the other, the regimented rule system under which they operate makes them, pace Rothgeb, naturally suspicious of motivic analysis. One can imagine two ways to reconcile these forces. One is to officially relax the rules of analysis to accommodate motives, but this has never been seriously considered. The other strategy, which is to inject some of the methodological rigor of Schenker into motivic analysis, has. Over the years, a number of authors have attempted a formal reconciliation of Schenkerian and Schoenbergian technique. Two recent essays by Allen Cadwallader (1988) and Jack Boss (1999) fit this description. Though their terminology differs, both operate according to the same principle of “limit[ing] what [is] called ‘motive’ to segments that are equivalent to diminutions in the Schenkerian sense or that combine such diminutions” (Boss 1999, §2). Cadwallader’s method produces a Schenkerian reading of a Beethoven

A History of Motives—Theory and analysis  93 Bagatelle in which there is near-​perfect correspondence between surface and middleground motives. Boss’s produces a Schoenbergian reading of Beethoven’s Piano Sonata in C minor, Op. 10, No. 1 that centers around the activity of two motives. These are identified as alpha, a double-​neighbor figure, and delta, a linear ascending-third gesture that is harmonized in parallels 10ths. The means by which Boss mingles Schoenberg and Schenker are highly subtle. Throughout his analysis, the tenets of Schenker remain in effect: he adheres to strict reduction techniques between surface and middleground layers. Yet the focus of the analysis is on the interaction of the motivic shapes. The resulting interpretations feel Schoenbergian because the motives are regarded in dynamic terms. To take one example, motive alpha, Boss notes, undertakes “a journey toward greater salience” that in the end is thwarted by delta’s resurgence, “pushing alpha back down into the inner voice” (1999, §11). While Boss’s approach holds much promise, it would be an exaggeration to say that it fully reconciles the two methodologies. The priority given to the one discipline over the other evokes a sense of Schoenberg’s baseball game being played out on Schenker’s home soccer pitch and according to its rules. The last major work to be noted in this category is David Epstein’s Beyond Orpheus (1973). The primary inspiration for this work is Schoenberg. As such, it relies heavily on Schoenberg’s presentation style and terminology; for example, in Epstein’s text, the recurring central material is referred to as the Grundgestalt. At the same time that he declares his Schoenbergian pedigree, however, Epstein also acknowledges the strong influence Schenkerian theory has on his theory. In Chapter 1, Epstein summarizes Schenker’s contribution to music, noting the particular value of his principles for distinguishing structural versus ornamental notes—​that is:  systematic reduction—​and of his multilayered graphs “to illustrate the coordination of foreground gestures with background structure”—​that is, hierarchy (Epstein 1979, 7). Epstein’s sincere admiration for these principles pervades all of the book’s large-​scale analyses, which are further unified by the common script he follows when carrying them out. Epstein first identifies the primary motives from the opening measures of a movement. For Beethoven’s Third Symphony (“Eroica”), there are two such motives, a triad-​gesture and a three-​note chromatic shape (see left and right brackets in Example 3.18(a)). He then accounts for each motive’s activity in multiple structural levels of the piece. The graphic in part (b) of the example resembles standard Schenkerian reduction; note, though, that the three-​note chromatic shape illuminated in the lower staff is derived from the surface in a rather free manner. The high-​priority tones in Epstein’s reduction are determined on the basis of melodic correspondences among phrase onsets; there is no consideration of counterpoint or harmony. A closer look reveals that the D5-​E♭-​D♭ shape in the lower staff transforms the three-​note shape from part (a) according to one of Réti’s least rigorous operations, interversion(!).55

94  Grounds for Motivic Analysis Example 3.18  Epstein’s analysis of motives in Beethoven’s Symphony No. 3, “Eroica” (I). (a) The main theme, mm. 3–​11.

(b) Reduction of the melody in mm. 83–​93 to a three-​note, chromatic shape (1979, 115).

Beyond Orpheus was criticized by its early reviewers for engaging in such analytic license, but these complaints never seriously tarnished its legacy (Agawu 1988). To this day, Epstein’s offering is remembered chiefly as a work that strengthened the credibility of Schoenbergian analysis by incorporating aspects of Schenkerian methodology.56 This characterization, though no doubt meant to be charitable, is patronizing. Epstein did not merely bring a Schenkerian sensibility to bear on Schoenberg’s motivic analytical tradition. More accurately, he wholly revived and refreshed motivic methodology in its own right. One way that Beyond Orpheus achieved this is by expanding the purview of motives. Although they chiefly manifest in his analyses as pitch and pitch-​class shapes, the motives at all times are understood to encode other kinds of musical information. Epstein notes early on that “harmonies are contrapuntally conceived” (1979, 7). Soon after, he extends the notion of “contrapuntal” to include motives. These claims of interdependence bear directly on methodology, as it encourages analysts to keep the harmonic implications of their proposed motives in mind, thus avoiding the kinds of errors that Rothgeb deplores. Another of the book’s achievements is that it improves the methodology for identifying and associating motives. Epstein cites the long-​standing lack of clear “criteria by which pitch shapes can be judged,” as “the greatest single cause of questionable studies of this sort in the past” (1979, 37). What is missing, in other words, is a rigorous procedure for reducing ornate textures. As a corrective, he offers his own set of criteria for linking two or more shapes, which are as follows: 1. Points of contour 2. Rhythm and meter

A History of Motives—Theory and analysis  95 3. Pattern: consistency and recurrence 4. Degree position of pitches within a key 5. Harmonic content Mostly, what is described in this list is not new. Some version of Epstein’s Point #3, wherein shapes attain structural status through repetition and patterning, is found in every methodology we have encountered. Point #4, as well, has long held sway in Schenkerian analysis to account for the migration of tonal works through key areas. If this condition were not in place, it would make it difficult to assert some common-​sense identities, for example, between a thematic gesture occurring in the dominant key in one part of a sonata and then in another key during the development or recapitulation. As a pitch shape’s letter names shift due to transposition, the scale degree correspondences among the motive forms ensure they sound identical. Epstein’s Point #5 acts as a corollary to #4, by claiming that motives, if truly related, will project similar harmonic profiles.57 There is also precedent for Epstein’s Point #1, which holds that structural pitches may be drawn from salient moments in phrases, specifically endpoints (onsets and cadences) as well as high and low points of pitch. In a passage from The Thematic Process, Réti claims that the basis for relating first-​and last-​movement themes in Beethoven’s “Moonlight” sonata inheres “not in the latter’s concrete melodic course, but . . . through a connection of some of its corner notes” (1979, 93; emphasis mine).58 Epstein’s close affinity with Réti, of all theorists, provides a clear signal that he is operating further beyond the boundaries of Schenkerian analysis than many assume. The substance of his Point #2 gives similar indication; it reads: Rhythm and Meter. Significant notes more often than not lie upon rhythmic and/​or metric strong points. This is not to exclude ornamental notes from consideration. Where they are significant, however, ornamental notes will usually lie in some close and prominent relationship to notes that themselves are structurally important. Discerning these relationships is of course a matter of judgment, and not all judgments may be definitive. (1983, 37)

The idea that a pitch’s structural weight is communicated through its rhythmic and/​or metric salience is intuitive, yet is in many ways antithetical to Schenkerian thought. The reason is spelled out where Epstein admits it is impossible to specify when this criterion will apply and when it will not. Schenkerian reduction avoids this hazard by minimizing rhythmic concerns. In that mode of analysis, the determination of whether a note is structural depends on other factors, such as its scale step and its contrapuntal relation to other voices. Epstein’s theory and technique, despite its flaws, shows promise as a pillar that could help support a new, refined system of motivic analysis. We have established

96  Grounds for Motivic Analysis that approaches that are too flexible are irresponsible. Stricter approaches that filter out important, salient tones, on the other hand, can be too limiting. A true compromise between the Schenkerian and Schoenbergian approaches is unlikely to ever occur; however, Epstein’s five criteria provide a glimpse of how the latter method might be resuscitated. What is missing is a means for judging the relative weight of pitches. Were we to find a way to uniformly implement his criteria in theory and analytic practice, motivic analysis could in the future be insulated from many of the critiques that have been lodged against it.

Method Category 3: Cognitive Approaches There exists a rich, long-​standing tradition of psychologists investigating music. Many of these scholars have done so with the hope of better understanding the brain overall. Examples include studying musical memory to better understand memory in general, or examining musical ability in people with communicative disorders (aphasias) to aid in brain mapping. More recently, scholars have worked to build an autonomous field centering specifically on the “psychology of music,” in which the study of brain function is carried out to better understand how humans conceive music. It is this subfield that has the closest bearing on the recent history of motive. It would be wholly appropriate for a study inquiring into the essence of motive to draw on the significant body of experimental literature on motivic cognition and perception that exists. Done right, this would entail our becoming fully versed in the data-​driven side of music theory; however, we do not have the time nor resources to accommodate that endeavor. Fortunately, there is a more expedient path into this subdiscipline. It comes by way of another activity that cognitive scientists partake in, one that frequently takes up as much of their time and effort as the actual running of experiments. This activity, known as “conceptual modeling,” translates thought processes—​which in reality are impossibly abstract and nonlinear—​into more concrete representations that typically take the form of networks and algorithms. Devising conceptual models for music cognition represents a highly robust form of theorizing. The most important feature of the models is that laboratory experiments can be engineered to test them: such usually involves measuring human and animal responses to aural stimuli and/​or by running rule-constrained computer programs that generate music.59 Another advantage of conceptual models is that they are designed according to the principles of cognitive science. In a refreshing break from the tradition that frames musical thinking as a discrete pursuit with its own symbology and rules, conceptual models resituate musical thinking as just another kind of knowledge. Conceptual modeling thus tends to

A History of Motives—Theory and analysis  97 be interdisciplinary, often relying on insights from fields as wide-​ranging as neuroscience, psychology, and linguistics.60 Our primary reference text from this category will be Lawrence Zbikowski’s Conceptualizing Music (2002). This work is meant to show how our “understanding of music draws on the same cognitive processes” that help us “organize [our] understanding of the world as a whole” (2002, 4). The first basis provided for this understanding is category, which is a mental network that each human consciousness assembles to describe every “thing” it knows. The tutorial Zbikowski offers on this subject describes the category of bird, shown in Example 3.19. This is a so-​called natural category that emerges “from the interaction of humans with their natural environments” (2002, 39). In the diagram, the category at far left is established on the basis of various general “attributes” that each admit a range of “values” (second and third columns, respectively). Some values are prioritized via the “prototype effect”:  these manifest where our strongest senses of attributes and commonality align. For example, most people, on being asked to think of “some bird, any bird,” will imagine a small, dull-​colored creature with wings and a beak; these values are indicated by the asterisks in the “values” column. According to cognitive psychology, Example 3.19  Diagram from Zbikowski 2002 of the category “Bird” (42). attributes size

values

individuals

large medium

wren

small* brown*

color

white

cardinal

red green

Bird

chirps*

sound

clucks

chicken

sings squawks

locomotion

flies* runs

parrot

98  Grounds for Motivic Analysis each time we encounter some new potential bird, we compare its attributes to our conception of the category and determine how well it fits. An illustration of this process is given in Example 3.19 for the category member, wren. The relative boldness of connector lines reflects the relative strengths of associations. This explains why wrens likely seem more bird-​like to you than other winged creatures: it all depends on your personal category structure(s) and prototype(s). Continuing this line of thought, it further makes sense that people’s category structures change over time as their experiences shift. This informs another key aspect of categories, which is that they are porous and changeable. Zbikowski reminds us in the strongest terms that categories are something our brains impose on reality, not the other way around: “Categories are not only not given by nature, but also they are subject to change and modification as our thought unfolds” (2002, 12). Shortly after category is established as a basis for thought in general, Zbikowski translates this phenomenon into musical terms. The musical concept that best instantiates the notion of category for Zbikowski is motive. To defend this view, he cites Schoenberg at length, specifically the passages that link musical comprehension to the repetition of clearly demarked and recognizable shapes. He then bolsters this view by systematically analogizing motives to more worldly, familiar categories. An important parallel in how we speak about the two worlds, physical and musical, pertains to a preference for labels that fall within a certain sweet spot of specificity. The average person, upon seeing a winged creature, will say it is a bird, as opposed to a “carbon-​based life form” (too general) or a “geococcyx californianas” (too specific). The common category name attaches to the so-​ called basic-​level, somewhere in the middle of the naming hierarchy where it provides “maximum utility” (Zbikowski 2002, 31). The same goes for motives in music. When discussing the opening of Stravinsky’s Rite of Spring, musicians and nonmusicians alike will not refer to the melody from m. 1 as “a bunch of notes” (too general), nor as “C5-​B4-​C5-​B4-​G-​E-​B-​A, with rhythm of a quarter note–​four sixteenth notes–​eighth note, also decorated with a shake on the second note” (too specific). They will instead employ a label that reflects a basic-​ level understanding, calling it “the bassoon motive from Rite” or, perhaps in the isolated context of the score itself, “Motive x.” Another parallel between category and motive pertains to how instances of the latter are stored in the mind. As listeners attend to a piece with prominent motivic activity, they are able to identify returns of the primary gesture even when it is altered in register, timbre, and—​to a lesser extent—​pitch and rhythm. To show how this kind of recognition is the same as the kind undergirding our workaday knowledge of birds, Zbikowski examines the relationships among motive forms in Beethoven’s Fifth Symphony, movement

A History of Motives—Theory and analysis  99 I. His diagram in Example 3.20, following the format of his “Bird” example, illustrates how a diverse set of “individual” forms of motive at the far right fit into a single category through the mediation of values in three musical domains (attributes). Of the many attractive aspects of the “motive as category” notion, the most compelling arises out of the way it models attributes. Each bubble in the leftmost column of Example 3.20 is an independent musical domain. More striking is that only one of them, “diatonic melodic profile,” expressly concerns pitch or pitch-​ class. Through aid of cognitive theory, Zbikowski restores some of the elements of motivic identity that, once essential, were “boiled off ” during the recent period of (de-​)evolution described earlier.

Example 3.20  Diagram from Zbikowski 2002 of the category structure of main motive forms in Beethoven’s Symphony 5 (I), mm. 1–​21 (44).

attributes

values tutti

orchestration

individuals mm. 1–2

solo

mm. 3–5

ensemble

mm. 6–7

mm. 7–8

f, ff

dynamic

cresc.

mm. 8–9

mm. 10–11

piano mm. 11–12

mm. 12–13

u, –2, –2 mm. 14–15

diatonic melodic profile

u, u, –2 mm. 15–16

u, u, –3 mm. 16–17

u, u, –4 mm. 17–18

u, +2, +2 mm. 18–19

100  Grounds for Motivic Analysis

Summary: The Bridge to Part II, Methods of Motivic Analysis This chapter has provided a historical overview of motive as a theoretic/​analytic concept. The account has been wide-​ranging, covering developments over several centuries; thus, it has been sketched in only rough strokes. It illustrates that the concept of motive has always fluctuated. This is because motives, which are in essence analytical and compositional tools, exist to serve the aesthetic and intellectual needs of the musicians who wield them. When seventeenth-​century analysts sought to explain the technical bases for the structural/​emotional form of madrigals and mass movements, they needed motives to take the form of figures. Nineteenth-​century musicians, who possessed a more lyric sensibility, required motives to have larger profiles and to enfold pitch and rhythm elements. Twentieth-​century musicians, working in an age when time itself was increasingly viewed as relative, shrunk motives to such an extent that they came to exist outside of time entirely. I asserted at the outset of this chapter that history will not furnish us with a ready-​ made system of analysis. It still can serve us another way. The issues it invokes, reformulated as a series of questions, offer a starting point for assembly of a new system. Here, a set of such questions, asked and answered, will deliver us to the second part of Musical Motives, the chapters covering methodology and analysis. Question 1: Should a motive manifest as a cell in the twentieth-​century sense, or should it manifest as a longer, memorable shape? Answer:  As both. In this study, the preferred length for motive—​the basic building block of music—​will be two to approximately seven ordered notes. In specifying a minimum length of two, this principle resists the notion that a motive can exist out of time as a chord. To allow for motives to manifest over several measures of music, they may (1) appear under rhythmic reduction, or (2) be chained together in the manner of  Theme = motive1 + motive2 + motive3. Question 2: On what basis should the tones of an ornamented surface be reduced in order to determine the structural pitches of a motive? Answer:  The looser, gestural approach favored by Schoenberg will be discarded. The spirit of Réti’s method, filtered through David Epstein’s approach, will serve as the model for reduction. In ­chapter 5 of this volume, Epstein’s five criteria, discussed earlier, will be revisited and distilled into a set of fixed rules for reduction that balance tonal and associative impulses. Question 3: Will motives be considered as pitch or pitch-​class phenomena? Answer:  As both. In line with the set-​theory understanding of motives, it will be possible to envision a specific pitch ​shape such as G4-​B-​E as an abstract,

A History of Motives—Theory and analysis  101 arpeggiating set of notes with varying contours, such as G4-​B-​E5 or C#4-​E3-​A. At the same time that we adopt this viewpoint, we will retain a pitch-​class understanding to observe parallelisms between local note shapes and larger-​scale key motions, since the latter properly have no specified pitch height. Question 4: Will a motive be considered to be a single-​line event or a polyphonic one? Answer: As both. The foundation for the method advanced early in Part II centers on a traditional, single-​line motive. This simpler, monophonic shape will ground what will be called basic motivic analysis (BMA), a mode of inquiry appropriate for novices or for experts looking to quickly ​or selectively analyze a work. In light of knowledge about how past composers wrote tonal music and how we conceive it now, however, this simplified model cannot stand as the final form of motive. A richer model, adumbrated by Carpenter’s multivoiced complexes and Zbikowski’s categories, will serve as the basis for complex motivic analysis (CMA). This form of motive, enfolding multiple voices and exhibiting textural, harmonic, articulative, and contrapuntal attributes, will be formally presented with attendant methodology in c­ hapter 7. Question 5: What role should traditionally nonstructural domains such as timbre, dynamics, and articulation play in the conception of motive? Answer: These domains play no role in BMA, but are accommodated in the model and methodology of CMA. Question 6: Should a motive be allowed to extend itself—​to develop, in the classic, Schoenbergian sense—​through alterations of its interval content? Answer: Officially, no. A motive, once defined, will only be associated with note configurations that perfectly preserve its relations. Despite this restriction, highly creative associations among motive forms will remain possible—​and indeed, desirable—​due to other flexibilities built into the method. Question 7: What motivic alterations are allowed, then? Answer: Motives may always be transformed by interval-​preserving operations, which are primarily transposition and inversion in the pitch/​pitch-​class domain and primarily duration scaling in the rhythm domain. They may also be discoverable under melodic reduction. Some enhanced flexibility, moreover, is available in CMA. Two motive forms may perfectly accord, but only in limited respects, for example, in contour but not pitch. The multifaceted nature of the complex motive will allow us to determine an approximate “degree of correspondence” between it and some other shape manifesting, say, roughly 50 percent or 80 percent of its features.

102  Grounds for Motivic Analysis Question 8:  How will the book’s strict methodology impact some of the more common-​sense intuitions analysts have about motivic relations? Will there be cases in which a clearly audible musical relationship must be excluded from analysis? Answer: Such exclusions will indeed occur, regrettable as that may seem. An example would be an ascending melodic third gesture that seems to expand as it is immediately succeeded by ascending fifth, sixth, and octave gestures. In contrast with past methods, there will be little allowance for “temporal proximity” of events to override a structural dissimilarity among two shapes (Zbikowski 2002, 161). The rigor of this method requires some sacrifice of findings; however, this “cost” will ultimately prove minimal, either as the finding itself proves inessential or as the method (particularly CMA) is adjusted to capture the intuited connection in some other way. The philosophies rooted in this last set of answers are embodied in the models, theories, and methods presented in Part II. The express concern of ­chapter 4 is establishing a universal nomenclature for motives; however, the exposition of motive types and labels will fulfill two aims at once. One is to resuscitate motivic analysis in our culture by working to standardize the language surrounding it. At present, when multiple analysts discuss the same work—​or different works featuring similar pitch and rhythm shapes—each, more often than not, will devise his or her own system of labels and terminology, thus discouraging communication. The other aim is to develop readers’ sense of what constitutes a properly formed motive. The labeling principles, through their innate design, intimate which shapes are well formed and which are not in this method. The foundational knowledge of basic motives provided in c­ hapter 4 will prepare readers for the subsequent demonstrations in ­chapters 5 and 6 of how such shapes may be deployed in analysis of full works.

PART II

MET HOD S OF MOT I V IC A NA LYSI S

4

A Universal Nomenclature for Pitch and Rhythm Motives Theorists and analysts have been working with motives for centuries, yet surprisingly no standard convention exists for naming them. The closest approximation to one is the practice of assigning motives arbitrary letter symbols from the Latin or Greek alphabets. It is difficult to say whether this approach, which requires no special musical training, is advantageous or not. On the one side, it allows novices to rapidly engage in analysis. On the other, this quick-​start philosophy is prone to backfire, as shapes proposed by novices often fail basic tests of audibility and/​or theoretic consistency. A more seductive aspect of traditional nomenclature is that it lends analyses a false air of certainty. Readers may recall Schoenberg’s approach of labeling motives and features with letters and using algebraic symbols to show their interaction; this was discussed at length in c­ hapter 3. His addition signs work as expected to show how musical shapes combine, for example in the “chain of derivations” given for the A major adagio from Brahms’s Quartet, Op. 51, No. 2.  His use of the division sign is, however, highly problematic. Example  3.13 reproduced his analysis of the adagio theme from Beethoven’s Piano Sonata 3, Op. 2, No. 3. He establishes motive b as the three-​note shape, G♯4-​A-​F♯. He writes “b/​2” to describe all instances of the second interval, A4-​F♯ in isolation. Importantly, b/​2 is never shown applying to the first of b’s intervals, G♯4-​A. We are left to wonder: are both b/​2 entities truly equal? Will combining them in reverse order also result in b, as logic requires? Almost assuredly not. Another problem with the letter-​naming approach is that it is inefficient. The act of establishing a set of arbitrary symbols to represent different motives is tantamount to writing a code. The author is obligated to provide a legend for all of the motive forms. Readers must periodically glance back at this legend as they follow an analysis. Memorizing it requires extra work, too. Worse is that such work rarely pays dividends, as one typically forgets an essay’s motivic code quickly, specifically the moment one turns to view the next motivic analysis. A more pressing concern is that analysts lack ready means to compare the motivic content of one analysis with another. Schoenberg, in analyzing the first movement of Beethoven’s Piano Sonata No. 5 in C minor, establishes five primary motives in mm. 1–16. In Example 4.1, motive a  =  a chordal triadic Musical Motives. Brent Auerbach, Oxford University Press. © Oxford University Press 2021. DOI: 10.1093/oso/9780197526026.003.0004.

106  Methods of Motivic Analysis Example 4.1  Example 52c from Schoenberg’s Fundamentals of Musical Composition.

utterance; motive b = upward, zigzagging arpeggiation; motive c = the rhythmic tag of two staccato quarter notes; motive d = the downward sigh, introduced via pickup; and motive e = descending linear motion of a third. His student, Josef Rufer, identifies three main motives for the same work (see Example 3.16 from ­chapter 3). In Rufer’s analysis, motive a is an arpeggiation idea, and motive b is a stepwise idea. Such a large discrepancy between analyses of the same movement, and so far we are only comparing the results of two very like-​minded scholars. It is not necessary to consider at present why their materials diverge. Our concern is that their analyses do not speak to each other, and that such is the prevailing condition in this field. Motive a for one author almost never means Motive a for another. Motive a rarely means the same thing for even the same author from one piece to another. To dispel this confusion, it makes sense to consider previous achievements in motive formatting and style. Two potential solutions for the nomenclature problem are suggested in the work of Rudolph Réti. First, he prefers more functionally descriptive labels over abstract symbols. The modest table of motives he gives for Beethoven’s Pathétique Sonata shown in Example Web.4.1 is more inviting than tables populated by long lists of arbitrary letter labels.1 Assuming one has a thorough knowledge of the piece at hand, it is easy to associate Réti’s labels with the compositional functions he describes.2

A Universal Nomenclature for Pitch and Rhythm Motives  107 A second aspect of Réti’s labeling approach with potentially far-​reaching application involves his recognition of the concept of universal musical shapes. He invokes this notion when discussing “cells,” which for him are special shapes that represent “the shortest extract of a motive.” The essential feature of a cell is its pitch interval content, so sensibly, he gives these entities labels such as “fifth,” “second,” and “third.” Réti is not the first or only analyst to conceive of motives in an atomistic, intervallic fashion. Schoenberg and Reicha prefer this approach, as do several present-​day theorists, such as Richard Cohn (2005) and Adam Ricci (2007). Réti’s straightforward approach suggests that a universal system for labeling motives is possible; however, no one has proposed one as far as I can determine. I do so here as a first step toward advancing the status of motivic analysis as a discipline. Having recourse to standard nomenclature affords analysts many benefits, starting with improved communication among scholars examining the same works from different vantage points. A  universal system, moreover, can offer guidance on how to properly identify and frame motives, and just as importantly, how not to. More immediately, this system should help to clear up much of the confusion that neophytes have with defining motives. More globally, it represents an important first step in improving the reputation of motivic analysis through the adoption of more objective and predictable analytic practices. I would like to pause to make clear the ramifications of situating the topic of nomenclature at the head of the methodology section. Nomenclature does not appear first because the act of identifying and naming motives comes first in analysis. It is because the naming system informs and impacts the structural logic of the full analytic system. Another point to remember is that the labeling system to follow has been developed to account for the majority of pitch and rhythm shapes that appear in tonal music. I have endeavored to make it as comprehensive as is practicable. It is not perfect, and some limitations must be kept in mind. First, it is unwise to assume that improved precision in discussing the content of musical shapes will resolve all of the methodological problems associated with motivic analysis. The nomenclature system applies to an art form, music, therefore it cannot claim universality or comprehensiveness, nor will it convey any special authority to analyses that rely on it in whole or in part. The system of nomenclature cannot even fully resolve ambiguity: when encountering any note shape “in the wild,” it will not restrict analysts from applying a number of different labels reflective of opposing interpretations. The formal presentation of the nomenclature commences with the musical domain of pitch (and, implicitly, pitch-​class). Once we have established guidelines for handling variations in length and disposition, we will move to discuss the rhythmic domain, which—​although equally important in the system—​tends to manifest less complexity.

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Rules for Labeling Pitch and Pitch-​Class Motives The system of nomenclature is founded on the principle that pitch and pitch-​class motives are essentially intervallic entities. In this domain, motives are named according to their interval content and their length in terms of “number of notes” (as opposed to their duration in time). There are two aspects of motive that will always be documented. We will, first, always account for the boundary interval measured from the starting point to the ending point. We will then examine the internal disposition of the motive, taking into account whether it is generally stepwise, leapy, unidirectional, zigzag-like, and so on. I mentioned earlier that the system has been fashioned for use with the tonal system. It follows that its terminology will correspond with shapes and figures common to this music. We frequently speak of “linear” and “arpeggiating” gestures in describing musical shapes, and so we will rely on that same terminology here. A practical place to begin is by considering the broadest categories of how notes can be arranged into shapes. The simplest shapes in music are unidirectional lines. Our nomenclature rules will apply first in this area, progressing from smaller shapes to larger ones. Soon after, supplementary rules will be provided to describe melodies that have more complex pitch contours, meaning melodies that twist and turn and/​or repeat notes. The following set of rules and examples will clarify and demonstrate how the naming procedure is put into practice. Rule P1. No one-​note pitch motives are recognized. Single-​note events, by definition, have no essential intervallic content, and thus no intrinsic pitch-​shape character.3 Importantly, excluding such phenomena from the pitch-​motive domain does not exclude the possibility of single-​note events manifesting as elements of a rhythmic, textural, and/​or rhetorical motive (for example, under complex motivic analysis). Rule P2. The simplest pitch motives, typically 2–​5 notes in length, are first labeled according to their intervallic content as measured between first and last notes. Three relevant guidelines should be cited here, not only because they clarify how this rule is imposed, but because they will apply quite generally to the full method. Guideline 1 (for Rule P2): Diatonic interval measurements are favored. A motion from a C to an E is usually assumed to be a third, and one from D down to A is assumed to be a fourth. Enharmonic substitutions are possible when the music calls for them, as in highly chromatic repertoires. This allows for some necessary flexibility in labeling, as in the case of a melody that moves from F down to C♯: that interval may be designated a descending fourth or descending

A Universal Nomenclature for Pitch and Rhythm Motives  109 third, depending on context. (In certain cases, a single label may apply to two different types of interval, such as “tritone” with regard to an augmented 4th or diminished 5th.) Guideline 2 (for Rule P2): Interval measurements are most commonly made in pitch space; however, pitch-​class (note name) space may be invoked to serve the interests of a particular analysis. For example, the default label for a motive spanning C4 to A is a “sixth,” and that for a motive spanning B♭5 down to F is a “fourth.” In cases when a motive spans more than one octave, for example A3 to C5, the expected label would be a “tenth.” The same, however, can also be called a “third” in pc-​space if one wishes to associate it with other pitch and pitch-​class thirds in a piece (or wishes to employ standard compound interval terminology). It is similarly possible, though rarer, to apply a pitch-​class label to a pitch interval. This can yield a counter-​intuitive result, for example, measuring the span G2 to F3, an ascent in pitch, as a “descending second” in pitch-​class space. Guideline 3 (for Rule P2): Whenever possible, the overall direction of a basic motive in pitch space is indicated by superscript and subscript text, e.g., 4th and 4th, respectively for ascending and descending motion. (This convention cannot apply to harmonic intervals in which boundary tones sound simultaneously.) The same superscript and subscript can also be used to represent pitch-​class motion, such as moving a 3rd through C-​D-​E, even if these notes descend in pitch space, e.g., C5-​D4-​E3. Rule P3. Basic motive labels are further qualified in terms of their internal intervallic disposition. In general, this refers to motives exhibiting stepwise versus leaping motion or having diatonic versus chromatic character. To signify the motive’s basic linear, leaping, or chromatic disposition, the number component will be notated respectively in plain, outline, and bold font.

Demonstration and Discussion We begin by considering a set of short, unidirectional motives. These simpler examples will be followed by others of increasing complexity and ambiguity. In labeling any motive of a second, one need not consider the controlling key, if any. The second-​ness or step-​like quality of a motive arises from the fact that it is composed of two notes a letter name apart. The corollary here is that the nomenclature generally does not distinguish between whole step and half step motion. In Example 4.2(a), the motion from a D♭5 up to E♭ is labeled as a second, specifically 2nd; in (b) the motion from G4 down to F♯ is also a second, 2nd. Examples 4.2(c) and (d) illustrate purely linear motions. The former is a 4th and the latter a 6th.

110  Methods of Motivic Analysis Example 4.2  Nomenclature for short, unidirectional motives. (a)

(b)

(e)

(c)

(f)

(d)

(g)

(h)

The motion from a D♭4 down to B3 in Example 4.2(e) is labeled 3rd, because one can only directly connect these letter names by leap. All other two-​note leaping motives will similarly appear in outline font when they occur. The interval in Example 4.2(f) is a 7th. Last, unidirectional linear motives may also exhibit chromaticism, filling in smaller boundary intervals with more and more notes. The motive in Example 4.2(g), though actually composed of three notes, is named a 2nd because it spans the second C4-​D. The motive in Example 4.2(h) is a 3rd, that fills the space between E♭5 and C. Rule P4Arp. Arpeggiation of triads and seventh chords constitutes a separate species of basic motive.4 The appropriate root label for such a motive, “Arp,” applies in the many cases in which chordal arpeggiation manifests as a recurring gesture. For this reason, the Arp designation typically supersedes the primary interval label from Rule P2. Additional information concerning the length and direction of the arpeggiation is appended to the root label as follows: Corollary 1 (for Rule P4Arp). A number can be added to Arp to indicate the number of notes in the shape, for example Arp4 and Arp5 to describe four-​and five-​note arpeggiations in ascent and descent, respectively. In the most basic case of ascending three-​note arpeggiation, the qualifying Arabic numeral is typically omitted. Corollary 2 (for Rule P4Arp). The overall direction of an arpeggiation can be indicated by altering the appearance of the label. Simple upward versus downward motions are shown via superscript and subscripts as described in Corollary 1. When necessary, internal directional changes can be represented by adjusting the relative height of the “Arp” label’s component letters. In cases of extremely complex pitch contour, this extra pictorial labeling convention should be curtailed o ​ r abandoned.

A Universal Nomenclature for Pitch and Rhythm Motives  111 Example 4.3  Nomenclature for arpeggiating motives. (a)

(b)

(c)

(d)

(e)

(f)

Demonstration and Discussion We begin once more with unidirectional motives. The three-​note, downward arpeggiation in Example 4.3(a) is labeled Arp3. So is the one shown in Example 4.3(b), despite the fact that it spans a fifth instead of a sixth. The shared label reflects the fact that the two motives express the same general musical idea.5 The six-​note, upward arpeggiation in Example 4.3(c) is labeled Arp6. Example 4.3(d) shows an equivalent motion that arpeggiates a seventh chord. It is important to note that the internal “stepwise” motion from B♭4 to C5 is in this case considered a leap and not a step. The Arp label has limited ability to capture the essence of more complicated arpeggiation patterns. In some cases, such as that suggested by the small motivic idea of Example 4.3(e), the letters of the label can be configured to approximate the shape’s contour. For more complicated arpeggiation patterns, the Arp label does not directly apply. In Example 4.3(f), for instance, Arp4 only accurately describes the larger patterns traced by each of the two implied melodic voices; these are the lines that emerge from a reduction, or pruning, of the surface figuration. If the analyst wishes to focus more on the surface, oscillating quality of the melody, it can be assigned a textural motive label in accordance with the rules of complex motivic analysis. Rule P4Neighbor. Full neighbor motion (away and back from a tone by step in either direction), another commonplace melodic shape in tonal music, is another separate category of pitch motive. There are two ways analysts can label such motives. The designation “N” works best for neighbor gestures that appear in relative isolation. An alternate, schematic notation with slashes indicating away-​and-​back motion—​e.g., /​ \ and \ /​for upper and lower neighbors—​is also possible. Double neighbor figures, which surround a note by its two adjacent pitches, may be labeled as DN.

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Demonstration and Discussion The opening, tenor melody of the Chopin Waltz shown in Example 4.4(a) is based on neighbor figures. These are bracketed at the surface and labeled as N. A larger N can be heard when the successive downbeats of mm. 1–​3 are extracted under reduction (see lines pointing to tenor). The opening of Beethoven’s Bagatelle, Op. 119, No. 1, shown in Example 4.4(b), furnishes a case of neighbor figures playing a supporting role to other motives. It is still permissible to label the first three notes of the melody, D5-​E♭-​D, as N. The /​\ slash notation is favored there because the first two notes do not stand on their own: they serve as a pickup to the more structurally important linear 4th that follows. The pickup to m. 3 is similar, but the first two pitches have been adjusted to accommodate the local V6 harmony, resulting in a double neighbor figure around B♭4. In this case, A4 is taken to be primary, hence the single /​sign. The advantage of the slash nomenclature Example 4.4  Two conventions for labeling neighbor figures. (a) Chopin Waltz in A minor, Op. 34, No. 2.

(b) Beethoven Bagatelle in G minor, Op. 119, No. 1.

A Universal Nomenclature for Pitch and Rhythm Motives  113 is that it tracks the presence of all of the neighbor figures, without clouding our view of mm. 1–​2 and 3–​4 as identical, fourth-​based melodies. The presence of the two linear 4ths running parallel in the bass voice (unmarked) supports this reading. Rule P5. Basic pitch motives are frequently decorated by prefix and suffix figures. These brief figures perform many duties, among them adjusting a motive’s​ harmonic profile by shifting its boundary tones or increasing a motive’s rhythmic interest. Stepwise prefixes and suffixes are indicated by slashes, /​ or \, to indicate ascent and descent. Leap prefixes and suffixes are indicated with hook notation. The symbols ⎡ and ⎣ are used to show ascending and descending leap approaches into motives; the symbols ⎦ and ⎤ are used to show ascending and descending leaps away.

Composers setting motives in tonal contexts frequently adjust them for variety’s sake or to align them with local harmony. As their name suggests, prefix and suffix tones lead into or out of a basic motive without impacting its shape.6 Very often, a piece will tend to attach particular forms of these figures to its primary motives. Because they are nonstructural elements, though, there is little need to analyze prefix/​suffix behavior. The value of recognizing prefixes and suffixes is that it allows analysts to distinguish the core content of a motive despite minor surface variations.

Demonstration and Discussion Due to relatively weak metric placement, an anacrusis (pickup) is likely to be heard attaching to an upcoming, structural motive. Example 4.5(a) provides two examples of stepwise prefixes attaching to a six-​note ascending shape. The first pickup note attaches by step; the latter substitutes a more generic downward leaping gesture. Stepwise prefixes are just as likely to attach to arpeggiating motives. A famous example can be heard in the first four notes of “I Won’t Grow Up” from the 1953 Broadway show, Peter Pan (Example 4.5(b)). Occasionally, as in the famous opening to Joplin’s rag, “The Entertainer,” a prefix gesture may take the form of two notes (Example 4.5(c)). The basic nomenclature is extended by placing a second slash next to the first. Stepwise suffixes are rarer. When they occur, it is often in the context of a melody employing an extra pitch to reach a critical scale degree, such as 2̂ or 7̂ to form a half cadence. This is what happens in the Haydn Sonata excerpt shown in Example 4.5(d). The melodic descent in mm. 3–​4 involving E5-​B4 and shadowed by the alto’s C♯5-​G♯4, is not a fourth as it first seems, but a linear third with an added pitch.

Example 4.5  Conventions for prefixes and suffixes. (a) Stepwise and leaping prefixes.

(b) Prefix stepwise motion in “I won’t grow up,” from Charlap, Styne, and Leigh’s Peter Pan.

(c) Double prefix stepwise motion in Joplin’s The Entertainer.

(d) Suffix use in Haydn’s Sonata 36 in C♯ minor, Hob. XVI: 36 (II).

A Universal Nomenclature for Pitch and Rhythm Motives  115 Labeling it in this way allows us to connect the motive with the salient surface thirds in mm. 1–​4 and 12–​13, as well as to the concluding melodic gesture in mm. 15–​16. The primary motivic motion at the end is revealed to be the 3rd C♯5-​A4; it is only in retrospect that we recognize it, in adorned form, in the alto voice of mm. 3–​4.7 Rule P6. Motives may be formed by combining two or more fundamental shapes. The proper label for a composite motive specifies the content of all linear, leaping, arpeggiating, and neighbor subshapes using addition signs to indicate discrete (+) and/​or elided (⊕) joinings. The resulting quasi-​mathematical expression can stand directly for the motive. Alternatively, a summary label may be assigned that takes the form: Bounding Interval/​Nickname = [total composite content]. Traditional nicknames should be avoided, except in cases in which a composite motive can be clearly associated with an iconic work such as Wagner’s Tristan Prelude or Rimsky-Korsakov’s Scheherazade.

Demonstration and Discussion While the motivic content of some works can be fully described by the shapes delineated by Rules P1–​5, many pieces rely on more complex motives that derive from the combination of more fundamental shapes. Rule P6 exists to treat such motives. Due to space limitations, the three examples in the present section illustrate basic procedures for identifying and labeling composite motives. The examples in the section that follows have been constructed to address pitch motive types that were escaped earlier mention, thus further illustrating the inherent flexibility of the nomenclature system. Example 4.6(a) presents a composite motive containing arpeggiating and linear elements. Assigning a label here is not difficult but not automatic. The primary concern is that there is no one way to determine the size of each sub-​ element. We may well ask: “Does the three-​note arpeggiation, G-​B-​D, end at the D3 before moving to a discrete 2nd starting on E (upper reading), or does the first Arp elide to a fuller, linear 3rd (lower reading)?” To avoid being swamped by minutiae, we should rely heavily on some reductive logic. Linear seconds are usually too generic to be significant, so the latter part of the ascent probably spans the third D3-​F♯. The initial leaping idea could be just two notes long as well, a G2-​B 3rd, but it is more likely an arpeggiation. Only in the face of strong evidence from elsewhere in the score would we opt for a different parsing. Last, two labels are possible for the lower, preferred reading. Using the special addition sign to signify the overlap, the motive can be called Arp⊕3rd. Alternatively, if we want to capitalize on the fact that its boundary interval is

116  Methods of Motivic Analysis significant elsewhere, a summary label can be given to the whole so that it is called 7th=Arp ⊕ 3rd. Example 4.6(b) presents a motive similar to that in Example 4.6(a). This shape reaches a full octave, which increases the inherent ambiguity of the figure. When deciding on how to join the arpeggiating and linear components, we chose elision in Example  4.6(a), because it favored a 3rd motive reading over the less useful 2nd. That strategy will not work here, so the two interpretations of this motive are equally viable. One may opt for the Arp⊕4th shown above the staff or the Arp + 3rd shown below.

Example 4.6  Nomenclature for compound motives. (a) Two readings of a motive of a 7th.

(b) Two readings of a motive of an octave.

(c) Bach Fugue in B major, WTC I: Two possible readings of subject motives in m. 2.

A Universal Nomenclature for Pitch and Rhythm Motives  117 Another class of composite motive involves linear gestures that change direction in their interior. By this I mean that the upward and downward linear stretches are both two or more notes long. In a situation that a one-note directional shift appears, it will surely register as a neighbor or prefix/suffix event. The corollary to the present point is that all basic motive prototypes, excluding the special N and Arp shapes, are unidirectional. The most direct way to label a truly multidirectional fragment is to use composite nomenclature. The second half of the subject from Bach’s B major Fugue from Well-​Tempered Clavier I traces an ascent from B3 to E4 and back (see m. 2 of Example 4.6(c)). One can use elision to create a fourths-​based reading as shown below the subject. Alternatively, the plain addition operator gives the “mixed” third and fourth reading shown above. This latter interpretation, being more motivically rich and connecting to the subject’s initial 3rd in m.  1, may be more analytically valuable.

Extensions to the Rules for Pitch and Pitch-​Class Nomenclature The six foregoing rules constitute the basis of the pitch and pitch-​class motive naming system. As far-​reaching as they are, the frequent need for extra “guidelines” makes it clear that many note configurations still fall outside their purview. In such cases, the self-​determining spirit of motivic analysis is appropriately honored by allowing musicians to adopt the rules as they like. I am all for this, but I wish to offer some suggestions for handling trickier shapes that are likely to confront analysts. The solutions suggested here are not the only ones possible. They are meant to serve as models for creatively employing the nomenclature and to show that the rules can be modified as needed. The first modification allows for flexible handling of prefixes and suffixes to accommodate common ornamentations of stock diatonic gestures. As Rule P5 was first presented, all prefix and suffix figures were attached at the edges of a motive. Often, it feels that a shape is better represented by having the prefixes or suffixes apply internally.8 Consider the case of Example 4.7(a), where the downward leap of a fifth (D3-​G2) is altered by the addition of the incomplete neighbor tone, A♭. To indicate that this 5th has an internal stepwise prefix to the latter note, we insert the appropriate slash into the notation: 5\th. The flexible, internal placement of prefix and suffix figures can also apply to arpeggiation. Here, creative use of the three letters designating the shape, “Arp,” can indicate where in the arpeggiation the prefix event occurs. Consider the emblematic motive from “The Jetsons” theme, shown at left in Example 4.7(b). The

118  Methods of Motivic Analysis B♮4 occurs after the A and attaches as a prefix to the third note, C5. The label Ar/​p literally represents the arrangement of arpeggiated and prefix tones. In contrast, the label A/​rp would apply to the “anti-​Jetsons” motto given at right, where the chromatic ornament has shifted to attach to the middle member of the F triad. These extended label conventions allow analysts to draw direct associations among shapes that might otherwise be overlooked. This point is illustrated in Example  4.7(c) by an aria excerpt from Gluck’s Orfeo ed Euridice, “Che fiero momento.” The reading given above the staff proceeds measure by measure, yielding four unrelated motives based on 2nds, 3rds, and 4ths. The preferred reading below identifies a common, arpeggiated basis for the two halves of the melody. The descending, internally-ornamented arpeggio in m.  9, “Ar\p,” is arrived at via prefix octave leap and left by stepwise descent. The ascending “internally ornamented” arpeggio in m. 11, Ar/​p, is both arrived at and quit via a descending semitone. The two halves are equivalent (Arp ~ Arp), with a natural boundary separating them at the augmented second, B♮-A♭. Example 4.7  Internal placement of prefix and suffixes. (a) An incomplete neighbor interposed between D3 and G2 creates a 5\th motive.

(b) Ornamented arpeggio from Jetsons motive and a hypothetical “anti-​Jetsons” motive.

(c) Two readings of  “Che fiero momento” from Gluck’s Orpheo.

A Universal Nomenclature for Pitch and Rhythm Motives  119 As advantageous as this ornamental nomenclature is in certain circumstances, it should not be used indiscriminately. One rarely needs to record every twist and turn of an ornate melody. Usually it is better to seek out the broad outline of the shape underlying it, reserving prefix/​suffix notation for cases where internal figuration tones are especially salient.

Rules for Labeling Rhythmic Motives The conventions for labeling rhythmic motives can be dispatched more rapidly than those for pitch and pitch-​class. Neither the placement nor the reduced footprint of this topic are meant to indicate it is of secondary importance, however. In motivic analysis, rhythm is regarded as a primary musical domain. The reason that fewer labeling conventions are necessary is that a piece’s rhythm shapes tend to be more consistent than its pitch shapes. They are, in other words, more tenacious, remaining stable for longer periods of time. As an example, consider the following common series of events. At the outset of a work, a motive is stated with a strong, recognizable profile. Upon repetition, it may retain both its pitch and rhythm elements: some slight alteration in either domain will do little to prevent recognition of it as the same idea. Yet given the option of strictly retaining either the rhythm or pitch content while varying the other, composers usually opt for the former. An example of this treatment is on display in the first phrase of Schubert’s “Neugierige” shown in Example 4.8. In this and similar cases, the immediately memorable quality of rhythmic ideas makes them sturdy enough to withstand transplantation to other spots in a piece and to support novel melodic shapes. We commence now with the rhythm labeling conventions. Rule R1. No one-​note rhythm motives are recognized. This follows from Rule P1, earlier; Q.E.D. Example 4.8  In Schubert’s Neugierige, two vocal phrase segments exhibit the same rhythm but different pitch content.

120  Methods of Motivic Analysis Rule R2. A basic rhythm motive, typically 2–​5 attacks in length, is first labeled according to its durations, which are assessed in relative terms as long (L), short (S), and, where necessary, medium (M). Sounding (note) events must always be accounted for; rest (silent) durations may be specified by parentheses or disregarded as the analyst sees fit. Guideline 1 (for Rule R2): A rhythmic event is typically initiated by a sounding note. In rare cases, a rest event can initiate a rhythmic shape; this may occur when a rest falls on a strong beat. Guideline 2 (for Rule R2): Rests that occur within or at the end of a rhythm are typically not accounted for by the rhythm label. In such cases, the previous sounding note is credited extra length that separates it from the next note attack. The final length of a rhythm, therefore, is often long (L)  or medium (M).

Demonstration and Discussion The first step in labeling a rhythmic shape is to assess its general arrangement of durations in relative terms. Generally, the basic distinction between long (L) and short (S) durations will suffice. If more specification is desired, the additional designation of “medium” (M) length can be used. In Example 4.9(a), a three-​ note rhythmic idea is twice repeated. The default manner of referring to two duration types, no matter the tempo, is Long and Short. The figure is thus labeled S-​S-​L. A similar rhythm appears in part b) of the example, except here the notation shifts so that it is built of all quarter notes. Assuming a moderate-​to-​allegro tempo, most listeners would judge these to be relatively short attacks. One correct, but less preferred label, is the S-​S-​S shown above the staff, with the final quarter rest of each measure acting to delimit the figure. The preferred interpretation, shown below, reflects the fact that listeners more readily perceive attack points than release points. Overlooking the terminal rest, we label this rhythm S-​S-​L, with the “Long” of m. 2 being of indeterminate length of at least a half note. More simple patterns of mixed duration are shown in Example 4.9(c). The S and L labels are favored, despite the fact that a wider range of durations are employed. In Example 4.9(d), an M label appears in m. 3. Note that we have not yet had any need for rest notation, even in part a), where rests actually appeared. This is because rests at either terminus of a rhythmic motive are generally not documented. Empty parentheses ( ) are used to signal rests, as in Example 4.9(e). Even in such cases, the need to indicate rests is frequently obviated by the strategy of considering only attack points.

A Universal Nomenclature for Pitch and Rhythm Motives  121 Example 4.9  Nomenclature for simple rhythms. (a)

(b)

(c)

(d)

(e)

Rule R3. Basic rhythm motives are frequently decorated by prefixes and suffixes. These one-​to two-​note figures, signified by dashes “–​”, typically serve a pickup function at the head or a rebound function at the tail of the shape. Rule R4. In cases in which a rhythmic motive exhibits a large number of attacks in a short span of time, longer duration values can substitute for the surface elements (e.g., a quarter note pulse may appear in place of four sixteenth notes). This ad hoc rhythmic reduction is indicated by applying sets of angled hash marks, /​and \ either above or below the basic S, L and M labeling components.

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Demonstration and Discussion Example 4.10 shows proper use of prefix/​suffix notation for rhythm. It is most applicable for showing how a prevalent motive recurs with one or occasionally multiple durations tacked on to either end. In Example 4.10, the same L-​S-​S motive appears four times with prefix and suffix durations attaching in mm. 1–​2 and  4–​6. We expect that a motivically dense segment of music will state its core material at the outset before offering it in decorated forms. In this manufactured excerpt, the gesture common to the four utterances, L-​S-​S, only literally appears in mm. 3–​4 and 7–​8. When the motive is heard in mm. 1–​2, it has a prefix attached and is labeled –​L-​S-​S. When it returns at the pickup to m. 5, it has both a prefix and suffix and is labeled –​L-​S-​S–​. Rule R4 establishes a convention of using angled hashmarks to show how a busy surface rhythm may project a more deep-​level duration. An analyst relying on this convention essentially performs an informal reduction to make a passage’s complex rhythms more manageable. In Example 4.11, a large four-​beat gesture first appears in mm. 3–​4 as L-​S-​S-​L-​L.9 It then repeats twice, with its first L attack dividing into two, equal spans (m. 5 and m. 7). Labeling the motives in this way allows us to acknowledge both the consistency of the shape and its surface variations. The flexibility of this tool may lead readers to wonder if the motive in mm. 3–​4 could also be designated L-​L-​L-​L, with both the first and second durations divided in half. Absolutely, it could. In fact, given musicians’ widely varying hearing habits, we may expect that some

Example 4.10  Convention for prefixes and suffixes (rhythm). Excerpt not from the literature.

Example 4.11  Measures 1–​8 of “Great Gate of Kiev” from Mussorgsky’s Pictures at an Exhibition.

A Universal Nomenclature for Pitch and Rhythm Motives  123 analysts will prefer surface-​like rhythmic labels and others more deep-​level motives. As either strategy will work, it is important not to swear blind allegiance to either. Engaging in only “deep-​beat” analyses can cause one to miss small surface level connections, for example microscopic S-​S-​L patterns in figuration that echo a larger, thematic one. Alternatively, assigning S and L labels to every single attack can lead to labels that look like gibberish, especially in instrumental pieces with rhythmically busy themes. Further extensions of the angled hashmark labeling method may be used to indicate a greater number of duration divisions or unequal divisions. Practically speaking, a long or short attack in moderate tempo will admit up to six divisions, after which point the faster notes will blur together. The excerpts in Example 4.12 illustrate labeling solutions for such subdivisions, including the use of a filled-​in triangle to indicate rapid subdivision as in a glissando; see part (e). In parts b) and c), some hashes are made bold to indicate the presence of unequal subdivisions, such as those stemming from dotted rhythms or compound meter. Rule R5. Rhythmic motives may be named according to total duration. The tool for labeling a motive in this way is the “summary label,” which takes the form Duration = [total S, L, M content]. In cases in which the last note attack is of indeterminate length, the number of beats may be estimated. Rule R6. Rhythmic motives may be composite, resulting from the combination of two or more fundamental shapes of the type described in Rules R1–​5. The proper label for a composite motive specifies the content of subshapes using addition signs to indicate discrete (+) and/​or elided (⊕) joinings.

Example 4.12  Conventions for handling subdivided durations.

124  Methods of Motivic Analysis

Demonstration and Discussion The summary label for rhythm motives serves the same purpose that it does for pitch and pitch-​class motives. It provides a shorthand name for a motive, while also clarifying its duration and specific content. To illustrate the process of deriving a rhythm summary label, Example 4.13 reprints select rhythms from Examples 4.9 and 4.10, with summary labels appended. The first thing to notice is that summary labels depend to a large extent on tempo and notation. The rhythm in Example 4.13(a) (originally 4.9(b)) is sensed as a three-​element shape in common time. The motive in part (c), in contrast, is felt in hypermetric terms as four beats in a brisk three-​quarter meter. The three shapes in Example 4.13(b) (originally 4.9(d)) exhibit both of these tendencies. The labels at far left and right, 4h = L-​S-​S-​S-​L, and 4qd = L-​S-​L-​S-​ S-​S-​S-​L, illustrate how two-​measure segments can yield four-​beat shapes. The center shape illustrates a seven-​quarter-​note rhythm that ignores the impact of

Example 4.13  Reprints of previous rhythm examples with new summary labels added. (a) Example 4.9(b) with summary label

(b) Example 4.9(c) with summary labels

(c) Example 4.9(d) with summary label

(d) Example 4.10 with summary labels

A Universal Nomenclature for Pitch and Rhythm Motives  125 syncopation: the 7q shape is free to occur in any beat of a measure in subsequent appearances. The last issue to note, as indicated by the labels given in Example 4.13(d), is that prefix and suffix events appearing as dashes do not figure into summary duration calculations. Rule R6 applies to rhythm in the same way it does for pitch and pitch-​class and thus requires no introductory demonstration.

Extensions to the Rules for Rhythmic Motive Nomenclature Earlier discussion noted that shorter motives can be assembled into composite motives using the familiar + and ⊕ operators. For any rhythmic gesture longer than three notes, it is likewise possible to employ additive nomenclature. Some caution should be exercised, however. Though composite labels are readily adaptable to rhythm, they offer only limited benefits. They are best suited to short, “hybrid” rhythmic motives like the unison gesture presented at the start of Mozart’s Piano Quartet in G minor, K. 478. In common time, it is h qd e | Ωçq; the preferred reading is 6q = M M - | S S L, where the latter component has a short prefix figure. The last convention to be presented allows analysts to document subtler rhythmic relationships, such as when a shape’s character depends on an irregular or phased metric placement. Rule R7. One or more bar line symbols, | , may be placed among the S, L, and M duration signs to indicate how a rhythmic shape intersects with meter. Bold text applied to an individual duration, e.g., S, L, M, indicates that it has a phenomenal accent that is independent of the written meter. Note, however, this convention need not apply to local maximal durations (agogic accent).

Discussion and Demonstration The final symbol to be incorporated into our nomenclature is the bar line, which provides information about a rhythm’s relation to a governing meter and, to a lesser extent, its stress profile. Metric stress is assumed for any duration occurring in a strong-​beat position, including the position immediately following the | symbol. Example 4.14 illustrates some ways that a simple L-​S-​S-​L rhythm may be set musically and represented with duration and bar line symbols. In Example 4.14(a) and (b), the rhythm shapes fit comfortably in the meter, resulting in unambiguous label forms. In Example 4.14(c), syncopation occurs as the longer durations are intersected by the bar lines. The practical solution for

126  Methods of Motivic Analysis Example 4.14  Barline notation for rhythmic motives. (b)

(c)

(d). Threefold motive presentation from the theme of Strauss’s Till Eulenspiegels Lustige Streiche.

(e) Shifting placement of barline notation to indicate phasing.

showing this condition is to allow the bar line symbol to migrate across the “L” labels as shown. The bar line notation aspect of this nomenclature is highly approximate. In 4.14​ (c), it reflects only the fact that some cross-​cutting of the long durations occurs, not the precise proportions of that division. Both of the split Ls look the same, although for the first the bar line falls halfway through (after the first of two quarter pulses) and for the second it falls a quarter way through (after the first of four). This is a mere quibble, however: the schematic line-​through notation communicates plenty about the presence of syncopation. For this reason, it is not necessary to seek perfect precision in placing the vertical line through the duration it intersects. The remaining examples will illustrate the bar line notation’s ability to make distinctions among rhythmic motive settings. In the course of surveying even just a few rhythmic analyses, extended strings of S and L characters quickly blur together. The bar lines help to break up this visual monotony and remind us of the characteristics of each gesture. A last benefit of barline notation is that it affords a useful means for documenting certain rhythmic transformations. To see how this works, we will apply the nomenclature to some basic rhythm shapes that occur in Strauss’s tone poem, Till Eulenspiegels Lustige Streiche. Example 4.14(d) reproduces Till’s theme from the start of the allegro section, mm. 6–​9. The core rhythmic gesture is S-​S-​S-​L-​S; the L value is given in plain text because its length, in the context of

A Universal Nomenclature for Pitch and Rhythm Motives  127 the S values nearby, lends it a natural, agogic accent. We note first that the three instances of the bracketed motive are not identical: in its third appearance, the duration of the G♯ is shaved down by one-​third of a beat. Even though the length of the long duration fluctuates, the original S-​S-​S-​L-​S label applies equally well to all three forms. That issue settled, we may turn to the task of overlaying the bar line notation on the durations. The results, shown in Example 4.14(e), take advantage of our ability to place the bar line at spots roughly two-​thirds and one-​third across the L duration. The shifting appearance of the labels reflects a dynamic rhythmic procedure in the music. The phasing is visually confirmed as we intuit the rhythmic shape drifting to the right across the bar line or, if you prefer, the bar line drifting to the left. The graphic in Example 4.14(e) is hardly momentous in itself, nor is it the only way to represent this rhythmic event. It is notable, however, for offering a way to distinguish between what otherwise would be regarded as three blandly equivalent patterns: motive Till, motive Till, motive Till. The very ways that the labels “speak” to each of us prompts our first exploration of multiple rhythmic/​metric narratives. It is possible to describe the succession of events in mm. 6–​9 passively, in terms of a static five-​note gesture that is pierced three times at three different locations. We could just as easily frame the process actively, in terms of the five-​note shape driving forward across bar lines in search of its final, resolved state. In this view, the L value experiences a “foreshift” within the work’s global, dotted quarter-​note pulse, where it migrates from the second subdivision in its triplet, to the third, and finally to the first. The effort put into conceiving this motive in such dynamic rhythmic terms would likely pay off handsomely in a full analysis of Strauss’s tone poem. Similar rhythmic shifts appear throughout the work, for example, during the solo flute’s extended hemiola passage at Rehearsal 7 and the murky canonic writing at Rehearsal Nos. 20–​21 that depicts Till confounding the scholars and philistines. The analysis printed above the flute staff in Example Web.4.2 ) illustrates the surface rhythmic reading. The classic interpretation of any hemiola is “backshifting,” where the two-​eighth gesture initiates on the first, then third, and then second subpulse of the triplet beat.10 Example 4.15 summarizes all of the rhythm notation conventions described in this section. The information given in the top portion of the chart details the core content of the system. The information below the dotted line pertains to common extensions to the nomenclature, specifically ornaments, subdivisions, and composite motive forms. The discussion of nomenclature for describing the pitch and rhythmic content of motives will conclude here. While not all potential configurations have been treated, the ones that have should be sufficient to provide at least a foundation for fluency with the label system. Readers who seek further guidance on

128  Methods of Motivic Analysis Example 4.15.  Summary chart of nomenclature for rhythmic motives.

the topic may consult the opening passages of the extended studies of pitch and rhythm printed in ­chapter 6 (the demonstrations of basic motivic analysis). They are encouraged also to incorporate this nomenclature in their own musical lives in the course of analyzing and discussing music with peers. At this point, all necessary groundwork concerning the history, theory, and premethodology of motive has been laid. Chapter  5 will commence immediately with the presentation of the theory and method of BMA, the first of the two modes of motivic analysis to be covered in this text. Discussion of nomenclature will adjourn until c­ hapter 7. At the time it becomes necessary to incorporate additional domains into our study of motive, we will reopen the topic to establish conventions for naming/​handling elements of contour, harmony, dynamics, articulation, texture, and so forth.

5

Basic Motivic Analysis The first mode of motivic analysis is limited to examining the pitch and rhythmic content of music. It is called basic motivic analysis (BMA). Were we to rush into simultaneous treatment of all of the methods needed to address texture, timbre, ornament, and so forth, chaos and confusion would result. Postponing discussion of those other domains allows the foundational principles of motivic analysis to emerge with more clarity. Another practical rationale exists for establishing a limited zone of inquiry here. Within the larger curriculum being presented in this book, BMA represents a minimum competency in studying motives. Many readers will likely choose to end their studies of motive upon reaching the conclusion of ­chapter 6. That is wholly appropriate: the amount of information contained in this and the following chapter—​comprising the method and two demonstrations—​can sustain lifelong investigation of motives. Indeed, those who opt to continue beyond ­chapter 6 will still likely spend the majority of their time in the future working on issues related to BMA, calling selectively on their complex motivic analysis skill set to supplement their core pitch and rhythm findings. The questions asked and answered at the close of Part I  communicated an initial sense of what is novel about the models being advanced in Musical Motives. In case it is still not fully clear what distinguishes BMA from traditional, Schoenbergian analysis of pitch and rhythm, one word should clarify the matter: rigor. While BMA operates in many of the same ways as traditional analysis, it will be rooted in a system of rules that govern motivic content and association and—​at the highest levels—​the proper construction of analyses. Addressing these concerns in order, this chapter will first introduce rules for deducing pitch and rhythm motives. In accordance with practices followed in chapters 1–4, the method will continue to allow for surface motives, shapes drawn directly from music that arise from contiguous notes in a single voice or register. From this point onward, however, it will concentrate on larger shapes formed of non-adjacent tones. The section titled “Principles of Reduction” will establish procedures for deducing these deeper-level, emergent shapes. The following section, “Principles for Linking Motives,” fills a procedural gap left in chapter 4. There, motives were formalized and named, but no means were provided for tying them together. This section provides those tools in the form of identity and association operations. The last stage in preparing readers to analyze on their own Musical Motives. Brent Auerbach, Oxford University Press. © Oxford University Press 2021. DOI: 10.1093/oso/9780197526026.003.0005.

130  Methods of Motivic Analysis calls for guidelines to structure motivic analyses. The section on “Assembling Analysis” addresses this need by providing a set of narrative archetypes. These are essentially analytic templates, akin to well-worn frameworks known to underlie myth and storytelling.

Principles of Reduction Justification for a Reduction Method Rooted in Auditory Salience It is not by chance that the topic of reduction is given top priority in this method. In a very real sense, the whole enterprise of music analysis depends on it. Without access to any paring-​down mechanisms, discussion about a work could only concern it in its entirety. For this reason, most theories of music include some means for reducing complex configurations of pitches and rhythms. This process, put simply, involves examining a given span of music, determining the relative importance of the events therein, and then rewriting the span with entities of lesser significance removed. The reductive process can be illustrated by a linguistic analogy. Most sentences such as the one printed in Line 1 of Example 5.1 contain words and clauses that qualify and give deeper meaning to a basic utterance. To determine the sentence’s essential communicative content, we can prune away these descriptive extras one stage at a time. It is true that each new sentence in the series seems barer and less interesting than the one above it. But then, the goal of performing reduction on a prose or musical statement is not to uncover a more beautiful version of it. It is to discern Example 5.1  Multistage reduction of a famous sentence. Sentence Input

Reduction Operation

1. The quick, brown, fox jumped over the lazy dog. one color adjective deleted 2. The quick fox jumped over the lazy dog. two character adjectives deleted 3. The fox jumped over the dog. one prepositional phrase deleted 4. (The) fox jumped. Core subject-verb sentence remains

Basic Motivic Analysis  131 the statement’s essence. We also employ reduction to increase our knowledge of the sentence and to better understand the manner in which it has been decorated. Such knowledge is eminently generalizable to our conceptions of linguistic grammar and human thought. Two common threads run through every prominent reduction method used in music.1 The first is that the reduction process is repeatable: the output of all reductions but the last can be fed back into the pruning machine to be reduced again. The approximate measure length of the musical span will remain the same, but it will be filled with less and less material. The second thread is that the reductive mechanism is rooted in some cognitive reality. In some reduction schemes, the criterion for retaining notes is aural salience, which means prioritizing events that stand out in register, rhythm, attack, or timbre. In others, decisions on event priority are made on the basis of musical syntax. In Example 5.1, syntactic knowledge allows us to determine which words may be removed from each sentence form. Musicians that have mastered counterpoint and/​or learned to improvise extensively on a given theme similarly possess specialized knowledge of musical syntax. They know, very often implicitly, which notes in a melody may be removed without altering its basic meaning.2 Having established that our methodology will incorporate reduction, we can now move to determine which basis it should rely on. Should it be salience, the approach traditionally favored by motivic analysts? Or should it be contrapuntal/​harmonic syntax, the approach born out of Schenkerian tradition? Time does not permit us the luxury of a full critique of their relative merits. Our decision instead will emerge after an informal side-​by-​side evaluation of reductions produced under the contrasting philosophies. The mode of reduction relying on musical salience shall be known as “equal duration reduction” (EDR). Under this procedure, pitches are prioritized on the basis of occurring (1)  on naturally stressed beats within a metric framework, and/or (2) at regular durational intervals (e.g., “every four eighth notes”). The contrasting mode of reduction relying on syntactic knowledge will be represented by Schenker-​style reduction, sometimes called “tonal reduction.” In this method, pitches are prioritized on the basis of harmonic and/​or contrapuntal patterns. At any given level of activity, one determines the vertical chords present and the voice-​leading between them. Non-​chord tones such as passing (P) and neighbor (N) notes are then removed to produce the next, “deeper” layer. The testing ground for the comparative analysis will be the opening phrase from Leeman’s March of the Belgian Paratroopers; the melody is given in Example 5.2(a) along with its harmonic context (Roman numerals). Most musicians would agree that all of the important tones appearing at the surface have been retained in the intuitive reduction shown in Line b). All that has happened is that the sixteenth notes occurring on the weakest subpulses have been pruned. As one

132  Methods of Motivic Analysis Example 5.2  Pierre Leemans’s March of the Belgian Paratroopers. (a) Paratroopers melody, mm. 1–​4, with harmonic context provided by Roman numeral analysis.

(b) First, intuitive reduction of the Paratroopers melody.

Example 5.3  A comparison of equal duration reduction (EDR) at left and tonal reduction at right. Line b), which reprints Example 5.2(b) with pitches numbered, serves as the basis for reduction in both left and right columns. (b)

(e)

(c)

(d)

(f)

would expect, something quite like this preliminary result would be returned by either of the two reduction strategies. More striking differences between the reduction methods emerge as the March of the Belgian Paratroopers melody is input into each. These are on display in Example 5.3. The multistage results of Equal Duration Reduction appear at left and those of tonal reduction appear at right. Note that the starting point for both reductions is Line b). The counting numbers that appear above the upper-​left staff are there to keep track of which notes are eliminated in different stages of reduction. A fair bit of agreement seems to emerge at first as we trace a downward path through each column; however, these surface similarities mask a deep methodological conflict. In transitioning from Line b) to Line c), a mechanical reduction excises tones 3 and 6 because they occur on unaccented portions of the beat.

Basic Motivic Analysis  133 Under tonal analysis—​compare the progression from Line e) to Line f)—​the same G4 and B♭ are removed because they are not members of the primary F-​A-​C triad being expressed. They are lesser tones that help “compose-​out” the tonic triad in mm. 1–​3; see harmonic analysis under the melody in part a).3 The most important comparison to be made is between Lines d) and f), which represent the local outcomes of the two reductive processes. (On both sides, the reduction could extend to more stages, but subsequent results would be increasingly bare). The shape that emerges at left, Arp\, is significant for balancing insight with familiarity. It is new in the sense that it was discovered by looking at the original melody in a new, reductive light. It is familiar in that it matches the original melody closely: if played in tempo it would aurally resemble Example 5.2(a). The final entry at right, Line f) in Example 5.3, shows a large-​scale pitch shape emerging from tonal reduction. Readers may initially find it peculiar that the fourth measure of f) does not appear to be reduced, as all the notes from the original melody remain; this includes the A4 that passes between B♭ and G. The reason for this is that tonal reduction takes into account other criteria in addition to duration. For example, it is generally accepted that the first and last events of any musical statement carry more weight than those that intervene; this is known as the principle of “structural accent” (Lehrdahl and Jackendoff 1983, 30–​35). With regard to the present four-​measure phrase, then, the tonal-​reductive viewpoint argues that the starting point on F4 and arrival-​point on G are structural events that must be retained.4 The second criterion deriving from Schenker’s understanding of global tone tendencies is that a hierarchy exists among the notes of the tonic triad that underlies a segment. (Again, said segment could be of any size, from four measures to an entire piece.) Of the F4, A, and C5 traced out in the first three measures, one of the latter two will serve as the high point from which the melody, under the influence of tonal gravity, will descend.5 In this case, I have prioritized the C5, which, as many melodies do, moves downward by step to the G4 that closes the phrase at the half cadence. We cannot place too much stock in a single side-​by-​side comparison, but we can draw some early impressions about the relative advantages of salience-​ based reduction (EDR) over tonal reduction. Let us consider practicality and efficiency. In terms of energy and time invested, EDR is easier to use. In contrast, learning tonal analysis demands prolonged study both of strict and free counterpoint. Despite this difference, the motivic output of the two methods at the base of Example 5.3 is roughly comparable. All but one of the shapes produced by tonal reduction are readily discoverable by the other method. The arpeggiation shown in Lines e) and f) for instance, emerged in Lines c) and d) through simple

134  Methods of Motivic Analysis extraction at the beat level and then the measure level. The “4-​line” from C5-​G4 beamed at far right can be accessed as a surface motive in the music back in Line a) of Example 5.2 (m. 4) with no reduction necessary at all! In contrast, we note that the equal duration reduction produces at least one aurally salient shape that is wholly invisible from the tonal viewpoint: Arp\. We shall return frequently to the notion of “invisibility” as we develop our methodology, employing it as a gauge to determine the limits and trade-​offs endemic to analytical techniques.

Rules for Salient Reduction Rooted in Principles from Epstein’s Beyond Orpheus The arguments made in previous pages imply that it is possible to design an effective method for motivic analysis that does not depend directly on tonal reductive techniques. To coax this implication further along, we must plug up the major conceptual gaps that still surround it. Taking our cue from the vociferous criticisms reported in c­ hapters 1–​3, our response will be to devise a set of reduction rules that apply consistently. With regard to salient reduction, this means strengthening the basic principles of EDR to accommodate more advanced musical issues, such as structural accent. “Strengthen” is the operative word; we need not build a method from the ground up. We have in fact already encountered a preliminary model for pitch-​ motive reduction in the form of David Epstein’s list from Chapter 3 of Beyond Orpheus. His first, second, and third criteria, reprinted and relabeled below as “Epstein Points 1–​3” (E.P. 1–​3), are most relevant here.6 E.P. 1. Points of contour: Structurally significant pitches usually achieve prominence through their location within thematic contexts, for instance, at high points or low points, at beginnings and closings (cadences) of motives or of longer musical ideas. E.P. 2. Rhythm and meter: Significant notes more often than not lie upon rhythmic and/​or metric strong points. This is not to exclude ornamental notes from consideration. Where they are significant, however, ornamental notes will usually lie in some close and prominent relationship to notes that themselves are structurally important. Discerning these relationships is . . . a matter of judgment. E.P. 3. Pattern: consistency and recurrence: These terms effect a partial description of motive itself. . . . Consistent and recurrent appearance of . . . notes within a pattern will give them greater musical and structural importance.

(Epstein 1979, 37–​38)

Basic Motivic Analysis  135 The list may seem limited, but the generous descriptions attached to each point go a long way to capture great subtleties. Again, consider the idea of structural accent. This esoteric idea, though not specifically named in Epstein’s list, is treated by the “beginning and closings” clause at the end of E.P. 1. Epstein’s Point 2, beyond establishing a preliminary basis for rhythmic/​metric reduction, identifies a further basis for determining if a pitch is structural, namely, on the basis of its adjacency to an ornament. The first step toward revising E.P. 1 involves expanding its scope to better harness the power of musical contour. When Beyond Orpheus was published, the term “contour” was in an early stage of development; in the few cases authors mentioned it, they nearly always meant relative pitch height. More recently, the concept has been expanded. First, more rigorous mathematic procedures have been established for documenting and processing pitch contour. Second and more importantly, the concept of contour has been generalized, allowing it to apply to any musical domain built of ordered elements, such as rhythm, duration, texture, and timbre. To assemble any contour reading, pitch or non-​pitch based, one readies an integer scale to apply within a domain. The n elements of interest (n notes, rhythms, etc.) are then normalized, meaning they are arranged in integer order from 0 to n-​1 according to the quality under investigation.7 That scale is last applied back to the events in their original musical context. To demonstrate, we will assemble a duration contour reading for the Belgian Paratroopers melody, mm. 1–​4. In the preassembly phase, we register the presence of four distinct durations. In increasing length, they are sixteenth note, eighth note, dotted eighth note, and quarter note. These durations are arbitrarily assigned the values 0, 1, 2, 3. These values reapplied to the source melody in order yield the following numerical string: < 2 0 1 1  2 0 1 1  0 0 1 1 1  0 0 1 3 >. Each wider space indicates the presence of a barline. This process translates all of the Paratrooper durations into an alternate format. For analysis to occur, these values must be interpreted, meaning reduced. Analysts performing reduction typically focus on maximal and minimal values—​in this case: 0s and 3s—​but also enjoy quite a bit of freedom in how to proceed. One possibility is to examine the full string, retaining the first and last values (structural accents) as well as the interior extremes.8 The only notable interior high point in this excerpt is the 2 that appears at the downbeat of m. 2. There are multiple low points, which occur whenever one or more 0s are surrounded by longer durations. Because very short durations have little impact on listeners, we will overlook them and assemble our duration contour reduction around three data points, the 2 from the beginning, the 3 from the end, and the aforementioned 2 in the middle. If we were to reattach the pitch content present during these three durations, the new melodic reduction, F4-​A-​G, would result.

136  Methods of Motivic Analysis Our second revision of Epstein Point 1 (contour reduction) involves qualifying what are “high and low points.” Just earlier we justified omitting minimal duration values on the basis of their limited salience: these tiny sixteenth-note events are the shortest and therefore have the least impact on consciousness. It may similarly be necessary to omit certain maximal and minimal contour values when ornamental gestures such as neighbor figures present. Consider a case in which an ascending melody’s highest note, G5, is decorated by an upper neighbor. Although the A a step above is technically the highest local tone, common sense dictates that we set it aside in favor of the G.  The same condition applies to lower neighbor figures for a descending line, and even to accented passing tones occurring on metrically strong beats. The new version of the contour reduction principle, given here as Reduction Rule 1 (RR1) takes account of such passing and neighbor tones. In addition, it specifically requires the analyst to account for the structural accents created at the start and end of any analytic span. Although it overlaps to an extent with tonal reduction, RR1 should be regarded mainly as an outgrowth of the philosophy of salience-​based reduction. Reduction Rule 1 (Contour): Structurally significant notes achieve prominence when they appear at high points or low points in any domain, including pitch, dynamics, articulation, duration, and timbre. These contour maxima and ­ minima appear in both global and local contexts. By definition, the start and end point of any chosen span of music undergoing reduction must be retained at all subsequent levels; such structural accents cannot be eliminated. Corollary (to RR1): A tone judged structural according to the salience model may be disregarded if, at the surface of the music, it is determined to be a nonstructural passing or neighbor tone.

The new rule for contour-​based reduction respects the spirit of Epstein’s original point but offers more guidance for analysts. Its chief strengths are its flexibility and its responsiveness to certain exigencies of musical composition. I refer here not only to structural accents, which must be accounted for in all cases, but also to the requirement that reduced pitches stand the test of musical relevance (RR1 Corollary). Another advantage of this recasting of E.P. 1 as RR1 is that it suggests a means for deciphering E.P. 3, which is unclear in its original formulation. One can only guess what Epstein means when he says that, “Consistent and recurrent appearance of . . . notes within a pattern” gives them greater “structural importance.” It is possible that E.P. 3 refers to figurated textures such as the one appearing in m. 11 of Chopin’s Nocturne in F♯, Op. 15, No. 2 (Example 5.4). It is well known that patterning can be created by means of slur marks, articulation, and pitch

Basic Motivic Analysis  137 Example 5.4  Slur pattern delineates a pitch motive in Chopin’s Nocturne in F​♯ Op. 15, No. 2, m. 11.

working independently or in coordination. In the case of m. 11 in this excerpt, it is the three-​note slurs that most clearly indicate the larger pattern, the 4th shape. (see stemmed notes). Again, none of the examples Epstein gives in support of E.P.3 at all resembles the nocturne excerpt. In light of his penchant for precision, it is appropriate to take Epstein at his nonword and assume that m. 11 is not the sort of event E.P. 3 is meant to apply to. The “recurrences” that Epstein does demonstrate occur at levels far removed from the musical surface. In discussion of Schumann’s Fourth Symphony, for example, he calls attention to the fact that many of the themes start with an upbeat. In this way, the idea of anacrusis itself becomes “significant to the unity of the symphony” (Epstein 1979, 37). The fuller context for this claim is that Epstein continually strives to expand the idea of motive beyond being a pitch or rhythmic cell. His formulation of E.P. 3 allows him to extend motive to extreme levels of abstraction, eventually allowing a general “premise” like ambiguity to be classified as motivic. This was a groundbreaking insight that deeply influenced all works on motivic analysis to follow, including this one. We have considered E.P.s 1 and 3, but not E.P. 2, the point that establishes rhythmic and metric salience as a criterion for reduction. The rule as Epstein formulates it works well for straightforward melodies such as that from Verdi’s “Stride la vampa!” aria from Il Trovatore (Example 5.5). The significant notes indeed “lie upon . . . metric strong points” in accordance with E.P. 2. An extraction of one downbeat note per measure creates the succession, B4-​B-​B-​B-​A-​A-​G-​F♯, which creates the larger 4th motive shown beamed. Epstein’s Point 2, however, lacks a clear means for handling cases in which pitch motives are masked by rhythmic techniques such as syncopation and

138  Methods of Motivic Analysis Example 5.5  Metric salience results in a linear motive in mm. 3–​10 of “Stride la Vampa” from Verdi’s Il Trovatore.

Example 5.6  Syncopation in Bach’s Fourth Partita, BWV 828. Structural melodic tones (treble staff) are metrically displaced at the music’s surface.

cross-​rhythm.9 Example 5.6, taken from the “Aria” movement of Bach’s Fourth Partita for keyboard, illustrates this point. Starting at E4 in the melody, all important melodic tones sound on weak parts of the beat. This syncopation poses a problem for a beat-​centric reduction, as that would mean no melodic events would be extracted from m. 2, not even at the downbeat. The analytic treble staff given above illustrates the melody’s underlying stucture, in which the tones, E4-​D-​C♯ and D are restored to their normative metric placement rather than being shifted a half beat ahead.10 To treat situations like this, we allow analysts to consider more than just note onsets. Instead of worrying about the fact that the E4 of the melody enters before beat two of the first notated measure, we concentrate on the fact that the

Basic Motivic Analysis  139 Example 5.7  Extraction windows lasting a duration of one eighth note occur on each of five beats.

E4 remains present as beat two arrives. Example 5.7 illustrates the process of establishing equal duration “windows” and allowing melodic events to intersect them. The windows yield the same ⎣ 3rd \ /​motive observed in the analytic staff of Example 5.6. In this instance, the windows were set to occur on each beat and to admit an eighth note’s duration of material. In other circumstances, an analyst might desire to set the windows on offbeats or spread them to occur every three, four, or even more beats apart. Example Web.5.1 illustrates how window extraction may be adjusted to extract motives in music that exhibit grouping dissonances, otherwise known as cross-​rhythms. Near the end of Beethoven’s Piano Sonata in D, Op. 14, No. 2, III, specifically in mm. 228–​232, novel accent patterns in 3/​4 time cause the music to behave as if it were in 2/​4 meter. In all cases that EDR is employed, analysts must strive to keep the windows at equal durations (i.e., no nudging allowed) and sufficiently close together to ensure that the motives they uncover remain perceptible. We now turn to the task of clarifying the remainder of E.P. 2. The text following Epstein’s first sentence on rhythmic/​metric strong points says, essentially, (1) that metrically accented ornamental tones need not always be excluded from consideration, and (2)  that these same accented ornamental tones often appear adjacent to structural pitches. The qualifier “need not always” implies that analysts can resolve this matter on a case-​by-​case basis with a clean, binary outcome: an accented ornamental tone is significant or not. The situation is actually more complicated than this. There are many cases in which accented ornamental tones are nonstructural. That first scenario is typified by an instrumental cliché of the Classical period, the ornamented arpeggio figure (see Example 5.8). Upon encountering the first theme from the finale of Mozart’s Piano Sonata in F, K. 332, one technically could extract the strong-​beat notes to generate the shape shown by dotted-​beam, B♭5-​ G-​D-​B♭4. No musician would attempt that in seriousness, though. All evidence

140  Methods of Motivic Analysis Example 5.8  Mozart Sonata in F, K. 332 (III), mm. 1–​3.

Example 5.9  Role of ornaments in Brahms’s Intermezzo in A, Op. 76, No. 6. (a) Ornamental tones as structural in the B theme, mm. 23–​28.

(b) Voice-​crossing 3rd motives in mm. 1–​4.

points to an F-​major tonic arpeggio descent as the first structural melodic event of the piece (solid beam). Beyond the obvious fact that the piece is billed in F major, the F arpeggio reading allows the right hand’s first note, C6, to function as the crowning note of the tonic chord (C6-​A5-​F-​C-​A4-​F5). In contrast, I know of no musical style, excepting maybe serial composition, in which accented ornamental tones can be shown to be purely structural. That would entail a logical impossibility, for tones cannot be ornamental and structural at the same time. This leaves us to ponder a gray area for accented ornamental tones. It may be possible that they function as structural tones in some cases but not in all.

Basic Motivic Analysis  141 A new, musical context afforded by the B section of Brahms’s Intermezzo in A, Op. 76, No. 6, will help frame an argument for treating ornamental notes as structural (Example 5.9). Grace notes are unusually prominent in this excerpt, with three appearing in one short phrase. Their placement is suspiciously uniform:  starting in m.  26, they always appear on the second eighth-​pulse of a measure. These factors draw attention to the graces themselves, as opposed to the tones they decorate. The decision to grant them structural status is made in light of two questions. The first is, “Does regarding the E5, D5, and A4 as structural clarify the nature of the melody here?” The answer to this is yes, as these notes help form a linear descent from the E5 all the way to the F♯4 of m. 28.11 The next question is, “Do the newly promoted tones resonate with any other significant motives of the piece?” The answer is again yes. In Example 5.9(a), the two grace note events, E5-​D and D-​C♯ are shown to assemble through addition into a larger linear 3rd. This same shape serves as the basis of the Intermezzo’s main theme from mm. 1–​2 in the A section. In Example 5.9(b), the 3rd = 2nd ⊕ 2nd is given in parallel tenths that are masked by a register swap: note the crossed lines below the music.12 Having noted a number of deficiencies surrounding Point E.P. 2, we are now prepared to state a revised version of it: Reduction Rule 2 (Rhythmic/​metric reduction): Notes coinciding with rhythmic and/​or metric strong points are typically structural. These strong points may reflect the written meter or those of temporary alternate meters created through displacement or grouping dissonance (syncopation or cross rhythms). Corollary (to RR2): Metrically stressed ornamental (non-​chord) tones should be disregarded except in cases where strong contextual evidence can be cited for deeming them structural. The strongest claims for retaining them will appeal to motivic resonances in the piece, local or remote.

Reduction Rules for Larger Musical Spans Moving past the relatively small-​scale reductions explored earlier, we turn to the issue of reduction as it pertains to larger motives that span multiple phrases. It will not be possible to apply RR1 and RR2 directly, without refinement. It is true that musical formulas tend to be recursive, allowing us to treat large-​level structures as if they were “blown-​up” versions of smaller ones. We routinely do this metrically with hypermeter and harmonically with tonal progressions. Upon shifting our attention to higher levels of musical activity, however, new complications arise.

142  Methods of Motivic Analysis The confounding issue is higher-​order salience. The reduction techniques in this book are founded on the principle that tones gain significance when they are emphasized metrically, rhythmically, or by jutting out in pitch. This is well and good when there is a limited, stable frame of reference. In moving phrase to phrase, though, one is likely to encounter radical shifts in the music’s disposition. A given span of music might be in a much higher or lower register than the one adjacent to it, the texture/​instrumentation might change, and so on. Were we to forge ahead without qualifying the guidelines from before, we might lose sight of significant pitches within a phrase if they fail to register as extremes in the larger span. This could happen if a segment of sixteen measures with a narrower tessitura were sandwiched between segments exploring wider pitch ranges. The reverse situation, also undesirable, results from prioritizing pitches that jut out of their local segments but that fail to assemble into any coherent shape. Students newly introduced to equal duration reduction are the ones most likely to propose such dubious shapes as they rashly extract precisely one salient pitch from each phrase. The best way to promote success is to establish parameters for creating the “limited and stable frames of reference” earlier called for in analysis. One such ready-​made framework is patterning, such as that furnished by melodic and/​ or harmonic sequences. In Example 5.10, which shows a later passage from Mozart’s Piano Sonata in F, K. 332, III, the tight patterning of texture and harmony suggests that it would be proper to extract a melodic tone from each Example 5.10  Mozart Piano Sonata in F, K. 332 (III), mm. 100–​112.

Basic Motivic Analysis  143 four-​bar span. In this case, the structural status of all upward-​stemmed notes is based on their being chord tones: this is why the E5 is selected in m. 104 and not the F. The soprano line’s chromatic descent through the pitches F5-​E-​E♭-D, is not the only motive that can be extracted. Starting with the B4 circled in m. 100, the alto voice can be shown to progress as a leading tone to the adjacent note name, C, at the start of the second system. The circled A3 and B♭ follow in measures 108 and 112. The shape that would emerge from connecting the four circled notes is B-​C-​A-​B♭, a sensible and hummable pitch-​class motive. Both of these four-​note motives fit within and are a product of the circle of fifths harmonic chord progression present (see chord symbols below music).13 A good many medium-​scale motives are easily identified; however, we cannot count on all musical surfaces as being as transparent as this one. Another kind of stabilizing reference frame can be of great help in murkier settings. Specifically, it will be necessary to coordinate higher-​order reduction procedures with the findings obtained through form analysis. Form in music refers to the rich system of knowledge describing the organization of musical works. In the most general sense, the study of form concerns the order and function of blocks of material, from the relatively small (phrase to phrase) to the largest (section to section) levels. When working close to the surface, the boundaries between formal units of music should inform reduction. In the eight-​measure melodic excerpt from Rossini’s Barber of Seville Overture shown in Example 5.11(a), the most intuitive shapes that emerge during reduction are the ones that respect the caesura (’) boundary between the phrase segments. These shapes are the G5-​A in mm. 92–​95 and the A5-​B in mm. 96–​99; the stems indicate the priority that attaches to these phrase-anchoring tones by virtue of structural accent.14 The point of this example is not to argue that motives can never cut across form boundaries. When they do, however, they should do so in a musically sensitive way. In the case of Rossini’s melody, the two segments are connected: the first four measures are in a sense answered by the second four. It is for this reason that it is appropriate to draw the larger G5-​A-​B beam shown in Example 5.11(b). This 3rd shape gains standing in two ways. First, it is built of structurally accented notes, and second, it occurs as a parallelism with the first surface motive expressed in the theme; see the brace in mm. 92–​93. Many syntactic musical elements nest recursively, and form is no exception. Multiple phrase segments typically combine to make phrases. Complete piece structures, typically binary forms, frequently nest within larger ternary or rondo forms. This implicit hierarchy provides the basis for allowing motives to cut across boundaries, since a division at one level will likely disappear at a higher one. This behavior is illustrated in the top-​down succession of the two analyses

144  Methods of Motivic Analysis Example 5.11  Motives crossing phrase boundaries in Rossini’s Overture to Barber of Seville. (a) mm. 92–​99.

(b) mm. 92–​103.

shown in Example 5.11. In the lower reading, the initially separate four-​measure segments fuse to assemble a larger formal unit. There are many situations in which close patterning of theme, orchestration, and text (if present) will support the decision to allow a motive to cross a phrase boundary. In contrast, there is only one in which that practice is counter-​indicated, that being when a piece engages in what I refer to as “full reset.” A full reset is a moment in which listeners are expected to freshly attend to starting music, which leads them to relinquish concerns about motivic activity heard before. The prime example of a full reset is the start of a new movement in a major work. Such moments are usually separated from the close of the previous movement by silence, a rhetorical element that Edward T. Cone likens to the frame around a painting (1968, 16–​25). It is true that composers often try to bridge these intermovement gaps. This can be achieved with the performance instruction, attacca. Another strategy for

Basic Motivic Analysis  145 Example 5.12  A three-​note motive echoes over two movements of Beethoven’s Sonata in F​♯ Major, Op. 78. (a) Movement. I, mm. 90–​93. The movement ends twelve measures later.

(b) Movement II, mm. 1–​4.

(c) Improper motive drawn across the “full reset” boundary of movements I and II.

linking movements is to reuse a closing gesture from near the end of the former at the start of the latter, as Beethoven does in his Piano Sonata in F-​sharp, Op. 78. In Example 5.12, the motive that does this is /​  ⎣, a stepwise prefix attached to a downward leap. The possibility of intermovement associations of the kind documented in Examples 5.12(a) and (b) is not problematic from the standpoint of reduction. It would be problematic if an analyst tried to draw a motive spanning the movements, as in Example 5.12(c). In that case, the provisional shape indicated by beam would violate the prohibition against motives spanning a full reset. Due to the frequency with which it occurs in Classical forms, I  should mention another circumstance that produces a full reset. It is “rounding,” the

146  Methods of Motivic Analysis ­ oment in a piece marked by the return of head material and tonic harmony. m Roundings occur often and in pieces of all sizes. In large-​scale sonata forms, the full reset event is so significant that it has earned its own term: recapitulation. Similar resets occur in rondo forms at the return of each refrain, as well as in binary forms appearing in instrumental suites and the interior movements of symphonies and sonatas. For pieces of modest scope, only a hint of head material is needed to bring about rounding, sometimes as little as two measures of melody. Yet even in such cases, the return of the main idea in tonic carries its full rhetorical significance such that a full reset can be said to occur. This prolonged treatment of rounding is offered in the hopes of preventing a common error made by analysts who are just beginning their studies in small-​ scale form and newly engaging with period and sentence structures. The excerpt appearing in Example 5.13, taken from a Haydn rondo in rounded binary form,

Example 5.13  Score of the theme of Haydn’s Piano Sonata in D, Hob XVI: 37 (III), with form annotated. Below, a dubious period is diagrammed spanning the digression and rounding.

Basic Motivic Analysis  147 will demonstrate. Its form is indicated by the markings of a, digression, and a’. Inexperienced analysts might note in mm. 9–​16 that one phrase ends on V and that the next ends on I. Their instinct might be to tie the two four-​bar phrases together into a kind of period, as diagrammed below the passage. The proposed period cannot be, because the rounding at m. 13 provides a hard reset of a material. As at the beginning of the work, the four-​measure melody that reappears at the rounding is itself answered by the phrase in mm. 17–​20. If the music of mm. 13–​16 serves as antecedent to the final phrase, it cannot also be a consequent answer to 9–​12.15 To reiterate, the rule against motives spanning a full reset prohibits shapes uncovered through reduction from occurring in gaps between movements or in the spaces before strong tonic recapitulations. This rule is firm except in the special situation of the “wind-​up” return, in which rising melodic energy and/​or additive phrase segments aid the music’s push toward the moment of recapitulation. In a concerto or song, this energy often takes the form of a miniature cadenza over a dominant seventh chord (i.e., an eingang).16 In a serenade or symphony movement, it might take the form of a sentence-like structure, in which smaller segments build energy toward a larger culmination segment that serves as the return. Example 5.14 illustrates a “wind-​up” passage in Beethoven’s Piano Sonata in C, Op. 2, No. 3, III. The annotations in the score illustrate the wind-​up gesture performing its typical duty, which is to elongate the dominant area. The arrival of V in m. 28 constitutes the structural close of the digression on a half cadence (HC). This is an event that, according to the earlier argument, cannot connect to the rounding at m. 40. The retransitional music in mm. 28–​39, however, is organically related to the rounding. The melody in m. 30 reclaims the high G5, and the expectant, Example 5.14  Beethoven, Sonata No. 3 in C, Op. 2, No. 3 (III), mm. 26–​43.

148  Methods of Motivic Analysis additive phrase rhythm suggests that an important thematic return is imminent. In this special case, it is the passage’s forward-​directed energy that allows for the medium-​sized motive, 2nd, to be posited for mm. 29–​40. The last of our rules concerning reduction will place a limit on its scope. Given the tremendous variation that works may exhibit in tempo and pacing, this can only be done in relative terms. Reduction Rule 3 (RR3) for medium-​scale reduction: Except in rare cases, motives discovered via reduction shall be constrained to a single, major formal section. Corollary 1 (to RR3): All phrases touched upon in reduction should furnish a roughly comparable number of tones. Corollary 2 (to RR3): Notes extracted from separate phrases may be treated as pitch-​class events. Corollary 3 (to RR3): Except in cases of extremely compact works, BMA will not admit motives that span a full piece.

The term “section” in RR3 refers to a major formal area of a piece as determined through study of harmonic, thematic, and rhetorical elements. Put simply, sections may be thought of as the building blocks of conventional forms. A simple binary form has two sections, or “reprises,” designated as || a || a’ || or || a || b || according to their thematic content. Rounded binary and sonata forms have three sections, designated || a || digression a’ || and || Exposition || Development Recapitulation ||, respectively. Rondo forms typically contain five or seven sections. When a piece is composed in nonstandard form, analysts call on their knowledge of the traditional models to parse it in as reasonable a manner as possible. The “rare case” clause in RR3 can be invoked when some energy—​melodic, harmonic, rhythmic, textural, or textual—​can be shown to flow across segments or sections, as in the case of the “wind-​up” condition described earlier. An argument can be made for linking formal areas if, for example, their harmonic centers exhibit a progression such as iv-​v-​VI (ascent through key area). (It is likely that other aspects of music in this same hypothetical piece would project over sectional boundaries at the same time the harmony does.) Speaking generally, the transition and retransition areas in sonata and rondo forms are the most likely to be involved in dynamic interrelation; however, the boundaries between any sections may be overrun. Corollary 1 to RR3 extends the original principle of reduction to greater spans. Its purpose is to ensure that reduction at this next level proceeds more or less “mechanically,” as before. Another way to say this is “evenly,” to avoid situations in which all of the pitches deemed structural are taken from too narrow a window

Basic Motivic Analysis  149 of events. Corollary 2 to RR3 reinforces the point brought up by the voice-​leading analysis in Example 5.10. In sequential passages, it is common for the material to rotate among the voices. Composers do this to generate sonic variety even while rigorous patterning is occurring. The same principle holds for the several phrases that constitute a section of a piece. While it is possible that the register of the voices may hold steady across phrases, it is just as likely that they will shift to bring forth new colors. To enable analysts to posit meaningful melodic shapes in such circumstances, pitch-​class motives must be allowed by the method. The point expressed in Corollary 3 is not truly independent of Reduction Rule 3. It rather serves to remind readers of the ultimate limitation of motivic analysis. There are many occasions in which a piece’s large-​scale form and harmonic structure can be productively seen as stemming from or entwined with motives. Yet even in these cases, the motivic events themselves tend to be of modest scope, occurring within the boundaries of one or several formal segments. This claim accords with Schoenberg’s original notion concerning motives’ size and with basic truths concerning the limits of human perception. It is well known, for example, that no real musical experience lasts more than a few seconds.17 In any instance that we attempt to apprehend (audiate, “hear,” etc.) a musical span longer than that, we substitute imagined sensation for actual sensation. This kind of grand thinking, which underpins entire areas of musical knowledge such as form, is by logical necessity almost entirely metaphorical. When this book was first conceived, I hoped it would be possible to develop a salience-​based reductive method that could reliably produce piece-​long motives. I soon came to realize that this desire was suspect. I know of no current theories that claim that concretely heard motives must—​or even could—​unfurl over the course of large pieces. While perhaps they could be engineered to do so, no purely musical reason exists to expand them to that extent. This led me to interrogate this pursuit: what was the motivation behind it? It was ambition, most likely, the desire to build a special functionality into motivic analysis to enhance its competitiveness with other analytic methods. That is a woefully insufficient cause for overextending the reach of a method. A Schenkerian analysis employs a piece-​spanning Ursatz because it must: the goal of that method is to show how the total structure of a work derives from its counterpoint and harmony. Motivic analysis, to the extent that it has evolved away from Schoenberg’s original theory, long ago ceded its claim of serving as a tool for revealing that kind of total organicism. The most likely effect of proposing piece-​long motives, ironically, would be to weaken the analytic enterprise. Any such shapes would be composed of motives with elements spread too far apart to be meaningful. Motives, in other words, generally do not dictate the grand formal designs of works. Their role, rather, is collaborative:  they run in tandem with other

150  Methods of Motivic Analysis organizational forces. Acknowledging this limitation does not in any way suggest that we must abandon the idea of comprehensive analysis involving motives. It means, rather, that we should temper expectations of what a motivic analysis of a large-​scale piece looks like. Instead of producing a single, grand shape, it will posit a slightly larger set of medium-​sized shapes that apply to the component sections. This sober recognition, if anything, strengthens both motivic theory and analysis. The firm upper limit on motivic scope, for one, productively limits our investigation of shapes to manageable—​yet still quite generous—​spans. Consider that a single section of a rounded binary form by Mahler can easily take up hundreds of measures and many minutes of time. For another, it discourages us from engaging in flights of fancy that could quickly erode this theory’s claims to systematic rigor.

Principles for Linking Motives Motivic analysis is concerned with identifying shapes in music and assembling them into a coherent whole. This portion of the methodology chapter pivots to address the latter activity by establishing rules for associating shapes within a work. It is necessary to reassert a guiding principle of the method, which is that associations among motives should be literal. This rule is global, in that it applies fully to both basic and complex motivic analysis. Rule 1 of Motivic Analysis: A relation between two motives is said to be literal when the second reproduces all of relevant aspects of the first, in order.

The essential identity of a melodic shape is encoded by its composite intervals. For a five-​note pitch string such as D4-​B♭-​A-​C5-​D, that means the four successive intervals between D4 and B♭, B♭ and A, A and C5, and C and D. These intervals can be measured diatonically in pitch space, resulting in the interval succession . If one desires more detail, the interval measurements can be further specified with tonal qualities, , or even in number of semitones, , although for our purposes both of these will usually be unnecessary. To say that a second pitch or pitch-​class motive is equivalent to a first one, the same intervals must appear in order. In tonal music, this occurs under the four operations illustrated in Example 5.15.18 Under transposition, shown in Example 5.15(a), the intervals of the starting pitch string (boxed) are fully preserved, but the new shape starts on a different note. Example  5.15(b)

Basic Motivic Analysis  151 illustrates transposition involving pitch-​class: in that case, the intervals dictate which letter-​name note will appear, but not in which octave it will appear. In the case of mirror inversion, illustrated in Example 5.15(c), all pitch interval magnitudes of the starting shape are preserved, while each ascending/​descending direction is flipped. This produces the contour of the original shape reflected upside-​down, as if a mirror lay horizontally where the “I” marking is. Under retrograde (Example 5.15(d)), the original string of notes is reversed, resulting in the interval values reversing both their order and ascending/​descending direction. Example 5.15(e) shows a case in which two operations in combination apply to the boxed shape to effect a retrograde inversion; this

Example 5.15  Illustration of the basic interval-​preserving operations for pitch and pc. All intervals shown are calculated diatonically, where 2 = step, 3 = third, etc. (a) Transposition preserves the melodic intervals of a pitch string.

(b) Transposition preserves the melodic intervals of a pitch-class string, but does not dictate the octave in which the notes of the new string appear.

(c) Mirror inversion reverses the up/​down direction of melodic intervals in a pitch string.

152  Methods of Motivic Analysis Example 5.15 Continued (d) Retrograde reverses both the order and up/ down direction of melodic intervals.

(e) Retrograde inversion reverses the order but not the up-down direction of intervals. At right, the two strings resulting from these last two operations are shown to be inversions of each other.

yields the shape at right, which preserves the original string’s interval values and orientations but reverses their order. A rhythmic gesture’s identity is encoded by its interval content as well; however, the distances between attacks in a rhythm are measured in duration. In discussing this type of distance, analysts often rely on the concept of “onset interval,” meaning the time between two events as measured in some musical unit value, such as a sixteenth or eighth note. For example, the rhythm h q e e h measured with a unit value of e would have the duration series . Importantly, each interval listed in that series is a pure time span, which unlike pitch has no upward or downward directed distance. That means that the operation of mirror inversion generally does not apply in the realm of rhythm.19 Having established that rhythms cannot be transposed the same way that pitches are, it is still possible to resize rhythmic shapes to occur as longer or shorter events. The rhythmic relationships recognized in Musical Motives are listed in Example 5.16. The primary operation of the method is duration scaling, which applies the same multiplier to all values of a rhythm. Consider the rhythm h q e e h. In Example 5.16(a), this rhythm is transformed to become w h q q w by multiplying all durations by two; the traditional name for this expansion is augmentation. In the lower line of the example, the

Basic Motivic Analysis  153 Example 5.16  Illustration of the basic interval-​preserving operations for rhythm. (a) Duration scaling preserves the durations of rhythmic shape.

(b) Retrograde reverses the duration series of the original rhythmic shape.

initial rhythm is transformed by a factor of ½ to become q e x x q. The traditional name for this acceleration-​like scaling is diminution. In both augmentation and diminution, the resultant rhythms preserve the essence of the original: the duration vector for each pair of rhythms remains the same as the unit value changes. All of the rhythms given in part a) of the example can thus be regarded as equivalent. With inversion excluded from the set of interval-​preserving rhythm operations, only retrograde remains. The retrograde relation, which is scarcely audible in the domain of pitch, is slightly more relevant to rhythm (Example 5.16(b)). It is, in fact, reasonable to assume musicians can sense when the elements of a differentiated duration series are reversed, and possibly even notice the symmetry. One caution to add about this operation arises in cases of

154  Methods of Motivic Analysis rhythms built of a single duration, such as q q q q. For an analyst coming upon a second instance of q q q q, the situation is fully ambiguous from the standpoint of transformation, since both basic repetition and retrograde performed on the original will produce it. In general, when pondering the proper label for describing an ambiguous transformation, one should prefer the more common, straightforward operation. In this case, simple repetition wins out. Example 5.17  Summary of all pitch, pitch-​class (pc), and duration preserving operations employed in motivic analysis.

Basic Motivic Analysis  155 All of the interval-​preserving operations described to this point are listed in Example 5.17, along with prescriptive symbols for indicating their presence. The chart is organized according to domain, with pitch and pitch-​class operations appearing in the topmost zone. Note that no special nomenclature is reserved for distinguishing between pitch and pitch-​class operations; it will be assumed that the audience for an analysis can discern the difference on their own.20 In cases where pitch and rhythm transformations occur jointly, a double barbed arrow is employed (e.g., the first, third, and fifth arrows). Single barbed arrows are used in cases in which pitch content alone transfers (e.g., the second, fourth, and sixth arrows). The center portion of the chart indicates the nomenclature for documenting rhythmic relationships. The most important of these is the one that appears second. This single-​barbed arrow indicates a full return of a rhythmic shape under duration scaling. The trivial case of scaling is “x1,” which is used to show the literal return of a rhythm motive (pitch content altered). Moving to the entry just above, the two-​barbed arrow carrying a multiplier signifies an operation in which an original shape’s durations are scaled rhythmically while its pitch/​pc content remains unaltered. (Note that in cases where a motive’s full pitch and rhythmic content returns, the unmarked “Transposition” arrow, which enfolds rhythm, is strongly preferred to the “x1” duration-​scaling arrow, although both technically apply.) The third and last arrow in this middle area is used to track rhythmic retrogrades; however, these will rarely be called upon in analyzing tonal works. Although it is possible that scaling and pitch retrograde could both apply simultaneously, no official nomenclature is offered to document that very rare transformation. One last motivic relationship is delineated in the lowest line of Example 5.17. The Sensed connection relation, signified by dashed arrow, violates this method’s guiding principle in that it does not track literal motivic recurrences. It should thus be regarded as an unofficial tool that retains an artifact from traditional motivic analysis, that being the sense of “intuited”—​which is to say: unprovable—​ relatedness. The Sensed connection tool should be used sparingly, if it all. Also, to minimize friction with the other transformations, it should only be used to document musical connections that could be shown to be literal, but simply are not for reasons of efficacy. One such scenario involves motivic fragmentation. Where it is technically possible to draw a plain pitch-​motive arrow from a source motive to a smaller, two-​note fragment, doing so frequently will compromise the logic of analysis by suggesting that all like two-​note gestures in a work are interrelated. It is methodologically safer to occasionally suggest that a local bit of fragmentation “can be heard” as a motivic connection. To avoid too many intuitions from piling up, I recommend a procedural restriction on “chaining” these arrows. A small number of dotted arrows may occur successively to show

156  Methods of Motivic Analysis the progression of a fragment, but these arrows as a group should be strictly confined to a local stretch of measures. The interval-​preserving operations presented in Example 5.17 cohere as a group. They complement each other such that, when employed creatively and judiciously, they will allow an analyst to comment meaningfully on the motivic content of nearly every gesture of a piece. The scope of this group, moreover, has been intentionally limited to discourage analysts from proposing ad hoc motivic transformations that, more often than not, are descriptive but not necessarily meaningful. A case in point is the informal transformation, “Syncopate,” which one might imagine applying in instances where an original rhythmic motive shifts the location of some of its attacks within the meter. This process, illustrated in Example Web.5.2 , involves the second theme from Beethoven’s Piano Sonata in C♯ Minor (“Moonlight”), III, in mm. 21–​28. Drawing an arrow between the two theme statements and labeling the latter a product of the “Syncopate” operation may afford some momentary satisfaction. Consider, though, the uncertainty that would result from admitting Syncopate to the group of rhythmic transformations. The term is highly vague; how would one know for certain when to apply it? Looking more closely at this one potential instance, we see that not all of the attacks of the second “Moonlight” theme in mm. 25–​28 are shifted; the downbeats certainly are not. Should the rule be that all attacks of the original shape must shift for Syncopate to be declared active? eighty percent of attacks? Another operation officially excluded from the list of motivic relationships in Example 5.17 is Fragmentation. Traditionally, this operation is said to manifest when, following the presentation of an idea, the music seemingly seizes on a short bit of it for developmental purposes. Common source materials for fragmentation are running-​note and cadential gestures. As ­chapter 3 noted, fragmentation has long been a concern of motivic analysis. And well it should be: it is nearly ubiquitous in Common Practice composition. For the purposes of assembling a new methodology, however, fragmentation is too inconsistent and illogical to be incorporated. On epistemological grounds, we have already seen how quickly the notion of a Fragment operation is undermined by the simple question, “What labels are appropriate for motive fragments?” Schoenberg’s answer to this question led him to postulate a set of quasi-​mathematic labels such as 3rd ÷ 2 to describe how two-​note fragments are derived from a three-​note idea. This type of label creates a new problem, however, which is that the new shape in question loses the ability to exist independently. If fragmentation of two unlike motives in separate locations happens to yield the exact same pitch shape, the two distinct “divide by” labels run counter to the common-​sense observation that the resultant shapes are identical.

Basic Motivic Analysis  157 The larger issue surrounding small melodic fragments is their generic nature. It is nigh impossible to determine the true origin of any two-​note melodic event. Is it a primary motive, recurring through the piece, or is it a local entity derived from a nearby idea? Or is it somehow both of these things? The present discussion cannot resolve this ambiguity, but does offer a suggestion for responding to it. In cases where analysts wish to show recurrences of a short motive, they should apply a unique label and track its influence with solid arrows. In cases where analysts wish to show the local dynamics of a fragment derived from a proximate theme, they may use dotted arrows for the limited span that the relationship is relevant. In exploring the inherent limitations of informal motives such as Syncopate and Fragment, we gain some deeper awareness of their nature. These operations and others like them, such as “voice swap,” are best understood as macroscale techniques that composers use to restate larger blocks of material. When employed consistently across a work, a gesture such as Syncopate can be viewed as a type of motive in itself. The gesture becomes a “premise,” to use Epstein’s terminology. Defining and tracking this sort of motivic activity is absolutely relevant to this study. The proper place for establishing procedures for doing so, however, is in the chapter that details complex motivic analysis.

Demonstration and Discussion The theoretical presentation of the relationships permitted in BMA concludes with a brief demonstration of proper technique for drawing and labeling operational arrows. The context for this demonstration will be roughly the first third (mm. 1–​124) of Beethoven’s Piano Sonata 7 in D Major, Op. 10, No. 3, I. The movement opens with a “14-​note” motto gesture. In Example 5.18, this shape Example 5.18  The presentation of the “motto” in mm. 1–​4 of Beethoven’s Piano Sonata in D, Op. 10, No. 3 (I).

158  Methods of Motivic Analysis is shown as the source of three primary motives, two pitch-​based and the other rhythm-​based. The main pitch motive of interest is a motive of a third that occurs in both descending and ascending (inverted) forms. The other motive bracketed is the stepwise-​prefix-​with-​arpeggio (/​Arp). The main rhythm motive of interest consists of fourteen rapid quarter notes leading to a longer, held note (see topmost brace in the example). The first pitch-​ based operation to be demonstrated is transposition. Transposition can occur diatonically or chromatically, in either pitch or pitch-​ class space. The arrows in Example 5.19(a) document pitch transpositions of a \3rd motive that starts first on D5 and then on B4 and G. Although instrumental doubling technically causes each instance of 3rd motive to appear in three voices, its presence is only tracked in the alto. Example 5.19(b) illustrates a second set of transpositions of the \3rd shape. One occurs entirely within the twelve measures of score shown. The expansive \3rd in whole notes that begins at m. 41 elides with a much faster \3rd that begins at m. 45. In addition to the common pitch content, the latter retains the rhythmic Example 5.19  Pitch motive activity in Beethoven, Op. 10, No. 3 (I). (a) Pitch transposition of \3rd motive, with rhythm retained.

(b) Pitch transpositions of \3rd motive, with rhythm altered.

Basic Motivic Analysis  159 Example 5.19 Continued (c) Mirror inversion involving multiple 3rd events, with rhythm retained.

proportions of the former but sounds it eight times faster. For this reason, the “x1/​8” arrow connecting them is double-​barbed. The other transposition arrow indicates that the \3rd beginning in m.41 originates from the “motto” segment of m. 1. This example introduces the convention of using a large filled-​in dot (see top left of the graphic) to represent motives appearing in distant segments. The reason a single barbed arrow is used is because the rhythm of the shape at m. 41 overextends the original’s first duration. True scaling of the motto would produce one whole note per pitch; therefore, only the pitch content is faithfully transmitted. Example 5.19(c), taken from the start of the exposition’s Second Tonal Area, demonstrates how to label inverted motives. In mm. 71–​74, the source \3rd in the left hand spawns an inversion of itself in the right hand at the pickup to m. 75. The diagonal lines in the following measures illustrate the subsequent register swaps. Rather than viewing the music one operation at a time—​which would require new Inversion arrows at the pickups to m. 77 and m. 78—​the analysis reduces the content to two basic forms of the motive, rectus and inversus. Both of these, it may be recalled, were present in the piece’s original “motto” gesture in mm. 1–​4. (Note that this is a compositional detail that would receive a great deal more attention if we were developing a full, formal BMA.) In contrast to the demonstration of pitch motive activity, where rhythmic issues were invoked tangentially, Example 5.20 concentrates exclusively on rhythm. Example  5.20(a) demonstrates the most critical rhythmic relation in motivic analysis, whereby a musical shape returns with new pitches but with its duration series intact. The single-​barbed “x1” arrow linking the 14-​note motto in mm. 1–​4 to the closing area theme of mm. 94–​97 communicates their identity relationship. The same relationship ties the 14-​note motto to the main theme of the development section, stated first in mm. 133–​137. Example 5.20(b)

160  Methods of Motivic Analysis Example 5.20  Rhythm motive activity in Beethoven, Op. 10, No. 3 (I). (a) Rhythmic duplication of the “14-note” motto; pitch content altered in mm. 91–​97 and mm. 133–​137.

(b) Diminution and augmentation of the original S-​S-​S-​S rhythmic motive.

documents both a diminution and augmentation of the motto’s first four notes. In the above case (m. 60), the retention of diatonic pitch-​class content calls for a double-​barbed arrow. In the case below (m. 105), the original rhythm is scaled by a factor of two and the pitch content is new. The last operation from the chart in Example 5.17, Sensed connection, is demonstrated in Example 5.21. A  set of provisional arrows are drawn in the example to depict the relation between the two-​note shapes in mm. 72–​75 and

Basic Motivic Analysis  161 Example 5.21  Potential “Fragment” operation in mm. 71–​75.

the upcoming, culminating /​3rd in m. 76. The first three of the forward-​directed arrows are printed in solid ink. The other arrows are printed as dotted lines to signal a looser, aural association. The two dotted arrows chart the same relationship in two different ways. The larger dotted arrow arcing to the left above the score indicates a more abstract fragmentation that takes place out of time. It views all of the C♯4-​D motions as pieces of the upcoming /​3rd motive. The smaller dotted arrow within the staves provides an opposite, “reverse-​fragmentation” interpretation: it views the C♯4-​D motions accumulating into the eventual /​3rd. In place of Fragment, analysts are encouraged to employ dotted arrows to indicate personal hearings of how similar-​yet-​unrelated shapes resonate. This discretion applies universally, both to authors of analyses and to readers. The two dotted arrows given in Example 5.21 may stand, as long as it is understood that they do not constitute motivic analysis, proper. They may be amended or altogether ignored. To state this as a principle: fragmentation may be illustrated and discussed in analysis but should not be debated.

Assembling Analysis: Preliminary Narrative Strategies The paired hairpin dynamics symbol, > < symbols in a score knows that they encode more than simple volume instructions. They portend

162  Methods of Motivic Analysis changes in air flow, bow stroke, and/​or arm weight. In the same way that a crescendo’s success may be dashed by fatigue, there is an ever-​present bugaboo that threatens to derail performances of motivic analyses. That obstacle inheres in motives’ microscopic nature, which can distract from the larger musical landscape. The danger is that analysts, becoming bogged down in minutiae, will fail to transcend them. The way to overcome this tendency is to mandate that all motivic analyses draw grand, synthetic points. A second global rule will help ensure that occurs: Rule 2 of Motivic Analysis: An analysis must be structured around a single source event called a Focal Point that can be shown to furnish all or nearly all relevant shapes in the piece.

This tenet shall hold for all works, irrespective of style. If we were to attempt a motivic analysis of even a twentieth-​century “moment form” piece, we would need to structure it around one or more primary events.21 Paradoxically, with regard to this hypothetical, modern piece, the notion of a central set of motives playing out organically would directly contradict the composer’s intent. For analysts adhering to this method, that contradiction must stand, unresolved and willfully ignored, as we concentrate on building our derivative artwork, the analysis.22 The graphic in Example 5.22 illustrates one way in which organicism manifests in music. It takes the form of a schematic showing an intuitive and traditional approach for assembling analysis. The original motivic source, the Focal Point, is located at or near a piece’s beginning, and its effects are traced forward in time. The transformational arrows that appear are unadorned, suggesting an idealized piece in which all motives recur literally. Solid circle nodes in this and all diagrams to follow represent musical segments. This representation implies that some kind of story or narrative underlies motivic analysis. That narrative may be better understood if reframed as a familiar, dramatic metaphor. A main character appears in the form of an initiating event. That character then exerts influence on the events that follow in time. The content Example 5.22  A model for cognizing motivic activity. Flow of information is from an early source event; solid circles represent musical segments.

Basic Motivic Analysis  163 and identity—​and energy, too, if one is amenable to that notion—​of Event 1 moves forward, propagating itself in left-​to-​right fashion through the work. We will explore this issue further in the book’s two Narrative Interludes (­chapters 5.5 and 6.5), noting the conditions necessary for proposing various plotlines to interpret musical works from the vantage point of motives. For now, the discussion of BMA’s methodology may be concluded with the proposal of one last rule: BMA Narrative Rule:  All analyses constructed via BMA shall adhere to the Propagation template, in which a motivic initiating event is shown returning literally or transformed over the course of a piece’s subsequent segments. Corollary (to BMA Narrative Rule):  All analyses constructed via BMA will ­locate their Focal Point at or very near the beginning of the piece.

This assembly rule plus corollary encapsulates a key aspect of BMA’s simplicity versus complex motivic analysis. In allowing analysts access to but a single plotline, BMA requires them to concentrate on the most basic aspects of investigation, such as identifying proper shapes in an opening source segment and seeking clear and meaningful correspondences in subsequent segments. The interpretation of the analysis is largely predetermined. Whatever drama unfolds, it will be shown to steadily progress from beginning to end. The corollary to the BMA Narrative Rule is in place to guide analysts in their selection of a Focal Point and to provide some necessary flexibility. For a BMA to follow the Propagation template, its source material must be located near the start. At the same time, analysts must endeavor to identify a Focal Point weighty enough to support a comprehensive analysis. Many pieces begin with segments that are bare in texture, exhibiting monophony, sustained tones, or repeating cadential figures; notable examples include Schubert’s Unfinished Symphony, Tchaikovsky’s Fourth Symphony, and Mahler’s Fifth Symphony. Upon encountering conditions of this sort, analysts are obligated to scan ahead to find the first segment of music capable of furnishing sufficiently rich analytical material. Such a segment might occur at the allegro onset immediately following the slow introduction. As long as the Focal Point selected can be reasonably said to occur “near the beginning” of a movement, the conditions of this rule may be said to be fulfilled.

Interlude 1 BMA Narrative Archetypes The Role of Narrative in Motivic Analysis in General and Its Role in BMA in Particular Although there has been little formal discussion of narrative up to now, the topic has played and will play a prominent role in this method. Many of the analyses presented to this point began by reporting on motivic content and succession, but then continued by casting the objective findings in dramatic terms. No formal justification has yet been given to support this interpretive activity. Here that will change, allowing narrative to officially take part in structuring large-​ scale analyses, and in so doing, support the original goal of having motives move and move us. This Interlude, the first of two, serves two purposes. The first is to fill a theoretical gap from earlier by offering arguments in favor of incorporating musical narratives into motivic analysis. The Interlude’s second purpose is to provide a last bit of guidance for assembling comprehensive basic motivic analyses (BMAs). Its last section presents four models, or archetypes, for organizing and animating motivic findings. One archetype models the activity of a single motive. The other three archetypes model multiple motives in dialogue. Once this task is complete, all of the foundational theoretical aspects of BMA will have been covered. Chapter 6 will address the remaining practical concerns of BMA by presenting and evaluating sample analyses and, last, offering final considerations of the method as a whole.

Theoretical Justification for Framing Motivic Analyses as Narratives There is no requirement that analysts relate a piece’s events as a narrative. It is one thing to document the connections among musical events. It is wholly another to impose a storyline on them by imputing agency and desire to the events themselves. This distinction is exemplified by two kinds of claims that can be made about the succession of events depicted at the close of c­ hapter 5 in Example 5.22.

Musical Motives. Brent Auerbach, Oxford University Press. © Oxford University Press 2021. DOI: 10.1093/oso/9780197526026.003.0006.

166  METHODS OF MOTIVIC ANALYSIS Claim 1: Motivic elements located in a piece’s early Focal Point are restated in later segments in a way that promotes smoothness and comprehensibility. Claim 2: A piece’s early Focal Point motivates its forward motion and development. Focal Point material from this early segment remains recognizable throughout, even when its surroundings shift. Focal Point content remains stable in all situations; however, its character may shift, much as a person’s character is shaped by life experiences.1

If it were our goal to make this analytic system as neat as possible, we would prefer statements like Claim 1 and outlaw those like Claim 2. Such could easily be done, and the results would remain rich. Even after quashing all impulses to indulge in metaphor and storytelling, one could still fashion impressive networks of nodes and arrows documenting motivic processes over time. One could, moreover, still make wide-​reaching claims about musical structure and process. A key element would be missing, however: emotion. An analysis written in the spirit of Claim 1 would largely fail to embody the First Proposition of Motive, that requiring these shapes to move and to move us. Here, then, is another compelling reason for requiring a Focal Point in motivic analysis. It provides a landmark around which narrative analysis is oriented. The idea that a musical work has the capability to suggest a real-​world event is centuries old. Famous examples are furnished by the literally “stormy” passages in Baroque operas, the bird calls in Beethoven’s Pastoral Symphony, the journey down Smetana’s Moldau, and the adventures of heroes and rogues in Strauss tone poems. Based on the descriptive titling of such works, we may in certain situations gather that the composers themselves meant for the music to relate such impressions. On the contrary, when dealing with a piece that lacks a documented program, we are on shakier ground when we attempt to assert that any plot, literal or otherwise, underlies it. The results of each person’s narrative musings on such works would no doubt make sense to him or her, but it is increasingly unlikely that they would be meaningful to anyone else. There are many reasons to doubt the possibility that instrumental music carries narrative. To counter them, we may cite evidence that widely shared views on specific musical meanings do in fact exist. One point of common ground is humanity’s universal impulse to impose narrative on successions of events. Here, readers may be surprised to learn that many of the nonmusical narratives they put faith in are, in fact, products of intent and of bias. One may take as example a set of facts comprising a classic history, such as the history of World War II. Viewed on their own, the facts and dates tell no overarching story; the cumulative significance of all of the events is imposed later (Nattiez 1990, 245–​246).2 A potential analogy can be made for music with respect to its motives, phrases,

BMA Narrative Archetypes  167 and formal areas. The sequence of these sonic events does not necessarily manifest any narrative until an interpreter supplies one. This practice emerges quite naturally for most: while “listening to a work, we recognize the evocations of actions, tensions, and dynamisms analogous to those for which the literary work is a vehicle” (Nattiez 1990, 248). Another argument for the presence of plotlines in instrumental music is the extensive set of grand narrative archetypes well known to generations of Classical music connoisseurs. Some of these are highly poetic, for example, the “darkness to light” plotline that is associated with symphonies that are billed in a minor mode but end in major. Others are more technical. Anthony Newcomb (1987) illustrates how the traditional formal models of music, such as sonata form, constitute plot paradigms in and of themselves. This view is well supported by the dozens of analytic essays that, upon noticing a deviation or deformation of an expected form, respond by imposing a vividly dramatic interpretation on the whole.3 The moment we allow that narratives can be posited for even instrumental pieces, a new question emerges. What kinds of stories can such music tell? Here we must take care to assemble narratives responsibly, to avoid basing them on details that are so personal that they resist generalization. One way to avoid this error is to dig into the cultural history of motives as they appear in the context of a composer’s career or a style period. One motive with a particularly famous history is the “sigh” motive, a two-​note 2nd shape, written to be performed with a “down-​up” feel through slurring or bowing. This shape proliferated throughout the Baroque era, coming eventually to be associated with grief due to its outsized role in pieces of lament such as Purcell’s “When I Am Laid in Earth” from Dido and Aeneas. Such historical examination is the purview of so-​called gesture studies. Robert Hatten and Janet Schmalfeldt, writing separately, convincingly argue that clues to the meaning of a particular gesture—​at least as the composer may have conceived it—​can be productively deduced from careful readings of his or her other works (Hatten 1994) or from the physicality of performing it (Schmalfeldt 2005). For example, if a composer of a song assigns the word, “misery” to a specific falling figure, then that shape can call to mind the idea of misery when it appears in one of their other untexted works. Another way to avoid the pitfall of making a story too specific is to cast it in freer terms. This entails a retreat from what Roman Jakobsen calls extroversive practice, which investigates sonic events’ “referential link with the outside world,” in favor of an introversive practice that investigates “the reference of each sonic event to other elements” (1970, 12–​13). It is of course impossible to actually achieve full introversion. Even when analysts intend to speak objectively about a “rising line,” a “fanfare gesture,” or a “contrasting tonality,” their understanding of these constructs is ineluctably bound to awareness of “outside” notions.4 (In this

168  METHODS OF MOTIVIC ANALYSIS case, these concepts, in order, conjure up associations of striving and success, of court brass ensembles, and of literal territory to be shared or fought over.5) While acknowledging that fact, we will continue to steer our narrative analysis craft toward the introversive horizon. There will be storytelling, but the stories will primarily concern the quasi-​adventures of musical shapes, unities, tensions, and emotions. To aid us in this endeavor, we will touch on some basic narrative principles. An extended tradition of literary scholarship has established that the particular details of a story are often less important than the general framework lying beneath it.6 Thus it is that a single framework can dictate the pathways of so many heroes. One might not immediately associate the character of Theseus from Greek myth with Luke Skywalker from the Star Wars film saga or Beatrix Kiddo (“The Bride”) from Tarantino’s Kill Bill films. As protagonists in epic dramas, they all experience roughly the same sequence of events. Each initially learns of a prophecy or undertakes a quest. From that point, each obtains a birthright such as a sword, ventures out to confront a host of enemies, faces a near-​death and/​or burial event, escapes, and ultimately triumphs.7 In acknowledgment of their debt to literary theory, the generalized musical plotlines to be advanced here are deemed “archetypes.” The archetypes formally proposed in this book’s two Narrative Interludes—​and employed throughout—​ are of my own design. Yet, if one were to read them alongside any modern treatise on musical narrative, one would observe a number of common traits. The first concerns the selection of subject matter; i.e., what motives are significant? Following Hatten, I take it that certain musical events, if known to be rare in a musical style, are intrinsically “marked” for meaning (1994, 29–​66).8 For example, fewer pieces in the Common Practice were written in minor. It thus follows that those that are cast in that mode possess an extra emotional dimension. (Specifically, they are more likely to be thought of as intensely “sad” or morose, whereas the mood of a piece written in “unmarked” major mode may not attract notice at all.) The same principle loosely extends to motive. A  jagged, chromatic motivic shape in a piece will naturally attract more attention than smoother and more normative diatonic shapes. In a similar vein, Fred Maus’s essay “Music as Drama” holds that events in music are conceived as actions and states of being, e.g., running, fleeing, conversing, or making an outburst (1988). We instinctively listen in this manner to make the music itself seem rational. More than simply hearing the music, we actively personify it, mapping a set of human behaviors and conditions onto what in actuality are soundwaves distinguished by frequency, volume, duration, and timbre. Consistent with the notion of deep metaphorical frameworks, Maus is keen to remind us that the identities of the agents committing all of these actions are unknowable. One may wonder what realm the imagined protagonist at any moment

BMA Narrative Archetypes  169 resides in. Is it a character or persona in the music, such as a cello theme seeking resolution, or is it a single note like a high G♯ struggling to break through to A and beyond? Is the protagonist the composer trying to solve a musical problem, or the listener trying to navigate a maze of themes and/​or tonalities? What is important to remember for each such pair of “or” questions is that answering yes to one does not require us to say no to the other. The fact that listeners regularly flit back and forth among these brief intuitions of agency is strong evidence, to Maus, of the archetypal basis of music. The piece, in his words, is “a drama that lacks determinate characters” (1988, 72).9 Past the issue of casting a story lies that of imagining its path. Following Almén 2003, all narratives presented in this study will proceed under the expectation that a piece of music will open by invoking one emotional/​dramatic condition and progress to at least one other. That progression in terms of tension, expectation, and satisfaction will relate to the motivic content; by this I mean the appearances and interplay of the motives. Our first task, then, will be to delineate the main narrative archetypes of basic motivic analysis. Following a theoretic account, the narratives prescribed will be illustrated by a small set of analytic and interpretive demonstrations.

The Four BMA Narrative Archetypes The Narrative Rule presented at the close of ­chapter 5 specifies that all analyses constructed within BMA will proceed linearly, modeling the music listening experience. The formal process label “Propagation” was assigned to this chronologic process, as was a representational flow-​chart schematic to track the development of a single motivic entity. The coupling of these two features results in the simplest narrative archetype possible. This archetype, called BMA-​1, is illustrated in Example 5.5.1. The one-​dimensional layout of BMA-​1 applies to analyses that concentrate on the activity and progress of a single motive. As currently formatted it suggests no

Example 5.5.1  BMA-​1, Propagation, the simplest narrative archetype for motives (rebrands Example 5.22). Material propagates

Focal Point

Event 1

2

3

4

5

6

7

8

170  METHODS OF MOTIVIC ANALYSIS means for modeling a piece that exposes two or more motives in its Focal Point segment. To address this shortcoming, the method will be extended to include multicharacter narratives such as “conflict” and “complementation.” The archetype of struggle or conflict has a long tradition in narrative accounts of music. For many Western listeners, it comes to mind unbidden when hearing music with repeating elements, which is to say: in most pieces from the Common Practice period. Upon hearing static repetition, one is likely to think, “The music keeps stating the same idea. If it has any intent to move onward, there must be an obstacle frustrating its progress.” Conflict-​based archetypes play a prominent role in BMA, as it is almost always possible to make a case for multiple agency in musical works. One does so by peering into a composite motive and reading it in terms of multiple, contrasting aspects. This approach may sound esoteric; however, it is so well entrenched that it may be considered the default mode of motivic analysis. One way to manufacture conflict out of a single entity is to cast the motive’s subelements—​note: they must all be proper shapes, not features!—​in oppositional terms. This strategy is exemplified in Almén’s 2003 narrative analysis of Chopin’s Prelude in C Minor, Op. 28. He reads the main melody in m.1 (G4-​A♭-​ G-​F-​E♭) in terms of two “interlocking” motives. Motive a is a half-​step neighbor established on the basis of the first three notes of m. 1’s melody. Motive b, a descending third, is based on the last three notes. (The two motives are illustrated in Example Web.5.5.1 .) According to Almén, the prelude undertakes a dialectic journey from order, into conflict, and to final resolution. He shows this narrative unfolding specifically through the dynamic interaction of his core motives.10 Where motive a is initially “prominent” over b in mm. 1–​4, its role diminishes over time. Almén reads this systematic “reining in” of motive a in terms of a “defeat,” a “tragic fate” solemnly marked by the prelude’s final, amelodic chordal statement in m. 13 (Almén 2003, 27). A motive’s singular image may also be diffracted into several shapes by establishing a set of individual, yet closely related forms for it. This is the approach favored throughout Zbikowski 2002. In analyzing the first movement of Beethoven’s String Quartet in B♭, Op. 18, No. 6, he identifies three closely related variants of the prime motive. These are shown in Example 5.5.2. The identity of each motive form, alpha, beta, and gamma, depends on the presence of attributes listed in its bubble network. Zbikowski’s strategy of allowing a single motive to manifest in three ways is a direct response to Joseph Kerman, who criticized this quartet movement specifically for its lack of motivic development (1966, 71–​74). As he mostly agrees with Kerman, Zbikowski repeatedly reminds readers that the three forms of motive, at the deepest level, express a unity. At the same time, he cannot seem to resist injecting narrative elements into his discussion. Near the beginning, Zbikowski

BMA Narrative Archetypes  171 Example 5.5.2  Figure 4.6 from Zbikowski 2002 showing “models for three forms of the principal motive” from Beethoven’s Quartet in B♭, Op. 18, No. 6 (I). (a)

(b)

(c)

refers to the alpha and beta forms of motive as the “musical Tweedledum and Tweedledee to the listener’s Alice” (2006, 169). He proceeds under the unexamined assumption that the three forms exhibit an observable “progress through the movement,” and that the presence of one versus another at key points is a source of its overall lighthearted, comic, sensibility (2006, 171). In Zbikowski’s account, this dramatic effect stems more from syntactic machination—​for example, having the “closing” form of the motive (beta) appear at a section’s opening—​than actual conflict among the forms. Nevertheless, said, his original decision to view a central motive in this way provides a precedent for doing so in other contexts. Having acknowledged the possibility of multiple agents in motivic analysis, we now adapt BMA’s theory to admit them. The narrative archetypes involving propagation of two or more motivic elements shall fall under the designation, BMA-​2, to distinguish them from BMA-​1 (single motive under Propagation). The three potential outcomes of BMA-​2 are listed in Example 5.5.3. In pieces exhibiting Complementation, the two main motive players are introduced and explored in separate formal areas, with direct juxtapositions kept to a minimum. As the topmost arrow in Example 5.5.3 indicates, there can be only one end result of a complementation interaction. Because the motives are prevented from interacting, they will fail to engage each other. Each motive will have its say in some portions of the piece; however, neither will establish dominance. This narrative archetype, “Non-​Engagement,” is assigned the label

172  METHODS OF MOTIVIC ANALYSIS Example 5.5.3  The three propagative narrative archetypes that manifest under the condition of divided or multiple motive entities. Nature of interaction Complementation

Conflict

produces

Narrative Archetype Non-Engagement

BMA–2˚

Synthesis

BMA–2•

Triumph

BMA–2+

BMA-​2o. The “2” aspect of the nomenclature signals membership in the second category of BMA motive. Mnemonically, the “2” can also be thought of as disunity, or that “more than one” motive form is involved. The superscript open circle, o, calls to mind the notion of a process left incomplete. When motives conflict, they are typically put into close contact, jostling and interrupting each other. One possible narrative outcome resulting from this conflict is, again, Non-​Engagement; note that Example 5.5.3 depicts two arrow pathways toward this archetype. Non-​Engagement may be thought of as the null outcome of a conflict, which results when the motivic struggle ceases without resolution. For an example, one may imagine a sonata form work in which a highly conflicted development is succeeded by a wholly conventional recapitulation that reasserts the independence of its contrasting themes with their attendant motives. The second type of narrative stemming from conflict is “Synthesis.” When Synthesis occurs, both of the main motive forms are maintained for the entirety of the piece or major section. At some point, likely near the end, they are assembled into a cooperative conglomerate. The label given to this archetype is BMA-​ 2•, with the filled-in circle suggesting a sense of completion or goal fulfillment. The last likely outcome of Conflict is one motive vanquishing or appearing to vanquish the other(s). Such is suggested when, over the course of the piece, the motive presumed to be subsidiary either vanishes suddenly or begins taking on aspects of the dominant motive. This narrative archetype is designated as “Triumph” and given the label BMA-​2+. (The plus sign loosely represents the increasing prominence of the “winning” motive.) The names assigned to the three BMA-​ 2 archetypes carry dramatic implications, calling to mind dynamic interactions among characters in a story.11 At the same time, I indicated early on that the narratives advanced in this book will be couched in primarily musical terms. Some may chafe at that restriction, preferring to translate the motivic activity they observe into fantastically dramatic accounts. The path in that direction—​a realm of motives personified, with their specific desires concretely articulated—​offers spiritual rewards but is

BMA Narrative Archetypes  173 methodologically treacherous. In the event we should be so bold to venture that way, it will be critical to equip ourselves with the sturdiest framework possible to support our musical storytelling. The framework I recommend originated with Northrop Frye, a literary theorist who wrote extensively on the origins and patterns of storytelling across cultures. In an essay from 1957 on myth creation, he posits that all dramatic narratives are reducible to four types: Romance, Comedy, Tragedy, and Irony (satire). His titles are Classically inspired, meaning that the romances do not necessarily pertain to love, nor the comedies to humor. Instead, each archetype is defined in terms of (1) its general trajectory of success versus failure and (2) its setting, meaning whether its events occur in the realm of idealized fantasy versus that of real experience. Frye’s four types were later adopted and refined by J. J. Liszka, who conceives the four narrative archetypes as a series of logical oppositions, as follows: I. Emphasis on Victory A. Comedy—​victory of transgression over order B. Romance—​victory of order over transgression II. Emphasis on Defeat A. Irony/​Satire—​defeat of order by transgression B. Tragedy—​defeat of transgression by order

(Liszka 1989, 133)

The four genres of comedy, romance, irony/​satire, and tragedy, are applied to individual literary works by determining who the protagonists are and then whether their victory upholds or overthrows/​subverts the social order. One must also determine whether the audience’s sympathies align with the victor or the vanquished. There is not time at present to offer a full demonstration of this procedure; however, those interested may consult Example Web.5.5.2 for an illustration of how Disney’s Sleeping Beauty is a romance, how the Wachovski’s Matrix film trilogy is a comedy, how the musical theater work West Side Story is a tragedy, and how Heller’s novel Catch-​22 embodies satire. The extra wrinkle in our branch of analysis is that one must take the extra steps of casting the musical motives as protagonists, establishing the rules of the piece—​its style, genre, language, and so forth—​as the social order, and identifying audience sympathy. This is no small task; thus, it will not be worth pursuing in all cases. (The Frye/​Liszka archetypes will, for example, shed little or no light on BMA-​2o type interactions.) In cases where high drama is sensed, however—​perhaps even once or twice in late chapters of this book—​it may be worthwhile to call on the four archetypes in the interest of creating a compelling, piece-​specific “story.”

174  METHODS OF MOTIVIC ANALYSIS

Demonstration and Discussion The final portion of this Interlude is given over to illustrating examples of BMA’s three multimotive archetypes. We begin with BMA-​2o. An analysis following the Non-​Engagement template will assiduously avoid projecting any sense of struggle; however, this does not mean it must be bland. Chopin’s Prelude in F♯, Op. 28, No. 13 is a quasi-ternary form work in which the A section, (mm. 1–​20) is marked by static double-​neighbor motives (“DN”) in the melody and accompaniment.12 The B section (mm. 21–​28) concentrates mostly on fourth-​based motives. These materials are shown in Example 5.5.4(a) and (b). The DN and 4th pitch shapes are constrained to their respective A and B areas, with two exceptions. The first such exception is in mm. 6–​7 (see Example 5.5.4(c)). Here the melody adopts a more soaring character as it leaps up to F♯5, then descends gently through a 4th to C♯. This moment foreshadows the 4th that will serve as the basis of the B theme. The 4th shape is presented once in this area and then evaporates. By declining to put it in dialogue with the DN motive, the music—​or whatever agency one prefers: the melody, the composer, the imagined protagonist—​expressly avoids any sense of conflict. A more pronounced blending of the two motive forms is found in mm. 34–​38. This moment of interest caps off the final section, which begins at m. 28 with a return of the left hand figuration from A. The DN shape is repeatedly expressed in the tenor’s eighth notes as before. It also appears in a new, drawn out form in the soprano that concludes the melody in mm. 34–​36; this is beamed in Example 5.5.4(d). Aside from the brief C♯5-​F♯ given in m. 30 (not shown), the 4th motive has all but disappeared. It returns in the final two measures, however, where the left hand material shifts to recall the texture from B. The large, gentle 4th in the tenor does not interrupt or threaten the hegemony of the DN shape, since the prelude essentially concluded at the downbeat of m. 36. Although the last two measures of the piece are structurally unnecessary, they do enrich its narrative. By having the music faintly recall an earlier theme, it causes audience members to partake in an act of reminiscence. That act will mean something different to all; however, one can predict their responses will register on the intellectual and emotional engagement spectrum somewhere in the vicinity of satisfied recognition and balance. Sectional forms, forms like rondo and ternary that are by nature additive and less organic, are the most likely to support Non-​Engagement narratives. To observe the behavior of multiple motives interacting (conflicting) in closer quarters, it makes sense to canvass movements written in sonata form. The clear articulation of both the exposition and recapitulation into First and Second Tonal Areas (FTA and STA) often entails the separate presentation of contrasting themes.13 These separate themes with their attendant contrasting motives are rarely kept

Example 5.5.4  Two-​motive interaction in Chopin’s Prelude in F♯, Op. 28, No. 13.

(a) Opening of A section, mm. 1–​4, marked by DN motives in pitch and pitch-​class.

(b) Opening of B section, mm. 21–​22, marked by 4th motives in soprano and tenor voices.

(c) Prominent 4th introduced in mm. 6–​7.

(d) Presence of both motives at the Prelude’s conclusion, mm. 34–​38.

176  METHODS OF MOTIVIC ANALYSIS apart for the whole work’s duration, however. The central development section typically explores a host of unpredictable transitions and sequences. (Some codas, when present, do this as well.) As the development juxtaposes snippets of old and new themes at a rapid rate, it creates a hotbed of motivic activity. In narrative terms, the rapid alternation of motivic ideas conveys, to many, a sense of Conflict. The precise nature and degree of this struggle are, of course, wholly unspecified. In a more tranquil sonata form piece, the alternation of ideas might call to mind an intellectual discussion between rational people, whereas in a grandstanding, full-​throated tone poem it might sound more like a battle being waged across a vast landscape. The next demonstration will center on the Synthetic narrative (BMA-​2•), which results when motive forms initially in conflict are later subsumed into a larger whole. The newly composite motive may be horizontally oriented, with the motives hitched together. Or the synthesis could be vertically oriented, achieved by stating the motives simultaneously in counterpoint. These two arrangements are modeled in Example 5.5.5. The locus classicus for the vertical synthesis of themes or motives is double fugue, although, for our purposes, there are many other genres that provide examples of this kind of contrapuntal combination. The so-​called cyclic symphony from the Romantic era is one. Example Web.5.5.3 illustrates a moment near the conclusion of Dvořák Ninth Symphony in which several melodic motives from previous movements are combined. The sudden escalation of contrapuntal complexity in this and like moments imparts heightened interest and emotional tension to the music. Such synthetic events are often found at rhetorically significant moments, such as at the crux of a sonata’s development section or near the end of a major work. Example 5.5.5  Two motives, 4th (diagonal line) and Neighbor (gable), that appear in conflict initially are later synthesized in horizontal and vertical arrangements.

BMA Narrative Archetypes  177 The third outcome of Conflict noted in Example 5.5.3 is that in which one motive overpowers the other(s). A Triumph narrative (BMA-​2+) typically unfolds as follows. A piece will first present a local span of conflict, ranging from at least thirty seconds to two minutes in length. The span will culminate in a forceful presentation of one of the motives, conveying to it an air of conquest. To constitute an authentic victory, the outcome of the conflict should have a measurable impact on the remainder of the piece. For instance, a secondary theme or motive, once “vanquished” in a sonata’s development section, shall be absent or play at most a measurably reduced role in the recapitulation. For a demonstration of the Triumph narrative from the literature, we turn to Beethoven’s Piano Sonata 3 in C, Op. 2, No. 3, I. The primary motivic players involved are DN and 3rd shapes, which trace their roots to the primary theme from mm. 1–​12. In Example 5.5.6, the DN motive is seen to occur when the melody is blocked in its initial attempt to descend from E4 to tonic (see beamed notes). Rather than being allowed to continue to C4 at the downbeat of m.3, the melody restarts on F4. This leap upward causes it to circle back, unfulfilled, to its starting pitch, E. The 3rd idea emerges more gradually. The first standalone 3rd motive appears in the bassline in mm. 7–​8. A G4-​E gesture immediately follows in the melody. It is stated first as a leaping third and then in filled-​in, linear versions. These new 3rds do little to tip the balance of power between the two motives. The DN motive dominates the structure of the primary theme in its h √∫∫µ Ωç | q q aspect, while the 3rd remains subsidiary. Even by mm. 9–​12, these thirds participate only in the countermelody, which is still unable to reach tonic, remaining locked in the 5̂-​3̂​ (sol-​mi) region of the C scale. Example 5.5.6  Measures 1–​8 of Beethoven’s Piano Sonata in C, Op. 2, No. 3 (I) introduce two motive forms, DN and 3rd.

178  METHODS OF MOTIVIC ANALYSIS Example 5.5.7  Large third-​based motives coordinate the voice-​leading and harmony in Stage 1 of the development section, mm. 97–​109. (Dashed slurs indicate enharmonic relationships; some high Fs are omitted.)

The relationship between these two motives, DN and 3rd, is explored at length in the work’s three-stage development. Stage 1, mm. 91–​108, prepares the conflict. The first theme to appear is the one just heard at the close of the exposition in mm. 77–​84. This choice of theme initially privileges the 3rd motive. This can be heard in the two-​beat melodic gestures that initiate measures 91 and 93 (D4-​B3 and then G4-​E, not shown). An even more impressive set of 3rds are composed out in mm. 97–​109, as indicated by the equal duration reduction shown in Example  5.5.7. The bassline of this section takes the form of a chromatically filled 3rd from B♭1 to D2. The full voice leading is provided so that some of the smaller 3rds can be seen in the alto and soprano voices (see beams). Although it is significant that Stage 1 of the development prioritizes the 3rd motive, this alone does not constitute its narrative victory over DN within the narrative. For Triumph to be invoked, there must be evidence of a struggle among the players. The first direct conflict between the motives occurs at the outset of Stage 2 of the development (this subarea in full spans mm. 109–​129). At m. 109, the brief return of the primary theme in D major interrupts the long string of 3rd motives with a clear presentation of DN (see Example 5.5.8). The initial theme is stated calmly and assuredly, but this music provides only a brief respite from the storm of the development. Its key, D major, is somewhat unusual in the context of a C major piece. Due to this segment’s impermanence and its sharp-​side tonicization, it seems almost appropriate to call it an “orange patch,” as a trope on Tovey’s “purple patch.” Although the music sounds peaceful, its equilibrium is highly unstable. It is almost as if a fuse has been lit at the downbeat of m. 109, with the wire hissing away in the four measures that follow.

BMA Narrative Archetypes  179 Example 5.5.8  In Stage 2 of the development, mm. 109–​129, third motives ascend to prominence.

The pyrotechnic event in m. 113 takes the form of an explosive dissolution of primary theme material. The melody attempts to assemble a DN motive—​see the incomplete dashed line in Example 5.5.8—​but the introduction of a new melodic sequence idea blocks the entry of the D5 expected at the downbeat of m. 114. For the first time in the piece, the 3rd motive seizes control at virtually all levels of activity. The music of mm. 115–​116 contrasts the drawn-out arpeggiation of D7 harmony in mm. 113–​114 with linear 3rds given out in syncopation. A beam in the example shows the melody’s progression through pitch-​classes D-​C-​B♭-A-G in mm. 115–​117; measures 117–​120 restates 113–​116 at the lower fifth. All of this 3rd activity culminates in mm. 123–​127, where the melody descends from C6 to D5. This last grand gesture, shown beamed in the example’s lowest system, can be heard as a cascade of elided thirds moving to 2̂ (re) , which awaits structural dominant support to close the development (HC). The present account of events advances a Triumph narrative for the development section. In order to claim that this narrative manifests at any higher level, we must determine whether the conflict spills over to impact the rest of the piece.

180  METHODS OF MOTIVIC ANALYSIS Example 5.5.9  Recapitulation area, mm. 139–​150. The recomposed transition of mm. 147–​155 significantly raises the profile of 3rd motives compared to the matching passage in mm. 9–​12.

Example 5.5.10  The cadenza from the coda, m. 233.

The critical locations to consider in the recapitulation and beyond are those that present new material. In this sonata, such passages occur in the recapitulation’s “rewrite” of the primary theme in mm. 139–​155 and in the extended coda in mm. 218ff. Neither of these areas provide enough evidence that the 3rd idea permanently vanquishes DN in the development section. The first seeming challenge to the Triumph claim is the recapitulation, which restores the DN idea in mm. 139–​142. The return of the opening theme here is more a bow to formal convention than anything else, and thus should not be given too much weight. The music that immediately follows, in contrast, is unexpected. Instead of recapitulating the music of mm. 5–​12, mm. 147–​155 substitute a bold recomposition. Example 5.5.9 illustrates how the new passagework there produces a novel flurry of chromaticized 3rd motives. Further indication of the DN motive’s tenacity is provided by the coda. As shown in Example 5.5.10, the last dramatic peak of the work is constituted out of chained DN motives. Granted latitude to wax poetic, we might say that this cadenza represents an apotheosis of this motivic idea. Taking this broader view of the movement puts a finer shade on the idea of how the Triumph archetype applies to this piece and, by extension, how motivic

BMA Narrative Archetypes  181 narratives work in general. There are many occasions in which a single work will support a single narrative. Just as often, multiple contradictory readings within a work will be possible. In the case of this sonata movement, we started by positing a single narrative for a limited span of music, specifically Triumph in the development. We sought to confirm this view by seeing whether the motivic trends initiated in the piece’s middle section carry over to its final one. On the basis of findings concerning the two passages from late in the piece, one could argue that the Triumph narrative, in the end, remains unfulfilled. That interpretation is reasonable, but unsatisfying because it leaves us with a null result. (This outcome is not all that dire, since the main aim of the analysis—​ illustrating the main characteristics of the Triumph archetype—​was successful within the limited frame of the development.) Rather than accepting this bleak view, I would seek to put the analysis of the coda in productive dialogue with that of the development. The key to doing so is observing the general trend in which the DN shape consistently progresses toward 3rd shapes. This conception invokes A. B. Marx’s view of Beethoven noted in chapter 3, in which each motive is associated with a general energetic character and function. The DN shape is always an expository idea, radiating calm, stasis, and symmetry. In contrast, the 3rd is a forward-​tilting shape that engenders development.14 This push-​and-​pull dynamic between motives is established in the first primary theme and applies, writ large, to the development. The two returns of the DN idea in the recapitulation are indisputable; however, neither is sufficiently strong enough to close out the movement. When the primary theme sounds for the last time in mm. 234–​237, it functions rhetorically as a springboard for the final push to the end. The moment itself is almost preternaturally calm. In contrast, the excited music of mm. 238–​258, in motivic terms, consists entirely of linear motion, with no hint of DN shapes. It is only in light of that last development that we may posit a final narrative outcome, one in which the 3rd motive emerges Triumphant as the piece’s agent of purpose and energy.

6

Exemplars of Basic Motivic Analysis The present chapter extends the work of ­chapter 5 and its attendant Interlude. That chapter established the purview of basic motivic analysis (BMA) as pitch and/​or rhythm motive activity. The first Interlude established guidelines for assembling a BMA as linear in time, with the essential core motive(s) situated at or near a work’s start. This short chapter will demonstrate the BMA method from start to finish by applying it to two complete sonata movements by Beethoven. The first section will present a pitch/​pitch-​class motivic analysis and the second a rhythm motive analysis.

A Pitch and Pitch-​Class BMA of Beethoven’s Op. 2, No. 1, Movement I The first movement of Beethoven’s Sonata No. 1 in F minor, Op. 2, No. 1, is a canonical work that has been analyzed countless times. It is a standard vehicle for introducing basic topics in undergraduate theory, among them motive, phrase structure, and sonata form.1 As such, it is an ideal subject for our first full demonstration of BMA. At first blush, this early work by Beethoven published in 1795 registers as Classical. It is characterized by thin textures and sleekly efficient lines. Though it avoids flashy figuration and flights of pianistic fancy, it is brimming with pathos. The performer must concentrate to keep the work’s fervent emotions in check behind its cool countenance, so that it merely bristles with nervous energy. The work begins in F minor, never venturing far beyond this gray realm. When, for example, it arrives in III (A♭ major) for the Second Tonal Area (STA), that key remains strongly tinged by F and C flats borrowed from the minor mode. The development section of mm. 49–​100, too, mostly explores minor keys, with a heavy emphasis on C minor (v). Contributing in equal measure to the movement’s gorgeous severity is its unusually tight motivic design. Much in the same way it dwells on minor modes, the piece radiates an aura of motivic single-​mindedness. Tradition holds that the opening melodic gesture in mm. 1–​2 is built of two motives (Tovey 1931, 12). These are provisionally labeled in Example 6.1(a) as “Arpeggiate” and “Turn.” The two motives are explored separately and together Musical Motives. Brent Auerbach, Oxford University Press. © Oxford University Press 2021. DOI: 10.1093/oso/9780197526026.003.0007.

184  Methods of Motivic Analysis Example 6.1  The theme of Beethoven’s First Piano Sonata in F minor, Op. 2, No. 1 (I) (a) Traditional view of gesture motives in mm. 1–​2. These return in loose mirror inversion in the second tonal area (STA) theme in m. 21.

(b) The first theme, with a potentially important new motive, the 6th, bracketed.

throughout the piece, most notably in the second theme, where they return in the same close succession but in loosely mirrored inversion (see lower staff, mm. 21–​23).2 Example 6.1(b) illustrates a third, potentially-important motive derived from the opening theme, the descending 6th figure in mm. 7–​8. This shape, which precipitates the climax of the first phrase, reappears throughout the work in many guises. The 6th lends unity to the music as it saturates all registers and ties together most of the thematic ideas and even key areas. As stated earlier, this movement’s status as a “standard” underlies its selection as a practice vehicle for our new nomenclature and BMA method. Couched as a rehearsal, the analysis will offer a new interpretation—​or better: a “performance”—​of the work that can be measured against all other readings. I will note at the outset one way in which this analysis will not distinguish itself from earlier views and several other ways in which it will. Like many previous analyses, this

Exemplars of Basic Motivic Analysis  185 one will limit itself to concerns of pitch and pitch-​class. Rhythm, texture, register, and articulation remain critical musical elements in all works. Here there simply isn’t time to cover these aspects in any detail beyond occasionally noting how some distinctive rhythms or articulations associate with the main pitch motives. Other analysts will surely reap the rewards of examining all of the syncopations and irregular hypermeter on display in the movement, and may well find ways to account for them motivically. Even as it remains restricted to matters of pitch and pitch-​class, this analysis will nevertheless break new ground. First, the scope of the analysis will be ambitious: not only will we investigate all the major themes of the movement, but we will peer into the figuration to illustrate how the accompanying voices participate in the motivic process. Second, the motives at all times will be attended to with particular care. This precision will allow us to identify novel motivic occurrences, and in turn to ponder a new nonstandard path of development. Motivic analysis begins with determining the prototypical forms of the motives and assigning labels to them. The way forward is already suggested by Example 6.1(a) and the inherited claim that the work’s first utterance is built of two motives. Let us proceed, then, by interrogating these first gestures. Starting with the first, we ask how many notes the arpeggiation is built of. Is it six spanning from the pickup C4 all the way to A♭5, or is it shorter? We can safely eliminate the first note as a necessary element of the shape: Beethoven performs this surgery himself when the theme is recapitulated at m. 101.3 So, off it comes. If readers are concerned that we might need the C4 later, we can always posit it as a “4th” fragment to explain the presence of other leaping or linear 4ths. We now consider the rest of the arpeggiation. Whenever it appears, it is a driving gesture that pushes toward a downbeat. For that reason, we will include the last A♭5 and designate the shape as Arp5. For the next motivic component, our options are to retain the Turn label from before or to use a more technical designation, such as 3rd\ /​. The latter has the advantage of allowing us to view connections between this filled-​in gesture in m.  2 and other 3rds, linear and leaping, that appear later. The solution I favor, as illustrated in Example 6.2, is to apply the summary label Turn = 3rd\ /​so as to incorporate both perspectives.4 The last motive from the opening phrase that requires definition is the scalar descent initiated by the high C6 at m.7. Most analysts regard this figure as a 6th because of the many prominent 6ths that return throughout the movement. Variations of it are common, however. The melody in mm. 7–​8 traces a clear 6th, but the bass voice in mm. 2–​8 does not. This raises more questions. Is the bass’s motive a sixth preceded by an ancillary tonic pitch (\6th), or is it

186  Methods of Motivic Analysis Example 6.2  Determination of the specific motive forms present in the theme, mm.  1–​2.

a neighbor-​note figure on F followed by an ascending fifth, (\ /​ 5th). The two readings, both eminently possible, are indicated above and below the staff in Example 6.3(a). Examining the rest of the piece does little to resolve this issue. On the one hand, the most salient motives of the development retrace the same 6th between C and E natural. For example, the soprano’s 6th in mm. 69–​81 is immediately answered by two similar 6ths in the tenor in mm. 81–​85 and 85–​89. A different result obtains when we examine the motivic content of the tense retransition in mm. 93–​101. The bass voice, shown in Example 6.3(b), moves through an unambiguous 5th. We should label it accordingly or somehow devise a way to call it a 6th with its last note deleted. In the coda, mm. 146ff., multiple scalar descents occur in multiple voices. As Example 6.3(c) indicates, the soprano shape’s identity there is complicated by the final, tacked-​on F5. Again, it may be read both as a 6th/​or a 5th\ /​. In contrast to the more trivial issue of establishing a uniform length for Arp (four versus five notes), establishing the model form of the sonata’s main linear motive has important ramifications. Here I declare that they are all linear fifths. The reason that some take the form they do is because they add one or two stepwise pitches at their head or tail ends. Making this determination promotes more efficient analysis. More significantly, it stakes a claim about the linear motive’s identity and function. That claim is as follows: the 5th is an expression of singular harmony, usually tonic in whichever key environment it appears. The subtle ways in which the fifth manifests result from adjustments that allow it to fit into various tonic and dominant harmonic environments. The label “5th\” for the melody in mm. 7–​8 indicates that the body of the motive expresses F minor and that the last E natural extends it, creating a suspenseful half cadence. The same explanation applies to the transition section in mm. 11–​20, where the melody repeatedly descends from E♭5 to G4. This is shown in Example 6.3(d).

Exemplars of Basic Motivic Analysis  187 The newly emerging tonic of A♭ major, murky at first, is signaled by the weak, contrapuntal cadence at m. 15. In the two cadential echoes that follow in mm. 16–​20, the harmonic support for the surface linear sixth is clarified, as well. In these faster E♭5-​G4 descents, most of the motive’s main pitches are supported by A♭ tonic chords. The arrival on the suffix note, G4, only occurs when the new key’s dominant chord (V) is reached. This novel interpretation of the linear motive as a 5th makes it possible for us to identify it where other analyses have overlooked it. One such location is at the climax of the development, mm. 81–​93, shown in Example 6.3(e). The ascending line from E♮3-​C4 in the left hand, shown circled, is identified in many other analyses. The material of interest begins in the melody at the pickup to m. 82. The C5 initiates a descent through pitch-​class space involving the notes C-​A♭-​F-​E♮. This is a triadic motion (Arp3) that fills out the fifth motion of C to F (see stemmed notes). Moments later, starting at the pickup to m. 84, the music distills this gesture down to its essence of a fifth-​plus-​stepwise exit: C-​F-​F-​E♮ . . . or again: 5th\.5 So far, we have identified three primary pitch motives deriving from mm. 1–​ 8: Arp5, 3rd \ /, and the linear 5th. With these motives at the ready, the BMA demonstration will take the form of an annotated score with commentary. The markings in the score given in Example 6.4 indicate most of the prominent recurrences of the main motives identified. Consistent with the guidelines set in ­chapter 5, many of these motives are found in inner voices. Readers should be aware that this analysis is not intended to be comprehensive; to draw beams or boxes around every clear motive would create too much visual clutter. It thus falls to the reader to infer some details from the analysis. The melody in mm. 49–​55 is completely unmarked, for example. Because this music so closely resembles mm. 1–​8, it follows that the same motives are present. Much of the bracketing and beaming speaks for itself, but some finer details merit further attention. The first narrative to be traced will be of the BMA-1 type concentrating on the progress of the linear 5th motive. The annotations in mm. 1–​8 (Example 6.4(a)) indicate a starting premise, in which 5ths appear in paired formation. The bass voice’s linear 5th ascent properly begins at m. 5. The soprano’s 5th enters at m. 7 and descends in contrary motion. This paired interaction intensifies as the piece progresses. In mm. 25–​28, for example, the /​5th occurs solely in the right hand, allowing for the G4-​E♭5 from the recent transition (mm. 11–​16) to sound again. Moments later in mm. 30–​33, the right hand reattempts the rising /​5th in a higher octave. This time, the left hand gives chase (paired) and helps propel the music to its first climax in mm. 33–​41; see Example 6.4(b). The next pair of linear 5th shapes appears in the development section (Example 6.4(c)). Once more, the right hand begins alone in mm. 69–​81, with

188  Methods of Motivic Analysis Example 6.3  Determination of the specific motive form for linear descent based on score evidence. (a) Measures 1–​8, bassline. Competing readings of the linear motive are shown above and below staff.

(b) Retransition, mm. 94–​101, lower voices.

(c) Close of the movement, mm. 146–​152.

(d) The transition, mm. 9–​19.

Exemplars of Basic Motivic Analysis  189 Example 6.3 Continued (e) Climax of development, mm. 81–​85. Pitch-​class motives in the melody.

a large-​scale descending 5th\; this is a direct echo of the original 5th\ from mm. 7–​8. Things get decidedly more interesting at m. 81. The first remarkable motivic event in this location is sounded in the tenor voice. It presents the ascending 5th idea that opened the piece in mm. 5–​8 not only at pitch, from E3, but at rhythm. In both cases, the line doubles its speed—​whole note to half note attacks—​upon reaching A♭3.6 The melody simultaneously declares its descending 5th material, with extreme emphasis. The new energy derives from the motive being reduced to its very essence and from being repeated so many times. The paired fifths in imitation occur as expected in the recapitulation, mm. 130–​134 (not shown). The new wrinkle here is that the left hand version is placed in a very low octave, allowing for a final, emphatic statement of the ascending motive form. The set of 5ths in the coda (mm. 146ff.) ends the piece by elevating the complexity of the pairing yet further; see Example 6.4(d). The bass line’s 5th, starting on the C4 at m. 145, moves down to the F3 in m. 150 before breaking off into a generic cadential motion in the last two measures. The soprano’s high 5th occurs in parallel thirds with the bass’s. It starts a measure after in m. 146 and can be heard “chasing” the bass descent. This interaction between the voices is made more audible through the new doublings, which paint the soprano and bass in wider brush strokes. The aforementioned bass descent from C4-​F3 is doubled at the upper sixth, starting with the A♭4 of m. 144 and continuing in the thumb of the left hand to C4 (see lines inside the system).7 There is yet one more descending line in the alto, an octave that starts at F5 in m. 145 and descends to the F4 at the very end. There are several ways to parse this shape. Analysts who wish to retain the sixth motive as a primary shape might argue that this final gesture elongates it into a seventh starting in m. 146 (E♭5-​F4).

190  Methods of Motivic Analysis Example 6.4  Motivic activity across the full movement. (a) Beethoven Op. 2, No. 1 (I), mm. 1–​24.

To support this view, they might make reference to other prominent surface sixths expressed in the low register, such as those that occurred in the first transition, mm. 11–​20. The idea of hearing a sixth “grow into” a seventh readily suggests a dramatic interpretation. To invest intentionality into this process, we say that the linear motive in this piece desires to descend from E♭5. It is repeatedly stymied, however, by the G4. It is only in the coda that the line breaks through that barrier, passing to F4. A central premise of this book is that the sentimental attraction of flexible motive forms does not outweigh the methodological hassle of explaining how sixths can somehow become sevenths, octaves, tenths, etc. It is preferable

Exemplars of Basic Motivic Analysis  191 Example 6.4 Continued (b) Beethoven Op. 2, No. 1 (I), mm. 25–​57.

to keep the motive forms distinct. It will still be possible to pursue dramatic interpretations; however, the narratives must be founded on facts. In adherence to this strategy, Example 6.4(d) reads the alto line in the coda as starting on F5: it is a linear 4th joined to a 5th. This view is supported by the phrase

192  Methods of Motivic Analysis Example 6.4  (c) Beethoven Op. 2, No. 1 (I), mm. 69–​101.

structure: note this voice’s pause and the sense of half-​finishedness at m. 149. Beyond that, this interpretation produces a more satisfying and elegant reading than simply calling the line an octave. The music can be shown “upping the ante,” compositionally, intensifying the contrapuntal complexity as a third 5th in the alto voice is injected and sent chasing the bass and soprano . . . both in similar-​motion descent for the first time. Remarkably, several of these final 5ths are pure, appearing with no prefixes or suffixes tacked on. Like the boiled-​down 5ths that emerged at the climax of the development, Beethoven’s

Exemplars of Basic Motivic Analysis  193 Example 6.4  Continued (d) Beethoven Op. 2, No. 1 (I), mm. 110–​119 and mm. 140-​152.

sonata movement ends with the most basic declaration of its essential motivic idea, C-​B♭-​A♭-​G-​F.

Loose Ends The markings across the large score example attest to the pervasiveness of the Arp, Turn, and 5th shapes. Indeed, at least one of these motives can be found in almost every measure of the movement. There are only two locations that are not

194  Methods of Motivic Analysis well explained by them. The first is mm. 37–​40, where the music repeats a portion of the previous passage, mm. 33–​36. Under fragmentation, the large /​5th from before is shortened to a 3rd in the left hand starting on C2 (not marked). The only related gesture sensed in this voice is generic, syncopated arpeggiation. The right hand explores a filled-​in 4th that relates only weakly to the open 4th pickup gesture that initiated the movement. This is indicated in Example 6.4(b) by the set of gray equal duration reduction (EDR) windows capturing downbeat events. The other passage not well explained by the three primary pitch motives is mm. 115–​117. This moment occurs in the recapitulation’s transition, which is typically a highly charged area of sonata form. Composers often deploy new material here rather than recycling ideas from the parallel location of the exposition, and this is what Beethoven does. These measures represent a problem for the motivic analyst. How do we reconcile this passage’s import with its seeming dearth of motivic content? One answer is to sharpen the search for relevant motivic material. With enough effort, one could probably knead and fold the melody line at this location so that it resembles two core shapes put together. The soprano in m. 115 makes a clear reference to the Turn idea; the melody that follows in mm. 116–​117 can be reduced at the half note level to an inverted arpeggiation: A♭5-​F-​C. This implicit association with m. 1 is unsatisfying, however. This melody has a completely different sensibility than the directed “Mannheim Rocket” arpeggiation that opened the movement. It is perhaps better to declare a distinct motive form here, one that recognizes the gesture as an ornamented arpeggiation of the F minor tonic. The label “/​A/​r/​p”, reflects the downward arpeggiation from A♭5 to F to C, with each structural pitch being given a short stepwise prefix. The descriptive portion of the summary label for this motive will be “prefix-​arpeggio” here in the text; in the score example, the shape will be labeled as Arp with multiple internal hashmarks. The identification of this last motive form will initiate another brief pass through the work, complete with its own, lesser BMA-​1 narrative. Although our attention to this shape was piqued by a “problem” spot in mm. 115–​117, a second look reveals this to be actually the third occurrence of it. Earlier instances of the “prefix arpeggio” motive are shown in Example 6.4 in mm. 11–​16, mm. 25–​29, and mm. 115–​117. The nonstructural tones display great variety in whether they lead upward (/​) or downward (\) to the main tones; the arpeggiating tones, in contrast, tend to descend. The only ambiguous case is the drawn-​out alto melody of mm. 11–​16. Its first two structural tones are the same, A♭4, which results in a chordal leap rather than a true downward arpeggiation (A♭4-​A♭-​E♭). The status of the “A\/r\p” in mm. 11–​16 is debatable, hence the quotation marks applied to it. We will retain it not merely because it is analytically legal to do so—​all of the six notes necessary appear in literal succession—​but because it is crucial to the narrative to be developed. The BMA-​1 plot we will assemble for the Arp motive traces its role as a secondary agent in the piece, whose job is to support the primary 5th-​based lines.

Exemplars of Basic Motivic Analysis  195 In mm. 11–​16, the loose form of “A\/r\p” in the alto, boxed, supports the soprano’s linear 5th. A  more robust form appears in mm. 25–​28:  the shape coalesces into \A/r\p as it migrates to the bass, where it is far more audible. Remarkably, it plays the exact same part as before (harmonizing a linear 5th motive), and directly echoes the sound of the first prefix-​arpeggio gesture. The last four pitch-​classes are again G-​A♭-​F-​E♭. When this motive returns in mm. 115–​119, the double presentation in the highest register indicates elevated importance. At the same time, it has not abandoned its accompaniment role. Example 6.4(d) shows it occurring in conjunction with F4-​E♮-​F-​G-​A♭.8 In addition to supporting this new, miniature BMA-​1 analysis, recognition of the motivic content here aids performance. The counterpoint is dense here, making these four measures difficult to memorize. I recommend keeping in mind, first, the inexact (mensuration?) canon at the octave involving the \ /​ 3rd gestures in m. 115; observe where the one \ /​3rd label applies to both staves. The next three measures can be remembered according to the mental script: “/A/r/p motive in m. 116, contrary motion in m. 117, and a repeat of /A/r/p in m. 118.” The arpeggiation motive’s last occurrence is in the left hand of mm. 124-​ 127. This passage in F minor, not shown, parallels the one in A♭ major from mm. 25–​28, so again the prefix-​arpeggio motive supports an ascending linear fifth. Curiously, the left-​hand figuration shifts, resulting in a steady descent on strong beats to each arpeggiated tone: /A/r/p . It is impossible to know whether Beethoven intended any sense of progression between the four forms of this recently discovered shape. Whether he did or not, one can happily be detected in the music. From free harmonization in mm. 11–​16, the motive is next clarified in mm. 25–​29, highlighted in mm. 115–​117, and rendered in a conclusive descending form near the piece’s end in mm. 124–​127.

A Rhythmic BMA of Beethoven’s Op. 10, No. 1, Movement III The finale of Beethoven’s Piano Sonata No. 5 in C minor, Op. 10, No. 1 is a short piece, lasting only about four minutes even when the indication to repeat the exposition is followed. The form of the work is straightforward as well; it is cast in sonata form with a coda spanning mm. 102–​122. Were we concerned with producing a conventional analysis of pitch and harmony, a certain set of events would likely catch our attention. One is the monophonic gesture that opens the work, shown in Example 6.5. Another is the “purple patch” spot in mm. 102–​112, where the tempo stretches out to allow an expansion of D♭, Neapolitan harmony (♭II). Though striking, both of these developments are actually quite commonplace in Beethoven’s music. With the form, pitch, and harmonic ideas emerging in so straightforward a manner, the likelihood increases that the movement’s

196  Methods of Motivic Analysis complexity might manifest in one or more other domains. Perhaps rhythm is one of them! The same disclaimer proffered in advance of the pitch-based BMA applies here. The analysis that follows does not presume to explain the full movement. It is intended to demonstrate the rhythm motivic theory and methodology introduced in c­ hapters 4 and 5, showing how to work with such shapes in vivo. That will be our starting point, at least. As more and more deep-​level motivic connections are suggested, we will hardly be able to resist the temptation to assemble them into some kind of propagative, forward-​tilting, narrative. Specifically, we will view the piece as exploring and then ultimately clarifying a pair of deceptively complex, core rhythm gestures. We begin by identifying the most prominent rhythmic motive of the piece, the six-​note shape (“6 note”) initiated at the anacrusis and lasting through the first downbeat (Example 6.5, mm. 0–​1). A fitting label for this first event is 6e = S S S S S | L. The label interprets the rhythm as five short durations, followed by a longer one. The bar line and the bold text applied to the second “S” indicate that there are two local stresses on the rhythm, one at the true downbeat and the other on

Example 6.5  Six-​note motives in the exposition’s of Beethoven’s Fifth Piano Sonata in C minor, Op. 10, No. 1 (III), mm. 1–​46.

Exemplars of Basic Motivic Analysis  197 Example 6.5 Continued

beat two of the alla breve measure. These stresses are associated with the motive, but do not necessarily define it. The most direct strategy for carrying out a full rhythmic analysis would be to identify all appearances of “6 note” in the score. In doing so, we would end up with a large number of such brackets, but many of them would serve to describe only surface and/​or generic events. A more efficient approach is to selectively

198  Methods of Motivic Analysis survey the piece for marked rhythmic moments that call out for explanation in motivic terms. The results of this more targeted approach are shown in Example 6.5, which encompasses the full exposition. An early moment that invites scrutiny is the music of mm. 14–​16. There, the syncopated sforzando attacks in the left hand announce the main motive in augmentation. A product of duration scaling, the new form of the motive occupies 6 quarter-​note pulses: 6q = S | S S S S | L.9 This larger form of the 6-​note motive has two functions. First, it punctuates the exposition by echoing the original motive heard throughout mm. 0–​11. The gesture closes the section with an emphatic, transformed version of the main rhythmic shape. Second, it prepares listeners to hear the STA theme that will enter after the fermata in m. 17. It turns out that this new, contrasting theme has much more in common, rhythmically with the primary theme than one might first guess. The core rhythm motive returns at m. 16.2, but with a shifted bar line. To reflect its new stress pattern, S S S | S S L, the motive is labeled as 6eSHIFT in the example. When analyzing rhythmic motives at the surface level, there is no rule against cutting off a shape mid-​stream, as I have done by ending it at G4. Doing so, in fact, invites productive speculation as to the function of the tones that follow. Consider, that the full two-​measure phrase segment is also composed of six essential pulses: five quarter notes drive towards, the half note at m. 18. The upper bracket there, 6q = S | S S S S | L, illustrates the 2x duration scaling of the original motive. Spotting the 6q form of the motive is admittedly a bit difficult, because the first quarter pulse has a prefix and is divided into eighth notes (see –​and /​ \ markings near the first and second S). The motive is there, though: all of the necessary attacks appear in precisely the right places. Once the 6q figure is intuited, it becomes difficult not to hear. The music makes its presence clear in a number of ways, such as 1) presenting it in close proximity to the 6q shape from the previous cadence; 2) setting it off in two-​measure phrase segments with pronounced rests; and 3) setting it so as to replicate the stress pattern of the 6e version. The unusual construction of the movement’s second theme provides a first clue on how to frame our emerging motivic analysis in narrative terms. Recall that over the course of mm. 0–​16, the central rhythmic motive was presented in two versions successively, the eighth-​pulse for fourteen measures followed by the quarter-​pulse one. Then, in mm. 16–18, the 6e and 6q forms are presented simultaneously. This prompts us to wonder about other ways this 6-​note shape might fit together with itself, and what dramatic effects will result each time it does. To rephrase this premise, the rhythmic interest in this movement can be thought of in terms of another motivic “game of pairs.” We posit that no single incidence of the 6-​note shape is remarkable in itself. The fireworks go off at places where two forms of the motive, once distinct, are imaginatively joined together. This conceptual framework influences our view of the STA and second theme. In the brief span of mm. 17–​28, the game of pairs is carried out in two ways. We have

Exemplars of Basic Motivic Analysis  199 Example 6.6  In mm. 23–​28, the rhythmic canon in the outer voices saturates quarter-​note pulse space. (Eighth-​note attacks have been reduced.)

already taken note of the first interaction with help of the nested brackets in mm. 16–18. Yet at the same time that the music introduces this first rhythmic complexity, it also seems, paradoxically, to devolve. The pacing in mm. 17–​23 is similar to that of mm. 1–​4, specifically with regard to its stop-​and-​start quality and the exaggerated separation of phrase segments. These gaps are not smoothed over until mm. 23–​28, where the next game of pairs begins. There, imitation between the hands results in a new, twofold presentation of the 6q motive. This arrangement, isolated in Example 6.6, allows the core rhythmic idea to saturate the music at the quarter-​note pulse level. This canon is somewhat more complex than the schematic lets on. Because each 6q figure continues to have a 6e shape embedded in it, there are actually six 6-​note motive forms contained in the three measures notated, not three. Having discovered that the rhythmic motive in mm. 17–​28 appears at two levels of scale, we next inquire into the possibility of a third(!) level. The twelve measures of the second theme proper are built from six 2-​measure phrase segments: 17–​18, 19–​20, 21–​22, and so forth. The first four constitute the body of the theme; the latter two extend it with echoes that serve to introduce the imitative element. Extending the theme by these means causes it to take the form of another, larger M M M M M L built of double-​whole note durations. The last L achieves its super-​downbeat status through the discharge of tonal and rhythmic energy at m. 28, which occurs as the dominant B♭ pedal resolves to E♭ and the right-​hand rhythms burst into tremolo sixteenths.10 The game of 6-​note motive pairs has to this point been dispatched through two configurations, nesting and imitation. A third type of interaction is broached at the closing area of the exposition, mm. 37–​45. At that point, the music briefly pursues a dialogue between in-​phase and out-​of-​phase statements of the six-​note motive. The new theme entering at m. 37 animates the surface with two rapid-​fire S-​S-​M gestures. At the next higher layer of pulse, this figure exhibits the duration profile, S S S S | S L. The metric stress on the fifth S and the sudden offbeat placement of L are unprecedented features that create strong syncopation. In response, the motive immediately repeats in mm. 38.2–​40, phased back into its normative metric setting. Upon reaching the close of the exposition, the game of pairs is suspended. Little of import happens in the recapitulation, where mm. 57–​101 essentially mirror mm.

200  Methods of Motivic Analysis 1–​44, nor, seemingly, in the compact development section. (We will revisit to this section near the end of discussion.) That leaves the coda. The first part of this section, mm. 102–​114, revisits the STA theme and its two-​level, nesting rhythmic motives. These appear in conjunction with the aforementioned exploration of Neapolitan harmony. It is the coda’s latter portion, mm. 115–​122, that is significant in our narrative for allowing the game of pairs to be invoked and explored one last time. Attentive listeners will note in mm. 115–​116 the return of the 6q shape assembled from two 6e shapes. The difference this time is that all of the eighth notes sound in one hand, where in mm. 22–​24 they occurred via bass and soprano imitation (see Example 6.7). The rhythmic combination in the coda is coincident with a pitch-​based, thematic combination: the primary and secondary themes are newly juxtaposed. This time, the order of themes is reversed: the STA version, 6eSHIFT comes first, followed by the First Tonal Area (FTA) version, 6e. This moment, importantly, enfolds much more than a surface-​level linkage of motives and themes. It sheds light on the meaning and origins of the work’s rhythmic motive material. I earlier noted the “start and stop” quality of mm. 1–​4, but avoided mentioning the FTA motive’s most peculiar feature, its metric ambiguity. The label given to it initially, S S S S S | L, can be said to be the authoritative one. It is possible, however, to hear it as S | S S S S L. In many performances of this work, the B♮s in measures 0, 1, and 2 sound stronger than the notated downbeats. Beethoven, almost certainly aware that the monophonic melody would be heard in this way by some listeners, plays a trick on them by waiting until m. 3 to reveal the true downbeat. Anyone who has been listening in the wrong metric orientation will feel a gentle bump at that point.11 Example 6.8 illustrates how the effect is created.12 Not everyone will hear the 6e motive from the beginning in this fashion. No matter how one hears it, though, most will agree it to be a quirky gesture calling into question the status of m. 0. Is this a proper measure of music, or an anacrusis only? The rhythmic developments in the coda indicate that Beethoven gave thought to this question as well. The novel, side-​by-​side pairing of 6e and 6eSHIFT forms Example 6.7  In the coda, the linking of FTA and STA forms of the central rhythm motive, 6e and 6eSHIFT, assembles the higher level, 6q motive.

Exemplars of Basic Motivic Analysis  201 Example 6.8  Metric ambiguity in mm. 1–​4. The horizontal, curving arrows represent “projections” of an imagined meter, which can persist only for so long (Hasty 1997).

of the motive calls direct attention to its duality. In addition, the metric ambiguity of that first theme form is finally resolved. In this context, the previously ambiguous rhythm can now only be heard as five pulses leading to a downbeat: S S S S S | L.13 This final combination of motive forms allows the piece to conclude its recurrent “game of pairs” by transcending it. Example 6.7 shows how linking the two forms of the 6e motive assembles the higher level, 6q motive. It turns out that three forms of the core motive are present in mm. 115–​122 at two metric levels. Having accounted for all appearances of the central 6-​note motive in the exposition and recapitulation, the rhythmic analysis is by and large concluded. Methodologically, it has constrained itself to discussion of only literal rhythmic motives; meaning, that no 5-​, 4-​, or 7-​note relatives of the main shape were entertained. Even while operating under this constraint, a fair bit of intellectual maneuvering—​particularly with regard to how 6-​note shapes under augmentation were seen to relate to surface shapes—​has allowed for a broad, synthetic reading. The only aspect in which the analysis remains incomplete is in its neglect of the development, mm. 46–​57. In the interests of time, I will offer only preliminary ideas on how it relates rhythmically to the other sections. To begin with a general observation, the development feels too short, even for this modestly sized sonata form movement. The development is terse from a harmonic standpoint, too. At the start (mm. 46–​50), the 2+2 measure construction alternating tonic and dominant harmony alludes to Classically balanced phrasing. From there, the music is given room only to tonicize F minor in mm. 50–​52 and to compose out a viio7 chord in the home key of C minor in mm. 54–​57.14 The rhythmic content of the development is somewhat threadbare, as well. The area opens with a clear statement of 6e. That motive is then obscured through two stages of fragmentation, the first occurring in mm. 47–​48 and the

202  Methods of Motivic Analysis second in mm. 50–​54. The eighth-​note form of the motive, saturating eighth-​ note pulse space, temporarily vaults to prominence over its relatives. That outcome seems almost churlish, as the constant repetition of the 6e gesture is more akin to babbling than anything else. This sensation intensifies in m. 52, where the right hand’s figuration abandons all pretense of stating a coherent melodic line. The cutting down of the six-​note motive down to 5-​, 4-​, and 3-​note units is not significant in itself, which is to say: we will not work to develop any kind of “acceleration” narrative. Rather, the patterns created by the fragmented forms point to more significant process illustrated in Example 6.9. The first unit of rhythmic content that could serve as a pattern model is initiated at m. 46 by the 6e shape, which is immediately followed by a five-​note and then a four-​note fragment. The entirety of this unit lasts four half-​note beats; this is indicated as S S S M by the bracket below the score. The pattern restarts in m. 48 with a full 6e shape, which this time is followed by a longer string of motive fragments. This second unit lasts six half-​note beats, and conforms to the central rhythmic model in length and stress pattern ( S | S S S S | L). This pattern of events suggests a purpose for the development, which is to explore the one form of the primary rhythmic motive that has been overlooked, namely 6h. After being broached in mm. 48–​51, the 6h form is twice confirmed in the measures that follow. The shift in melodic figuration in m. 51 introduces the third patterned statement, which continues to the

Example 6.9  The development is built of four melodic statements that progress from four to six half notes in length. This formal area explores 6h, the one form of the central rhythm not yet treated.

Exemplars of Basic Motivic Analysis  203 downbeat of m. 54. Upon reaching the climactic melodic tone of the development, F6, the deluge of rapid S-​S-​S-​L shapes in eighth notes decorates the last 6h shape. The last few paragraphs have offered new information about the rhythmic motives of the development. Though these local details are plain enough, they are not easily absorbed into the overarching plotline staked earlier for the movement. The problem is that the development’s fierce monothematicism actively avoids pairwise presentations of motives. Put another way, it feels as if the music in mm. 46–​57 is only allowed to develop by means of fragmentation. The formal area that results, which traditionally would serve as a high point of the sonata, feels like a collapse. It is curiously stunted, short, and abrupt. Motivically, it fails to combine any motive forms in a novel way. Its aim, instead, is to take a clear 6e form of the motive (mm. 46–​47) and to systematically dissolve it into four-​note fragments over its twelve-​measure span. Ultimately, it is the mingling of rhythmic processes, combined with sensations of success and failure, that creates listener interest in this local section and over the piece as a whole. The development seems to be “up to something,” motivically. (Again, in scanning the other domains of music, we observe no sign of a melodic, harmonic, textural, or lyric agenda; the possible exception is, of course, register.) By pausing the main rhythmic motive’s evolution, the development serves to tease listeners and to keep them in suspense for the climactic developments that will only appear in the final measures of the coda.

Afterword The two BMA-​1 readings given in this section complement each other to reveal the several benefits of this mode of analysis. The constraints imposed on motive labeling, as is true for many artistic pursuits, unlock a new set of freedoms. Analysts using BMA are tasked with defining motives rigorously. Yet they remain free to set the enforced parameters loosely, yielding a rich assortment of moderately sized—​i.e., phrase-​length—​events. The goal in doing so is not simply to fill the score space with brackets and beams. It is to put the discovered shapes in dialogue with each other. The result of investigation across these two pieces is discovery of an important shared trait. Both works pose a prime motive at the start and telegraph a set of expectations of how that motive will combine with itself. Paired fifth pitch/​pitch-​ class motives chase each other over the course of Beethoven’s First Piano Sonata, I; paired 6-​note rhythmic motives do the same over the course of his Fifth Piano Sonata, III. The pairs are always in flux, continually redefining their interrelations

204  Methods of Motivic Analysis across sections. Each reconfiguration seems like a small adjustment, until the end, where a final presentation of the pairing idea is amplified by a new motivic extension, a new player, or even a new dimension of activity. All this from a composer still in his twenties and just embarking on a lengthy publication career! As one may gather from the impeccable construction of these pieces in terms of their formal, thematic, and—​now more clearly—​motivic content, Beethoven’s inimitable technique was well honed even in his early development.

Interlude 2 CMA Narrative Archetypes New Freedoms on the Focal Point’s Content and Location This second Interlude on narrative serves to bridge basic motivic analysis (BMA) and complex motivic analysis (CMA). By definition, all BMA plotlines are Propagative, meaning that they locate the Focal Point, or central motivic event, at or near the beginning of a piece. All other events are conceived as flowing from it in musical time. Moreover, the Focal Point in BMA is conceived in terms of pitch and rhythm only. In Interlude 1, these constraints gave rise to four narrative archetypes. The simplest is BMA-​1, in which a single pitch and/​or rhythmic motive plays out over the course of a piece. In cases in which an analyst senses that a work harbors two or more pitch/​rhythm motives, three BMA-​2 archetypes can be called on to explain their piece-​long interaction. The narratives of “Non-​Engagement,” “Synthesis,” and “Triumph” stem from two interaction types, complementation and conflict. The main aspect distinguishing CMA from BMA is that nearly all of the former restrictions are lifted. Chapter 7, which formally presents CMA, will explore the ramifications of broadening the Focal Point to include domains beyond pitch and rhythm—​namely harmony, contour, articulation, and so forth. The Focal Point, moreover, will be allowed to occur anywhere in a piece, not just at the beginning. Technically, the proper placement for this Interlude on complex narrative types would be in Chapter 7, between the CMA presentation phase and demonstration phase. I have decided to introduce the expanded set of narrative archetypes early, however, to avoid interrupting the next chapter’s flow of discussion.

CMA Archetypes Stemming from an Expanded Focal Point We first consider the effect that broadening the scope of a Focal Point has on analysis. The first narrative archetype of complex motivic analysis, diagrammed in Example 6.5.1, corresponds closely with BMA-​1 in that it, too, follows the flow of time. (Readers should note that in these models, the transformational arrows that appear are unadorned, suggesting that the motives recur literally or under duration scaling.) The main aspect that has changed is that the central Musical Motives. Brent Auerbach, Oxford University Press. © Oxford University Press 2021. DOI: 10.1093/oso/9780197526026.003.0008.

206  METHODS OF MOTIVIC ANALYSIS Example 6.5.1  The Propagative archetype, CMA-​1→, is analogous to BMA-​1. The starting event in this case is broadened to occur as a Focal Point with additional domains beyond pitch and rhythm. Material propagates

Focal Point Segment 1

2

3

4

5

6

7

8

pitch/rhythm/harmony articulation/dynamics/etc.

analytic entity occurring near the beginning is expanded. That is to say, the event no longer manifests as a singular pitch and/​or rhythm motive, but rather as a complex of musical ideas that can be thought of as a kind of Schoenbergian Grundgestalt. The first task of the following chapter on CMA will be to establish parameters for the proper scope and content of this Complex. With regard to our present and more limited aim of establishing narrative types in CMA, however, the Focal Point can remain a “black box” entity. Two narrative impulses are associated with CMA-​1. The dominant one, represented by the label CMA-​1→, is designated simply as “Propagation.” For a Propagation narrative to properly manifest, the influence of the Focal Point must be maintained for the entire length of the piece. This does not mean that all of its submotivic elements must appear in every segment; the Focal Point’s influence will naturally wax and wane over time. There is a minimum requirement, though, that at least one of its elements be present at all times. The diagram in Example 6.5.1 indicates the simplest mechanism by which a motivic complex can propagate over the course of a unipart work. To accommodate more substantial pieces with pronounced formal divisions, such as sonata form, it is necessary to posit a multilevel—​that is to say: a hierarchic—​path of motivic influence. Example 6.5.2(a) models how a Propagation narrative unfolds in such works. As before, the Focal Point appears at or near the beginning of the piece and carries out local development over its first major section. Contrasting material, in terms of mood, mode, theme, melody, and harmony is expected at the beginning of the Second Tonal Area and the development. The Focal Point impacts these subsidiary formal areas by radiating packets of motivic subelements to their starting points. These initiating events, henceforth called Local Points, head smaller propagative processes within their sections. Example 6.5.2(a) illustrates the most common arrangement of this narrative, in which Focal Point material literally appears in the body of the work. In this case, it coincides with the music of Segment 1. Example 6.5.2(b) illustrates a

Example 6.5.2  Variants on CMA-​1→ that apply in the case of multisection works. (a) The CMA-​1→ narrative across a large work is structured hierarchically. The Focal Point radiates its materials to two or more “Local Points,” that spawn the successive content in each section. Focal Point

Local Point

3

2

1

5

4

8

7

6

Section 2

Section 1

(b) A variant of CMA-​1→ in which Focal Point material does not occur literally in any segment of the piece, but is deducible from surveying large-​scale motives and motivic processes. Focal Point

Local Point

Local Point

1

2

3

4

5

Section 1

6

7

8

Section 2

(c) The Dissolution archetype, CMA-​1>. Focal Point

1 pitch/rhythm/ harmony articulation/

Development via gradual subtraction of elements

2

3

4

5

6

7

8

208  METHODS OF MOTIVIC ANALYSIS more unusual circumstance. In this case, the Focal Point is placed outside the linear frame of the piece to signify that it does not appear in any given segment. In other words, the Focal Point’s “idealized” content—​its pitches, rhythms, and other aspects—​never appears all at once at the surface of the music. At most, an approximation of it will appear, requiring the analyst to deduce the full structure.1 The last type of Propagation narrative for CMA appears only rarely. Example 6.5.2(c) depicts a condition in which a Complex, again posited near the beginning of a piece, is seen to have a diminishing influence over its course. This narrative process, to be known as “Dissolution,” is represented by the label CMA-​1>. This archetype is best suited to pieces that expressly invoke the notion of Dissolution through programmatic means, for example, of titling and staging. Examples of this phenomenon include Haydn’s famous “Farewell” from the end of his Symphony No. 45, in which the players are instructed to depart the stage in small groups, and Schoenberg’s “O Alter Duft,” the closing song from Pierrot Lunaire that describes an age lost to history. In the graphic showing the Dissolution archetype, the graying out of the segment nodes indicates their increasingly weaker material connection with the Focal Point. Note that the curving horizontal arrows remain unlabeled in this model. In actual practice, it would be the analyst’s responsibility to specify which motivic elements are being shed over time.

CMA Narratives Stemming from Delayed Focal Point Appearance The remaining CMA archetypes arise from lifting the second constraint on BMA, which newly allows for the Focal Point to be located in any segment within a composition. As we consider the impact of this conceptual maneuver, we will be aided by an image that illustrates two basic types of informational flow. The first type, Propagation, shown in the top line of Example 6.5.3(a), will be familiar from BMA-​1 and CMA-​1. The second type of flow, Accretion, is shown in the line below. Though couched as opposites, the two models shown in part a) of the example are actually quite similar. Both exhibit a single point of unity, a Focal Point. The difference between them is the conceptual direction of information flow at the higher levels. In Propagation, the motives at the beginning are conceived as having a forward trajectory. In Accretion, the Focal Point appears late in the work, such that all related motivic events that occur in advance are seen both as foreshadowing and evolving toward it. There is surprisingly scant theoretical

CMA Narrative Archetypes  209 Example 6.5.3  Two ways of viewing flow of information. (a) In Propagation, shown above, flow is from an early source event (reprint of Example 5.5.1). In Accretion, shown below, flow is toward a late source point. Focal Point 2

1

3

7

6

5

4

8 Focal Point

1

2

3

4

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Influence/ Foreshadowing (b) Accretion archetype with multi-sectional hierarchy.

Local Point 1

Section 1

2

Section 2

Local Point 3

4

5

Influence/ Foreshadowing

6

Focal Point

7

8

pitch/rhythm/harmony articulation/dynamics/etc.

precedent for this interpretive practice, which essentially reverses the trajectory of Propagation; however, the mechanism by which it proceeds is straightforward enough.2 The arrows appearing in the Accretion-​type narrative carry the same information about transformations as those in the Propagation narrative. The rightward pointing arrows appearing “in line” with the piece, critically, still track the experience of hearing the music in time. It matters not whether musicians are experiencing the piece live or rehearsing its sound in their heads. Either way, they are constrained to process events one at a time, from left to right, as it were. Note that these surface arrows cannot communicate the sense in which the central or

210  METHODS OF MOTIVIC ANALYSIS late “core” motivic material might influence or cause the earlier motives to exist, say, in a piece in which it is known or surmised that such material was conceived first. To represent that notion, the graphic employs a separate set of leftward, back-​relating arrows. In Example 6.5.3(b), the Accretion model is expanded; here, the late core material is depicted generating the first segments in each of two major sections. Similar to Examples 6.5.2(a) and (b)  this scheme is hierarchical. The single Focal Point informs multiple Local Points. The Local Points then head each large section of music, generating subsequent events in their proximity in customary, left-​ to-​right fashion. To reiterate, the similarities between the Propagation and Accretion narrative types are greater than their differences. This is borne out by their analogous node structure: either one could easily be translated into the other. Despite the temptation to collapse these two conceptions into a single narrative script, I have retained the distinction between them in order to enrich analysis. Doing so expands the number of archetypes possible among pieces. Moreover, it allows and encourages an analyst to entertain multiple, contrasting narrative accounts of even one individual work. One musician studying a string quartet movement by Haydn might decide the central motivic point occurs at its beginning, in effect, launching the piece. This strategy aligns with the traditional view of music. (It happens to be Schoenberg’s view, which is why he unfailingly places the Grundgestalt at the beginning of his analyses.) Another musician might prefer to locate the main motivic event at a later point in the piece. Her preference in this regard might stem from a pragmatic desire for an optimally elegant analysis. She may observe the richest conglomeration of motives occupying a location other than the beginning. Alternatively, she may wish for the analysis to reflect a more “out of time” (synchronic) view of the piece. For those possessing a deep familiarity with a work, it is possible to have this kind of omniscient score sense, so that musical events can be appreciated locally but conceived globally. Edward T. Cone likens this experience to that of reading the same mystery story multiple times to better savor it (1977). Although the plot of a piece or work of fiction is no longer a secret after the first encounter with it, in repeat hearings or readings, one still feels a degree of rising and falling suspense/​emotion while experiencing any segment within. The emotional impact of any such moment is typically diminished, though, because one’s consciousness is split. While some of our attention is dedicated to experiencing the segment “in the moment,” some mental effort is given over to gauging the present experience in relation to the precognized Narrative curve of the work.3 As analysts begin to explore the new freedom to analyze forward, backward, and even “out of time,” it is important that they remain aware of their own

CMA Narrative Archetypes  211 proclivities. The decision to adopt a Propagative versus an Accretive viewpoint is highly personal, a fact that recalls the central notion of motive—​or perhaps now: motivic analysis, writ large—​moving us. Each time we pose to ourselves the question, “In what direction am I thinking about this music?,” we gain information not only about our knowledge of the piece at hand but also about our own analytical temperaments.4 To avoid running too far afield from pressing methodological issues, we return at this point to laying out and defining specific CMA narrative types. The essential concepts of Accretion—​specifically, the changed flow of time at high levels and of omniscient score awareness—​are communicated well by Example 6.5.3(b). For the purposes of delineating the next class of complex motivic analysis archetypes, it should be sufficient to simply rebrand this image as the model for all of them. In the same way that CMA-​1 generally aligns with BMA-​1, it is proper to regard CMA-​2 and BMA-​2 narratives in similar terms. Readers will recall that BMA-​2 narratives manifest in three forms, depending on how their motivic elements interact (Example 5.5.3). If two shapes are put into conflict with one another, at some point it may seem that one has prevailed and the other has been vanquished. This instantiates BMA-​2+, the Triumph plotline. If the two elements are peaceably rejoined, then a BMA-​2•, or Synthesis plotline is said to manifest. With the Focal Point broadened to the extent that it embeds a multitude of pitch/​rhythm motives—​as well as motives of harmony, articulation, texture, and dynamics—​it becomes increasingly difficult to imagine how one subaspect of the central motivic complex could fully triumph over the others. In observing a large-​scale work, we are more likely to observe the various elements fluctuating in prominence. One pitch motive derived from the Focal Point may be dominant in one formal section, whereas a separate set of pitch and articulation motives may come to the fore in another. All of this is to say that the BMA-​2 narratives do not enjoy equal representation in CMA-​2. As the idea of Triumph is called into doubt, certain branches of the CMA-​2 narrative tree fade, specifically BMA-​2+ and BMA-​2o. Example 6.5.4 shows that, as this occurs, the Synthesis narrative comes to the fore. All accretive Example 6.5.4  The split-​aspect Narratives in BMA yield only one meaningful analog under CMA (cf. Example 5.5.3).

Nature of interaction Complementation

Conflict

produces

Narrative Archetype Non-Engagement

BMA–2˚

Synthesis

BMA–2•

Triumph

BMA–2+

212  METHODS OF MOTIVIC ANALYSIS views of music may be regarded as synthetic to some extent. This sense emerges more naturally in analyses that posit the Focal Point at or near a work’s conclusion: if the full motivic complex only occurs in a late location, then all preceding segments will be heard foreshadowing it. In contrast, if an analyst locates the Focal Point in a more central location within a work, the synthetic narrative will strictly apply only to the segments up to and including the central motivic complex. The remaining segments will exhibit Dissolution. Both of the scenarios depicted in Example 6.5.5 exhibit the Synthetic narrative; they merely differ in the degree to which it applies. A reading with a late Focal Point will be considered more purely synthetic, and will receive the designation CMA-​2) appears when the motivic climax of the work appears midway through a work. Following this pattern, we institute a variant of CMA-​3, the “Modified Cyclic” profile, that applies to pieces that blend cyclic and progressive tendencies. An example of such a piece is a rondo form that features significant recompositions of refrain material. Consider, for example, an eight-​segment rondo similar to that depicted in Example 6.5.6(a), but that features a new chromatic countermelody in its sixth segment. Such a piece is modeled by Example 6.5.7, in which a single refrain event is elevated above the others due to this new content. The designation CMA-​3↑ applies to such Modified Cyclic works. In addition to the overarching, circular process expected of all CMA-​3 readings, the Modified Cyclic model accounts for inequality among the subcycles. Narratively speaking, the unique status of Segment 6 reintroduces an element of directionality to the analysis, which may be felt in terms of a growth process that builds across Segments 1 and 3, peaks in Segment 6, and last dissipates at the final refrain statement in Segment 8.

216  METHODS OF MOTIVIC ANALYSIS Example 6.5.7  Modified Cyclic Archetype (CMA-​3↑). Variant in which one instance of the central, recurring events is promoted due to enhanced content. Focal Point 6

1,3,8

Relative unity w/Focal Point

Passage of time

7

2

5

4

Summary of BMA and CMA Narratives The two Interlude segments of Musical Motives provide narrative frameworks for motivic analyses. One reason for developing these plotlines is to counteract the inherently small-​scale nature of motivic analysis. Motivic analyses that lack these frameworks present visually as a jumble of circles, beams, and labels. Even if the author’s overall sense of logic and meaning is clear to them, in the absence of some plotline their reading will likely not translate to anyone else in print or in person. The full set of archetypes developed for use in BMA and CMA appear in the summary chart in Example 6.5.8. According to the theory and methodology developed in this book, the motivic analysis of any stretch of music beyond a few phrases in length should be couched in these or comparable terms. The narratives are grouped according to patterns of informational flow. The most intuitive analyses are Propagative. Both BMA-​1 and CMA-​1 exhibit this tendency; they differ merely in how many motivic elements they track. BMA-​1 follows the evolution of pitch and rhythm motives, whereas CMA-​1 tracks the progression of a broader complex of motives. The three BMA-​2 narratives, also Propagative, are on offer to address the dynamic interplay between two or more primary pitch and/​or rhythmic motives. In earlier discussion, I  described how the BMA-​2 narratives, when reassessed in light of a

Example 6.5.8  Summary chart of BMA and CMA narrative types.

218  METHODS OF MOTIVIC ANALYSIS larger Focal Point complex, collapse to one synthetic CMA-​2 narrative type. Both CMA-​2 entries in the summary chart are Accretive and Synthetic; they diverge only in where they locate the Focal Point in the music, closer to the end (CMA-​2). The final narrative entries, CMA-​3 and CMA-​3↑, describe fluctuations in motivic unity in works in which the Focal Point returns more than once. Here, as always, the insistent tone of argument and the seeming formality of the summary chart belie a great many flexibilities. An analyst facing a piece may choose to employ BMA or CMA as he wishes, and then any narrative type within. He may feel at one time that a particular CMA model applies best, and then decide a day later that another CMA narrative better captures a different shading of the work. The possibility mentioned at the outset of this section of structuring analyses in “comparable terms,” moreover, allows for the development of additional archetypes. The ten narratives presently recognized by this theory are those that emerged naturally as I attempted to marry musico-​literary precedents with a flexible understanding of musical temporality. In the future, interactions among literary, musical, and other aesthetic and temporal domains will no doubt furnish further compelling and useful plotlines. We are nigh approaching the close of this second of two Interludes. On that occasion, I caution readers not to assume that this means that all theorizing on this topic will cease. We are still in the midst of transitioning from BMA to CMA, a move that entails a conceptual broadening of musical space. BMA narratives occur in essentially one linear dimension, that of time. The CMA narratives retain that first dimension, but add a second that gauges the relative relatedness of segments. The most rudimentary CMA plotlines, CMA-​1 and CMA-​2, invoke the notion of hierarchy. If we grant that a central motivic complex is able to project some or all of its material backward or forward in time, then it is fair to say that it exists out of time to an extent. That is to say: Focal Point material exists in its own space, allowing relative relatedness to be charted on a second, (typically vertical) axis. The models for CMA-​3, the cyclic narratives, most clearly reflect this two-​dimensionality of musical segments; however, it applies to all of the CMA plotlines. We shall explore this topic further in the next chapter, where the CMA method expressly prescribes a means for comparing the motivic content of all of a piece’s segments.

7

Complex Motivic Analysis Introduction: A Rationale for CMA Two defining aspects of BMA are its prioritization of pitch and rhythm and its reliance on propagative (chronological, “left-​to-​right”) processes for interpretation. These features confer many advantages to the method, not least of which is accessibility. A further advantage is the impact they have on BMA’s overall character, causing it to approximate how first-​time and/​or curious listeners experience pieces by emphasizing discovery and quick association. Ironically, these same aspects that benefit BMA within its own sphere manifest as shortcomings for a method that aspires to analyze more comprehensively. If a technique focuses purely on pitch and rhythm, it will fail to account for activity in other important domains of music, among them harmony, dynamics, articulation, timbre, and ornamentation.1 The most direct solution to address this shortfall is to propose a method that engages all of the same attributes as in BMA plus additional ones that it excludes. Almost any passage from the Common Practice can be called on to illustrate the potential value of such enrichment. As an example, consider the unremarkable moment from the exposition of Haydn’s Symphony No. 103, I, shown in Example 7.1. The BMA-​style brackets show this allegro theme to be built of a set of routine rhythmic and pitch motives. This information is useful for knowing how the surface coheres, but reveals little else. The desire to know more about a piece’s full content opens up an informed dialogue with all of the musicians who have engaged or will engage with it, composer, performers, and listeners alike. Starting with the first, it is reasonable to assume that Haydn had more than just a set of pitch shapes in mind when he wrote this passage. Like any trained European composer of the eighteenth century, he would also have been concerned with •​ coordinating the note-​to-​note interactions of the voices, in particular the functional soprano and bass, which is to say: counterpoint. •​ ensuring that all lines cooperate to produce intelligible chords and, where relevant, functional progressions, which is to say: harmony. •​ concluding the utterance with a cadence, which is to say:  local phrasing and form. •​ imbuing the whole with a vibrant, overall character. Musical Motives. Brent Auerbach, Oxford University Press (2021). © Oxford University Press. DOI: 10.1093/oso/9780197526026.003.0009.

220  METHODS OF MOTIVIC ANALYSIS Example 7.1  The allegro theme of Haydn Symphony 103 (I), mm. 40–​42 as viewed under BMA.

It follows that if we wish for motivic analysis to say something about these additional kinds of relationships in music, it must be expanded to engage them. For many of these new domains, such as counterpoint, harmony, and form, it will be possible to import terminology and techniques from already-​established music theories. For other domains, more creative solutions will be necessary. Indeed, aspects of music as vague as character or gesture cannot be conceived of in singular terms at all. Each emanates from the joint agency of many factors, among them articulation, dynamics, timbre, and intra-​/​extramusical allusion. If Propagation is the only framework available for structuring findings, analysts will be unable to access nonlinear archetypes such as Accretion and Cycle. These plotlines, as discussed in the previous Interlude, represent alternative means for conceiving music. Specifically, the nonlinear accounts model kinds of nonlinear thinking that expert musicians of all stripes—​performers, composers, and academics—​regularly rely on. (Recall that when one has a deep knowledge of a piece, one is not constrained by time or ordering when sensing associations among its events.) Nonlinear plots have a further value, too, in fostering creativity in analysis. As analysts gain awareness of the novel archetypes, they may be inspired to craft multiple narratives for a single piece. A further hope is that the archetypes will, over time, influence motivic analysis as a whole to continue evolving beyond the one-​way, chronological thinking that has long dominated it.2 A few last comments will prepare readers for the presentation of the extended methodology for complex motivic analysis. The definitions and methods given in this chapter are intended for expert users, those who have mastered BMA and who are well acquainted with the history and theory of motive. The chapter’s organization will loosely follow that of c­ hapter  5. The content in each corresponding area will shift, however, to fit the changing priorities of the new mode of analysis. For instance, there is no need to reopen the discussion on techniques

Complex Motivic Analysis  221 of reduction; the “salient” approach developed earlier will suffice. The first section of this chapter will concentrate on introducing the terms and techniques necessary for charting and then coordinating musical domains beyond pitch and rhythm. It will culminate in the unveiling of the complex motive model. There is similarly no need to rehash the motivic transformation rules established for BMA. The second section of this chapter will instead turn to the issue of interpretation. I mean this term not in its subjective, aesthetic sense, but literally. At the outset, readers should be aware that elevating a motive’s degree of complexity—​where now many gestures are charted in many domains—​results in a veritable explosion of data points. A piece’s primary motive under this approach is no longer conceived as a single shape, but rather as a group of many. The system that handles these complex motives must account for every attribute’s recurrence through all segments of a piece. Imagine, for example, a piece that is viewed in twenty segments with a Focal Point encompassing fifteen separate aspects. A simple, back-​of-​the-​envelope calculation tells us that that analysis will give rise to approximately 300 data points. As larger quantities of information come under view in CMA, this branch of analysis should, in accordance with tradition, continue to affirm motivic analysis’s perennially intuitive disposition. As such, CMA’s interpretive machinery has been designed to allow musicians to meaningfully chart the flow of gestures through pieces. In the latter part of this chapter, two pathways toward that end will be delineated. The first, more informal method of organizing findings allows analysts to use the arrow notation established in ­chapter  5 to trace the path of select attributes of the Complex across the piece. This graphical approach may be thought of as “BMA Plus”. The second mechanism, known as Quantitative Analysis, examines all data points generated through CMA. The theory that establishes Quantitative Analysis includes procedures for valuing all of a complex motive’s attributes and for charting the relative degree to which it returns in segments. This last interpretive act, entailing a near-​comprehensive motivic comparison, will be aligned with the more humanistic aspects of musical interpretation, among them narrative, hermeneutics, and performance practice.

Formalizing Complex Motives Introduction to the Expanded Format As was the case for the basic motive, the concept of the complex motive draws on many structural elements from Schoenbergian theory. This borrowing, however, is neither simple nor wholesale. Though my complex motive is inspired by Schoenberg, it is not a Grundgestalt by another name. All aspects of that

222  METHODS OF MOTIVIC ANALYSIS traditional entity, encompassing both form and function, have been redesigned. In terms of literal scope, the newer analytic entity occupies a larger footprint. The expanded breadth of the complex motive results from supplementing treatment of the classic musical domains—​pitch, rhythm, harmony, and articulation—​with new ones such as texture, gesture, and rhetoric. In this way, the complex motive explicitly formalizes attributes that traditionally were treated in ad hoc fashion, if at all. An increase in this analytic entity’s length is mandated by two interdependent requirements: Rule CMA1: Complex motives must exhibit at least one significant harmonic root motion. Guideline 1 (to Rule CMA1): The length of a complex motive is commensurate with the segment, a prototypical phrase that (1) represents a complete musical thought and (2) can be apprehended (audiated) as a simultaneity, which is to say, retained in the mind’s eye.

The segment, as described in the rule, may be thought of as the common, “musician’s phrase,” meaning a coherent portion of music that lasts a few seconds and has a clear beginning and end.3 I make no secret of the fact that Rule CMA1 stems from a pragmatic analytical concern. Making complex motives—​and, just as important: the formal units of music—​uniform in length and content is prerequisite for making direct comparisons among them as they return in their varied incarnations. Immediately we may begin to note some of Rule CMA1’s effects. The first is that complex motives are extended beyond their typical length in BMA. Another is that these motives are more crisply demarcated. Complex motives do not “run out of notes” at the point, say, where the analyst feels that enough component shapes have been bracketed. Their endpoints are determined, rather, on the basis of small-​scale formal issues. In this way, complex motives manifest as viable segments of a piece. This last point implies that some form of cadence will appear at the end of every complex motive. Though this idea will hold in general, I am reluctant to strictly police it. For all practical purposes, keeping the cadence guideline in mind should be sufficient. We therefore prefer that all complex motive parsings conclude with harmonic cadences. Where no conventional points of punctuation can be identified, closure may be signaled by other means such as marked shifts in rhythm and texture. Failing that, as in rare cases of music built of longer, undifferentiated stretches, complex motives may be parsed subjectively. Again, in the spirit of Requirement (2) from Guideline 1 of the rule, a segment’s length

Complex Motivic Analysis  223 may be defined as the amount of space and material that an analyst is capable of apprehending as “now.”4 Armed with a clearer sense of complex motives, we may begin to model them. Example 7.2 revisits the Haydn symphonic excerpt from earlier, rendering it as a complex motive. The motive takes the form of a multiformat inventory, or more properly:  a network. The suggestion that networks could serve as the framework for motivic analysis was initially broached in ­chapter 3 in the context of describing Zbikowski’s categories (2002). In this chapter, the network concept comes to fruition as it is established as the basis of the complex motive.5 Example 7.2  The allegro theme of the symphony formatted as a motivic complex.

224  METHODS OF MOTIVIC ANALYSIS It is important to note from the start that Example 7.2 depicts a mere instance of a complex motive; it does not show the model in its entirety. The present introduction to the complex motive is meant to lay groundwork for the fuller theoretical account of it appearing in the next section of this chapter. The pitch and rhythm motives, in a holdover from BMA, are again represented in musical notation with brackets and labels. The rhythmic content, indicated above the score, is analyzed as a four-​beat gesture in 6/​8 time composed of medium-​sized beats. (It would be acceptable to view the rhythm in terms of a smaller, two-​beat shape that sounds twice.) All of the M rhythms can be subdivided into eighth notes with hashmarks ( /​| \ ); however, in this case, only the last beat receives that treatment. Further details of the rhythm are signaled through the use of the bar line signs (|) and bold typescript. Together, these conventions indicate the shape’s irregular metric placement. When performed in isolation, this excerpt sounds like it begins on a strong beat. In fact, it begins on beat two, an “off-​beat” opening, as in the style of a gavotte. The bolded M attacks indicate the unusually strong quality of the “beat two” events in 6/​8 time.6 The set of descriptive domains that are listed below pitch and rhythm are formatted individually to express their content as efficiently as possible. Harmony, for example, is here represented both as a Roman numeral succession involving tonic (I) and dominant (V) chords in E♭ major and, more generally, as an upward-​ fifth harmonic root motion (↑5th). The five domains that follow harmony detail the segment’s more coloristic aspects through combined use of musical symbols and text. The “Articulations” entry notes the prevalence of staccato attacks, as well as snapped, down-​up slurring. The content of “Dynamics” is used to note volume and changes in volume, if significant. The “Orchestration/​Texture/​Timbre” domain describes the arrangement of the voices. In the present case, the designation “high strings” signals both a literal scoring decision, meaning orchestration, and a sonic connotation of lighter, silkier sound—​in other words: timbre. This domain is also fitting for documenting standard voice configurations and arpeggiation patterns that influence a segment’s overall sound, with examples being “planing,” “Alberti bass,” and “parallel thirds.” It may seem counterintuitive to include that last designation here and not separately in Counterpoint. Counterpoint, as will be explained later, is a “derivative” domain used to loosely track the behavior of a texture’s outer voices. In contrast, textural arrangements such as parallel thirds and sixths are often restricted to the upper voices of a texture, where they serve to thicken the sound of moving lines. Contour information in this preliminary example is tracked schematically, with priority given to the melody (black line) over the more static bass voice

Complex Motivic Analysis  225 (gray line). This information may be denoted in other formats. Two possibilities include using prose to describe the melody line as “gradually descending from 3̂, followed by upward sweep,” or using a contour vector, such as < 3 4 3 2 1 0 1 3 5 >. The segment’s contrapuntal content is captured in two ways. The first employs the traditional designations, “parallel,” “contrary,” “oblique,” and “static” to broadly indicate the type of interaction. In this case, oblique motion at the start gives over to contrary motion at the end. Below these labels, the counterpoint is described in finer detail, in terms of diatonic intervals measured between the bass and soprano. If desired, other intervals among alternate voice pairings can be listed. The advantages of this expanded network format will be revealed gradually throughout this chapter and the next. Our more immediate concern, as we move beyond the overview stage of the complex motive model, is noting the many challenges of working with it. Chief among these is the model’s multivalence. Consider that each one of the domains listed in the Haydn example is complicated enough to stand alone as an area of theoretic inquiry. How daunting it is, then, to see them all yoked together in one network. It is not merely a matter of finding a balance among harmony, rhythm, contour, and character. There is reason to worry that, in attempting to address so many richly descriptive domains, that all will be given short shrift. These concerns are valid but do not invalidate this line of inquiry. On the contrary, they support it. Present-​day music theory has become so fragmented that it is common for individuals to spend their whole careers investigating one or more of a small set of musical domains. The philosophy of CMA runs counter to that trend, implicitly arguing that all of these disparate domains should be rebundled to better reflect their a priori, bound-​together state in music. But for a few ambitious, “network-​aware” approaches, relatively few modern analytic systems fully engage the interplay of melody, harmony, counterpoint, articulation, and timbre. Most give priority to one or perhaps two of those areas. One impetus behind the development of CMA is providing analysts with an avenue of investigation that, at least in spirit, aspires to be comprehensive. A further reason for courage in pressing ahead is that the volume and quality of results afforded by CMA will outweigh methodological shortcomings. It is only natural that, as more domains are incorporated into a system, that some watering down will occur for each. It will be possible to encode some pitch contour information for melodic gestures within CMA, for instance, but not with the exactitude of a dedicated, expert-​level contour analysis. In other words, we must continually seek out compromise solutions that offer a workable level of detail that is neither burdensome nor threadbare.

226  METHODS OF MOTIVIC ANALYSIS

Theorizing the Content of the Complex Motive Preliminary discussion of the Haydn symphonic excerpt offered a glimpse into the form and function of complex motives. To now formalize such motives, we briefly abandon concrete examples in favor of a more abstract approach. No single, isolated segment of music taken from the literature is rich enough to support an assembly demonstration encompassing all potential domains of a complex motive. Indeed, most excerpts one regularly encounters wholly lack content in one or more domains. For instance, the passage given in Examples 7.1 and 7.2 contains no ornaments, dynamic contrast, tempo fluctuation, nor any outstanding rhetorical gestures. The format for complex motives is illustrated in Example 7.3. The leftmost column lists the standard domains; the center column indicates the type of information tracked by each. Most of these domains are intuitive and have already received some theoretic attention. Some are new, such as the domain accounting for “Special Effects.” This domain is reserved for documenting events that are deemed motivic by virtue of their outstanding character. An analyst has much latitude in deciding whether an event is sufficiently “marked” for attention to merit inclusion in this domain. For example, commonplace volume gestures such as mezzo forte or “hairpin crescendo” fall under the purview of Dynamics. If, however, a segment were to feature a prominent sforzando or many of them in series, then that could be counted as a Special Effect. Similarly, basic trills and grace notes typically count as Ornaments, whereas a more impressive rolled chord or glissando might count as a Special Effect.7 The new domain appearing below Special Effects is “Embodiment/​Allusion.” This area serves as a repository for two kinds of information. The first, embodiment, refers to distinctive (“marked”) physical movements that are required of performers to execute certain passages. Examples of embodiment include a pianist “crossing” the hands to realize certain textures, a string player shifting to all “down-​bows” for emphasis, or brass players following a score instruction to play with “bells up.” This domain’s second aspect, Allusion, refers to robust extramusical associations that may accompany certain shapes. For a motive to qualify as musically allusive, it must refer to a previously existing piece that the composer knows or can be reasonably assumed to have known. The allusion may be to other musical works or prominent motives from those works.8 Often, the shape in question will have earned iconic status through citation in other pieces or the written literature; it may carry a name such as the “Bach” motive (B♭-​A-​C-​ B♮), or “Tristan chord” (half-​diminished seventh chord). Last, it should feature prominently in the work being analyzed. Dallapiccola’s use of the “Bach” motive throughout “Simbolo,” from his Quaderno Musicale di Annilibera, for example, would constitute a valid allusion (Lewin 1993). More generally, Allusion may

Example 7.3  The standard content of and modes of representation for a complex motive.

228  METHODS OF MOTIVIC ANALYSIS also manifest as a reference to a genre or topic, usually in the sphere of music. It would be appropriate, for example, to list content in this domain for a motive that projects a sense of the “pastoral,” the “hunt,” the “military,” or “storm and stress.” Embodiment and Allusion may seem to make an awkward pairing; however, sound reasons exist for placing them together in one domain. Both aspects, for one, depend on knowledge located outside of a work’s aural soundscape and score. Consider Embodiment. For a pianist’s crossing of the hands to register to analysts working from a score, they need to be able to visualize it. This requires some first-​hand experience of piano playing, of using one’s one hands to turn noteheads into notes. (The same argument applies to the other instrumental subcultures, of course.) For a performer’s physical gesture to register with an audience, they must see it, either live or on video. For Allusion, the outside knowledge comes from immersion in musical culture. Motives gain fame via discourse, first as composers write letters to acquaintances and dedicate pieces to them, and then as historians and theorists dive into that documentary history and disclose their findings to the public. A further benefit of causing Embodiment and Allusion to overlap is that it allows us to resituate the classic rhetorical figure within motivic analysis. According the “Sigh” shape figure status, for instance, alludes not just to a set of melancholy gestures in melancholy pieces, but to a long pedagogical tradition concerned with interpreting and performing a phrasing convention. Invoking that figure’s name constitutes literal embodiment as well, as the word “sigh” denotes a movement-​sound derived from the human animal. On these bases, the Embodiment/​Allusion domain effectively charts a complex motive in both its physical and associative aspects. The column at right in Example 7.3 prescribes the means for representing content in each domain. For Pitch and Rhythm, the nomenclature is the same as it is for BMA (see c­ hapter 4). For Harmony, three labeling systems are recommended. They may be drawn on freely, depending on the level of specificity desired. The first is the conventional set of Roman numerals, which indicate chord root and quality. Any information one wishes to convey about chordal inversion (bass identity and arrangement of voices) may be relegated to other categories, such as Counterpoint and Orchestration/​Texture/​Timbre. The second system is based on the harmonic function labels, T(onic), D(ominant) and P(re-​Dominant).9 The third system, also quite general, tracks root successions as directed distances in pitch-​class space—​e.g., “Ascending fifth (A5)” and “Descending Second (D2),” with aspects of key functionality ignored. This third approach is particularly well suited to CMA, as a high degree of generality improves an analyst’s chance of finding literal matches in other segments.

Complex Motivic Analysis  229 The visual format of Example 7.3 relates further relevant information about the model. The domains are shown grouped in three areas, the top-​to-​bottom ordering of which reflects their relative importance from the standpoint of tradition. (Note that soon, when the domains are combined for the purposes of calculating similarity across segments, this ordering will inform relative numerical weighting.) The three entries that appear above the first bolded divider are “essential” (also: “primary”) domains that must be accounted for whenever CMA is applied to Common Practice pieces. The remaining eight domains are of secondary import, tracking aspects of music typically regarded as more decorative. A typical CMA will engage at least two or three of these domains. Only sometimes will it be necessary to invoke most or all of them. The domains given in the lowest group are Counterpoint and Contour.10 They are placed here because they are inherently derivative: the information they encode is deducible in whole or in part from other domains.11 A string of vertical intervals in a contrapuntal analysis, for example, can usually be derived from voices already appearing in the Pitch domain.12 The same holds for a contour-​ based description posited for a motive. The pitch contour < 0 2 1 3 >, for example, conveys a new shade of information about, say, the notes C3-​F-​D-​G, but not unique information. Contour vectors generalize but also overlap note-​specific content, and for this reason they are accorded lesser status. We will forego additional domain-​by-​domain accounting of the model, allowing the example to speak largely for itself. Curtailing the discussion allows us to proceed more quickly to the demonstration of complex motive assembly. It further promotes efficiency by sidestepping overtly technical accounts of the domains, which in the end might prove extraneous anyway. While this chapter goes to great lengths to suggest specific mechanisms for working with domains, analysts are free to jettison approaches they disfavor and to institute their own. I have only a few words to add about this methodological freedom, which at first appears sweeping. First, it must be employed responsibly. No specific means are prescribed for representing any and all of the domains; however, analysts are still charged with accounting for these domains in a rigorous manner. To wit:  substitute nomenclatures must pass methodological muster. Alternative symbol systems need not be traditional, nor even preestablished, but they must be legitimate in the sense that they are reproducible and make musical sense. Second, this freedom does not apply beyond the level of the domains. The general format of the complex motive remains a central, nonnegotiable aspect of CMA. I noted earlier that this framework dictates how a full motivic analysis is constructed. To say this another way: Complex motives and CMAs interpenetrate one other. Therefore, failing to conceive a segment of music as a complex

230  METHODS OF MOTIVIC ANALYSIS motive necessarily entails a loss of access to the interpretive techniques associated with it.

Further Aspects of Working with Complex Motives The next phase of discussion will flesh out the complex motive concept by raising three practical concerns. The explanations provided in response to them directly inform the process of crafting a complex motive and selecting systems of representation for its domains. This portion of the chapter, dedicated to balancing the domains and maximizing their interpretive power, will connect the abstract model detailed in the previous section to the concrete demonstrations to follow. Final reinforcement of this material will take the form of a sample analysis in which a complex motive is assembled from scratch from a short Brahms waltz.

Concern 1: Unified and Conflicting Harmony We noted earlier that harmony frequently plays a major role in establishing the boundaries of complex motives; however, this is not its primary function. This domain exists to document the characteristic harmonic content of motives. This includes noting the presence of a conventional cadence and describing the beginning and ending harmonic states, when different. (If they are the same, some opposed harmonic state must occur internally, as per the “significant tonal motion” clause of Rule CMA1.) No matter how bare a segment under study may initially appear, the default assumption should be that some harmonic element is present. In many cases, this tonal motion will be salient. Such is the case for mm. 1–​4 of the minuet from Schubert’s Quartet No. 9 in G minor, shown in Example 7.4. The opening of this minuet has a strong harmonic sensibility, in that all of its on-​beat simultaneities (chords) are tertian and adhere to Common Practice syntax. Although there is always room for variance, most trained musicians will agree that the Roman numerals shown below accurately interpret its chord content. (We will have more to say about the harmonic function labels later in this section.) Example Web.7.1 illustrates a situation in which the harmonic content is murkier; it occurs in mm. 1–​8 of the finale of Haydn’s Piano Sonata in E♭, Hob. XVI: 52. The passage, in one sense, embodies harmonic stasis by means of a tonic pedal point. Upon noticing this pedal, the analyst need not give up and declare the harmonic domain empty. Further investigation in cases like this often reveals the presence of triadic structures functioning harmonically. In the web example we can see how the melody expresses tonic and dominant states in alternation.

Complex Motivic Analysis  231 Example 7.4  Derivation of harmonic motives from mm. 1–​4 of Schubert’s Ninth String Quartet in G minor, D. 173 (III), through segmentation and reduction. The “+6” indicates the presence of an augmented sixth chord.

There is a persistent unfolding of E♭ major I chords and D diminished viio chords, the latter of which contains both tendency tones in the key, 7̂ (ti) and 4 ̂ (fa). Harmonic analysis in every context is subjective. This holds particularly for Common Practice tonal works, though, because the separate voices project harmony at different rates and intensities. Pedal points, non-​chord tones, canonic imitation:  all of these are common techniques that generate small-​scale harmonic conflict. Analysts should attempt to document such clashes in a Complex’s Harmony domain when they are relevant. To do so, they will need to cultivate an

232  METHODS OF MOTIVIC ANALYSIS attitude of openness. They must be willing and able to flexibly employ notation to engage harmonic blending events. Again, due to subjectivity, it is difficult to place absolute restrictions on the kinds of claims one may make in this domain. The only guideline that will be offered is as follows: Guideline 2 (to Rule CMA1): Harmonic claims should never intentionally violate the aesthetic premises of a work.

It would, for example, be misguided to attribute functional harmonic content to a work of Musique concrète or a spoken word piece by Steve Reich. On the other hand, an expressly antiharmonic aesthetic can manifest in isolated moments within an otherwise traditionally tonal piece. It is easy to imagine, for example, the final segment of a Romantic symphony that is built exclusively of tonic chords sounding at loud volume and in various rhythms. This hypothetical passage certainly possesses a harmonic identity, tonic, but no meaningful harmonic-​motivic shapes. Guideline 2 need not apply blindly. For example, I generally advise against ascribing harmonic-​motivic quality to unpitched segments like the first eight measures of Movement II from Bartok’s Concerto for Orchestra. Yet, I also acknowledge that cases exist in which it may be appropriate to do so. Here I refer readers to the phenomenon of the “percussion break” that approximates a pitched event, as in the case of drum set fills or solo segments that exploit drum-​ head tuning. Jazz drummers are exquisitely sensitive to harmonic progression from their experience navigating charts and standards. It follows that they would tap into all available resources of their kits to project drum-​based analogs of common harmonic tropes, including suspenseful dominants at half cadences and in ii-​V-​I turnarounds. There are, in other words, few limitations as to where one may creatively intuit harmonic gestures in music. This type of projection need not apply only to nonpitched segments within larger pieces. It can apply to whole works that resist standard harmonic nomenclature. It is often worthwhile to scout out harmonic gestures in genres that presumably resist them, such as medieval works and spoken-​word art pieces. Mostly, this kind of postmodern projection does not constitute an “intentional violation of aesthetic principle.” There is nothing, for example, untoward about applying set theory methodology to probe harmony in a High Classical composition.13 It is safe to assume that Mozart did not create and organize chords according to pitch-​class set principles that postdate him by centuries. It is, at the same time, eminently reasonable to imagine that he would have been aware of the sonic impact of recurring pitch cells in his pieces, both in the horizontal and vertical dimensions.14

Complex Motivic Analysis  233

Concern 2: Preference for Binary Representation in the Domains The transformational tools of BMA—​transposition, inversion, duration scaling, etc.—​are designed to track exact pitch and rhythm correspondences. The reason for preferring absolute over partial matches is that the former are more methodologically straightforward and thus easier to defend. The same impulse in the realm of CMA leads to the following guideline: Guideline 3 (to Rule CMA1): The informational attributes within the domains of CMA should be formatted in binary terms whenever possible.

Beyond bolstering the strength of individual associative claims, this convention promotes efficiency at two different points in the analytic process. It does so first at the outset of analysis, when the content of the Focal Point complex is defined. The binary condition encourages analysts to build only as much detail into their Complexes as necessary to yield results. It also promotes efficiency at the stage in which all of the piece’s component segments are compared. For each pair of segments, relative relatedness is determined by a series of yes or no questions addressing the presence or absence of a specific attribute.15 Binary formatting is more straightforward for the secondary domains, in which attributes such as “trill” for Ornament or “Petrushka chord” for Allusion can be thought of in all-​or-​nothing terms. It is far more complicated for Harmony, however. To illustrate why this is, we revisit the Schubert minuet that was earlier held up as an exemplar of harmonic clarity (Example 7.4). The root identities and functions of the individual chords are relatively unambiguous. The problem is that the string of chord function labels given in line a) is highly detailed and specific, which impedes our ability to directly link this segment with others in the movement. Were we to uphold the requirement for absolute matches, we would likely only observe connections among segments containing fully literal returns of this music. To reduce the specificity of a segment’s content, we can treat harmony in the same manner that BMA treated complex melodic strings. This calls for viewing a segment’s harmonic content in terms of its component parts. Analysts have freedom to establish any harmonic sub-​element in a Complex they like, provided that it adheres to Rule CMA1. The lower area of Example 7.4 illustrates a set of potential harmonic motives that might define a Complex; many others are possible. These “attributes” are derived from the initial string of harmonies in area a) in two ways, segmentation and reduction. Under segmentation, abbreviated strings of adjacent harmonies are extracted from the original. Five potential attributes are shown to result from this process in area b) of the example. The other procedure this method recognizes is harmonic reduction, which entails pruning out a passage’s more decorative harmonies and retaining its more structural ones.

234  METHODS OF MOTIVIC ANALYSIS Reduction, too, can be performed on strings of Roman numerals and harmonic function designations alike. Unlike segmentation, though, this procedure requires training far beyond the primer materials given in c­ hapter 5. To be fluent with reduction, an analyst should have studied college-​level theory for at least one year. That experience is helpful for learning about how harmony is hierarchic, meaning:  how a single chord can be stretched out—​but not supplanted—​by chords that follow. It is likely that anyone surveying the function labels in line a), could guess that the first tonic (T) and final dominant (D)  will be retained under reduction on the basis of their structural accents. Only those familiar with Schenker’s concept of “composing out” and/​ or Riemann’s concept of harmonic functions, however, would be able to explain why the second and third function symbols in line a), D and T, are absent in line c). The reason, to be clear, is that the V chord in m. 2 is a weaker, decorative chord. Its 6/​3 inversion, occurring in the context of a large-​scale G3-​F♯-​G bassline, acts as a “neighboring” harmony that connects the i chords in measures 1 and 3.

Concern 3: Potential Redundancy of Complex Material The present method grants analysts a high degree of freedom in formatting Complexes in that, for every domain, they may specify as many or as few attributes as desired. With no rules to constrain this stage of analysis, this section offers two further guidelines. The first of these, made only implicitly earlier, is as follows: Guideline 4 (to Rule CMA1): In formatting a complex motive, there is never an obligation to account for all events within a span. This applies to all domains, including rhythm.

The second addresses an inherently ambiguous condition that occurs when working with many domains and attributes: Guideline 5 (to Rule CMA1): Material overlap (redundancy), which is inevitable, should be minimized wherever possible.

Looking back one last time at the attributes listed in Example 7.4, we note a large degree of overlap between the shorter ones uncovered through segmentation and the longer one uncovered through reduction. If one wished to incorporate both harmonic attributes 1 and 6 in the complex motive, that would double count the starting chord. Guideline 5 to Rule CMA1 permits that. No outright limit is established in this method for how many times a single musical

Complex Motivic Analysis  235 element might appear in a Complex. Yet at the same time that analysts take advantage of this interpretive freedom, they should exercise restraint in employing it. Elegance and efficiency, the hallmarks of a well-​built Complex, will be hampered if domains are crowded by redundant bits of data. Such redundancy would occur, for example, if an analyst were to select Attributes 2, 3, and 5 for inclusion.

Complex Motive Assembly In this section, we will construct a complex motive. The piece serving as the basis for the demonstration will be Brahms’s Waltz in B minor, Op. 39, No. 11. The work is of modest scope, yet rich enough in content to ensure a compelling Complex. An annotated score of the waltz is provided in Example 7.5. The bold, lowercase letter notation and Roman numerals, respectively, detail essential aspects of the form and harmonic content. The bold lines reflect the piece’s divisions into surface segments, the raw starting material of CMA work.16 Among the first things to note is how the segmentation respects the piece’s regular phrasing. Other segmentation schemes are possible, provided they are well formed: one cannot, for instance, segment a piece in such a way as to leave out any passages. For example, analysts need not restrict themselves to four-​bar segments; some readers may already be feeling that mm. 17–​24 cohere as one unit.17 The reason I have parsed the digression in two parts instead of one is because the thematic material and articulation style shift at m. 21. With any segment capable of serving as the Focal Point, we arbitrarily select Segment 1 to do so.18 The first of the three essential domains to be tackled is that of pitch motive. This content, arranged in four voices (SATB) on three staves, is shown in Example 7.6. Beginning with the soprano, we note a surface N shape expressed in measures 1 and 3. This shape recurs in nearly all segments that follow. So does the rising third gesture initiated in m. 2 at C♯5. The question is whether this shape spans a 3rd or 4th. There is a good case for the latter, as the melodic ascent to F♯5 is quite audible. The 3rd reading will be preferred, however, because in some subsequent iterations, such as mm. 18–​19, the three notes of the gesture do not always attain their fourth note. We consider next whether any pitch motives are supplied by the remaining voices. The example indicates that none are present in the alto and bass. The alto runs in parallel with the soprano, a behavior that can be documented in the orchestration domain. The bass does move by 2nd. This generic motion can be accounted for with a contrapuntal and/​or harmonic designation, though. This leaves the tenor voice, which traverses a true 4th in its second

236  METHODS OF MOTIVIC ANALYSIS Example 7.5  Full score of Brahms’s Waltz in B minor, Op. 39, No. 11, with segmentation indicated.

half. It begins at the F♯4 of m. 2. Its last two notes, D and C♯, run an octave below the alto. This “shadowing,” which clouds the tenor’s independence, is indicated by the dotted curving arrow between the voices. (Such “coupling” arrows should not be confused with the dashed arrows used to show informal, Sensed connections.) Turning to Rhythm, a survey of the piece confirms the importance of two shapes, the M-​S-​S-​M rhythm from m.1 and the M-​M-​M rhythm from m.  2. Because this is a waltz, it is important to establish the melodic pedigree of the M-​ M-​M gesture. Otherwise, readers might assume that it pertains to the left hand’s pervasive oom-​pah-​pahs, a connection that would manifest as analytic white

Complex Motivic Analysis  237 Example 7.6  A complex motive derived from mm. 1–​4 of the waltz.

noise, trivially present in every segment.19 For the Harmony domain, we establish a single attribute. The chordal motion from tonic in m. 1 to minor dominant in m. 4 receives the designation, T-​D. In assembling the secondary domains, we first attempt to determine which are needed. One domain that may be quickly excluded from consideration is Articulation. It is true that the source segment exhibits a characteristic set of staccato and legato attacks, but these recur throughout the piece as generic elements. The domain of Dynamics is slightly more remarkable. Though sparing in its use of common dynamic designations, the waltz does exhibit one notable gesture. The crescendo of mm. 3–​4 will be claimed as a motivic

238  METHODS OF MOTIVIC ANALYSIS element and symbolized in Example 7.6 by a hairpin graphic. The next domain, Orchestration/​Texture/​Timbre, can be thought of as performing a complementary role to Pitch. Where the Pitch domain describes the specific notes in the voices, this one describes relationships among voices, such as the alto shadowing of the soprano at a third below. To capture this relationship, the Complex’s Orchestration/​Texture area contains a stylized symbol indicating the attribute, “Parallel Thirds.” Only one type of Ornament occurs in Segment 1, that being the grace note decoration that appears in measures 1 and 3. The grace attacks are brief, but their impact is significant for imparting a Hungarian snap to the melodic rhythm.20 This ornament type returns in many but not all subsequent segments, rendering it nontrivial. For the model we are building, the Ornamentation category is assigned a single, binary attribute called, “grace notes,” to document the presence or absence of these decorative gestures. The last of the secondary domains, “Special Effects,” accounts for the only musical gesture in mm. 1–​4 that could at all be considered extraordinary, the fp marking. In many instances, a mild accent like this would not merit including this domain at all. In this case, the accent is made an attribute because of its resonance with a later accent, the climactic sforzando that appears in m. 25. Appearing at the bottom, the domain of Counterpoint accounts for two voice-​ leading behaviors manifesting in the outer voices. One of these is the “bass pedal” that is held below the shifting surface harmonies in mm. 1–​3. The other is the 5–​6 intervallic progression that occurs over mm. 1–​4; see the Arabic numbers above the bass staff. The initial pitch-​class fifth from B-​F♯ expands to a sixth, A-​F♯ when the bass moves downward by step. This completes the assembly of our complex motive. Example 7.6 represents all of this information as a summary network, one that will serve as the basis for the first full pass through the CMA method in the upcoming section.

The Paired End Products of CMA: Organic Map and Narrative All motivic analysis is concerned with comparing musical entities. In BMA, the entities take the form of pitch and rhythm motives. In CMA, the entities are expanded into attribute complexes that each occupy a full segment of music. The purpose of Interlude 2 was to establish the narrative frameworks by which CMA will proceed. The CMA narratives exhibit a great deal of diversity in terms of how their nodes are laid out in temporal and—​with regard to the graphic representations—​visual space. In terms of structure, though, they are quite unified. For one, all of the narratives are built of nodes reflecting a piece’s

Complex Motivic Analysis  239 division into discrete segments. For another, those segments relate to each other organically and in strict hierarchical fashion. A  single Focal Point segment spawns all the content of the other nodes. It may do so directly, or, in the case of a multisection work, through the presence of one or more intermediary Local Points. Recognition of these two structural aspects of this mode of analysis logically determines the procedure for carrying out CMA. The steps are as follows: 1. The analyst divides the work under study into phrase segments according to principles of form analysis. Each surface segment constitutes a complex motivic entity. 2. Taking the full work into consideration, the analyst selects/​derives a Focal Point segment on the basis of its potential for generating all others and its rhetorical impact. 3. If the piece is composed of more than one main section, the analyst selects Local Point segments for each on the same basis as in Step 2. 4. The analyst examines all segments of the piece with regard to a) how motivic attributes flow from Focal Point to the surface, and b) the specific degree to which each surface segment exhibits Focal Point material. While all of the steps are of equal import, Step 4 is the one in which the findings are organized and presented. To that end, the method of CMA prescribes two means for carrying out segment-​to-​segment comparison. The first mode of analysis adopts the arrow-​based approach of BMA, meaning that it depicts the flow of motivic information among segments. The analysis that results is in essence a vastly expanded BMA graphic. This is called the Organic Map. The second mode of analysis takes a quantitative approach to the segments, tracking their degrees of similarity with regard to the Focal Point. The result is a line graph that tracks relative motivic unity on the vertical axis against time on the horizontal axis. This end product is called the CMA Narrative. Rule CMA2: The findings of a CMA are communicated by a pair of complementary modes of representation, the Organic Map that illustrates the flow of motivic associations in the score and the CMA Narrative that documents in detail the number of Complex attributes retained in each musical segment.

Example 7.7 represents the four-​step procedure of CMA as a flow chart that culminates in the two end products of Map and Narrative. The Map and the Narrative fulfill complementary roles, such that a complex analysis cannot be said to be exhaustive unless both are present. The two processes are, at the same time, autonomous. A piece’s Map and Narrative can be assembled independently,

240  METHODS OF MOTIVIC ANALYSIS Example 7.7  Flow chart representing the full process of complex motivic analysis. 1. Segment Piece

2. Select Focal Point

3. Select Local Points

4. Construct Organic Map

Construct Musical Narrative

(final product is an unordered set)

and either can be generated first. One may even be presented in isolation without the other, for example, to make briefer points about a piece. The CMA Map and Narrative diverge in how they handle and present data; however, at their core they are unified as aspects of CMA. For that reason, any fundamental principles established for one mode—​e.g., those constraining Focal Point selection and multilevel formal hierarchy—​will apply to the other. This point should be kept firmly in mind as we concentrate now on the lowest left branch of the schematic, examining the act of Map construction. The purpose of the upcoming sections will be to describe this process and then apply it specifically to the Brahms waltz still at hand.

CMA Map Assembly In CMA, analysts are no longer constrained by the Propagational model of information flow. They are free to experiment with placing a work’s Focal Point at any location. In doing so, analysts will gain the ability to cultivate different or even multiple interpretations of a work. In addition to this new analytic freedom in the horizontal dimension, there is also a new freedom on offer in the vertical, synchronic (“total-​now”) dimension. Although it may not be immediately obvious, the annotated score of the Brahms waltz in Example 7.5 invokes three coordinated levels of structure. The whole piece manifests at the highest level. At the level below this we find the piece’s sections, each composed of two or more segments. (Although it is possible to divide it in three sections to reflect its a digression a’ thematic layout, the present analysis will divide it in two in accordance with its binary reprise

Complex Motivic Analysis  241 structure). Last, there are the surface segments. The strict hierarchy that controls these structures dictates that we treat the events of each level equally. Just as a piece contains a Focal Point, each section must orient around a segment that has been promoted to primary importance on the basis of motivic richness and/​or rhetorical significance. The characteristics of the Focal Point have now been well documented. The designation, “Local Point,” refers to the same phenomenon manifesting one level below. The principles described here can be expressed more formally by an assembly rule with corollaries: CMA Map Rule: All Maps must reflect the strict formal hierarchy of piece > section > segment. Graphically, this entails a pyramid-​like structure in which elements from the Focal Point connect downward to a set of mediating Local Points that occur once per formal section. The motivic content of the Local Points connects to the surface segments of the piece. Corollary 1 (to CMA Map Rule): For a CMA Map to be properly formed, every Local Point must be connected to the Focal Point by one or more transformational arrows. At the surface level, every segment in a section must connect to a Local Point, either directly or via an unbroken chain of arrows. Corollary 2 (to CMA Map Rule): The strength of a connection among segments is roughly proportional to the number of motivic attributes it entails. A connection may be established on the basis of a single attribute, such as a common rhythm or pitch shape.

The basic framework for an Organic Map is shown in Example 7.8. The Map contains a set of nodes, which represent segments, and solid arrows, which indicate standard motivic associations. As always, an arrow can signal a wide range of relationships, from a single textural attribute to a full match in all domains (identity relation). The graphic captures a number of essential Map characteristics, including multilevel vertical design and the presence of mediating Local Points, one for each section, shown as larger, bold nodes. In keeping with Corollary 1, none of the six surface segments is untethered. The genesis of each can be traced through its Local Point connectivity back to the Focal Point. The goal of the Map—​to borrow a term from Schoenberg—​is to offer a “two-​dimensional” reading of organicism, depicting both the top-​down, synchronic process by which a Focal Point generates a work and the left-​to-​right, diachronic process by which the surface unfolds. The arrows’ directions in the example are particularly important. For the hypothetical piece represented, the Focal Point connects with the first segment

242  METHODS OF MOTIVIC ANALYSIS of Section 1. This predicates a Propagational flow of arrows within. In Section 2, the Focal Point connects to a later segment, which creates a miniature Accretional flow. The schematic shown in Example 7.8—​and indeed, the larger process of Map building—​owes much to the “time-​span reduction” method pioneered by Lehrdahl and Jackendoff 1983. According to the rules of that method, “a piece must be exhaustively segmented into time-​spans at every level,” from the sub-​ beat and beat, to measure and phrase, to the largest sections (Lehrdahl and Jackendoff 1983, 146). The analyst identifies a “head” event for each segment based on the strength of its metrical, harmonic, and/​or structural accent and attaches a longer stem to signal retention at the next higher level. The process, carried out recursively, produces a hierarchic tree diagram. The most significant overlaps between CMA Map construction and L&J-​style time-​span reduction are the shared reliance on segmentation and the prioritization of “head” events. Both methods, similarly, allow for prioritized (head) material to appear at any point within the span, allowing for Accretion narratives. There are significant differences between the methods as well. CMA Map construction, for instance, does not require segmentation at all metric levels; this results in a structure that has fewer levels than typical for their trees . On a related note, the “head” event of any CMA Map segment is determined based on organic content and perception of rhetorical strength, which more often than not is distinct from Lehrdahl and Jackendoff ’s “accent” paradigm. Sufficient groundwork has been laid for us to develop a CMA Map for the Brahms waltz. Preliminary discussion of the work indicated its division into two sections, mm. 1–​16 and 17–​40, and ten segments. We first treat Section 1, which requires a Local Point. There are four candidate segments in mm. 1–​16. In this Example 7.8  Schematic of an Organic Map for a piece built of two sections. All nodes represent segments, including the “Focal Point,” a promoted segment. Solid arrows represent unspecified motivic associations of the type familiar from BMA.

FOCAL POINT

1

2 Section 1

3

4

5 Section 2

6

Complex Motivic Analysis  243 case, though, the Local Point must occur at Segment 1, the one whose material is coincident with the preselected Focal Point. This identity relation is shown in Example 7.9 by the thick bold arrow at left. It is unadorned, signaling a full transfer of motive attributes. (Note: a slight change has been made to the Focal Point derived in Example 7.6, that being the “+” added to allow the N and 3rd elements to behave as a composite motive.) Having made this selection, the analyst fills out the Map by documenting the flow of Local Point elements into nearby segments. Starting on the left side, the Map posits a full transfer of pitch and rhythm shapes in the upper voices from Segment 1 into Segment 2 (see boxed material). The first motive attribute we will observe is the neighbor (N) shape. This motive appears in m. 1 with an M-​S-​S-​M rhythm. Plain arrows indicate the literal transfer of its pitch and rhythm to the melody in m. 3, m. 5, and m. 7. Remarkably, in the present interpretation, no direct connection is asserted between these early neighbor figures and the last one appearing in mm. 15–​16. The N figure from m. 3 first links with the tenor in mm. 5–​7. The “I” above the downward-​sloping arrow indicates the pitch inversion, while the single-​barbed point indicates the shedding of rhythmic content. (The N shape in mm. 5–​8 is partially augmented.) From m.7, the F♯4-​E♯-​F♯ N motion connects via a long, single headed arrow to the last N shape in the melody at mm. 15–​16. The multistage path, involving transfers from the soprano to the tenor and back, could be shortened by means of one single-​barbed “I” arrow linking the N shapes of m. 1 and 15–​16. The advantage of positing this more meandering route is that the aural associations between all of the little, neighboring figures are strengthened by the literal pitch-​class correspondences. The remainder of the Map excerpt given in Example 7.9 concentrates on the activity of the other main pitch motives. The rising 3rd motive from m. 2 returns literally in m. 6. It then undergoes both inversion and duration scaling (x3) to yield the stretched out 3rd in the alto in Segment 4. The arrow linking this most recent 3rd to the soprano 3rd that follows a measure later indicates a literal, surface association. It also invokes a highly specialized compositional technique. Specifically, the topic of “canon” emerges as a potential higher-​ order motive, or “premise,” to use David Epstein’s term. Presently, canon is not accorded a place in the Focal Point’s motivic complex. Were it to appear later in this CMA, we would only be able to track the association informally with the dotted, Sensed connection arrow. Of course, we could restart the analysis, selecting a different segment as the Focal Point. We will not do so in this first demonstration; however, this recent discovery should drive home the importance of diligent pre-​analysis. If one is surprised by a major compositional premise midway through study of a piece, that is a sign that one was not fully prepared to begin that analysis.

Example 7.9  Organic Map for the first section of Brahms’s Waltz in B minor, segments 1–​4.

Complex Motivic Analysis  245 We last trace the activity of the linear 4th motive. After appearing in the tenor of Segment 1, it moves to the bass of Segment 2, where it elongates into a more regular attack rhythm of dotted-​half notes. The lowest arrow linking Segment 1 to 2 specifies the pitch and contrapuntal correspondences between them. The shared bass motive ensures that the “5–​6 motion” from mm. 3–​4 recurs in mm. 7–​8 between the outer voice pair as F♯3-​C♯6 stretches out to become to E3-​C♯6. Both the pitches and regular rhythms of Segment 2’s bass 4th carry over to Segment 3. To avoid cluttering the graphic, no arrows attach to the other 4ths that appear in the soprano and alto in mm. 9–​12. This omission should inspire readers to practice developing their own explanations for these beamed figures. We could, for instance, draw three separate arrows fanning out from Segment 2’s bass 4th motive to the three beamed 4ths in Segment 3. Alternatively, we could retain the lowest curving arrow that points to the bass voice of Segment 3 and view the alto line as an upper shadow; a faint dotted arrow has been used in past examples to illustrate similar relationships. No matter which view is taken of Segment 3’s alto, I advocate using an arrow to derive the subsequent 4th in the soprano from it. In this way, the staggered 4th motives in Segment 3 can be seen presaging the overlapping canonic 3rd motives in Segment 4. Most of the meaningful content of Example 7.9 is treated by the above discussion. This leaves one or two last methodological matters to address, among them the issue of coverage. This particular Map excerpt reproduces nearly all of the pitches from Brahms’s piece, but there is no requirement that it do so. Other fine Maps are possible for this and other works that omit gestures for clarity and/​or to streamline analysis.21 There is yet another property specific to this Map that should not be generalized, its de-​emphasis on the rhythmic domain. It tracks rhythm only by means of the “x3” duration scaling sign and by maintaining the distinction between double-​and single-​barbed arrowheads. This arrow symbology is sufficient for noting how Focal Point gestures generally shed their duration profiles to manifest as pure pitch motives. For pieces in which rhythmic motives are sensed to play a more prominent role, it would be appropriate to track them in more detail. The remaining portion of the CMA Map for Brahms’s Waltz is given in Example 7.10 The notable difference in this second section is that its Local Point occurs midway through at Segment 7, which necessitates the use of back-​ relating arrows to reach Segments 5 and 6. The leftward arrow linking Segment 7 to Segment 5 is double barbed, indicating that all of the right hand’s pitch and rhythm material transfers faithfully. The leftward arrow appearing below the staves indicates that a contrapuntal attribute, the “pedal point,” transfers as well. The contents of Segments 5 and 6 are of particular interest due to their sensitive formal location. They constitute the digression area, the area of rounded binary form tasked with creating a sense of contrast with the main, thematic sections. This contrast manifests subtly at first, partly by means of delaying the

Example 7.10  Organic Map for the second section of Brahms’s Waltz in B minor, segments 5–​10.

Complex Motivic Analysis  247 linear 4th motive’s appearance. The contrast is more keenly felt in the following segment, where the intense clustering of beamed gestures appears. The pitch material in the soprano, alto, and tenor voices in mm. 21–​24 is dutifully parsed into familiar pitch shapes, 3rds and 4ths. There is also, however, a new effect created by their arrangement, a chromaticized descent in parallel sixths. The latter portions of the Map should be mostly self-​explanatory. Segment 7 does not perfectly match Segment 1. The later event is cast in major mode instead of minor and opens with a novel three-​note flourish in the right hand. Critically, because the Focal Point was defined in this mock analysis as simply possessing “grace notes,” we are obligated to treat this Local Point as identical to it. For Segments 8–​ 10, a quick scouting of their contents suggests that a kind of motivic “balancing” strategy informs the waltz’s final measures. This sense emerges as we become sensitive to two long-​range echoes of material. The first echo occurs among the pairs of segments closing each of the two main sections. In the first section, Segment 3 expresses primarily 4th-​based motives and Segment 4 mainly 3rd-​based motives. Segments 9 and 10 (end of second section) emulate this strategy. This correspondence allows for a nuanced understanding of the relationship between the segment pairs. On the one hand, the sameness of pitch motivic materials ensures continuity. Yet there is also deep harmonic contrast in the sectional closing gestures. Where Segment 3 favors parallel six-​three chord motion, Segment 9 employs a chromaticized circle-​of-​fifths chord progression. Contrast and continuity end up being different sides of one coin: the latter passage simply reharmonizes the former. The other long-range balancing idea involves the arch-​forms projected by each section’s beginning and end points. The soprano’s last melodic shape in mm. 39–​40 is a neighbor figure, which caps the descent from D♯5 initiated in m. 36. Grouped together as a “3rd + N” gesture, an informal composite motive, this passage echoes a similar shape seen at the start of this section in Segment 5. This aural association is noted by the dotted arrow arching over Example 7.10, though it also of course applies all the way back to mm. 1–​2. Recognition of this association invites scrutiny of the melody at the close of Segment 4. A similar composite motive is noted there in Example 7.9. The difference in treatment is that the N there is elided and decorated by grace notes. This last bit of discussion has concentrated on the unifying role played by the N + 3rd composite pitch motive. This Focal Point element appears at all of the waltz’s sectional boundary points in subtly varied forms. As effective as the Map is in laying bare the shifting arrangement of the N + 3rd elements, it offers no mechanism for quantifying how related the four instances of the shape are. The CMA Narrative is better suited to discern and interpret such small-​scale distinctions. By the time readers have completed their study of how Narratives are constructed, they will be in a better position to articulate the role and meaning of these N + 3rd composite motives. Narratives, as we shall see, are further valuable for handling portions of the music in which there are fewer

248  METHODS OF MOTIVIC ANALYSIS demonstrable motivic connections, meaning more desolate regions of the Map such as Segment 10.

CMA Narrative Assembly We may continue developing a sense of how CMA Maps and Narratives differ by comparing their source materials. CMA Maps investigate musical shapes directly, meaning that they traffic primarily in musical notation and terminology. Their interpretive arrow networks afford many advantages, but also drawbacks in that they can be difficult to interpret. This characterization refers not only to their dense visual fields but also to the ambiguity of arrow labels, which are not always optimal for documenting the fine differences between motivic events. Musical Narratives track content through more of an accounting strategy, meaning a mode of analysis that traffics largely in numbers. The process of Narrative construction will be briefly summarized and then illustrated in detail. As always, we begin by identifying the Focal Point in accordance with Rule 2 of Motivic Analysis. The selection will have a strong and near-​ immediate impact on the type of narrative the analysis will pursue. CMA Narrative Rule: The Focal Point of analysis shall be a motive complex coincident with a segment of the piece. The location(s) of the Focal Point will determine the species of narrative (Propagative, Accretional, Cyclic, etc.)

After selecting a Focal Point, the analyst quantifies its sub-​elements by assigning values to each domain such that they sum to 1. Next, the piece’s other segments are surveyed. Each is assigned a relative value that represents how many Focal Point elements are present. The Focal Point is automatically assigned the highest value, causing all others to be less than or equal to it. The segment values are, last, charted against time. The result is a line graph that illustrates the overall organic trajectory of the piece, the profile of which may be interpreted in narrative terms. For example, most works in which the Focal Point appears early will generate a Propagational curve that peaks immediately or very early. This high point might be followed by a lengthy decline, indicating a gradual dissolution of central materials, or by a series of upward spikes, indicating a cyclical return of Focal Point material. Works in which the Focal Point is delayed will exhibit Accretional peaks closer to the middle or right side of their graphs. It is now possible to commence with the CMA Narrative assembly process. To ensure continuity with the Map analysis, we will for the time being allow Segment 1 of Brahms’s Waltz in B minor to retain its Focal Point status. Our attention will

Complex Motivic Analysis  249 therefore concentrate on the same motivic complex from before (Example 7.6) as we transmute it to numerical form to facilitate cross-​segment comparison.

Step 1. Establish Unity Value of Focal Point The CMA Narrative assembly begins with establishing a unity. The Focal Point segment is identified and arbitrarily assigned the value of 1. Step 2. Quantify Focal Point by Assigning Values to Its Attributes If the Focal Point segment is valued at 1 (100%), all other segments will either tie this value or be scored lower. To determine how much each element within the Focal Point is worth, it is necessary to work backward, one domain at a time. Each domain within the Focal Point is initially assigned a preliminary value of 1 as well. At a later time, these will be scaled and combined to allow segments to be compared to the Focal Point. Whenever a single motivic attribute is present, the domain will be scored in binary fashion. Taking, for example, the Harmony domain, the presence of the sole “T–​D” (A5) attribute returns a value of 1 for Segment 1. It does the same for Segment 2, where the same functions apply to the boundary harmonies, F♯ minor and C♯ minor (m. 5 and m. 8). It returns zero values for Segments 3 and 4. For any domain that admits multiple elements—​ e.g., the several pitch and rhythm motives for this waltz—​fractional and/​or decimal values indicate that an incomplete set of subelements return. It is a simple matter of proportion. If the value of 1 is associated with the appearance of four pitch elements, then later segments containing 0, 1, 2, or 3 of them should be scored 0, 0.25, 0.50, or 0.75. The last step involved in quantifying Focal Point content is to determine how the domains combine, numerically. Referring back to Example 7.6, we see that the current Focal Point for the waltz is composed of eight domains, the three primary ones appearing above the bold line and the five secondary and derivative ones below. With each of the eight domains exhibiting a value of 1, one possibility is to simply average them to obtain the Focal Point’s score. That strategy, however, sets an unworkable precedent. A seeming contradiction arises, in that the five secondary domains that combine to make up 62.5 percent (5/​8) of the resultant value outweigh the three primary domains. Under an averaging scheme, this imbalance would be further exacerbated for Complexes that incorporate more secondary domains, essentially “packing the court” in favor of coloristic musical elements. Another flaw of the domain-​averaging method is that it breeds inconsistency across analyses. In one case, the pitch motive domain might be cataloged with four other domains, resulting in an effective weighting of 20 percent, where in another it might appear alongside six other domains and count for only 14 percent. My strategy for minimizing this variability calls for assigning equal weight,

250  METHODS OF MOTIVIC ANALYSIS 50 percent, to each of the main domain groupings, primary and secondary/derivative. This solution stabilizes the value of the primary domains, ensuring that each always contributes 16.67 percent (1/​6) toward the Complex’s total value. Similarly, each of the secondary and derivative domains will contribute a portion toward 50 percent of the total unity score.22 Example 7.11 illustrates how the subelements of the waltz’s Focal Point are translated into the percent values that apply in analysis. The weighting for each individual attribute depends on two factors: the value of its coordinating domain and the number of attributes it shares occupancy with.

Example 7.11  Determination of relative values of unity for each motivic element of Brahms’s waltz, domain by domain.

Complex Motivic Analysis  251 It is easier to see how weighting is determined for the lower half area of the example, comprising Orch/​Texture through Special Effects. The five domains listed there share 50 percent weighting; that means each will contribute 10 percent. And indeed, for four of these domains, the reported weighting is 10 percent. The outlying secondary domain is Counterpoint, which houses two elements that must share its 10 percent value. Dividing by two yields 5 percent weightings that are assigned to the “5–​6 motion” and the “Bass pedal” attributes. The three domains in the Primary area share the other 50 percent of the total Focal Point value, which works out to 16.67 percent for each. The last of these, Harmony, contains a single element that receives its full share of value. For the other two domains, the 16.67 percent is apportioned. It divides into three parts for the three pitch motives (three entries at 5.56 percent) and into two parts for the two rhythm motives (two at 8.33 percent). At the very bottom of the chart, all domains and elements sum to 100 percent, the value that stands for complete organic unity.

Step 3. Apply Values Template to Segments The template of attribute values developed in Step 2 is next applied to the full waltz; this is shown in Example 7.12. For each segment, the analyst considers each motivic attribute in turn. If present, it receives its full value. The 1s and 0s in the example’s spreadsheet, shorthand for “yes” and “no,” reinforce the notion that evaluating motivic elements is a binary process. Each 1 that is scored is multiplied by its “weight” before it contributes to the Total value at the bottom of its column. To demonstrate the tallying procedure, we examine the column for Segment 2. The first ten 1 values communicate that most of the Focal Point’s elements return in Segment 2; the two 0 values at the bottom indicate that the bass pedal and sforzando marking are absent. The ten 1s, multiplied by the weightings shown in the weight (%) column (third from left), yield a total of 85 percent for Segment 2, a value that accords well with our sense that the passage is highly similar to Segment 1. The advantage of listing the comprehensive cell content in Quantitative Analysis is that it offers a means for holding analysts accountable for every individual claim. In studying any segment, readers may quickly observe how its content diverges from the Focal Point. This information is highly useful if one wishes to dispute a result. The transparency of the calculation allows readers to peer inside segments and formulate a response, for example: “No N motive is present in Segment 8, despite what Auerbach claims.” The organization of Example 7.12, with its columns, percentages, and tallies, exudes objectivity. I assure readers that, in practice, narrative analysis is fluid and subjective. Cataloging the presence of an attribute is a binary process, yes, but not always a straightforward one. For example, Segment 3 registers a “yes” (1) for Orchestration/​Texture in its seventh row. This is because the parallel thirds that

Example 7.12  Full tally of motivic complex elements, with 1 and 0 values indicating their presence/absence in each segment. If yes (1), the weighted value is added to the segment’s TOTAL.

Complex Motivic Analysis  253 originally manifested among the soprano and alto now arise between the alto and bass. (The larger context for this attribute is the grander series of parallel six-​ three chords that guide mm. 9–​12; see the three beams appearing in this segment in Example 7.9). Another ambiguous event occurs in the rhythm domain in Segment 4. The triplet in m.  13 seems to hearken back to the melody of m.  1. Read literally, the triplet rhythm here diverges from the M-​S-​S-​M shape that was established as a central rhythmic motive. To my ear, though, the last G♯5 of the triplet is swallowed up by the first two notes as shown in Example Web.7.2 . Based on this hearing and its demonstrably genetic relation to M-​S-​S-​M, this rhythm attribute is scored as present in the spreadsheet. At this time, no formal mechanism exists to fully document the decision process behind scoring choices. It thus falls to analysts to find ways to share such information, for example, in a texted gloss accompanying the Quantitative Analysis spreadsheet. If an analyst does choose to include supplemental argumentation, they should do so sparingly. For one, this mode of CMA was designed to be detailed in precisely a way so as to preclude extended discussion. For another, analysts who adhere to the rules of reduction and assembly established in c­ hapters 5 and 6 will ideally already conform with peer views on motivic associations.

Step 4. Graph and Interpret Segment Totals The two Interludes of this book establish a basis for comprehending motivic succession in narrative terms. They further prescribe a means for representing these narratives. Specifically, they suggest the medium of the Narrative Curve, a line graph charting the recurrences of musical elements over time. The curves we will draw resemble those employed in literary theory to depict a plot’s rising action, climax, and denouement. There is ample precedent in music analysis, too, for curves of this type, dating back to Wallace Berry’s Structural Functions in Music. Berry’s intensity curves track “directions of growth and decline” in various domains that encode a piece’s structure (1976, 9–​10). More recently, John Rink has used such curves to reveal “the patterns of oscillation and flux . . . manifested throughout [a]‌work” (1999, 234). The main purpose of Rink’s graphs is to inform musical performance by tracing and controlling pieces’ fluctuating energies. In contrast, our graphs will primarily concern analysis and listener interpretation—​although, naturally, this information may be of interest to performers as well! We have considered the CMA archetype models only; we have yet to generate any of our own Narrative Curves. We shall do so presently in Example 7.13, using the data generated by the earlier Narrative tally. The two axes of the graph are set up according to the guidelines established in Interlude 2. The vertical axis charts each segment’s degree of relatedness to the Focal Point as a percentage value. The

254  METHODS OF MOTIVIC ANALYSIS Example 7.13  Narrative Curve resulting from graphing the total values from Example 7.12. a

digression

a’

5 6 Segment

7

Relative Unity (%) with Focal Point

100 90 80 70 60 50 40 30 20 10 0

1

2

3

4

8

9

10

horizontal axis lays out the segments in temporal order. Dashed vertical lines are drawn to indicate the division of the work into formal regions. This is done not only to aid in reading the piece in graphical format. It also communicates important information about the status of segments within the hierarchy of the piece. The Focal Point will appear as a global maximum. Within any section, the Local Point will appear as a local peak: for example, in Brahms’s waltz, Segment 5 serves as the Local Point of the digression. The main purpose of the line graph is to communicate the results of the data-​ driven analysis in visual terms. In addition, the trend line in the graph may be considered dynamically, in terms of motions away from and back toward the state of motivic unity embodied by Segments 1 and 7. The same motions may be felt as fluctuating levels of musical tension. The presence of two Focal Point events, it should be recalled, is emblematic of a Cyclic narrative. The act of classifying a piece’s main plotline is a milestone in the narrative analysis; nevertheless, we may glean yet more useful information about the Narrative Curve by inquiring into its behavior within the formal sections. For instance, we note that all three sections of the waltz exhibit the same downward trend. The descents are remarkably consistent across Segments 1–​4 and 7–​10: not a single uptick value registers. Even the digression, despite starting at a relatively low point in Segment 5, decreases in value over the course of its short length.

Complex Motivic Analysis  255 The Narrative developed in this first pass through Brahms’s waltz is one in which a larger Cyclic structure nests smaller Dissolution-​type curves. If we wished to press forward, investing this Narrative with further emotional weight, the guidelines established in Interlude 1 suggest that the initial dramatic interpretation should be conveyed in musical terms. In the case of this waltz, the motivic complex of mm. 1–​2 itself will represent the protagonist. The complex’s inclination, as indicated by the curve patterns among sections, is to gradually shed its elements. Specifically, in the span of Segments 1–​4, the soprano and alto that are at first bound together in tight double thirds relax into a looser, two-​ voice counterpoint. The strict alternation of the rhythmic motives M-​S-​S-​M and M-​M-​M that characterizes Segments 1 and 2 gives way to freer rhythmic elements, such as the triplets and dotted rhythms in Segments 3 and 4. This dissolution process is interrupted at Segment 5, mm. 17–​20, where the original pitch, rhythm, and orchestration motives return. The Complex, in response to being partially restored, again attempts to rid itself of identity-​ establishing components. In Segment 6, this is reflected in the domains of Orchestration/Texture and Rhythm, as the M-​S-​S-​M shape is dropped in favor of the more generic M-​M-​M rhythm. It must be noted that much of the tension generated in the digression, importantly, has little or nothing to do with motive at all. There are powerful formal and harmonic conventions at play. By sounding fragments of the main theme over an extended, F♯ dominant harmony, Segments 5 and 6 create a strong expectation that the full theme will soon return in tonic. This occurs at m. 25, where the Complex is fully restored. Upon its return, the waltz makes one final attempt at dissolution, which is, at last, successful. The descent of the Narrative Curve in Segments 7–​10 is steep, reflecting the rapid loss of even more attributes than across Segments 1–​4. Nearly all of the Focal Point’s complexity evaporates by Segment 10, which helps to explain the relaxed sense of closure achieved there.

Re-​Casting the Narrative: A Fuller Set of Criteria Informs Focal Point Selection The just-​completed assembly of a Map and Narrative constitutes our first complete complex motivic analysis. All parts of the construction process contained in Example 7.7’s flowchart were demonstrated, save one: “Step 2: Select a Focal Point.” In the interest of simplifying the first demonstration, we opted to base our analysis on a predetermined Focal Point, that being Segment 1. Doing so caused us to model the highly idealized situation in which a musician proceeds through analysis without any revisions or doubts. In reality, false starts and second thoughts often necessitate adjustments to an analysis even as it is taking shape. To properly

256  METHODS OF MOTIVIC ANALYSIS and responsibly demonstrate the CMA process in full, then, it is necessary to address the revision process. We will conclude our discussion of the Brahms B minor Waltz by recasting the Narrative on the basis of a different Focal Point.23 Upon first segmenting a piece, one is faced with a great many candidate spans for the Focal Point. This is not to say that all segments will produce a workable CMA: there are factors that impact the number of options. On one side, the field of candidate segments is narrowed by recognizing that not all Focal Point choices are equally good. On the other, the field is kept open by the realization that there is no such thing as an absolutely correct choice. Every candidate segment offers its own set of advantages and disadvantages. No absolute criteria can be posited for selecting a Focal Point segment. In their place, this method prescribes three guidelines to help analysts develop instincts for determining which segments will work best. Guideline 1 (to CMA Narrative Rule): Privilege musical segments exhibiting multivoice (polyphonic) complexity.

This recommendation follows from our long-​standing interest in making the Focal Point as analytically versatile a tool as possible. CMA strives to relate attributes from the Focal Point to those appearing in every other segment of the piece. The analyst’s task becomes easier as the Focal Point encompasses more and more raw material. It is further recommended that analysts choose a segment that enfolds both diatonic and chromatic gestures. Again, this preference is largely pragmatic, as it obviates the need to derive diatonic motives from chromatic ones and vice versa, analytic feats which are difficult to perform convincingly. Guideline 2 (to CMA Narrative Rule): Favor segments that are emphasized rhetorically in the music.

Such emphasis may result from a segment’s placement at the beginning or ending of a work or major section. It may also be signaled by extremes in dynamics, texture, or articulation. This second guideline is offered in the interest of creating coherent Narratives. It is easiest to defend claims that a certain musical passage is centrally important when it appears that the composer has lavished special attention on it. Guideline 3 (to CMA Narrative Rule): Favor segments that, when plotted, produce curves that conform to Narrative archetypes.

This last recommendation raises a new challenge of chronology. Previous discussion established that quantification and Narrative plotting directly depend on

Complex Motivic Analysis  257 the identity of the Focal Point. Strictly speaking, however, it is impossible to envision a Narrative Curve without a Focal Point already in place. The way out of this dilemma is to create a set of simpler, provisional analyses. To create one, the analyst picks a potential Focal Point and subjects it to the full quantification process to generate a first segment tally and curve. One then repeats the process as many times as desired, weighing various outcomes at even this early stage of analysis. In the abstract, the idea of assembling multiple analyses seems wasteful and burdensome. In practice it need not be. One can dramatically streamline the analytic process by examining a small group of potential Focal Points and seeking ways to accelerate the tallying process. One solution for speeding up quantification and tally is through automation. For those with programming experience and access to a score coded in a computer language, rendering a Focal Point into a fully fleshed graph would require little more than establishing a weighting scheme for the attributes and pushing the enter key. Alternatively, it is quite easy to pare down the scope of a provisional analysis by concentrating on a reduced set of domains, for example, only Pitch, Harmony, and Orchestration. The Narrative Curve that results would be somewhat approximate, but would exhibit enough of a profile to aid in making an informed decision. Taking into account the new selection guidelines, Segment 7 of the B minor Waltz emerges as a stronger candidate for a Focal Point than Segment 1. This argument hinges in part on Segment 7’s enhanced rhetorical weight. As the rounding is initiated at m. 25, the music experiences a miniature breakthrough as it shifts permanently into major mode. The full, two-​handed flourish at the first downbeat plays a role in this development as well. To properly account for this gesture, it will be necessary to reformat at least one of the domains from the previous analysis. One option is to account for it as an ornament related to the grace notes. Another is to recalibrate the Orchestration domain by granting full credit only to segments in which a sonority of at least five notes appears. In recognition of the flourish’s highly unique sonic quality, however, I have opted to list it as a Special Effect. Fortunately, only minimal adjustments are necessary to reconfigure our previous Focal Point complex to accommodate Segment 7. They are so few, in fact, that we can omit the step of reprinting the full image of the Complex and proceed directly to generating a new segment tally for the piece. This is provided in Example 7.14. The new, “Chord roll” attribute appears in the Special Effects row, just above the Total values. In this new tally, the attribute returns a 0 value in mm. 1–​4, reducing Segment 1 to a value of 95 percent. The only places where the roll occurs are in Segment 7, where the new Focal Point is located, and in Segment 6, where it serves as a retransition element preparing listeners for the upcoming climactic arrival.

Example 7.14  New tally of motivic complex elements based on selection of Segment 7 as Focal Point (requires tracking the presence of a new Special Effect element).

Complex Motivic Analysis  259 Example 7.15  Narrative Curve resulting from graphing the total values from Example 7.14. a

digression

a’

5 6 Segment

7

100 Relative Unity (%) with Focal Point

90 80 70 60 50 40 30 20 10 0

1

2

3

4

8

9

10

The new values in Example  7.14’s Special Effects column impact the final segment totals in a subtle but profound way. Plotting these new values yields the curve shown in Example 7.15. Comparison of this with the original in Example 7.13 reveals that the entire narrative structure has shifted. The Cyclic aspect has disappeared, replaced by a Modified Synthetic (CMA2< >) plotline. To reframe the narrative interpretation, we might say the waltz begins in media res, in a state that closely approximates the core content. The first downward sweep in Segments 1–​4 and intermediate hill in Segments 5 and 6 are retained from the earlier plot. The difference comes at Segment 7, where the music surges to its singular high point. This is where the Focal Point material, originally heard in Segment 1 in a weakened, incomplete state, emerges in major mode and at full volume. Performing the waltz live opens up the possibility for pianists to gild this moment further with a dash of expressive choreography. As they roll out the paired wide chords in the two hands at m. 25, they will naturally sway the arms and body in the grand manner of a conductor. On the occasion of recasting the Complex to generate a new Narrative Curve, we will make a single, earnest attempt to fit a specific, extroversive storyline to it. The central Complex will again serve as protagonist, with its purest form appearing in Segment 7. This interpretation will assume that listeners’ sympathies are aligned with this motive, given that its presence can be sensed in nearly all measures.

260  METHODS OF MOTIVIC ANALYSIS As we translate our musical Narrative into a more literary one, we will look to fit it into one of four archetypes suggested by Frye and Liszka. The question is whether the Complex should be viewed as a member of the social order or as transgressor. Our initial impression was that it is repeatedly attempting to shed its elements. That impulse will be reframed here as a desire to disappear, or to “escape” the waltz’s environment. With the protagonist wishing one outcome—​and the harmony and form of the piece working to constrain it—​the archetype at hand quickly takes shape. This waltz is a comedy. It begins in Segment 1 with a presentation of the Complex in slight distress. It initially appears in a subdued, minor mode. It is obligated by local tonal and formal forces to repeat in Segment 2 and to ascend in registral space. In the following two segments, it makes its own wishes clearer by sinking in register and shrugging off some of its identifying elements. In the digression, the portion of the form traditionally associated with high tension, the protagonist must adapt to a new tonal setting, the dominant minor key. It does so uneasily, reappearing in mostly recognizable form but also actively searching for a way out. Note where the inexact repetition of mm. 17–​18 into the following two measures results in a new, leaping contour in the melody at m. 20. This represents a temporary abandonment of the linear 3rd shape first established in m. 2. In the throes of this small identity crisis, the protagonist gathers its strength in Segment 6 and arrives in triumphant form at m. 25. At that moment, the core Complex reappears in major and in its loudest, most confident form. Whatever forces had earlier caused it distress now seem wholly absent. In Segment 8, it rises in pitch register, but not nearly as high as it did in Segment 2. Having transformed the mode and sound of the waltz—​in other words: having triumphed over the social order—​the protagonist skips, lighthearted, to a contented conclusion. The glib repetition in Segments 9 and 10 of the M-​S-​S-​M rhythmic element, along with the “pat” circular-​fifths harmonic progression, confirms the lingering impact of the Complex’s transgressive act in Segment 7. The piece will end in major and in its lowest register. The comedy archetype advanced here allows for listeners to graft any number of stories onto this waltz. Presuming Liszka’s formulation remains in effect, however, makes it likely that those stories will exhibit a fair bit of overlap. There are only so many ways to frame a tale of a protagonist confronting and overcoming a social constraint. One could, for example, imagine the waltz depicting a teenager challenging the exclusionary rules of his school or club, or a moral politician who effects change on a corrupt government by working from the inside. My own inclination is to view the protagonist as a paired couple in a forbidden romance, who persevere through adversity and win the approval of their families. Or maybe they just elope. All of these are equally possible. One can choose one plotline, or

Complex Motivic Analysis  261 many, or none, depending on the answer to the question: does the presence of a story enhance one’s intellectual and emotional response to the music?

Conclusion to the Methodology Area The analytic cadence closing out the CMA demonstration of the Brahms waltz also marks the structural conclusion of Musical Motives’s methodology section. The first task of this brief, final coda to c­ hapters 4–​7 will be to encapsulate its material. To that end, Example 7.16 retrieves all of the main rules for BMA and CMA and condenses them into a single chart. Example 7.16  Summary of rules for motivic analysis. Preliminary Rules Reduction Rule 1 (RR1): Contour Reduction Rule 2 (RR2): Rhythm/Meter Reduction Rule 3 (RR3): Larger span conditions Global Rules

Rule 2 of Motivic Analysis: Presence of Focal Point BMA and CMA Specific Rules

Archetypes Propagation

Rule CMA1: harmonic root motion

Rule CMA2: Map and Narrative

CMA Map Rule (hierarchy)

CMA Narrative Rule yields

BMA Narrative Rule: Focal Point at outset yields

Approximate order in which rules apply

Rule 1 of Motivic Analysis: literal associations

Archetypes Propagation Accretion Cyclic

262  METHODS OF MOTIVIC ANALYSIS The top-​down organization of Example  7.16 loosely reflects the order in which the rules apply in analysis. The Reduction Rules from ­chapter 5, designated as Preliminary Rules, apply even in the pre-​analytic stages, when one is surveying a score to determine what motives of significance may lurk within its highly active textures. (They, of course, continue to apply to all subsequent stages of analysis). The Global Rules are central to the philosophy of both BMA and CMA, and apply as soon as an analysis proper is initiated. The latter of these, Rule 2 of Motivic Analysis, entails the bifurcation of the method into the BMA and CMA approaches. If the Focal Point of a piece is determined to be a simple pitch-​ and-​rhythm event located at the start, BMA analysis will commence along with its attendant archetype shown in the left region of the lowest box. If the Focal Point is determined to be complex and/​or is located at a central or late segment of the piece, CMA analysis will commence in the right region. This southeast path entails a further split into Map and Narrative assembly, with the latter attended by its three potential interpretive plotlines. The moment that the presentation stage of an analytic methodology concludes is the moment where critical evaluation, and hopefully constructive revision, may come to bear on it. To facilitate that endeavor, I have strived to maintain transparency in all authorial choices. To defuse any potential misinterpretation of CMA, I would like to make a few last comments to clarify its significance and scope, which—​despite its far-​reaching applications—​are both meant to be modest. At the outset, I wish to dispel any notion that the techniques of narrative analysis put forth in this chapter offer the only path toward dramatic readings. It is safe, in other words, to assume that the plotlines proposed for this waltz are discernable by other means, including engaged listening. Our initial classification of Brahms’s waltz as a rounded binary form piece, for example, hinged on an awareness that core material from the beginning returns in its latter half. This fact makes it likely that any Narrative Curve posited for it will exhibit some kind of two-​peak profile. A more accurate and productive view of narrative analysis is as a member of a conceptual triad. Sounding music, motive, dramatic/​emotional narrative: all three aspects must be accounted for because they inform and support each other. We noted the importance of musical intuition for guiding us at all stages of analysis, from the initial parsing of segments and form, to the formatting of pitch-​ rhythm and coloristic motives, all the way to gauging the “fit” of the Narrative plotline. Of course, intuition is too subjective to stand on its own. Its insights must be grounded in concrete details. In CMA, such details are supplied by the complex motive and, in the end, the meta-​narrative, be it musical or otherwise. The inclusion of this broad array of elements provides a means for evaluating our musical intuitions with a raised degree of exactitude.

Complex Motivic Analysis  263 Another point to keep in mind is that the results obtained through CMA do not represent secret knowledge unobtainable by other means. Much of the novelty of the CMA method is, in fact, couched in quite pedestrian terms, specifically, the quantification and tallying mechanisms. Not all of it is, of course. The exception in this regard is the new explanatory power offered through CMA’s dual output branches. Complex motivic analysis is most effective when it is put in dialogue with itself, as when the visual plot of the Narrative is read in the context of the Organic Map graphic. This strategy helps analysts to pinpoint the influence of specific events within the larger trends shown by the curve. In the case of the Brahms waltz, for example, the claim that the Focal Point “dissolves” or “evaporates” over the final four segments is supported by reading the Organic Map and observing how the 4th motive quite literally vanishes from sight and hearing.

PART III

ANALYSE S A N D C ONCLU SION

8

Analysis of Three Works in Contrasting Styles The three analyses presented in this chapter expound on the theory and methodology presented in ­chapters 5–​7. The first of these, an abbreviated complex motivic analysis (CMA) of a piano piece by Cécile Chaminade, reinforces the content of ­chapter 7 by again taking readers through the processes of Narrative construction:  segmentation, Focal Point selection, quantification and tally, and the drawing of the Narrative graph. The other analyses, one BMA and one CMA, examine modern works in other genres, a Broadway number by Marvin Hamlisch and a song by Radiohead. These two works are texted, offering readers a model for how to integrate a piece’s literal poetic and/​or theatric meaning into an account of its motivic activity. As a group, the three analyses are intended to bolster the claim that motivic analysis applies broadly to music. These selections are steeped in Western traditions, so are not terribly diverse as measured on a global scale. They do diverge with regard to their time periods and aesthetics, however. As such, it is hoped that this brief foray into the late nineteenth-century salon, the Broadway playhouse, and the alternative art-​rock album can point the way toward a future in which motivic analysis is extravagantly applied to any music that might stir readers’ passions.

“L’Ondine,” Op. 101, by Cécile Chaminade Method: Complex Motivic Analysis Narrative Profile: Modified Cyclic The first analysis examines “L’Ondine,” Op. 101, a character piece for piano by Cécile Chaminade (1857–​1944). Although she is a somewhat lesser-​known figure today, in her time Chaminade enjoyed great success both as a touring performer and composer throughout Europe and America.1 For better or worse, she is best known for her smaller, salon-​type compositions, songs and solo piano works that number into the hundreds. Of course, a work’s size implies no indication of its quality. It is only fair, then, to assume that examination of a polished Musical Motives. Brent Auerbach, Oxford University Press. © Oxford University Press 2021. DOI: 10.1093/oso/9780197526026.003.0010.

268  Analyses and Conclusion miniature by this expert French composer would repay similar analytical dividends as of any by a close contemporary of hers, such as Maurice Ravel, Amy Beach, or Gabriel Fauré. “L’Ondine” is an engaging work that takes approximately three minutes to perform. The score of the piece, with segmentation, appears in Example Web.8.1 . The work is loosely programmatic in that its title names a water sprite. The short lead-​in of mm. 1–​2 introduces an arpeggiated texture, a figure long associated with flowing water. This arpeggiation is explored throughout the work, with longer and longer stretches of it creating a wave-​play effect of notes sweeping up and down in register. The design of the piece is straightforward in many respects, including its phrase structure and tonality. Most of the phrases of “L’Ondine” take up four or eight measures and feature clear cadences: many of these are perfect authentic cadences (PACs), though a good number of plagal cadences appear, too.2 Tonally, the piece is firmly rooted in E-​flat major, with all but one or two of its phrases beginning on a tonic or dominant harmony. In declining to pursue some of the more traditional avenues of development, such as directed tonality, the piece achieves its dramatic effects primarily by means of its novel formal organization and motivic development. In its first minute, the piece lays out all three of its compositional modules. The first, occurring as a material in mm. 3–​10, features a graceful melody that starts on E♭6 and descends an octave; the melody floats above supporting arpeggios in the left hand that emphasize beats one and three. The b idea, first introduced in mm. 11–​ 14 (Segment 3a), presents another simple melody. This one, however, appears more calmly in mezzo-​forte dynamics and in chorale-​like block chords. Upon its immediate repetition at m. 15, the b idea is ornamented by triplet-​sixteenth figuration, with melodic guide tones sounding in the pinky of the right hand. The c material, first appearing in mm. 19–​23 (Segment 4) also employs block chords, but the sound is more severe. The dynamics are fortissimo, with heavy accents written in. There is also no longer any real melody to speak of: all we hear is repetition of a three-​note fanfare, followed by a low-​register echo. Most returns of the three modules, the main melody (a), repose melody (b), and fanfare (c), are literal. The only music that resists classification is mm. 32–​41 (Segments 7–​8). The texture and melody in the first two measures, 32–​33, derive from a, but a new cadence appears in mm. 34–​35 that features a curious new rising figure in the melody. This music leads to what feels like truly novel material in mm. 36–​41. The texture in this effervescent, veloce segment is almost completely overtaken by arpeggiating triplet-​sixteenth notes. There is little sense of melody aside from the brief fragments expressed in the top voice of the right hand, and little sense of harmony beyond the alternation of B♭s and Gs in the bass voice’s strong beat attacks.

Analysis of Three Works in Contrasting Styles  269 One question about “L’Ondine” that presents early on concerns the role of mm. 33–​41 within the form. It is possible to say that the segment constitutes an altered a section, with four measures of conventional a material followed by a new transition leading to the return of b in m. 42. The alternative view regards mm. 36–​41 as autonomous and wholly new. Under the terms of that reading, remarkably, the a material, mm. 32–​35 would act as transition to new d material starting in m. 36. Either reading can work; however, the latter is preferable due to an important reprise of the veloce section. When the d material returns in mm. 67–​74, its status is elevated. In contrast to before, where it served a transitional role, it here acts as a concluding gesture that is appropriately set in tonic. The next question about form asks whether a coda is present and where it might begin. To advocate for a coda, we would note that the piece feels thematically and tonally closed at m. 67, when the a material cadences in E♭ major one last time. The passages that follow recapitulate the fanfare, c material and—​as just discussed—​the flowing d veloce music. This late return of material is satisfying, but is it organically necessary? (If yes, then it participates in closing the body of the piece and therefore does not provide “extra,” coda padding.). There are a number of ways to argue that it is, beginning with the appeal to the sonata principle. The c and d materials originally occurred in the dominant key; at the end of “L’Ondine,” they settle into the tonic, providing long-​range tonal resolution. Proceeding in accordance with decisions made in the previous discussion, Example 8.1 diagrams the areas, themes, and keys in the work. “L’Ondine” presents as a rotational form, in which the starting set of ideas, a-​b-​c, is traversed three times. The first rotation, taking up mm. 1–​23, presents the core segments in order. The second rotation of material begins with the return of a at m. 24, and then incorporates a brief bit of new material, d, before continuing on to the b and c sections. The final rotation beginning at m. 55 omits b, but compensates listeners with a final set of cadences that confirm tonic and help balance the durational proportions of the rotations. The modest dimensions and mostly monochrome tonality of “L’Ondine” point to a deeper analytic challenge, which is identifying the source of its drama. The piece is quite tempered in its emotions. Entire sections, in fact, unfold in soft, simply built 4+4 phrases in E♭ major. Even the flowing d material, though faster and chromatic, is restrained by piano dynamics and even, legato phrasing.3 At first glance, only the c idea stands out as at all passionate. It is extroverted, with grand dynamics and thick chords in alternating registers. It is also harmonically the most adventurous music, introducing the tonally remote chords, G♭ major, B♭ minor, and an augmented sixth chord and fully diminished seventh chord, both built on G♭. These chords come about in part from the descending chromatic line in the soprano voice, which descends measure by measure from G♭6 through F, F♭, and E♭.

Example 8.1  Form of Chaminade’s “L’Ondine,” Op. 101.

Analysis of Three Works in Contrasting Styles  271

Analysis of “L’Ondine” The standard procedure in motivic analysis is to scan the opening of the piece in search of pitch and/​or rhythm shapes of potential future significance. The texture in mm. 1–​2 already suggests some motives of interest. There is, first, the undulating 4ths idea expressed in the bass voice as E-​flats and A-​flats alternate on strong beats. The top voice of each measure’s arpeggios, the B♭4-​C5 melody stated on beats 2 and 4, create a 2nd shape. Both of these shapes are retained in the accompaniment in mm. 3–​7, where the first fully realized melody enters and the piece truly begins. This music introduces two new motivic ideas, the dotted quarter-​and-​eighth note rhythms in mm. 3–​4 and the longer melodic descent taking up mm. 4–​5. All of the motives cited so far resonate throughout the piece, meaning that any could serve as the basis for a BMA. The problem is that they return often and unvaried, which will make for rather uninspired analysis. They are also completely diatonic, which diminishes our ability to associate them with the contrasting, chromatic materials introduced in the c fanfares and the veloce passages. Any full BMA that results, then, will likely skip over these passages, leaving many score events unilluminated. To address this shortcoming, we shall opt for an abbreviated CMA. This frees us to seek out the most distinctive musical ideas—​whose appearance may be delayed well beyond the start—​and to use them to interpret the full piece. We begin with the preliminary segmentation having already been carried out; this is, again, shown in Example Web.8.1 . We initiate the CMA by seeking the segment that will serve as Focal Point. The strongest candidates will exhibit high complexity in terms of their counterpoint and their chromatic content. We may immediately exclude Segments 8 and 14a/​ b: although the surface harmonies in these veloce areas are remarkably varied and contain many chromatic tones, there is no counterpoint to speak of. (The boundary tones of the right and left hands are the same note, indicating basic chordal planing.) This leaves Segments 3b and 4 (along with their close matches in segments 9b, 10, and 13)  and Segment 7 as the strongest possibilities. The attributes that make Segment 4 attractive are its forte dynamics and bold accents, the grand leaps among the voices in wide register, and the aforementioned chromatic line in the soprano, descending from G♭6-​E♭. Segment 7 carries a forte indication and marcato accents, and it features a chromatic linear fragment in the alto voice in mm. 33–​34: C♭6-​B♭5-​A. This segment, critically, includes all of the main elements listed for Segment 4, plus others, such as grace notes and a quarter-​note triplet rhythm in the melody in m. 33. (These elements are all present in Example 8.2.) It is true that this specific form of triplet does not occur elsewhere; however, its general “triplet-​ness” can

272  Analyses and Conclusion Example 8.2  Segment 7, mm. 32–​35, as Focal Point.

Example 8.3  View of the fanfare material in mm. 19–​23, as structured by two motives in counterpoint.

be associated with all of the passages that contain triplet sixteenth figuration. The most compelling aspect of this segment is the novel melodic idea that concludes it in mm. 34–​35. The plagal cadence there supports the rising line, F5-​G♭-​A♭-​B♭, which owes its distinctive, modal sound to the presence of whole tones below its tonic. This motive will be labeled by its functional solfege in the local key of B♭ major as sol-​le-​te-​do (5̂ ↓6̂ ↓7̂ 1). A quick, comparative survey of the other segments confirms Segment 7’s suitability as a Focal Point. Our new interest in seeking out sol-​le-​te-​do gestures, for instance, leads us to note first that the main theme of the piece as stated in mm. 1–​10 avoids stating any notes on D. There is, in other words, a conspicuous lack of any type of 7̂, ti or te. This is a status (problem) that calls for redress at some point in the form of a melodic fill. Choosing Segment 7 also allows a more cogent reading of the fanfare, c material from mm. 19–​23 (Segment 4). Earlier discussion fixated on the most obvious motive in that passage, which is the soprano’s chromatic descent. Looking again, it is possible to view the c material as grounded by the pitch-​class 2nd, D♭-​E♭. In Example 8.3, an enlarged version of this shape is shown occurring in the tenor among all downbeats. The last E♭, transfers to the soprano in a way that allows the motive to ingeniously bridge the formal boundary leading to the return of a in m. 24. The pitch motive content of Segment 4 reveals this c fanfare material to be highly organic to the rest of the piece. Once one looks past the shocking new

Analysis of Three Works in Contrasting Styles  273 sound of the texture and chromatic triads, one can see the two-​voice motivic counterpoint undergirding it (see beams). The next steps of the CMA call for defining/​quantifying the Focal Point’s attributes and documenting their presence in Segments 1–​15. The former task is easily dispatched. In the primary domains, the pitch and pitch-​class motives have been established as the D♭-​E♭ second and the sol-​le-​te-​do (5̂ ↓6̂ ↓7̂ 1) melodic ascent. In some cases, the two attributes appear together and their score is compounded, but this is not always the case. The rhythm motives are “dotted rhythms” and “triplets” of any size. No harmony attribute is listed in this abbreviated CMA; the piece is tightly unified in this primary domain by the strong plagal progressions that appear in every segment but the last. This leaves the secondary domains, which are defined as the Texture attribute, “arpeggiation,” the Dynamics attribute, forte, and the Special Effects attribute, “grace notes.” Each of these domains and attributes is listed at left in Example 8.4(a), along with its weighting. Segment 7 is scored as 100, as required by CMA. All but one of the chart’s attributes are scored as 1s or 0s. An anomalous 0.5 value appears in Segment 8’s Grace note category. This improvised score describes the faux-​grace note, G6, that occurs in m. 39 when the left hand reaches over the right. The effect is not a true grace note, but it is not exactly not a grace note, either. The Narrative Curve is printed in part b) of the example. Due to the rotational form of the piece, the Curve accords most closely with the Modified Cyclic archetype. Though there is only one peak, there is a clear correspondence in the Curve between the first irregular “M” shape traced in Segments 1–​6 and the second traced in 8–​12. The close similarity in profile between these two regions of the Narrative Curve is remarkable, first, in that it appears despite significant differences in material. The starting points of each, Segments 1 and 8, differ strongly in their sound and mood. The former presents a relaxed, lyric melody, in contrast to the latter’s less tuneful, virtuosic passage. They differ in their degree of relatedness to the Focal Point, but only by about 8 percentage points. Further comparison of their column attributes confirms they have much in common. Both segments feature arpeggiation, even if it unspools at wildly different rates, and both fully lack any pitch-​motive content established as central in Segment 7. These masked correspondences facilitate an interpretation of Segment 8 as a varied return of Segment 1. The piece would be fully Cyclic all the way through Segment 12 if not for the isolated peak at Segment 7. That means that, in the context of this particular Narrative, the Focal Point’s appearance interrupts the work’s even keel. The intrusion occurs specifically in the domain of pitch, as the melody states the linear D♭-​E♭ shape in both measures 32 and 33 and then concludes with the novel sol-​le-​te-​do formula in m. 34–​35. What of this seeming paradox, that a Focal Point could somehow intrude on the work generated from its content?

(b) Resulting Narrative curve, with rising trendline (dotted).

(a) Tally of Complex elements.

Example 8.4  The Narrative of Chaminade’s “L’Ondine,” Op. 101

Analysis of Three Works in Contrasting Styles  275 To resolve this potential conflict, we note the long-​range, accumulative impact of the Focal Point’s “new” pitch materials. The stepwise D♭-​E♭ gesture, first of all, is not truly new here; it is introduced as early as Segment 4. As earlier discussion indicated, this 2nd gesture is hidden in plain sight in mm. 19–​23 below the descending-​chromatic line of the soprano. It functions there to imbue the music with its first real sense of harmonic variety through the introduction of flatted-​ root chords (mixture). More importantly, it contributes to the moderate upswing in relatedness values in this area of the Curve: compare the hill of Segments 3b–​5 with the valleys of Segments 2, 3a, and 6. The pitch motives in the Focal Point segment individually fulfill the conditions of “D♭-​E♭” motion and sol-​le-​te-​do. The two gestures are separated in time, however, with the D♭ motive occurring in mm. 32–​33 and the sol-​le-​te-​do motive occurring in mm. 34–​35. The latter gesture, moreover, cadences strongly but on the “wrong do” of B♭. Although the motivic content is fully unified in Segment 7, the piece remains tonally unresolved and will press further on. Spurred on by the requirement to seek a final E♭ tonic resolution, the music launches a highly energetic, veloce segment (Segment 8) that explores arpeggiation and flat-​inflected harmony to an even greater extent. Near its end in m.41, the segment attempts to reconcile/​normalize sol-​le-​te-​do by steering the soprano melody through sol-​la-​ti-​do in E♭ major. The music declines the offer to cadence, and instead employs B♭5-​C6-​D-​E♭ as a bridge gesture to reach b material in the dominant key at m. 42. The Narrative Curve descends precipitously in Segment 8, reflecting the music’s failure to retain the primary pitch motives explored in the previous segment. Once it is diverted back to b material, the piece retraces its steps by literally restating Segments 3a/​b, 4, 5, and 6 as Segments 9a/​b, 10, 11, and 12. What remains is for “L’Ondine” to solve the question of the relationship between the primary motives. It does so in Segment 13, and the motives are fused together in the tonic key. The last melodic gesture of the work comprises the four downbeats in mm. 64–​67. B♭-​C♭-​D♭-​E♭ are the sol-​le-​te-​do that leads to tonic. This gesture, it may be noted, literally includes the D♭-​E♭ 2nd motive, and it restores the scale degree 7 tone that was missing in the melody in mm. 3–​10. It is true that the presence of the Focal Point’s two pitch/​pc attributes does not have nearly the same impact on the Narrative Curve here as it did in Segment 7; however, it is significant enough to elevate Segments 13, 14a, and 14b to a new plateau. The higher scores of these last four segments nudge the overall trajectory of the Curve upward, as indicated by the dotted trend line drawn across Example 8.4(b). The gently positive slope of this line indicates the work’s gradual rise in organicism. Awareness of this fact expands our appreciation of the piece’s subtle pacing and meticulous design. In one sense, it embraces a lyrical, almost timeless aesthetic, in that it is built of blocks of material that seem to alternate

276  Analyses and Conclusion more than to progress. In another, though, it bows just enough to tonal and narrative conventions of forward development to allow it to register with Western-​ trained listeners as directed and purposeful.

“Paranoid Android,” by Radiohead Method: Complex Motivic Analysis Narrative Profile: Cyclic Radiohead’s “Paranoid Android,” from the 1997 album OK Computer, is widely recognized as a triumph of modern popular music. Lasting over six minutes, it is considerably longer than the average rock song, and its span is loaded with an impressive richness of ideas. According to Radiohead’s bassist, Colin Greenwood, the song was in fact created by fusing together three works under separate development by band members (Jabba 1998). Traces of its additive origins can be heard in the work’s heavily demarcated ABCB structure: the final formal area briefly recapitulates the energetic B section, causing the song to end in a high-​energy state. There are many more ways in which “Paranoid Android” is exceptional. There is, for one, the matter of its lyrical and textural content. The sung text, reprinted in Example Web.8.2 , is replete with vivid, violent imagery and raw emotion. The lines of the A section communicate the singer/​protagonist’s malaise, exhaustion, and misery. At a prominent place in that section’s refrain area, a computerized voice accompanies the singer’s human wail of “What’s that?” with the sotto voce statement, “I may be paranoid, but (I’m) not an android.”4 The text in the B section reorients the singer’s point of view outward as he observes a parade of despised “others.” The people, listed in a series of unnamed “you”s, are projections of nameless young-​urban-​professionals that he imagines being subjected to punishment. Allusions are made to firing squads, beheadings, and cleansings by fire. The anger within the text gives rise to the most explosive passages of the album, marked by screams and heavy distortion. The last block of text in C manages to contrast with both of the sections preceding it. The primary content is a plea to an unknown entity to “Rain down on me From a great height.” The protagonist seems to be seeking some response from the heavens, either absolution for his sins in the form of a cleansing rain, or further punishment for them in the form of more torments. After its first presentation, the verse repeats two more times. In its third and last iteration, another text that revives the B section’s imagery (“crackling pigskin,” “screams,” “yuppies,” “panic,” and “vomit”) sounds against it in verbal counterpoint. The final line of the C section relates the

Analysis of Three Works in Contrasting Styles  277 aphorism, “God loves His children,” in a perfunctory, sarcastic manner that all but obliterates its sentiments of consolation.5 This first gloss on the lyrics notes two separate locations in which the words emerge out of separate channels, literally invoking a sense of fractured identity. The interplay of voices in A is particularly confounding. Is the quiet, unnerving computer voice an outside consciousness, or is it a subliminal aspect of the protagonist’s mind? (One may, of course, wonder whether there is any difference between the two possibilities.) The whole of OK Computer is pervaded by a specific type of anxiety, specifically that concerning the human identity in an increasingly digital world. Many tracks on the album incorporate the sounds of static crackles and distortion that render both sung and instrumental tones into feedback. The computer voice appears elsewhere, too. It is the most prominent element of “Fitter, Happier,” a short piece that features the voice reciting a human welfare “checklist” (e.g., “Not drinking too much, Regular exercise at the gym”) over a wash of tones and Musique concrète-style sound samples. The goal of this analysis is to illustrate how the motives of “Paranoid Android” contribute to its powerful statement on anxiety, anger, and modern-​day self-​ construction. It should be noted that this argument for unity will gently contradict Radiohead’s own comments about the song. Colin Greenwood at one point declared that “Paranoid Android” is about “nothing” of significance, and that they assembled it in this fashion “as a gag” (Jabba 1998).6 This claim holds more than a kernel of truth, certainly. The band’s general irreverence toward the song is confirmed by accounts given of early performances of the work: “When we started playing it live, it was completely hilarious,” recalled O’Brien. “There was a rave down section and a Hammond organ outro, and we’d be pissing ourselves while we played. We’d bring out the glockenspiel and it would be really, really funny.” (Doheny 2002, 62)

This attitude is further reflected by their choice of the Swedish animator, Magnus Carlsson to create the song’s music video. He did so in the unpolished style of his animated series, Robin, which follows the exploits of a young, unemployed city dweller who wears a distinctive purple hat. In the video for “Paranoid Android,” Robin and his friend, Benjamin, encounter a host of surreal, seedy people. Most of them threaten Robin and Benjamin in some way: verbally, sexually, and physically. Despite this, the main characters remain curiously unfazed and emerge from the cartoonish violence unscathed.7 The band’s comments on “Paranoid Android,” while revealing, are also ambivalent. Radiohead’s denials that the song holds any deep significance are so many and so forceful as to render them suspect. Artists of all stripes are well known to make nihilistic comments about their work so as to close

278  Analyses and Conclusion off questions from fans and critics that they have grown tired of answering. Brahms, for example, upon being asked what he had learned from his mentor, Robert Schumann, responded: “nothing but how to play chess” (Kalbeck 1908, 125). Beyond general supposition, the strongest evidence attesting to the band’s serious regard for “Paranoid Android” is that, following its recorded release, they rehearsed it for more than a year in order to perform it live (Rip It Up, 2001).

Analysis of “Paranoid Android” The compositional complexity of “Paranoid Android” has attracted the attention of many previous analysts. René Rusch and Brad Osborn, writing separately, both investigate technical aspects of the work. Their goal in doing so is more to lay bare Radiohead’s compositional process than to provide an interpretive reading of the song. Nevertheless, many of their observations will resonate with the account given in this section. A common thread in these authors’ studies is interest in explaining the work’s seeming harmonic disunity. Section A, which begins in the key of C minor, also implies G minor as tonic. The B section, which begins in A minor, shifts toward a C tonal center for its vamp interludes in 7/​8 meter.  The C section, written as a passacaglia (ground bass), is tonally ambivalent as well, orienting around both C minor and D minor tonality, the latter of which is supported by numerous prominent A major chords. Rusch 2013 is content to leave the tonal ambiguity of the piece unresolved, citing the ever-​present pull between each section’s pair of tonic candidates as a steady source of “tension” in the music. Osborn’s harmonic analysis, which focuses on Part C as opposed to the full work, closely aligns with Rusch’s. The difference is that, instead of concentrating on the harmonic poles of C and D themselves, he is more concerned with the wrenching harmonic transitions between them, as when the A major chord at the end of the Passacaglia moves directly to C minor to restart its loop instead of “resolving” to D minor as expected (Osborn 2017, 156–​158).8 Another trait shared by the two authors is their ambivalence on the matter of whether “Paranoid Android” coheres as a whole. Osborn states in an early chapter that the work resists unity at multiple levels. Parts A, B, and C, he notes, “are not only completely independent of one another thematically, but also feature different organizational strategies” (2017, 35). He later retreats slightly on this point by associating “the immediate juxtaposition of C minor and D minor pitch centers” in the C area with tonal pairings heard “in each of the song’s [other] major sections” (2017, 158). The three formal areas, in other words, are unified in their reliance on double-​tonic complexes.

Analysis of Three Works in Contrasting Styles  279 Rusch similarly begins with an observation about disunity, pointing out that “each main section” of the song “features its own motives, phrase rhythm, and tonal areas.” Soon after, however, she makes two specifically motivic claims about connections between the song’s formal areas. One of these concerns the prominent, descending chromatic bass lines of the Passacaglia (C3-​B2-​B♭-​A), which “can be heard as a variant of the bassline that connects “A minor and C major in the B section” (Rusch 2013, §2.8). Elsewhere, she makes an important aural association between separate moments in A that arise from the note collection G-​A-​B♭-​E. In Example 8.5, this collection is shown appearing in the context of a Gmin+6 cadence sonority in mm. 3–​6; it returns in mm.17–​19, where it composes out a three-​measure gesture that transforms a G minor chord into an E7 chord (Rusch 2017, §2.5). The same four-​note sonority will play a central role in the analysis to follow. When the time comes for listing the reasons for selecting Segment 7 as Focal Point, the connection Rusch observes will be cited. With this short literature review concluded, it is now possible to initiate the CMA process for “Paranoid Android.” Segmentation of the work is not difficult, due to its straightforward phrase structure. The patterning of the harmonies and textures strongly suggest that, at an assumed tempo of q = 100, most phrases last 4–​8 measures.9 Strong cadences appear regularly. Closure within the B area is routinely signaled by syncopated, descending 3rd chromatic gestures on C3-​B2-​B♭-​A stated in unison by the guitars. Conventional half and full cadences appear throughout the chorale-​like C section. The transcription of the work given in Example Web.8.3 will serve as the basis for our analysis. The graphic indicates the basic segmentation of the work, as well. The only complication that arises when parsing “Paranoid Android” is posed by all of the material repetition in C. Strictly speaking, the music of Example 8.5  Rusch’s Example 2b (2013), showing shared harmonic content across segments in Radiohead’s “Paranoid Android.” Transformative arrows at the bottom are added by the author.

280  Analyses and Conclusion mm. 74–​105 takes up eight four-​measure units of music. At the same time, the passacaglia-​like progression, which is built on a “lament bass” of sorts, produces the effect of a fourfold repetition of a two-​segment idea. This interpretation is reflected in the use of the lowercase letters a-​d, which respectively signal the first, second, third, and fourth passes through each recurrence of Segments 12–​13. For those who lack access to the full score, the summary diagram in Example 8.6 will likely be of aid. The next stage of CMA that follows segmentation is selecting a Focal Point event. To make this decision, we first survey the piece to determine where the dramatic high points are and to gain a sense of what motives recur. The list of segments with enhanced rhetorical significance includes numbers 1, 4, 7 (this essentially a written out repeat of 4), 10, 11, 12d, 13d, and 15. Of these, the weakest candidate segments are numbers 1, 10, and 11. Segment 1 is, in this case, listed mostly out of habit. Due to its placement at the outset, listeners attend fully to it and are transported into the sound world of the piece. A further, pragmatic reason for always reserving consideration for Segment 1 pertains to Narrative construction. We have not yet begun assembling a dramatic reading of this piece. In case that we eventually want to posit a Propagation plotline, it makes sense to argue for Segment 1’s privileged status early on. Segments 10 and 11 are included because they exhibit high levels of intensity. The first of these follows up the bareness of Segment 9—​which consists of little more than a menacing, semitonal undulation—​by adding a vocal scream element. Segment 11 continues with a no-​holds-​barred guitar solo characterized by “screams” created with high notes, tremolo, and feedback. While the raised energy of these segments merits their inclusion in the original list, other factors weaken their bid for rhetorical preeminence. Segment 10 is in nearly all regards weaker than 11 in volume and intensity, so it cannot serve as a high point. Segment 11’s standing is compromised by a noteworthy textural deficiency, in that it has no vocal component at all. Each remaining candidate segment can be thought of as the most complex and/​or intense unit of its section. Segment 4 (and its mirror, 7) acts as the representative for the A material. Segments 12d and 13d, constituting the densest rotation of all music stated in mm. 74–​105, act as the rhetorical representatives for C material. Segment 15, which caps the piece off with even more extreme feedback and electronica effects, serves as the most extreme version of B material. A further important development in this segment is the reintroduction of distorted human voices as a noise element. The presence of this element not only fills the textural gap noted in Segment 11. It also will successfully register as a scorable element if we, as one may fairly expect, find a way to establish the topic of human/​computer duality as a Focal Point attribute.

Example 8.6  Form of “Paranoid Android” in terms of sections harmony, and segments.

282  Analyses and Conclusion As we survey the score for prominent recurring motives, we must be vigilant for shapes residing in both Primary and Secondary (i.e., the structural vs. coloristic) domain categories. We begin with rhythm. We need not look far for signs of a recurring shape: the rhythm guitar presents it at the outset in mm. 1–​3. The rhythm in question is a stylized backbeat gesture that activates beats 2 and 4. A key characteristic of this “Backbeat” motive is the presence of submetrical syncopation, which results in some of the surface attacks to be “pushed” ahead by a sixteenth-​note pulse, as shown in Example 8.7(a). The Backbeat motive is maintained throughout the A section, including in Segment 4 where it forms the basis for the synthesizer’s more ornate figuration (Example 8.7(b)). The question of whether the Backbeat idea appears in the B area is open to debate. Its presence may be felt in many of the 4/​4 measures, such as at m. 42, where the unison melodic leaps to pitch-​class C cause beats 2 and 4 to be accented. Overall, though, Backbeat’s role is weakened here, as cross-​rhythms are introduced to the texture (see the last half of m. 42) and as contrasting grooves in 7/​8 time are explored. The Backbeat motive returns strongly in the C area, however. It appears in m. 74 in the foundational layer of the passacaglia (Segments 12a and 13a). Notably, in the last 12d–​13d rotation, this motive provides the backbone of the last vocal countermelody.

Example 8.7  An important rhythm motive in “Paranoid Android.” (a) “Backbeat” emphasis in Segment 1. Submetrical syncopation, shown by dashed arrows, sharpens the sense of accent on beats 2 and 4, shown in bold arrows.

(b) “Backbeat” returns ornamented in the synth voice in Segment 4.

Analysis of Three Works in Contrasting Styles  283 In the realm of pitch, we note the prominence of linear 3rds as early as Segment 1. (Readers may refer to the full score of the piece to verify the presence of all of the following motives.) The bass ascent from G2 to B♭ in m. 3 is immediately answered in mm. 4–​5 by the lead guitar’s descent from B♭4 to G. Throughout the rest of the A section, the 3rd motive appears as an element of the vocal line; it occurs in mm. 7–​9 (C5-​E♭ and G-​B♭ ascents) and later in measures 24 and 30–​34 (C-​A and B♭-​G descents). The 3rd motive is less prominent in the B section, manifesting most often as a surface leaping gesture involving Cs and As. The shape gains significance when the main tonal areas of this section, A and C, are viewed as an outgrowth of the bass’s first two notes in m. 41: this is an unsophisticated yet powerful parallelism. The same relation, involving the same pitch-​classes, is further explored in the piece’s C area. Motions between the pitch-​classes C and A occur in the bassline both at the beginning of Segment 12, where it is chromaticized, and at the end of Segment 13, where a half-​cadence on an A chord is reached. This placement at both edges of the fourfold-​repeating unit casts the C-​A third as the glue that binds this loop of music together. While all of that occurs, the other linear thirds remain prominent in the interior of the passacaglia. The most exposed of these is the lead singer’s D-​F motions in mm. 81–​82 and  84–​85. Another pitch motive we might wish to include in our Focal Point is the motive of a 2nd. Although 2nds are often generic, those in “Paranoid Android” bear mention because of how exposed they are and how expressively they are employed. In the A section, the 2nd in descending minor form is associated with misery and exhaustion, as when the lead guitar accompanies the singer with a mournful pitch bend in mm. 15–​16 (E♭4-​D). Moments later in mm. 17–​18, the same motive turned upward and made major (“What’s that?” sung on D5-​E♮), communicates confusion and alarm. This motive grows yet more prominent in the B section. It undergirds the A-​A♭ undulation that gives this music its sinister feel. The next pitch-​based motive to consider is the tritone. This motive comes to the fore early: the first vocal utterance in mm. 7–​10 concludes with a motion from B♭5 to E♮ on the words, “tryin’ to get some rest.” The stepwise descent in this instance suggests an affinity with the 3rd motive noted earlier, since a diminished fifth tritone can be viewed as a composite set of thirds, 3rd ⊕ 3rd. In addition, there are many cases where direct tritone motion is exposed; most of these employ the boundary tones, B♭ and E. The earliest appears in mm. 3–​4 in the bass, providing a preview of the first line of melody to be sung. The gesture returns in mm. 5–​6, 9–​10, 11–​12, and 15–​16, running loosely parallel with the voice in the last occurrence. The tritone (TT) shape is more hidden in the B section, providing the boundary tones for the main vamp gesture spanning m. 41 (A♭-​D). In the C section it constitutes a structural element of segment 13: in mm. 78–​81, the bass and choral melody both express the same B♭-​E linear descent heard back in the A area.

284  Analyses and Conclusion The last pitch motive to emerge as central does so as the result of a decision on how to account for chromaticism in the song. The first chromatic fragment to actually appear is the B♭4-​A-​G♯ sounded in the synth voice in Segment 4. It is always possible to classify a motive on the basis of its span. In this case, that would mean labeling the shape as a specialized, filled-​in form of third (3rd). That interpretation will not work here. First, it is not at all clear that this motive even is a third. Although the last note is transcribed as a G♯, one could argue that it is A♭, and that it might be the same A♭ explored by the semitonal bass motion in the B section. Another issue to consider is that this piece’s chromatic gestures vary greatly in length. Some take up three notes, but others take up four or five. The fact that these shapes often overlap in pitch-​class content further problematizes the span-​label approach. Of what value is it, for example, to distinguish B♭-​A♭ 2nd motives from filled in B♭-​A-​G♯ 3rd motives? A more direct solution is called for. Here, we will recognize the presence of “chromaticism” (Chr), in general, as a binary motivic element, present or not present as a pitch/​pitch-​class attribute. The pitch motive content of the piece remains fairly consistent throughout. In contrast, the harmonic syntax shifts drastically among the A, B, and C sections, serving as a primary agent for shifting the color and mood. The challenge in working with this domain is to identify salient harmonic gestures that occur in more than one section of the form. There is no single chord progression, such as Tonic-​Dominant, that qualifies. Instead, there is but a single sonority that plays a central role in the piece. It is the chord mentioned earlier, built of the notes G, B♭, D, and E♮. While the chord is made of pitch-​classes that can appear in any vertical order, it tends to appear in the “inversion” that puts G in the bass. This chord could be called a half-​diminished seventh chord on E in second inversion, meaning a iiØ6/​5 chord in the key of D minor. In “Paranoid Android,” this sonority behaves more like a G minor triad with an E natural added to it, in the manner of an “add 6” chord in jazz. The Gmin+6 harmony plays a conspicuous role in the outer sections of the song. It is first heard in m. 4, where the lead guitar enters, with its special timbre helping to embellish the moment. This arrival produces the effect of a cadence, which is then echoed in m. 6. (The chord operates in identical fashion in Segments 2 and 3.) The Gmin+6 harmony is next heard in Segment 4. Here it migrates to the head of the segment. More accurately, the chord is composed out, so that the whole segment expresses it. The lead guitar’s ostinato in this area continually sounds the upper two notes of the chord, D5 and E. At the same time, the bass guitar follows a smooth path from G down to E. The result is a three-​ measure expression of the sonority in mm. 17–​19 that repeats in 20–​22.10 The Gmin+6 chord plays a prominent role in the C area as well. It returns at its original pitch-​class level in mm. 79–​80 to prepare the cadential motion of

Analysis of Three Works in Contrasting Styles  285 Segment 13. As before, the sonority is horizontalized (or “composed out”) by an impressive descent in the bass in mm. 77–​80 that links D3 to E2. The fourfold presentation of the passacaglia causes this gesture to be restated four times. Our survey of events in the primary domains has winnowed the original field of segment candidates down to four: Segments 4, 12, 13, and 15. To decide which should serve as the Focal Point, we will extend the survey to consider secondary domains. It will not be necessary to exhaustively account for the activity in every potential coloristic area. Instead, the process can be abridged by concentrating on a single, “tiebreaker” domain. (To be sure, the domains of Orchestration/​ Texture/​Timbre and Ornament are both critical to the sound of “Paranoid Android,” and both will play a role in the CMA.) The attribute in question is the one that was cited at the outset as central and definitive to “Paranoid Android,” that being the theme of (split) Identity. Even within a piece that is, as a whole, about the human and digital interpenetrating one another, some segments will embody that process more than others. The Focal Point, if it is to constitute the essence of the work, should do so as well. The attribute at hand is perhaps the most expansive one we have yet encountered. The notion of split Identity is, in fact, a humanistic theme that has been explored in many fields, among them philosophy, literature, and psychology. The most appropriate domain for placing such an attribute is Embodiment/​Allusion. On each occasion that a segment of the piece invokes split Identity, it is quite literally alluding to that much larger topic. Having established where the attribute of split Identity resides, it must next be defined so that analysts are clear on what it is and how the piece toggles it.11 As to the former, “Identity” will be said to manifest where humanity and technology strive to evoke one another. The clearest type of Identity events in “Paranoid Android” arise mimetically, such as when the computer voice “speaks” in Segment 4 (mm. 17–​23). This phenomenon manifests in the opposite direction as well. When Thom Yorke quietly intones nonsense syllables on G5-​A♭ in mm. 45–​47, his voice mimics an overmodulated sound signal, meaning technological gibberish. A less direct form of imitation occurs through gestural echo. At the climax of the first B section, for example, the voice caps off its most emphatic declaration, “I guess he does,” with a long C4 that bends upward an octave. Moments later in mm. 64–​65, the lead guitar, in full electric mode, reproduces this pitch bend, compressing it to one beat to launch the solo that will take up most of Segment 11. Upon taking Identity into account, Segment 4 emerges as an outstanding choice for the Focal Point. The disjunction between the voices, human and computer, is most intense here. It is further significant that Segment 4 is the one that delivers the song’s title, which makes literal mention of a troubled, irrational mental state.

286  Analyses and Conclusion Segment 4, the Focal Point, is represented as a complex motive in Example 8.8. The staves above depict all four of the primary pitch and pitch-​class motives noted earlier. The exposed 2nd involving D5-​E♮ appears in the voice. The three other pitch-​based motives appearing in the synthesizer and bass guitar are the tritone (TT), the linear 3rd, and all-​or-​nothing chromaticism (Chr.). The first rhythmic motive, “Backbeat,” which appeared as early as Segment 1, appears in the rhythm guitar part. There is also a new rhythmic motive, the S-​S-​S-​L duration pattern given in the computerized voice. Further justification for including the S-​S-​S-​L arises from noting its appearance elsewhere, such as in Segments 1–​3 in the lead guitar riffs and Segments 9–​11 in the bassline. The Harmony domain, for reasons already discussed, manifests as the Gmin+6 chord. Of the many secondary domains that can be tracked in CMA, only three will be accounted for in this analysis: Orchestration, Ornament, and Allusion. The last of these, wherein the Identity occurs, has already been fully treated. The Orchestration attribute takes the form of parallel-​tenths voice leading, which in this segment coordinates the synth voice and bass. The Ornamentation domain is centered on the “escape-​tone” (ET) gesture shown bracketed in the last beat of m. 17. The quick motion up to B♭2 is not structural; it is a surface motion that decorates the bass’s downbeat-​to-​downbeat motion from G2 to F. Although the Example 8.8  A complex motive derived from the music of Segment 4.

Analysis of Three Works in Contrasting Styles  287 ET gesture manifests as a rising third in Segment 7, it should be conceived generally so that other, similar forms can be accounted for. This includes inverted third presentations, such as the F5-​E-​D vocal bends that Yorke often uses to ornament motion among longer notes. With regard to weighting the Complex’s domains and attributes, we start by assigning 50  percent unity to the Primary and Secondary domain groups. The three Secondary domains elements split their 50 percent equally, resulting in a 16.67 percent weighting for each. The same apportionment applies to the Primary domains, although further subdivision is required to handle the presence of multiple pitch and rhythm motives. The 16.67 percent unity value for pitch-​based motives is divided equally among the TT, 3rd, 2nd, and Chr motives. Similarly, the 16.67 percent divides in half for each of the two rhythmic motives identified.

Data Interpretation and Narrative Template in hand, we proceed with scoring the remaining segments of “Paranoid Android.” The results of this work appear in Example 8.9(a). The Segment totals in the lowest row are graphed to produce the work’s Narrative Curve, shown in Example 8.9(b). Note that in this graph, the x-​axis folds on itself in two places to reflect the large-​scale repetitions of material. At left, Segments 2–​4 share space with Segments 5–​7. At right, the fourfold repetition of Segments 12 and 13 is charted in one region. In both cases, the shaped nodes—triangles, x marks, and so forth—distinguish segment content across rotations, with small arrows showing the flow of time. The Narrative profile of the work is Cyclic. The piece opens in a neutral state in terms of unity and emotion, with its thin scoring expressing only a portion of Focal Point material. The degree of unity remains fairly level through the first three segments of the A section, then rocket to a peak at Segment 4. The music traces a similar path in Segments 5–​7, but at a slightly depressed level (see dotted plotline below the solid line). Some subtle changes account for the altered profile. For example, in Segment 5, the voice descends instead of rising in pitch. In so doing it covers a smaller range and fails to state the B♭-​E tritone as before. The B section, though highly agitated with regard to rhythm and texture, is marked by an overall lull in motivic activity. Upon arriving at Section B, the level of motivic interest drops dramatically, yet the level of tension does not. In contrast, the transition to Segment 12a and the C section effects a sharp rise in complexity. What is more, this segment initiates an eight-​segment climb that results from the steady addition of more and more Focal Point elements. Peak unity is achieved once more in Segment 13d. The moment after this occurs, the piece reverts to B material. The Curve plunges down in Segment 14 to its lowest level

(a) The full tally of complex elements for “Paranoid Android” based on the Segment 4 as Focal Point. Empty cells signal “0” values..

Example 8.9  The Narrative of “Paranoid Android.”

0

10

20

30

40

50

60

70

80

90

100

A

1

5

2 6

3

4/7

B

8

10

Segments 1–15

9 11

12a

12b,c

12d

C

13a

13b,c

13d

14

B

15

(b) Narrative Curve resulting from graphing the total values from Example 8.9(a) tallies. Additional dotted arrow paths show motion among segments under material repetition.

Relative Unity (%) with Focal Point

290  Analyses and Conclusion yet seen. It recovers to an extent in the final segment, but only to a level roughly commensurate with the starting value back in Segment 1. The largely neutral account of “Paranoid Android’s” Narrative is here concluded. We have proceeded just about as far as is possible without invoking an outside program (extroversive semiosis). Yet, a wholly technical reading seems insufficient for a piece as charged and evocative as this. The song’s title, lyrics, and digitally engineered soundscapes are all integral to the experience of hearing/​ knowing the work. It seems only fitting, then, that these elements inform our analysis. We can ensure they do so by following the procedure outlined in Interlude 2, which calls for taking our discovered archetype (in this case: Cycle), and layering relevant program elements onto it. The program element that will serve that purpose in this next, more imaginative reading, will be the titular mental state, paranoia. By virtue of this piece being a song with lyrics, we are acquainted with a fictional, presumably male protagonist, who is afflicted with the condition. The Focal Point event will be said to correspond to a maximal state of paranoia; other segment scores will indicate the protagonist’s shifting levels of it. Note that even within this interpretation, we remain free to posit a wide range of storylines. In one reading, paranoia might be viewed as a malady one wishes to be cured of. In another, the paranoid state might be viewed more neutrally, not as a condition to be feared, but one that, as experienced, affords a person new views on the self and others. The next question to be addressed is that of agency, which asks what, specifically, causes the shifts in unity/​tension value from one segment to the next? Almost immediately, we may cast aside the notion that the song depicts specific character actions. The lyrics are far too fragmentary and enigmatic for that. Abandoning the search for a literally representative plot, however, does not equate to saying that the song must lack a dramatic narrative. The song’s additive design, exhibiting dramatic contrasts among the sections, communicates the bare outline of a story. Over the course of the piece, the protagonist experiences anxiety and despair, rage, a moment of acceptance and/​or resignation, and, lastly, rage once more. The triggering events for this succession of emotions cannot be known and do not matter. It would, in fact, be just as correct to designate them as moods, which means they may not even originate as responses to the environment at all. Moods are as likely to be brought on by the vagaries of brain activity as by actual experiences. This framework deprives the protagonist of agency, meaning that he cannot do anything to escape these thoughts. If any agency be present, it must derive from another source. Here it will be taken to be the anatomy, physiology, and chemistry of the brain, which is to say: the condition of paranoia, itself. In most people’s experience, being paranoid affords very few, if any, advantages. Individuals that harbor extreme distrust and

Analysis of Three Works in Contrasting Styles  291 suspicion toward humanity have the potential to suffer greatly, as they alienate others and run themselves down emotionally through the prolonged rehearsal of irrational fears (Davey 2014, 496). In the realm of art, in contrast, deleterious health conditions are frequently seen to exude a kind of seductive beauty. The Romantics, for example, are well known to have regarded sickness, and even madness, as “pure” human experiences, by virtue of the fact that these conditions betray no trace of societal constraint.12 The notion of paranoia as a rarefied, strangely beautiful state applies well to this song. The music that sounds at the arrival of Segment 4, the spot at which paranoia reaches its first apex, is an exceptionally beautiful moment. The new texture, created via the introduction of synthesized sound layers and the disembodied, computer voice, is fantastical. “Dreamlike” is perhaps a better word for the wash of sound, as if the protagonist has fallen into a fugue state.13 The profile of the Narrative Curve at Segment 4 supports this reading: the motion is steeply upward, indicative of an unexpected transition. The surprise of this moment in “Paranoid Android” is further amplified by its location in the piece: it is first introduced just forty-​seven seconds after the song begins. The early placement of this peak has further narrative consequences. Once the moment of peak prominence passes for the second time at the close of Segment 7, listeners are left wondering whether it may return. The open question, formulated technically, is whether they are in the process of experiencing a Propagative or Cyclic narrative. But it can also be phrased more dynamically: the sudden absence of peak material in the B section causes listeners to want to experience it again. How and when will it return? The remainder of this account will elaborate on a narrative that frames maximized paranoia as state of grace. Each of the four main sections of the piece exhbits the same Curve profile, which translates to each section presenting an initial level of paranoia that subsequently rises. Given this similarity, the analytical interest derives from examining the subtler differences among the A, B, C, and B areas. The first pass through the A material coincides with our first window into the protagonist’s state of mind. The relatively low scores exhibited in the CMA Narrative at Segments 2 and 3, 42 percent and 46 percent, indicates that he harbors some paranoia at the outset but not to an extreme degree. Our preliminary diagnosis is that the subject’s condition is stable, as evidenced by the nearly flat portion of the curve between Segments 2 and 3. At Segment 4, the texture is suddenly flooded by Focal Point elements. This is not a development that could have been predicted nor rationalized. This is the moment that his fugue state begins, a hallucinatory event induced either by natural brain chemistry or possibly the ingestion of drugs.14 The arrival into Segment 4 is meant to disorient listeners. At the moment the protagonist expresses confusion (“What’s that?”), the voice of his identity fractures. It is here that listeners

292  Analyses and Conclusion first experience the most extreme level of paranoia and partake in its associated sonic beauty. After a few seconds, the fugue state evaporates, returning the protagonist to his original state of mind. In the second pass through A, Segments 5–​6, the main character begins to meditate on paranoia. The lyrics here signal his attempts to externalize his pain, envisioning punishments that would befall his real or imagined enemies were he to attain power over them. The scores for this pair of segments decrease approximately 4 and 8 percentage points, implying that this shift in thinking takes him further away from the idealized state. The deliverance he seeks, it seems, cannot be attained by violence, nor by dwelling upon others. At this early point in the music, the onset of paranoia occurs only through blind chance, as at Segment 7, when lightning strikes again and he is transported back to the rarefied state. The motivic activity in the B section confirms that violent, outward-​directed thought is counterproductive. Segments 8–​ 11 exhibit the most aggressive sentiments both in the text and music, yet the Narrative Curve languishes in a zone of middling unity values. This section, remarkably, is the only one of the four in which the local peak does not occur at the end, meaning there is no proper culmination or end-​capped moment. The regional peak that does occur at Segment 6 is also the lowest of the piece. As a whole, the four segments of the B section are the furthest removed from unity, averaging a score of only 46. In stark contrast with B, the passacaglia-​like C Section is highly directed, narratively speaking. The four passes through Segments 12 and 13 allow for motivic elements to accumulate:  this explains the consistently upward trend in values (see arrows in Example 8.9(b)). Significantly, this climb back toward unity occurs in conjunction with a host of new reflections and sentiments concerning paranoia. In the first pass through the material, the protagonist adopts an air of acceptance. He does not specify what he wants to “rain/​continue raining down” on him, but from context we may assume it refers to troubles and suffering, in general. By the numbers, this new mental tack elevates his level of paranoia significantly, from 71 percent unity at the beginning of Segment 12a all the way to 92 percent by the close of Segment 13d. Due to how the segmentation is carried out, the entirety of mm. 102–​105 is credited as a narrative peak. More precisely, it is the events of the last two measures of Segment 13d that facilitate the upward surge. In its first three notes, the rhythm of the words “God loves his,” is indistinguishable from the previous S-​S-​S utterances of “The panic, the vomit.” Unlike the previous fragments, though, in mm. 104–​105, he continues into beats 3 and 4 of each measure. The change is critical, rhythmically: it restores the long-​absent S-​S-​S-​L motive. The resultant texture, patiently assembled over four rotations of the passacaglia, achieves Focal Point status with a score of 100. This marks the goal of the piece, motivically

Analysis of Three Works in Contrasting Styles  293 speaking. Importantly, this moment of arrival is also the moment in the text that the main character lashes out with the song’s bitterest sentiment. The delivery of the words, “God loves his children” is thick with irony. The sense of attainment felt at this moment is bound up with the cumulative process that produced it. The peaks experienced in Segments 4 and 7 are sensational; however, we noted there is something not fully satisfying about them. They come upon listeners like an epiphany, vividly present one moment and gone the next. Their sudden absence spurs the protagonist to action. In his quest to reattain the transcendent state, he explores several approaches. Violent thoughts in the B section accomplish little; adopting a posture of acceptance proves decidedly more effective. After cultivating that sentiment for the duration of the C section, the final flash of irony (“God loves his children”) is what removes the final barrier to ascendancy to peak paranoia. The bitter sentiment here is no more uplifting than the confused and alarmed state of Segment 4/​7; however, it does express a similar kind of perfect–meaning: a truly maximal–​state of distrusting humanity. The song, of course, does not conclude in that state. In the final two segments, it turns away from the C material in such an abrupt, angry fashion, as to make a dark song even more bleak. It is depressing to imagine a damaged person whose goal is to recapture a state of paranoia. Is he not even more pitiable if he fails to achieve even that? Nevertheless, the protagonist attains his desired state of grace briefly in Segments 12 and 13. The shocking return of B material at Segment 14, however, wrenches it away. Whatever enlightenment the protagonist experiences in Segment 13d, it is only transient. The return of B is fairly literal, except for some alterations that yield new scores for Segments 14 and 15. Segments 8–​11 were angry; here, the level of rage rises yet further as all sense of restraint falls away. All proper lyrics disappear, replaced by the screeches of solo guitar and warbling synthesizer tones. Note that in Example 8.9(a) these segments receive credit in the Allusion domain. Buried within this texture are quieter fragments of nonsense human utterances, such as the “na na na” syllables sung in mm. 119–​122. Earlier, in the song’s calmer moments, it seemed that the crisis of Identity could possibly be resolved. By the end, the swirl of static-y anger offers a more dire prediction on the outcome of the modern experiment of humanity and technology. As the protagonist’s voice in “Paranoid Android” goes, so may very well go the voice of humankind. In other words: it will be lost.

Coda The preceding Narrative account of “Paranoid Android” endeavors to be comprehensive, at least to the extent that it observes motives in every segment and treats the whole as a unified musical/​aesthetic utterance. As we pause to

294  Analyses and Conclusion recover from the recent onslaught of minutiae, the last thing we might wish to do is reopen the discussion of motive! To dwell further on the microscopic patterns in the music is to court obsession. Surely we should refrain . . . unless, perhaps, we have overlooked any crucial motivic correspondences or interpretive themes? It turns out that we have. So far, we have lavished attention on the main character’s state of mind, putting great stock in his delusions of persecution and exaggerated self-​importance. No comment has been made on a secondary aspect of paranoia frequently diagnosed by medical professionals, that involving subjects’ conspiratorial views of their surroundings. It is typical for paranoid people to become irrationally upset by chance events and encounters. This response is closely associated with their propensity for “elaborating” their delusions “into an organized system” that opposes them (American Psychiatric Association 2013, 301.0). Rarely do the stars align such that the overall disposition of an analytic method aligns with the sentiment of the artwork under study to the extent that happens here. Fully aware that the act of seeking a hidden meaning in an artwork on the basis of its smallest patterned events may seem a bit paranoid, I shall press forward nonetheless. Moving beyond the idea that the Focal Point unifies the song, in this analytic coda I will seek out an even deeper source of organicism in the work. For reasons that will become clear, the main domain under study will be Rhythm. We begin with a brief survey of the piece so as to attach literal, texted meanings to the two central rhythmic motives. The table in Example 8.10 lists the most outstanding occurrences of the S-​S-​S-​L and Backbeat shapes, along with a brief description of the text or musical associative affect for each. This list is useful for uncovering relationships that project both forward and backward in time. For example, the guitar’s Backbeat in mm. 1–​2 corresponds to the text’s rhythm sung in m. 57. The spectre of paranoia is thus raised at the outset by the rhythm guitar. Its G4-​E♭ gestures perseverate on a ghostly version of “(You don’t re-​)mem-​ber” in which only the last two syllables sound. A similar back-​relation links mm. 51 with 50, where the untexted bassline pre-​echoes the “(Gu)-​cci little Piggie,” comment. Nearer to the end of the piece, another rhythmic evolution occurs: fragmented forms of S-​S-​S-​L in mm. 98–​103 (“The panic; the vomit”) lead to a true S-​S-​S-​L at mm. 104 (“God loves his child-​). That dense network of small-​scale rhythm relations results from a hitherto-​ unrecognized, composite Ur-​motive. The structure of Example 8.10 provides a first clue to its source. Reading from the top to bottom, the chart conveys a sense of progression. From m. 1 to m. 56, the S-​S-​S-​L motive emerges as increasingly prominent. At m. 57, the protagonist’s anger boils over, causing the rhythm to be extended. The result, shown in bold text in Example 8.10 and notationally in Example 8.11, is the joining of the two main rhythmic motives, S-​S-​S-​L and Backbeat.

Analysis of Three Works in Contrasting Styles  295 Example 8.10  Chart of S-​S-​S-​L and Backbeat rhythmic motives in “Paranoid Android.”

Example 8.11  Elision of S-​S-​S-​L and Backbeat motives at m. 57.

It is tempting to view the composite rhythm form in m. 57 as the source of all S-​S-​S-​L and Backbeat gestures. The problem is that the rhythm there does not fully apply to all of the rhythmic motives noted in the chart. Note, for example, that in m. 105, the word “children” occurs on a strong beat, which does not fit the “Backbeat” condition. For us to say that a single rhythmic gesture underlies all of the others, it needs to be adjusted. Specifically, it is necessary to relax the Backbeat provision. Doing so produces a similar composite motive that starts with S-​S-​S-​L but recasts Backbeat as a more generic “Two-note Tail” gesture. This more general shape derives from Segment 4, where it is embedded in the speech pattern of the AI voice; see Example 8.12. Although the words only loosely intersect the meter, the relative duration of the syllables creates a free meter. Most remarkably, the two rhythmic gestures here occur as S-​S-​S-​L on the words, “be paranoid” and as the Two-​note Tail on the word, “android.”

296  Analyses and Conclusion Example 8.12  The computerized speech utterance in “Paranoid Android” as an instance of the composite rhythm, S-​S-​S-​L + “Two-note Tail”.

This last investigation has resulted in us circling back one last time to the Focal Point segment. The unrelenting scrutiny of the materials leads to one last conclusion regarding Segment 4. By aid of this reading, one may claim that Radiohead has found a means to integrate the cryptic AI utterance into the full song. No foreign sound bite, the words themselves embody both texted and musical meaning. To say the song’s title, “Paranoid Android,” is an act that brings its central composite rhythm to life: S-​S-​S-​L + Two-​note Tail. In the hands of most bands, the compositional element of the computerized voice might have remained a novelty. Radiohead puts it in the service of forging the deepest kind of motivic association. In addition to the digital voice appearing elsewhere on OK Computer, imparting textural organicism to the album, in the context of this one song it conveys multiple meanings. There is the texted meaning of the words, the timbral meaning of the split, human/​computer Identity, and, in the end, a sweeping, multilevel meaning in which the rhythms of the utterance relate to the surface materials of the music, itself. The presence of this sort of connection, along with the myriad conventional pitch and harmonic associations pointed out in the Narrative analysis, make a strong argument that “Paranoid Android” is tightly unified. With regard to the “accidental” assembly of the song as related in Doheny 2002, we have no reason to doubt that the core sections of the piece were conceived separately. The present findings apply to the life of the work long past that inception point, when the independent sections merged. The finished song can no longer be regarded as a nonorganic, additive structure. It is an obsessive, almost overly-​ordered creation, constructed such that the sound of any one moment suggests and informs all others.

“At the Ballet,” by Marvin Hamlisch Method: Basic Motivic Analysis Narrative Profile: Triumph of 3rd shape

Analysis of Three Works in Contrasting Styles  297 “At the Ballet” is a song by Marvin Hamlisch from the Broadway musical A Chorus Line. The show was a juggernaut, winning nine Tony awards and the Pulitzer Prize for Drama in 1975. It remained on Broadway for fifteen years, closing in 1990 after running for more than 6,000 performances.15 This “show about a show” dramatizes an audition in which eighteen performers aspire to join the background dance troupe of an unnamed production. In addition to being judged on their dancing and singing, they are asked by the producer to divulge details about their pasts. They stand on a white line drawn on an empty stage and deliver. A Chorus Line unfolds, then, as a series of vignettes that are at turns amusing, reflective, and poignant. The song “At the Ballet,” in many ways represents the heart of A Chorus Line. Marvin Hamlisch once said that “the song set the tone for all the music in the show; once [it] was written, the creators understood the shape and color of the piece as a whole” (Wolf 2011, 122). Its subject, the transcendent power of dance, stemmed directly from show creator Michael Bennett’s primary passions and very identity as a choreographer. “At the Ballet,” is sung by three women, Sheila, Bebe, and Maggie; the text of the song is given in Example Web.8.4 . The women reflect on shared experiences in which the institution of the ballet has provided them escape from dysfunctional family lives. Their accounts center specifically around emotional wounds from childhood. Sheila tells of watching her mother discover a mysterious set of earrings in their car, clear evidence of infidelity by a man who was routinely “cold” to both of them. Bebe, in the second verse, relates the experience of hating her mother as a youth. The mother’s specific infraction is her condescension, of describing her daughter Bebe as merely “different,” which is to say: distinctly not “pretty.” This comment, which is symptomatic of a long pattern of slights, results in Bebe’s self-​worth being damaged from that point forward. Maggie, last, tells of her father abandoning the family at her birth, and of how, to comfort herself, she developed a rich fantasy life in which she imagined dancing with him around the living room. There are several weighty themes explored by “At the Ballet.” The pattern of topics is similar for all three soloists. In two of the three women’s accounts, there is early mention of an absent father figure. This pain is erased in the realm of ballet, where, in Sheila’s words, “Graceful men lift lovely girls in white.” Tellingly, the word “men” is paired not with “women,’ but with “girls” to encode father-​ daughter age asymmetry. For Maggie, it is important that whenever you “Raise your arms”—​i.e., when you are in need of support—​“someone’s always there.” When Bebe reaches the parallel location in her chorus, she notes that, “Ev’ry prince has got to have his swan.” Despite having made no earlier mention of her father, her words here reflect a concern about males being absent from her life, possibly on account of her failing to attract their attention.

298  Analyses and Conclusion The women relate how, in response to these traumas, they set out to find a more inviting home with a new, surrogate family. Example 8.13 sketches the path of their journey, tracking events in terms of form, speaker, and key. Approximately the first half of “At the Ballet” is given over to introducing the three women in three rotations. The model for presenting expositional material is established by Sheila in mm. 1–​47. She sings a single verse (Vs) about her childhood, followed by two contrasting Choruses (Ch1s and Ch2s) that describe her experiences with ballet. Bebe’s section, mm. 48–​94 is formally identical to Sheila’s. Maggie’s exposition follows, but this last rotation is heavily altered. In mm. 95–​110, she speaks her verse text instead of singing it, and does so over the music corresponding to Sheila and Bebe’s Chorus 1. The result is a blended verse and chorus event, Vm/​C1m. At m. 111, the music enters a turbulent area in which the Chorus1 music appears in C-​sharp minor, and the three women revisit melodic fragments associated with “childhood doubt.” This “Crisis” area is exited at m. 127, with a return of Chorus1 material sung by a more confident Maggie. This time, her music rises and crescendos to a grand orchestral climax at m. 143, followed by a brief Denouement section that begins at m. 151. “At the Ballet” flits rapidly among past and present and between real and imagined scenes. Motions across time and space are communicated and amplified by dramatic shifts in rhythm, texture, and tempo. Before considering the whole work in detail, we will concentrate on the formal and motivic content of the first main section, mm. 1–​48, which will here be called “Sheila’s section.” This area, which communicates its own narrative in miniature, will serve as a reference point for Maggie and Bebe’s sections. Example 8.14 illustrates the form of Sheila’s section. The vertical, hashed lines indicate boundary points where dramatic shifts in text and texture occur. The section employs an unconventional three-​part structure to communicate an unconventional story. The first portion of music in mm. 1–​21, the Verse in “Rock-​ strong four,” sets Sheila’s account of her childhood family life. Next comes a chorus (Ch1s) in mm. 22–​37, in which the song’s title is stated. As it specifically denotes the ballet, the music in this area shifts to 3/​4 meter and lighter, classical orchestration. All hints of drums and rock beat cease, replaced by crisp arabesque figures played by flute and oboe. Surprisingly, this chorus section is not the endpoint of Sheila’s music. At m. 38, she exits the idealized, fantasy realm of the ballet to initiate a second chorus (Chorus 2s) marked by a return of the rock beat. The music of mm. 38–​48, by means of its triple time, minor key, serious mood, and hypnotic beat, loosely evokes the dance studio setting, a place of discipline and group effort. In addition to tracking musical features such as meter and key, Example 8.14 in its lowest line interprets the “plot” of Sheila’s section. Two events of special import are listed. The first, in mm. 9–​11, is a brief segment of ballet-​like music

Example 8.13  Form of Hamlisch’s “At the Ballet.” Bold hashed lines divide work into Sheila’s (s), Bebe’s (b), and Maggie’s (m) sections.

300  Analyses and Conclusion Example 8.14  Form of Sheila’s section, mm. 1–​47. Verses m. 1

Chorus 1s

Chorus 2s

m. 9

m. 12

m. 22

m. 38

m. 44

Meter 4/4

3/4

4/4

3/4

3/4

3/4

Feel

Rock

Waltz

Rock

Waltz

Rock

Waltz

Key

G minor

G major

G minor

A major

A minor

A minor

Plot

Situation

Epiphany

React/Cope

“At the Ballet”

Discipline

“Home”

that interrupts the Verse. This moment is labeled “epiphany” to signal its role marking a character’s sudden insight or pivotal decision. In this case, it depicts Sheila’s mother’s decision to marry an emotionally abusive man. The moment of epiphany divides the Verse into three parts, serving as a calm moment in between the first episode naming the abuser and the last describing her silent witness to the abuse. The other event of note is the final cadence of the section that appears in mm. 44–​48. It is significant that Sheila finally gives name to her desire here for a “home.” But she is saying more than that. The melody and rhythm of “But it was home” fully match how “at the Ballet” is set at the close of Chorus 1. The two realms, ballet and home, are literally woven together. To this point we have concentrated on the text and texture of Sheila’s section, but of course musical motives play a pivotal role in it as well. Our discussion of motives will focus on the progress of four pitch shapes and one globally recurring rhetorical gesture that takes the form of Threefold Repetition. The singers, in verses and choruses alike, frequently employ this spoken/​sung formula to emphasize their points. To gain a better sense of these motives’ forms and functions, we will complete a brief circuit of Sheila’s section with aid of Example 8.15. The pitch content of Sheila’s utterances in mm. 1–​2 is based primarily on the interval of a fourth. The double iteration, “That’s what he said; that’s what he said,” strings two such intervals together. The effect is unsettling, perfectly imitating the forehand and backhand cadence of physical abuse. (Although no physical harm is intimated, the setting makes it clear that these words land as harshly as blows would.) In mm. 4–​5,  the spirit-​crushing ultimatum/​marriage proposal extended by her father—​“He was probably her very last chance”—​concludes with another prominent, stretched out fourth. During the entire time that these shapes are sung in the voice, the supporting instruments, guitar and bass, imbue the texture with

Analysis of Three Works in Contrasting Styles  301 the same motive to further suggest discomfort and dread (see vamp material bracketed in m.0). Sheila’s text in the Verse is deployed rapidly, in a manner halfway between speech and song. To accommodate all of this text, the vocal line contains many repeated notes and neighbor motions. The lower neighbor shape (LN) is most prevalent, occurring sometimes within longer 4th spans (mm. 3–​4) and sometimes on its own. Serving as a vehicle for Sheila’s agitated speech, the LN motive in its wilder, undulating form immediately associates itself with topics of cruelty and self-​doubt. (In later contexts, the LN shape will return in a more poised, measured fashion and shed these negative associations). The LN motive’s influence expands in the second pass through the verse’s bleak music, starting at m. 12. There we observe an almost constant alternation of Ds and Cs. This motion, expressed in heavily syncopated rhythm, signals the anxiety of a young girl witnessing a discovery of infidelity and not knowing how to respond. Example 8.15  Primary pitch and rhythm motives in Sheila’s section. (a) Motives of anxiety (4ths and LN) in Sheila’s verse, mm. 1–​4.

(b) Threefold Repetition generates a descending 6th, followed by ephiphany (2nd) in Sheila’s verse, mm. 5–​9.

302  Analyses and Conclusion Example 8.15  Continued (c) Stately, assured 3rds in Sheila’s verse, mm. 22–​33.

The other two motives of interest in this verse segment work in concert to amplify the impact of the Epiphany moment. As Example 8.15(b) illustrates, this occurs by way of comic misdirection. In mm. 6–​9, Sheila sings a lyrical, descending melody. The music builds suspense with the rhetorical motive as the text, “Though she was twenty-​two. . . ,” repeats three times. This set-​up is followed at m. 10 by the punchline, “she married him!” Her mother’s momentous decision is marked by a hopeful, “upturned glance” in the form of a motive of a rising second (2nd). The irony, in this case, is sharpened by the musical setting. The announcement of this fateful mistake is incongruously haloed by “pretty” music:  Classical orchestration, triple time, and a surprising major-​chord sonority. The barest hope of redemption is signaled by this Picardy third and 2nd motive; however, the moment of salvation is transient. The bleak music from the beginning returns in force at m. 12, indicating how inadequate her mother’s decision is for effecting lasting change. Example 8.15(c) details the motivic content in Sheila’s Chorus1. The new shape appearing here is the linear 3rd, shown beamed. By virtue of the fact that it first occurs in the “Ballet” area, this motive acquires an association with the notion of escape from Sheila’s unhappy situation. Two other motives return from

Analysis of Three Works in Contrasting Styles  303 earlier, but are treated differently. Lower neighbors are again present (see slurs) but no longer teeter, nervously, in syncopation. The LN motives here are instead tightly regimented, carefully patterned in rhythm, signaling that Sheila’s doubts are present but under control. The Threefold Repetition motive returns as well, but does so to express empowerment instead of irony. Following the two quick presentations of the 3rd motive in mm. 22–​27, we expect the sentence structure that is forming to flower into its last, continuation phase. As anticipated, another linear 3rd motive initiates at G4 in m. 30. This slight leap to begin higher in register signals an escape from the gravity of pitch space, but only a temporary one: the melody in mm. 30–​32 descends as before to C4. Remarkably, two ascending forms of the 3rd motive occur here in the accompaniment. These ascending 3rds (see beams) nest at two metric levels, in quarter notes sounded by the harp and clarinet and in dotted half notes in the brass. Their light scoring readily suggests a narrative interpretation, which is that the linear 3rd motive aspires to ascend. It is in fact now demonstrating its ability to do so, but it is not yet ready to take full flight over the music. The last significant motivic event in Chorus1 is the return of the upturned glance motive in mm. 32–​33. When this 2nd appeared in the verse, it relayed the punchline of a dark joke: “she married him.” Here, it returns to communicate another type of fleeting, joyful surprise. Surprise, because this may well be the moment that Sheila herself becomes aware of an avenue leading away from her unhappy situation. The singer is already at the high point of her vocal line at G4. The “Hey” that follows provides an unexpected boost to A4. At m. 38, Sheila’s music takes its leave from the ballet theater and initiates the second chorus, Ch2s (not shown). The music of mm. 38–​48, evoking the dance studio setting, recalls that of the verse. The mode is cast back into minor, and the steady rock beat returns, despite the music’s remaining in triple time. The motives associated with doubt return as well: we can hear Sheila’s voice wavering once more in lower-​neighbor figures. Her melody at the larger level traces a linear descending 4th on the words “Up a steep and very narrow stairway, To the voice like a metronome.” The close correspondences in mood between this area and the verse makes sense, narratively. The young Sheila may be enamored of ballet, but arriving at her studio nevertheless may provoke anxiety. Ballet training is well known to be rigorous. Some form of pain in rehearsal is all but assured, in the form of muscle and tendon strain and/​or verbal lashing from the studio instructor. It is appropriate that some musically coded elements of fear and doubt should return in this section. Here, though, their impact is softened by new developments. The text in Sheila’s second chorus recalls the experience of

304  Analyses and Conclusion walking toward “the voice like a metronome.” Musicians and dancers defer to the metronome, which is to say they obey it. The lyric signals Sheila has found an authority figure to replace her father, a teacher she respects. Another development is Bebe’s voice joining hers at m. 40. In this setting, Sheila is no longer fully alone. The last event of note in Chorus 2 is the final cadence, which was previously noted for its role tying together the concepts of ballet and home. The findings concerning the textual narrative and material elements of Sheila’s section can now be applied to the full piece. The analysis will proceed by coordinating the previous diagram in Example 8.13 with the narrative associations for the core motives listed in Example 8.16. The 4ths and undulating LN shapes are associated with doubt and uncertainty, the upturned 2nd with hope and epiphany, and the linear 3rd with escape. In addition to these pitch-​based motives, we noted a gesture of Threefold Repetition occurring in all three subsegments of Sheila’s section. This rhetorical motive adds emphasis to whatever sentiment that is being expressed, whether it be wry humor, hope, or happiness. Moving forward past Sheila’s section takes us to Bebe’s. The same Verse-​ Chorus1-​Chorus2 structure governs here, but Bebe begins her verse in A minor instead of G minor and sings her choruses in D major and minor. This means that “At the Ballet” exhibits directional tonality. In the same way that the linear third motives aspire to ascend, so does the key and pitch structure of “At the Ballet” as a whole.16 Bebe’s epiphany moment at mm. 58–​59 further differs in that the humor is darker (“I hated her”). Also, this time, the epiphany is felt by Bebe herself, not her mother. Nevertheless, Bebe’s first response of viewing her mother as a toxic influence only serves, as before, as an imperfect and impermanent solution. The child Bebe may have earned some solace in asserting herself. This defense mechanism, however, proves insufficient for redeeming her. Following the close of Bebe’s section, the form loosens as the narrative pursues new developments. Maggie’s section, beginning at m. 95, has no 4/​4 rock beat. Instead, her character exposition is delivered in spoken word. While the Chorus1, “ballet” music accompanies her, she describes her childhood ritual of dancing with an imaginary Native American chief. Maggie’s role in this piece is not simply to round out the trio. Shortly after she begins her verse, she changes the course of the trio’s spiritual journey. She is the first to plunge into the turbulent waters of the Crisis section (mm. 111–​126) and will be the first to emerge at the song’s climax. In contrast to Sheila and Bebe’s stories of their pasts, which were compartmentalized, Maggie’s memories are related in real-​time in more immediate terms. The music of her verse quite literally depicts a psychological rupturing, one so strong that it draws all the women together into a shared moment of Crisis. The closing portion of this analysis shall investigate the content and drama of the Crisis and Denouement areas.

Example 8.16  Listing of motives of “At the Ballet” with narrative associations.

306  Analyses and Conclusion Our account will concentrate initially on events occurring in the domains of key, harmony, and motive; see Example 8.17. The music of Maggie’s section begins in a highly stable state. As she speaks in mm. 95–​110, a solo flute playing the “At the Ballet” melody in G major accompanies her. At m. 106, the mention of her “fantasy life” initiates a transition segment. The break with reality occurs specifically at m. 106; fittingly, this is the moment where the imaginary father figure is named. The music at this point is radically upended. Harmonically, an A7 chord with flatted fifth and ninth appears that functions in G major as an altered ii chord. By enharmonic respelling, it is an augmented sixth pivot chord that shifts the music to the key of C♯. In the span of four measures, then, the music wrenches from a placid setting in G major to a turbulent passage set in C♯ minor. This latter key is highly unstable both in relation to “At the Ballet’s” starting key, G minor, and its closing key, D major. The rupture event that happens during this transition has a motivic component as well. At m. 106, the flute line once more attempts an ascending linear 3rd motive at the crest of its line on the notes F5-​G. Every time we have heard this melody so far, the line has stopped at the first “Hey.” Could it be that this motion might finally continue, such that the upturned glance is transformed into a purposeful, ascending 3rd? This very nearly occurs, but no. The pitch-​class G continues only by semitone. The G♯ that follows in m. 110 is a shy substitute for A♮, the note that would more effectively proclaim a triumphant linear 3rd. The melody’s failure to attain A can be viewed as a literal “off the tracks” moment that triggers the Crisis section. The other two women are swept up into the storm that ensues in m.  111 (Example 8.18(a)). They sing a ghostly version of the “ballet” tune in “doo doo doo” vocables, as if the redemptive power of the beloved discipline has been Example 8.17  Maggie’s Verse/Chorus and the pre-Crisis area (mm. 95–110).

Analysis of Three Works in Contrasting Styles  307 called into question. More significantly, the women revisit and recite a host of hurtful quotations from before, which appropriately return as 4ths and oscillating neighbor note motives. Narratively speaking, the forward emotional progress of the song has been halted, and the women have been cast back fully into doubt. The Crisis area, in the narrowest sense, acts to remind listeners of earlier musical materials. Within the family-​forging narrative being advanced here, though, mm. 111–​126 have a more profound function. This segment of music serves as the crucible into which the three women pour their anxieties. By means of the fragments they trade, we hear their identities dissolving and begin to see that each is helping shoulder the pain of the others. The three have come to embody sisterhood. The forging of their bond within the Crisis section is also what precipitates its end (see Example 8.18(a)). The section closes in mm. 126–​127, where Maggie reattempts the earlier dialogue with her fantasy father: “Maggie, do you wanna dance?” The words are the same as before, but the outcome is different. This time the music corrects the harmonic and motivic deviation from earlier. First, the nervous, semitonal neighbors from the Crisis area are set aside. They are replaced in mm. 123–​125 by more confident major 2nds involving G♯ and A♯. At m. 127, the key of D major is reclaimed, permanently vanquishing the unstable C♯ tonality. Simultaneously, Maggie attains the pitch-​class A, the long-​ delayed note capping the motion from F5 and G that the flute projected in mm. 108–​109. This is shown by the large beam in Example 8.18(a). Once the Crisis is overcome, no doubts or fears remain to inhibit the piece’s upward trajectory. The song’s final Chorus1 area savors this shift, motivically. This time, when the climactic “At the ballet” lyric is reached in m. 137, the music at last surges beyond a single upturned glance. Maggie is not limited to a single, shy, “Hey” expressed as an upturned 2nd. Instead, a large-​scale C5-​D-​E stretches over mm. 137–​142, triggering the work’s emotional and musical high point. Where before the music explored crisis, here it is finally free to reach its climax (see Example 8.18(b)). Remarkably, when the dramatic peak arrives at m. 143 with the entrance of the high brass, the three soloists go silent. The decision to have no singing in this section makes sense in light of the song’s grand theme concerning the fate-​altering power of dance. At this point in the number, the back stage is illuminated to show the full cast gracefully dancing: the spectacle of ballet is capable of speaking for itself.17 The narrative of Triumph through dance is confirmed in the closing segment of the work, the Denouement section in mm. 151–​163 (Example 8.18(c)). The only motives that return here are those with positive associations. There is one last “Hey” in m. 154, which prompts the three women to proclaim their individual salvation. As a family speaking in turn, they invoke the Threefold

(b) Soon after the first 3rd is completed, another, sung by Maggie, ushers in the climax of the song at m. 143.

(a) The Crisis area, mm. 111–​122. Crisis resolves at m. 127 as the aspiring Ascending 3rd from m. 103 is finally completed (large beam).

Example 8.18  Motives shape the main crisis and resolution of “At the Ballet.”

(c) Motivic counterpoint and softer, satisfied 3rds in the final bars of “Ballet.”

310  Analyses and Conclusion Repetition scheme one last time: I was pretty, I was happy, I would love to. As they sing, the horn and vibraphone in mm. 155–​157, support their melody with a slow ascent through A4-​A♯-​B. This filled in chromatic 2nd places the upturned glance motive in counterpoint with the threefold declaration of what the ballet has meant to Sheila, Bebe, and Maggie. This upward glance motive has undergone a significant journey. Present from the outset as a seed of hope, it returns at the end to literally flower in the presence of the women’s achievement. Sheila, Bebe, and Maggie’s final, unified declaration is that everything they needed was found “At the ballet.” The final cadence of the piece gilds the lily. The brass section murmurs one last linear third motive in its ascending, aspiring form (mm. 160–​162). The ♭VI-​♭VII-​I succession confirms the women’s triumph in such a way that, once more, words seem almost unnecessary.

9

Conclusion Motivic Theory in Context Motives are near-​ubiquitous due to their intersection with all of music’s structural domains. This book’s focus has been on Western music, which in the past three centuries has evolved to prioritize the domains of melody, counterpoint, rhythm, harmony, form, and narrative. Much of the discussion in previous chapters is dedicated to exploring the nature of those intersections, which explains the expansive nature of the book’s methodology area, c­ hapters 4–​7. The material on extracting basic motives from complicated surface textures delves into reduction, a learned practice that enfolds melody, counterpoint, and rhythm. The material describing how prefix and suffix gestures decorate a core shape is dependent on an awareness of harmony. The restrictions imposed at the end of ­chapter 5, prohibiting motives from crossing strong phrase and section boundaries, turn on issues of small-​and medium-​scale form. The rules for assembling and framing the analysis of full works, such as the Focal Point requirement, are guided by narrative principles. Were we to imagine a township populated by all available analytic methods, the motivic analysis personage would reside near the center of that society. An apt adage for characterizing this citizen would be, “jack of all trades,” in recognition of its great flexibility. As noted in ­chapters 1–​3, analysts of all stripes enlist motivic analysis regularly. It matters not whether their specialty is set-​theory analysis, Schenkerian analysis, performance-​and-​analysis, or computer-​aided analysis. A finding derived from any of these areas can nearly always be reinforced by restating or analogizing it in terms of a traditional motivic connection. The suitability of the term “jack of all trades” increases in light of two witty extensions that the adage has acquired more recently. The first of these, “and master of none,” suggests with good-​natured humor that our factotum cannot perform any single task perfectly. Motivic analysis is often not the best tool for analyzing the full pitch content of a work, nor the rhythm content, nor the whole work, itself! Consider the following situation involving an analyst who is in the process of developing a complex motivic analysis (CMA). She has taken pains to select a content-​rich Focal Point segment and to posit a robust Complex to serve as the source of all motivic material. In deploying this Complex, she may still encounter segments that are only tenuously related to the Focal Point. The Musical Motives. Brent Auerbach, Oxford University Press. © Oxford University Press 2021. DOI: 10.1093/oso/9780197526026.003.0011.

312  Analyses and Conclusion “problem” segments in question will almost assuredly receive some value, based on the presence of at least one source rhythm or interval. Still, fitting these low-​ scoring segments into analysis may nonetheless feel “forced” to her. My concern regarding that situation is not that a later reader will object to our hypothetical analyst’s CMA. The reader may simply disagree with the analyst’s decisions about which motives are prominent or with her choice of Focal Point. I am more concerned about the dissatisfaction our analyst is experiencing. After devoting all of that time to studying the piece, should she not expect to have a near-​complete understanding of all of its shapes and gestures, and how they go together? The first reason why the answer to that question is no is systemic: the piece at hand might simply resist motivic analysis. As this methodology was largely derived from western European, nineteenth-​century aesthetic/​cultural sensibilities, it applies most readily to compositions steeped in that tradition. This body of work includes most pieces by Haydn, Beethoven, Mozart, Verdi, Chopin, Dvořák, Tchaikovsky, and Grieg, and their Common-Practice colleagues. Critically, it does not include all of their works. Particular care should be taken when engaging these composers’ incidental works, such as short parlor pieces or miscellaneous offerings known to be dashed off to raise funds or support state functions. For works outside of the Western Common Practice, some caution at the outset can prevent wasted effort later. It is certainly possible to apply motivic analysis to twentieth-​century, nonpitched percussion pieces, to fourteenth-​ century motets, and to modern day pop tunes from around the globe. The chances of generating a meaningful analysis for any given piece deriving from those traditions, though, will vary to some extent based on how closely they hew to the Western, organic tradition. Another reason the answer is no stems from the built-​in limits of interpretive musical knowledge. Pieces of music are artworks that support myriad interpretations. It is for this reason that analysts revisit the same pieces many times over the years, much in the same way that a performer might master a work and then return to it periodically (Agawu 2004, 275–​277). It is also the reason that a wide variety of analytic systems have been developed by theorists. Each method returns its own type of answer about how a piece’s components fit together. As such, in cases where motivic analysis points strongly to the influence of a recurring gesture—​be it melodic, textural, or even physically embodied motion—​the analyst may need to open up a separate, specialized investigation of it. Motivic analysis, in other words, can stand alone, but is most potent when it doesn’t. A further aspect of “and master of none” applies to this book’s author and to its potentially bifurcating readership. Near the close of ­chapter 1, I expressed a hope that a new approach to motives might raise the general public’s interest in reading and carrying out technical music analysis. In truth, most academics harbor some

Conclusion  313 form of this ambition. In this case, however, I can assure readers that this hope does not stem from vanity. It is rooted in the firm belief that motives truly are intuitive. Anyone who has hummed a fragment of a song or can immediately recall guitar riffs from their favorite piece of rock music is capable of thinking motivically. This “anyone” is most people; is that not exciting? Chapters  1, 2, 4, 5, and 6 are written in a more conversational tone in the hope of reaching past the earshot of academic musicians to that of a more general audience. As one might imagine, it is difficult in most places to simultaneously engage both types of reader; in all other places, it is nigh impossible. In ­chapters 1 and 2, lay readers can follow the main text, while specialists will likely wish to delve into the citations and endnotes. Simple enough. When it comes to ­chapter 5’s treatment of BMA, this balancing act becomes much more difficult. It may very well be that the primer on melodic reduction given at the start of that chapter is too complicated for novices and too basic for experts. If I have succeeded in positioning that material anywhere near the center on this spectrum of expertise, it should provide some value to everyone. For true beginners, it serves as an invitation to step into the world of analysis by laying bare its basic underlying principles: reduction, recursion, and unity. For experienced analysts, it offers a new opportunity to ponder the benefits of tinkering with the principles of reduction. A traditional, tonal counterpoint-​based approach will yield generic shapes that are more likely to resonate at multiple levels, while a salience-​based approach is more likely to yield idiosyncratic shapes that are more emblematic of individual pieces. The same rationale supports the decision to include primers on the historical role of motive in composition in ­chapter 2, on motivic nomenclature in ­chapter 4, and on musical form and narrative analysis in ­chapters 5 and 6 and Interludes. Each of the areas in this list represents a well-​developed subspecialty practiced by a vibrant scholarly community that possesses a rich set of conventions and literature. In the act of summarizing, one could not hope to fully represent even one of these subdisciplines, let alone all of them. I have therefore endeavored to adhere to the guiding principles of each on the basis of a small sampling of prominent treatises. It is here that I feel that the “master of none” sentiment is most apropos. I expect that seasoned academics from every field impinged on will feel inclined to protest that their area has been inaccurately represented. In cases where that has happened, I apologize, especially in cases where my characterizations appear dismissive. Any perceived affronts should be attributed to inelegant writing or expression and not to malice. In light of motivic analysis’s voraciously expansive nature, we can amusedly observe how “jack of all trades, and master of none,” is modified by the last colloquial extension, “but better than one.” The last four words broker the compromise between the generalized nature of motivic analysis and the specialized

314  Analyses and Conclusion nature of adjacent theoretic and analytic subdisciplines. Analysts who are used to working in more established fields may be tempted to write off motivic analysis as immature or for providing results that are too diffuse. The explanatory power of this discipline should not be underestimated. The recurrences of shape in music are responsible for its content, flow, and a great deal of its meaning. The patterns of pitch, rhythm, harmony, texture, and so forth offer insight into the thought patterns of composers writing music, performers interpreting it, and listeners experiencing it.

What Motives May and May Not Be Motivic analysis, as this book has formulated it, cannot offer a single, expert ruling on how a piece is constructed. What it does do is allow analysts to quickly and productively engage many dimensions of a musical work. In asking how simple motives interact with harmony and form, for example, we are prompted to study the work’s harmony and form in greater depth. In asking how complex motives are in part harmonic, we arrive upon a view of harmonic progressions as patterned, repeating, memorable units. There is a class of uncharitable adjectives sometimes applied to theoretic entities that apply with great facility, meaning: in many circumstances. Specifically, words like “extravagance” and “promiscuous,” carry connotations of moral fallibility and decadence (Downes 2010, 6). A classic example of an “extravagant” harmony is the half-diminished seventh chord, which is capable of pointing to many resolutions in many keys at once (Smith 1986). Closer to home, motivic analysis, writ large, may be viewed as extravagant in that essentially a) any piece can be analyzed by it and b) any gesture in a work can be viewed as a motive. The wide-​ranging utility of motivic analysis need not be viewed in negative terms, however. Reflective of the fact that music is multidimensional, most convincing analyses—​even those relying heavily on a single technique, such as set theory—​ typically augment their findings with information gleaned from examining melodic contour, rhythm and meter, and a text or program (if known). The advantage of motivic analysis being a “jack of all trades” is that it has this type of cross-​modal sensibility “baked into it” from the start. While maintaining the view that extravagance is generally beneficial, that quality becomes a disadvantage if it is allowed to run rampant. Consider the danger of broadening an established field to enfold increasingly more musical domains. That system, sufficiently extended beyond its initial focus, would outgrow its purpose and threaten to engulf all competing systems. Though such a development is still far from coming to pass at the present time, this is not a moot point. Already, within the corner of speculative theory staked out in this book,

Conclusion  315 complex motives have been formatted to allow them to engage all domains of music. Their purview, moreover, is not limited to the most common domains. Room has been set aside for motives to accommodate any further domains that later theorists might wish to add. This maneuver invites the question, “Can everything in music be conceived as a kind of motive?” The technical limits imposed on motive in the early chapters should be sufficient to show that the answer to this is “no.” Such limits, appropriately enough, stem from the central proposition that motives must move and move us: they must exist in time and be memorable. A motive is disallowed from having too short a duration. As defined, it cannot be a single, isolated event, no matter how compelling. A grand pause is not a motive, nor is the first, brilliant E-​flat chord of Beethoven’s Eroica Symphony. (Though note: that sound event grouped with the silence that immediately follows could be a motive). Nor is a motive allowed to be too large. Excepting the rare case of miniscule novelty pieces, such as the “Sphynxes” from Schumann’s Carnaval, a full-​length piece cannot be a motive. Taking into account the restrictions on working memory, ­chapter 5 set an upper limit on motive length as “the length of a major section” of a work, for example, the A or B area of ternary form or the recapitulation of sonata form. As we retreat from the clearest cases of too small and too large, the answer to “Can any event be framed as motive?” admittedly becomes less clear. Basic motives will, by definition, always manifest as pitch and rhythm events. It is complex motives that run the greatest risk of slipping their perch of clear identity and falling into the “anything goes” category. This peril is felt keenly when one faces an audience’s inevitable set of hypothetical qualifying questions. Examples include: “What about fugue subjects?” and “What about the opening guitar lick from the Rolling Stones’s ‘Satisfaction’ that returns in every refrain-​chorus?” In each case, the inquirer wants to know: can’t each of these be a motive? We begin with fugue subjects. (Here, “subject” should be understood as encompassing all main theme entries, no matter their tonal profile.) Analysts may consider a fugue subject a motive, but they should not unless there is a compelling reason to do so. Most fugue subjects do not function on the whole as motives, but as themes assembled out of motives. This generalization holds especially for lengthy subjects, such as the one found in movement II of Handel’s Concerto Grosso, Op. 6, No. 4 in A minor. The subject of that fugal work, given in Example 9.1(a), uses twenty-​one notes to state four separate gestures. The first is a syncopated Lower Neighbor. The second is a four-​quarter-​note gesture read as a two 2nds added together: D5-​C + F-​E. Next, there is a climactic high 2nd that could be interpreted as extending the previous shape (presently, it is not). In the last two measures, there is a continuation idea stated in eighth notes. Equal duration reduction (EDR) at the quarter note level reveals an /​/​

316  Analyses and Conclusion Example 9.1  Fugal works by Handel and Bach. (a) The subject of Handel’s Concerto Grosso in A minor, Op. 6, No. 4 (II).

(b) Climax of the Handel movement, mm. 97–​104, explores new combinations of motives from the subject.

(c) The subject of Bach’s Fugue in G♯ minor from Book I of the WTC.

Arp3 shape: C5-​D-​E-​C-​A4. Over the course of the piece, these shapes are explored separately and in novel combinations, most notably in the final climactic measures, as shown in Example 9.1(b). The same claim applies to medium-​ length subjects, such as those found throughout Bach’s Well-​Tempered Clavier. The subject of the Fugue in G♯ minor from Book I is two measures long and takes up fifteen notes; it is shown in Example 9.1(c). The subject opens with a drawn-​out 2nd, which leads to a short arch built of two elided 3rds. It closes with a steady eighth-​note fa-​sol-​do figure that serves as the backbone of a iio6-​V-​i cadential progression. The 4-​̂ 5-​̂ 1̂ (fa-​sol-​do) idea frequently appears on its own, notably in all of the fugue’s modulatory episodes. The subject’s last and arguably most important motive is the three-​note gesture that first appears in the first half of m.2. This leap-​to-​a-​semitone is labeled in the example as ⎡2nd.

Conclusion  317 For generations, musicians preparing to learn a fugue have been instructed by their teachers to identify all complete subject and answer entries. This activity does help to lay bare the basic thematic and tonal form. By our standards, though, this circling and labeling of themes does not constitute deep analysis. It is more akin to the armchair or word search-​type observation that we saw Charles Rosen denigrating in c­ hapter 1. If analysts aspire beyond that level of understanding, a richer avenue of inquiry is to examine the motivic activity that frequently occurs independently of the themes. In the case of this Bach fugue, the semitone at the top of the ⎡2nd is highly exposed in its first presentation. It juts out in register, and it highlights the dissonant tritone interval, G♯3-​C𝄪4. There is nothing about this motive that is inherently aggressive or violent; however, the abrupt dissonance causes me to hear it as a cry or “wail,” of sorts. Whether it is human or not, I cannot say, but it is definitely visceral to an extent. The forward drive of the G♯ minor Fugue results from activity in several domains as, for example, the texture increases from one to four voices, and the register climbs from the low, tenor opening to the B5 that eventually enters in m. 26, two and a half octaves above. The specific activity of the “wail” motive correlates particularly well with the piece’s forward-​leaning, accumulative emotional arc. This process is illustrated in Example Web.9 . Discounting the fact that the highest tone sounds at m. 26, the climax of the work actually occurs in mm. 32–​ 41. Within this final segment, we hear the original 3rd⊕3rd arch stretch to span a major third G♯3-​A♯-​B♯. This form of the subject in m. 32 is novel. It is, moreover, aurally grating and difficult to play. There is also in this span a dramatic uptick in intensity of fa-​sol-​do gestures, which repeat in many instances in thicker, doubled orchestration. The peak moment within this span centers on a “wail” event (m. 39). The prominence of the ⎡2nd motive has, in fact, been steadily increasing all along. Following its fourfold introduction in the fugue’s exposition, it spawns rapid copies in mm. 17–​18 while providing a new counterpoint to the subject in the tenor. In mm. 21–​23, it serves as the basis for an ascending sequence as it is rapidly exchanged (twice per measure) between the alto and bass voices. Just after that, the soprano reaches its highest pitch in m. 26 specifically by means of two chained ⎡2nds. Returning attention to the final segment, we see Bach applying the most powerful rhetorical tools in fugue, homorhythm and silence, to privilege the “wail” gesture. It sounds, completely alone in the soprano, one last time in m. 39 (G♯4-​B♯-​C♯5). The final exposed statement of the ⎡2nd motive confirms the dour, hopeless mood of the piece, and supports Bach’s choice in the last measure to deny the music a Picardy third, the major-​inflected form of tonic. Having considered fugue subjects of great and medium length leaves open the issue of whether the shortest fugue subjects can be motives. Two pieces from

318  Analyses and Conclusion Bach’s Well-​Tempered Clavier come to mind, the C♯ minor Fugue in Book I and the E Major Fugue from Book II. It is certainly possible to declare these subjects pitch motives unto themselves and to trace their development. As one does this, I advocate that one should impose a similar kind of narrative on these motives as we did for the G♯ minor Fugue to prevent the analysis from devolving into an artless search for subjects and answers. The foregoing discussion indicates that fugues are fully amenable to BMA. Yet for those familiar with fugues, that point should provoke a bit of cognitive dissonance. Although fugue subjects are monophonic entities, fugues are, in the purest sense, polyphonic. As is well known, a subject is predesigned by the composer to work with its countersubject(s).1 A complex motive, then, will be far better suited than a basic one to probe a fugue’s organicism and narrative. Following the guidelines in c­ hapter 6, the Focal Point that is posited should be rich, containing both diatonic and chromatic elements as well as paired subject and countersubject material. For the G♯ minor Fugue, an ideal candidate segment is mm. 32–​34, which presents the subject in the tenor, the two countersubjects in the soprano and alto, and, a running-​sixteenth note idea in the bass that appeared once before in m. 25. On the basis of these materials, a fuller narrative could be constructed around the basic “wail” interpretation sketched earlier. Our last answer to the question of fugue subjects as motives is this: a monophonic subject is generally not a standalone motive, but will in all likelihood furnish some of the pitch and rhythm attributes of a fugue’s central complex motive. The other “what-​about” challenge from earlier asked if the first riff from the Rolling Stones’s song “Satisfaction” qualifies as a motive. Here the answer must be yes. The riff, depicted in Example 9.2, is one of the most famous in all of classic rock. Clearly, it is memorable, and for decades it has moved listeners. Set in E blues and 4/​4 time, the motive sounds two B3s on its first two beats, then traces a syncopated arch motion up to D4 and back. The genius of the motive lies partly in this two-​part, “Hits” and “Arch” arrangement, which is designed to complement the rhythms and pauses of the chorus lyrics. Well before the first verse arrives, the guitar hits on B in the intro foreshadow how Mick Jagger will deliver the most aggressive attacks in his lyric (see italics in the example). The downward Example 9.2  The main guitar riff (hook) of “Satisfaction” by the Rolling Stones. Schematic representation of notes, rhythms, and text.

Conclusion  319 3rd portion of the arch in the guitar riff serves as a windup gesture for driving the music back to the downbeat of every odd measure. Quick consideration of the “Satisfaction” riff reveals how motive-​like it is, but also opens the lid on a greater conundrum in pop and rock analysis. The “Satisfaction” riff is not just a motive. It is a hook, a “musical or lyrical phrase that sticks out and is easily remembered” (Monaco and Riordan 1980, 178 quoted in Burns 1987, 1). Musical hooks, which are named after their ability to immediately catch and hold listeners’ attention, are the lifeblood of pop. Most of pop music’s greatest hits feature one or more hooks. The most famous hook in Aretha Franklin’s “Respect” occurs where the band falls silent and she spells out the song’s title, a capella. In “Hey Ya,” a 2003 hit by André 3000 with OutKast, it is difficult to say whether the hook is the basic groove material, the repeating cycle of G-​C-​D-​E chords occurring in six-​and-​a-​half measures of 4/​4 time, or the version of it given in the chorus (0:33–​1:06), where the groove supports a set of hypnotic “Hey Ya”s and a new line of synthesizer counterpoint. Other famous hooks, as compiled by the staff at Billboard magazine, include the opening riff/​groove of “Under Pressure” by Queen with David Bowie, and the choruses of Carly Rae Jepson’s “Call Me Maybe” and the Beach Boys’ “Good Vibrations” (11/​12/​15). All of these examples intuitively fit the concept of hook despite their great variety in textures. The “Satisfaction” lick is a two-​bar solo for guitar. Aretha Franklin’s solo break explores a new texture and lyrical treatment: spelling a song’s title is a common trope in pop music. The chorus of “Good Vibrations” conveys the song title over a wash of sound full of electronica, a pulsing beat, and thick, high, vocal planing in the signature Beach Boys manner.2 Are hooks motives, then? Perhaps. All of the hooks noted here are of modest length and could readily be poured into the complex motive mold. The problem for most of them is their overexposure. In the case of “Hey Ya,” the hook cycles continuously, rendering it generic. The same can be said for “Under Pressure.” There is a steady crescendo of instrumental layering and volume that occurs throughout the song, but these add little interest to the original idea. In “Call Me Maybe,” the reverse situation obtains, where the hook is walled off from the rest of the piece. The verse and pre-​chorus of “Call Me Maybe” are thinly scored and quiet. These areas delay the arrival of the loud, eclectic, and—​this is meant in the best way—​ bubble-​gum chorus. The song is essentially a one-​trick pony, in which the main element the audience truly wants to partake in is hook material. The potential hook-​motives in all three of these songs fail to develop. In the first two cases, it is because they stagnate; in the third, it is because the hook fails to connect organically with other segments. This condition of failing to develop is incompatible with motivic analysis as this theory formulates it, which leads me to recapitulate a point I have made before: An analyst can consider a hook a motive, but should not unless there is a compelling reason to do so. The preceding examples

320  Analyses and Conclusion are not anomalous. There there are thousands of songs like “Hey Ya” and “Call Me Maybe” that will resist analysis when the hook is selected as the Focal Point. All that said, there are also thousands of popular songs in which the hook event does appears to be motivically significant. Aretha Franklin’s “Respect” is one of them. In its 1967 version, the famous R-​E-​S-​P-​E-​C-​T hook is delayed to 1:49, which is more than two-​thirds of the way through the song. Although the “stop time” texture there seems novel, the spell-​it-​out moment closely resembles the other choruses found at 0:21, 0:41, 1:03, and 1:40. All of those earlier arrivals similarly mention “Respect” and spotlight the backup chorus material of alternating D tonic and G subdominant harmonies.3 In “Good Vibrations” and “Stayin’ Alive,” the main hooks similarly resonate across each song. The chorus of the former is sufficiently rich, orchestrally and contrapuntally, to allow elements such as the theremin’s ghostly sound to bleed into the verse, bridge, and outro areas. The latter tune, “Stayin’ Alive,” is likewise unified across its form by rhythm and harmony. The way it avoids the “Hey Ya” condition is by exhibiting a series of closely related ​yet ​distinct hooks. The hook from the introduction (0:00–​0:12) features syncopated guitar riffs and an upward pitch bend in the strings, while the hook in the chorus (0:32–​0:57) subtracts the guitar while adding in the song’s title and stylized panting on “Ha.” Either of these segments could very well serve as a Focal Point within a fuller CMA. This last line of argument might seem to imply that motivic analyses of pop and rock music should aspire to be comprehensive. While CMA is a fine tool, BMA remains viable in cases where a single aspect of a hook attracts attention. As an example, Traut 2005 notes a delightful motivic parallelism lurking inside “My Sharona” by The Knack. It involves the repeated utterances of “My my my.” When these “my”s appear “spread out over a two measure span” at the build-​ up area of the chorus, they “create a nice elongation of the much shorter title hook, M-​M-​M-​My Sharona” heard shortly afterward (Traut 2005, 69). This point stands on its own merits, but also could be expanded into an investigation of how the text’s “S-​S-​S-​L” rhythm resonates elsewhere, such as in the staccato, popped, register-​leap gestures given in the drums and bass, starting in m. 1. A host of similar “Can’t X be a motive?” queries can be directed toward other theoretic entities. One such structure is the schema, as recently formalized by Robert Gjerdingen’s Music in the Galant Style. Schemata (plural) are compositional modules that eighteenth-​century composers linked together to build phrases, periods, and larger sections of music (Gjerdingen 2007, 10–​16, 29). Schemata are short, usually occupying only a few measures, and are conceived as networks simultaneously enfolding information about melody, harmony, and counterpoint. Does this mean that compositional schemata are motives? I would say, despite their sharing a significant strand of DNA with complex motives, that mostly they are not.4 Gjerdingen’s interest in schemata is historical and sociological: he characterizes them as common formulas that composers learned by rote and deployed in their music, much as people at formal gatherings deploy prescribed conventions of greeting, speaking,

Conclusion  321 and taking leave. In music, as in life, various schemata succeed each other rapidly. A schema analysis of a work is thus more interested in disunity than in the kind of organicism prioritized in motivic analysis.5 In addition, the components within each schema’s network are bound together. They are not meant to be reduced, extracted, and sought out elsewhere as separable elements. Gjerdingen’s analytic practice notwithstanding, it is easy to see how closely schema theory and motivic analysis overlap and how they could productively interact. The primary aspects listed in a schema’s network translate readily to the analogous areas of a complex motive; only minor adjustment is needed to recast Gjerdingen’s scale degree patterns and Roman numeral analysis as melodic and harmonic motives. What is more, the names of the schemata, which boast descriptive titles such as Romanesca, Prinner, and Pastorella, already encode information about topic and allusion, an important secondary domain element of complex motives. The main factor limiting the integration of the methods is that schema theory is in a relatively early phase of development. To analyze with schemata, one must necessarily select for pieces in a tradition for which a full set of schemata have been defined. Originally, this meant instrumental pieces from the Galant period (roughly 1720–​1780); however, since the publication of Gjerdingen’s book, scholars have been steadily working to propose schemata for other genres and traditions. Recent work by Sherrill and Boyle, for example, establishes fifteen new schemata for recitative passages in Galant opera (2015). Recitative, importantly, is a vocal tradition that, prior to now, might be seen as resistant to motivic analysis because of its highly unpredictable surface melodies and rhythms. Sherill and Boyle’s method is effective for parsing recitative passages into formulaic modules of the type shown in Example 9.3. Their approach could potentially inform motivic analysis by suggesting the kinds of motives that are appropriate for a passage. At the surface, short melodic motives can be seen to associate with their schema labels, such as the A3-​ D4 4th leap appearing inside their Schema #2 (“Prua”), and the F♯3-​A scalar 3rd inside their Schema #5 (“Vela”). Their segmentation further suggests a means for applying reduction to recitative. EDR, by nature, is an awkward fit for freely measured music. A better strategy would be to draw either one or two representative pitches from each of Boyle and Sherrill’s modules, or all of them when a conjunct melody appears (Schema #8). Motivic analysis has the potential for enriching schema theory, as well. That discipline presently offers few guidelines about schema ordering (Gjerdingen 2007, 377). The few it does are general, concerning formal function: for example, Sherrill and Boyle suggest that a set of interchangeable “initiatory” schemata will proceed to “medial” and “closing” schemata (2015, 13). On the basis of the tones extracted from segments, other forces might be called on to explain segment ordering. Example 9.3 subjects one of their segmentation schemes to reduction in two voices as indicated by upward and downward stemmed notes. Once the large linear 5th is imposed, the

322  Analyses and Conclusion Example 9.3  Example 24 from Sherrill and Boyle 2015. Galant schema segmentation informs reduction (newly added stems and beams).

syntactic function of the schemata can be rationalized as 1) providing the high tone D4, 2) elongating the phrase by pausing the long-​range descent, and 3) concluding the phrase with rapid descent. Much has been made of the present method’s open-​endedness, specifically in regard to the operations allowed for associating motives and the domains included within CMA. In both cases, readers are encouraged to augment the original prescribed lists with their own rigorous, stylistically-​relevant operations and domains. In addition to these extensions, we here note one more. Readers will recall that the two Interlude sections of Musical Motives explored a set of archetypes borrowed from literary theory for the purposes of structuring comprehensive and moving accounts of pieces. The specific plotlines prescribed—​ Propagative, Accretive, and Cyclic—​are in no way definitive. Depending on the cultural sensibilities of the music and the analyst, a host of other plotlines could be devised. One can easily imagine abandoning the linear, time-​directed narratives that have long held sway in Western aesthetic discourse in favor of other worldviews. Doing so would introduce intriguing new wrinkles into BMA and CMA, not least with respect to their graphic representations. In place of left-​ to-​right oriented flow charts and clockwise loops, analysts could explore alternate criteria for representing motivic activity and relatedness. Inspiration for these alternate schemes could come from nonrepresentative artworks such as those shown in Example 9.4 by Wassily Kandinsky (1866–​1944). In Kandinsky’s Several Circles (Example  9.4(a)), the bursts of activity in the northwest and southeast regions of the canvas suggest two main motivic conglomerations. In crafting a CMA narrative of a ternary form piece, an analyst

Example 9.4  Nonrepresentative artworks as inspiration for further narrative archetypes. (a) Vasily Kandinsky, Several Circles (Einige Kreise), 1926. Oil on canvas, 55 1/​4 x 55 3/​8 inches (140.3 x 140.7 cm). Solomon R. Guggenheim Museum, New York, Solomon R. Guggenheim Founding Collection, By gift. 

(b) Vasily Kandinsky, Little Accents (Petits accents), 1940. Oil on wood panel, 12 5/​ 8 x 16 1/​2 inches (32 x 42 cm). Solomon R. Guggenheim Museum, New York, The Hilla Rebay Collection.

324  Analyses and Conclusion could generate a roughly analogous image by depicting the music’s A and B sections as two main regions, with like motives grouped inside by color or proximity. Kandinsky’s Little Accents (Example 9.4(b)) could serve as a blueprint for an alternate motivic scheme. In this case, groups of like motives—​even those separated by great distances in the score—​could be organized atemporally in linear regions, with size and shape used to represent surface variations.”6

The Persistent Limitations and Future Promise of Motivic Analysis With all of the effort given over to building flexibility into this method, it is acutely ironic that it exhibits such consistent unease with the one aspect of Schoenberg’s theory that was created to treat issues of musical ambiguity. I am referring here to developing variation. If a melody opens with an ascending 3rd motive with arsis-​to-​thesis energy, Schoenbergian theory holds that that shape, under repetition and subtle alteration, can grow to become a 5th, 6th, and then eventually an octave or more. The argument that the shape transforms over time is sustained by appeals to listener memory and to general musical “logic.” To clarify, the method prescribed in this book does allow musicians to engage with developing variation to a limited extent. If we wish to trace the evolution of that hypothetical, two-​note gesture, we can define it as a complex motive possessing pitch, rhythm, and contour attributes. Every time the shape returns spanning a larger interval, the rhythm and ascending contour will be retained. Mathematically speaking, this amounts to two-​thirds (66.66  percent) of the shape returning. The light that CMA shines on, say, the varied presentations of a melodic-​rhythmic shape thus is more comprehensive in some ways than a Schoenbergian reading, in that it selectively tracks which aspects of the motive are retained. In many other ways, of course, it says less. What falls to the wayside, mostly, is the poetry. A process that Schoenberg would have viewed as evolution or a yearning for growth is, in this method, rendered clinically as “a pickup figure occurring three times in succession with x and y degrees of alteration.” I am exaggerating a bit here. It remains true that this method aspires to inject poetry and narrative concerns into analysis whenever possible, at the same time that it privileges literal over varied repetition. It is that last shift in philosophy that ensures that this analytical approach could never be mistaken for Schoenberg’s. I  am quite certain that he would have detested the “improvements” Musical Motives makes to his method. Its new rules, which are offered in the spirit of making Schoenberg’s system more rigorous, at times will block analysts from commenting on some motivic connections that feel true but cannot be proved. Having died in 1951, Schoenberg cannot have known the extent to which music

Conclusion  325 theory would flourish as a scholarly discipline. His prescience concerning the potential fate of his own theories is, however, remarkable: I would have  .  .  . liked to have brought one or another idea into the world, and still more to have stood up for it, spoken for it, and fought for it. I would have liked to have done for myself what my disciples will do. I would also have liked—​I cannot deny it—​to have won the glory for it. Now I suppose I must do without all that, and content myself with what is really there, with all that I have borne, whose paternity will undeniably be granted to me, and not begrudge recalling ideas, undoubtedly brought forth by my creative will, that will now be adopted by others. Unfortunately, I know only too well how disciples differ from the prophet. How what was free and agile, perhaps even seemingly full of contradictions, now becomes rigid, pedantic, orthodox, exaggerated, but uniform—​for the talented, all that is great, like nature is full of contradictions because they don’t see the real connections, and thus the essential deludes them. This damned uniformity!



(Auner 2003, 53–​54)

These are the words of a musician who ranks artistry above all other concerns, who would disavow any elegant comprehensive theory were it to require him to sacrifice even a single intuited insight. But of course, Schoenberg always viewed himself primarily as a composer, where I view myself primarily as a music theorist. My aim in pointing out the irony of Musical Motives—​a book that, by the act of strengthening the terms of a pre-​existing theory causes its collapse—​is to first point out the gulf between our philosophies. More generally, it is to remind readers of the inevitable trade-​offs that theorists must always make when seeking to establish and obey rules that apply to the musical arts. Not everyone will be satisfied with that answer. For any who feel that the present method is too literal and restrictive, they may establish and newly include operations that recognize inexact repetition. In addition to developing variation analysis, which is still in practice, a number of more rigorous theories have been developed for this purpose. Among the most promising is the area of theory concerned with “similarity” relations, in which the degree of overlap between two entities is determined through comparison of their total pitch, pitch-​class, and interval content.7 The challenge, if one hopes to incorporate any kind of nonliteral viewpoint into motivic analysis, will not arise at the local level. Modern music theory already possesses many ways to answer the question, “How similar, exactly, are these two events?” It will arise at the macro level, where the number of motives an analyst juggles at once expands beyond two, three, or four, as here, to dozens or hundreds, whose individual identities will be difficult to establish.

326  Analyses and Conclusion One reason, then, that the present method excludes developing variationtype transformations procedures is to ensure neater frameworks for BMA and CMA. Another is that many of the more advanced techniques for calculating similarity require computer-​aided analysis. Analyzing music via computer is not beyond the reach of the average, musically literate reader. Getting started with computer analysis, however, does require a longer period of training, in which one must become familiar with the language of encoded music and with running analytic software. Just as important, one must become adept in developing the right questions to ask the computer to obtain usable results. There are many advantages to employing a computer in analysis, such as efficiency and infallibility. If asked to locate a motive in a piece, a computer can perform the task millions of times faster than a human and will do so perfectly, not overlooking any literal repetitions.8 A computer enlisted to calculate levels of organicism for the data charts used in CMA will never omit a value or average the applicable domains incorrectly. Its capacity for analyzing many pieces at once allows researchers to investigate other kinds of “big” theory questions. To inquire into the topic of compositional influence, one can isolate an iconic motive from one composer—​say, Beethoven’s “fate” motive—​and seek it out in works by predecessors and successors. This same procedure, applied to many thousands of pieces, can inform style analysis by establishing which types of motives are favored in certain time periods and regions. These extended techniques are worth pursuing. The reason they are not accommodated here is, again, due to my own analytic proclivities. In traditional, hermeneutic analysis, one begins working on a piece by applying whatever background knowledge and expertise one possesses. The decisions one makes on what motives are important and what form they take are circular: one intuits a starting set of shapes from the piece, tries out analysis, and then retools the motive bank in the hopes of improving the result. This kind of give and take approach, in which one concentrates attention on a single work for a long period of time, might strike some as myopic. Others, who see the value of this approach, are more likely to view analysis as an opportunity to actively engage with a piece of music, to re-​perform it, if you will. Through the continual refining and adjustment of motives, analysts retrace the steps by which composers assemble their pieces out of shape and gesture. The process I am describing should sound familiar to anyone who has received training in musical analysis, no matter the type. Set theory analysts engage in dialogue with pieces by customizing their analytic toolbox in real time. Perhaps the trichord they initially selected would have more explanatory power if it were a tetrachord that included other interval types, or perhaps a more compelling story would emerge from circling alternate sets in the score. Schenkerian analysts devote long hours to drafting multiple

Conclusion  327 voice-​leading graphs of a single work, which amounts to recomposing it several times over. Human beings are innately musical, meaning that most everyone seeks out music. The degrees to which they choose to do this vary tremendously, however. Some people enjoy hearing it and moving to it when it is present, but that is all. Some dedicate time to performing it as experts (trained instrumentalists) or as amateurs (dancing, tapping, and singing along). Some create their own music, composing new works with the aid of technology and/​or by improvising alone or in groups. In modern Western culture, these activities are informally ordered in a type of progression. Young musicians typically start with singing and dancing, and then—​time and opportunity permitting—​take up trained performance. Ultimately, those in the Classical stream may opt to study advanced-​level music in academies or universities and pursue a career in music. Those in the popular music stream may simply find in their young adult years that more and more of their time is spent making music. When a musician at any level of proficiency thinks about moving to the next, he takes stock of himself, asking “do I wish to know more?” Those content with their level of ability and knowledge will answer “no,” or will not entertain the question at all. Passionate connoisseurs of music, who wish to experience it more deeply, in more ways and at new levels, will answer “yes.” Professional and pre-​ professional musicians rarely think about these choices anymore; for them, a day of playing, making, and analyzing music is simply their way of life. Amateur musicians, in contrast, confront this issue often, since it is their precious spare time that must be bartered for that needed to read up on their favorite bands, play music with friends, seek out lead sheets and transcriptions online, or follow reddit threads on theory and analysis. This book opened with an appeal to those amateur musicians and will close with another. If your appreciation for music has at all stagnated—​if you feel your favorite old recordings or your old instrumental noodling patterns are growing stale—​the problem may not be that your attention span has diminished. It is likely that you have temporarily run out of ways to experience music. If you listen only, you can get more involved in the making of music by taking up an instrument and/​or composing. If you listen and play already, you should explore new artists and genres . . . but also, you should strive to know more about the music and musical works you love. Before the age of the Internet, this meant reading and attending public lectures. Those resources remain. Now, however, they are supplemented by a host of online video essays that examine the hidden technical features of well-​written music. Some of these video essays are of extremely high quality, boasting sufficient creativity, polish, and insight to inspire just about anyone. The video medium has an inherent weakness, however, which is that it promotes passive learning.

328  Analyses and Conclusion The viewer watches and listens, but does not create. To truly engage the brain, musically, it is necessary to do something musical. It is in this respect that music analysis shines. It is this technical, detail-​driven practice that allows us to get our hands on the music as we ask questions of it. For anyone who feels that they have exhausted all the usual pathways toward musical wonderment, I prescribe a regimen of music analysis. It is one thing to listen to an expert point out hidden connections that enhance your appreciation of your favorite works. Such an experience can be of great value, especially in providing analytic models worthy of emulation. But know this: no claim or insight into a piece of music you come across, no matter how complex or poetically perfect it seems, will mean anything to you unless you are able to experience it for yourself. This is a tall order for the average music fan, who lacks the time and resources to become versed in diatonic and chromatic harmony, species counterpoint, and twelve-​tone space, and all of this before immersing themselves in Schenker and set-​theory. (In truth, it is a sizable task even for professional music theorists!) Fortunately, there is a way forward through this seeming morass. There are many pathways to choose from when preparing to embark into the deep woods of music analysis. Some are short and return a quick data point, while others are long and lead to deeper routines of questioning. Some of the paths have been attended to for decades by theorists pruning away inconsistencies and posting signs for proper analytic conduct. These routes are pretty and well manicured, but often very narrow. This book stands as an invitation for curious travelers to stroll down a decidedly different type of promenade. The pathway representing the practice of motivic analysis is exceptionally wide. It will accommodate specialists pursuing the most complex strains of analysis as well as amateurs seeking information about the most basic (yet still highly satisfying!) echoes and re-​echoes of basic melodic and rhythmic shapes. This path, however, is also a bit unkempt, with fewer traditions and rules in place than others. Hopefully, readers will not find it quite so wild and woolly as they did before beginning this book. To anyone that passes this way, I bid you good fortune and happy hunting. I take cheer in your enthusiasm and await your findings with great anticipation. The last advice I offer to ensure the best possible results is to analyze responsibly, which entails treating the system with care and keeping its limitations in mind. Remember that, within the realm of motivic analysis, there are no absolute truths waiting to be discovered. There are only a myriad of smaller truths. The first emergence of any of these truths will apply to a single consciousness, the investigator relying on motives to interrogate her or his own habits of hearing, understanding, and feeling. This analyst will look to communicate this truth to others, and this is what a theory of music is for. Musical Motives exists to facilitate such conversations. It is offered in the hopes that in future discussions that involve motives, musicians will come closer to speaking the same language.

Notes Chapter 1 1. Victor Zuckerkandl (1956, 75–​79) identifies the music–​motion connection in the writings of Hegel, Helmholtz, Hanslick, Schenker, and perhaps most famously, Roger Sessions. An alternate account is explored in Rowell 1983 (170–​172). 2. This book follows scientific pitch notation, in which all pitches within an octave, C ascending to B, receive the same numerical designation. For example, the lowest note on an eighty-​eight-​key piano is A0 and middle C is C4. When describing strings of melodic pitches, the first note will be given a register designation. All subsequent notes will be assumed to lie in the same octave unless a new octave is specified (e.g., E4-​C-​D-​B3-​A-​E4 starts above middle C, crosses below it for two notes, and then ends on the E above). 3. In further support of the argument that all music moves, Gjerdingen 1999 (142) cites “the conjecture that many motion percepts . . . may be a product of the same type of neural circuitry” proposed by Grossberg and Rudd 1989 for vision. Sidestepping the thorniest questions of how the brain responds to music, we will concern ourselves only with post-​listening contemplation. At that stage, it is reasonable to assume any musician would perceive a series of nonoverlapping pitches that are proximate in register as a single, moving line. 4. A precedent for Schoenberg’s account of motive is found in Hugo Riemann’s definition from the previous century: “A melodic fragment which in itself constitutes the smallest unit of expressive meaning” (Riemann 1903, 14, cited in McCreless 1990, 227). 5. The connection to the opening soprano idea is actually slightly stronger: its four-​note shape, C3-​D♭-​C-​F is sounded by the bass in mm. 5–​8. See also: the semitone trill! 6. Korsyn 2003 cites a like demonstration from Sigmund Spaeth in which the melody of the song “Yes! We Have No Bananas!” is shown emerging from the absurd combination of Handel’s Hallelujah Chorus and “My Bonnie Lies over the Ocean” (98). Korsyn’s example opens an important discussion on the “policing” of motivic associations, which is to say, deciding whether to limit them to one movement or to allow them to serve as the bases of inter-​movement and inter-​opus allusions. 7. A more politic way to state this would be to say that forward momentum strongly correlates with motives and stasis with their absence. I favor the main text’s wording because it invites us to question common assumptions about motive and motion. Most would not immediately regard a homophonic chorale as composed of motives (though one may certainly discern their presence), but to the extent it exhibits forward energy it must be. In contrast, a moment form piece, such as Kontakte by Stockhausen, may initially appear to exhibit motives at least in the interior of its

330 Notes nonlinear texture-​blocks. But if one interprets these blocks occurring out of time, as representative of some “now” and completely devoid of forward motion, then those shapes do not function as motives. 8. “In 1942, Von Békésy was the first to observe that at every point along its length, [the basilar membrane, a region in the ear] vibrates with maximum amplitude for specific frequency. This finding confirmed the hypothesis launched eighty years earlier by Helmholtz, that the cochlea performs a frequency analysis” (Rasch and Plomp 1999, 92). 9. In experiments carried out by Eitan and Granot, a mixed population of musicians and nonmusicians were exposed to paired sound stimuli in the domains of pitch (ascent and descent), dynamics (crescendo and diminuendo), and duration (elongation and contraction). They report that “pitch ‘rises’ suggest, as expected spatial ascent” but are also “significantly associated with moving away (contrary to the Doppler effect), with acceleration, and with higher energy” (2004, 232–​233). In other words, the up/down pitch metaphor is hardly universal. 10. This series of events is described by Daniel Levitin with regard to brain scans taken of participants in a listening experiment: “Listening to music caused a cascade of brain regions to become activated in a particular order: first, auditory cortex for initial processing of the components of the sound. Then the frontal regions . . . that we had previously identified as being involved in processing musical structure and expectations. Finally, a network of regions—​the mesolimbic system—​involved in arousal, pleasure, and the transmission of opioids and the production of dopamine” (2006, 187). 11. The specific quality of an interval, for example major (G4–​E♭) versus minor (F4–​D) for thirds, is usually disregarded as an identity marker for tonal motives. 12. The same analogy between motif and motive is noted in Laitz 2008 (768–​769). 13. Degeorge and Porter note the role of tile patterns for “bringing out architectural forms—​the verticals, the soffits of an arch.” This role was sufficiently established that tenth-​century “Geometry treatises were even written with the architectural decorator in mind” (2002, 28). 14. Sims, Marshak, and Grube 2002 describe this piece in similar terms: “The decoration consists of abstract geometrical motifs, and birds and animals of a particularly elegant stylization that was hardly ever surpassed, anywhere, at any time. Features are elongated to the point of abstraction, like the long necks of the water-​birds pacing around the rim and the bodies of the hounds, perpetually pursuing themselves in the next register. Natural shapes are exaggerated, as seen in the extravagantly curved horns of the bearded mountain goat in the widest register of the beaker.” 15. In modeling perception, Alexander’s graphic represents one of the first of several “conceptual models” that will be encountered in this study. A fuller definition and account of conceptual modeling is given in c­ hapter 3. 16. The term for motives that have acquired such meaning, originating with Wagner, is Leitmotive. Famous examples from his Ring cycle symbolize Valhalla, Siegfried, and the “curse” on the Rheingold; famous examples from popular cinema include the “Empire” theme from the George Lucas’s Star Wars trilogy and the “Shire” music from Peter Jackson’s The Lord of the Rings trilogy.

Notes  331 17. In support of this notion, we note first that dramatic music is possible without words. That fact is evidenced by thousands of Classical instrumental pieces written in the “absolute music” tradition as well as by the existence of untexted works written in jazz, folk, country, and rock idioms. Second, in cases where words appear, they may be regarded as serving a subsidiary purpose. A song may begin its existence as a poem, but once music is added, the text’s status changes. In three models of text–​music relationships proposed by Agawu 1992, words are relegated to a lesser position by virtue of either being dependent on the musical aspect or being subsumed by it (or by the song genre). 18. The emphasis given here to motives’ structural behavior is not meant to enshrine formalism. A host of scholars, among them Robert Hatten, Lawrence Kramer, and Susan McClary, have convincingly argued not only that music carries meaning but also that all such meaning is culturally encoded. Harold Bloom wrote, “There is no such thing as a poem in itself ” (1997, 43). It follows that there is no such thing as a piece of music in itself: a musical work is “a relational event, embodying impulses . . . from a variety of sources” (Straus 1990, 12). All who come in contact with a musical work bring their experiences to bear on it. There is no cause to investigate that chain of awareness here. I make reference to it to allow us to separate upper-​level musical meaning—​which will always be ineffable to an extent—​from the type of modest, baseline meaning referenced earlier in the main text. Such meaning, which turns on recognition of the abstract patterning of motives, in my view entails nothing more than actively listening to a work. 19. Further discussion and argument for this “introversive” mode of analyzing will be given in ­Interlude 1. 20. Merriam-​Webster, s.v. “motive.” 21. Truly listening to music, often referred to as “active listening,” means preparing ourselves to receive intelligent communication. 22. See Lakoff and Johnson 2003 for discussion of how conceptual thinking is rooted in bodily experience. Further discussion of how metaphor applies to musical knowledge is given in Brower 2000, including specific narrative schemas like “departure,” “return,” and “overcoming blockage” (353).

Chapter 2 1. Information theory is a subdivision of mathematics that treats modes of communication such as speech, sonic waveforms, and alpha-​numerical codes. An introduction to and brief history of the discipline is given in Bose 2008 (1–​9). 2. As discussed at length in Straus 1987, Dubiel 1990, and Cohn and Dempster 1992, counterpoint depends on a set of requirements. Chief among these are a vocabulary of standard chords and a sense of hierarchy, which holds that a set of two or more faster notes stand in for or “reduce to” a single, longer representative note. A fuller discussion of issues surrounding counterpoint will appear in c­ hapter 5 in the section on melodic reduction.

332 Notes 3. Of the many oversimplifications present in Example 2.3, the design and content of the far right columns may be the most egregious. To carry out a responsible style analysis, it would be necessary to devote many pages to each of the three streams shown. Within the sphere of popular music, for example, the roles of harmony and motive are radically different across different subgenres. These two domains play a more dominant role in structuring Motown songs and piano-​based rock pieces by the Beatles and Elton John; in contrast, they generally play a more textural, formulaic role in repetitive blues-​based rock and sample-​track rap music. Moreover, it is common for artists to explore many types of subgenre as they develop, such that the relative prominence of all the listed style elements fluctuates. 4. The Lydian mode is a diatonic collection that uses the same intervals as a major scale, but arranges them in a different order over the central note (similar to a “tonic,” but called a modal “final”). In practice, it sounds like a major scale with a raised fourth scale degree. 5. This two-​word term is fraught with complexity (see Crocker 1962, 16–​17, and Tymoczko 2011, 226–​230). Used in this text, it refers to musics that, first, exhibit a preference for triadic vertical harmonies and, second, favor certain orderings of those harmonies to produce a forward-​tilting sensation commonly referred to as “progression.” Under this definition, Common-​Practice Classical music can be said to exhibit functional harmony in the form of standard root chord progressions, while world musics like Gamelan do not. 6. This revolution was initiated by Jean-​Philippe Rameau, a composer-​theorist whose active period wholly coincides with J.S. Bach’s. A set of early chapters in Rameau’s 1722 Treatise on Harmony are remarkable for recognizing inversional equivalence among chords. (Hard as it may be to believe, it was not at all common before Rameau to regard two D7 chords, one with a D in the bass versus one with an A in the bass, as the same creature.) Later chapters in his treatise set out rules for the allowable successions of chords based on their root motions, a precursor to what became Common-​Practice chord-​progression theory. 7. The gigue’s opening gesture, in other words, functions somewhat in the manner of an opening argument in an oration. There is a long tradition of conceiving purely musical processes in terms of rhetoric (Butler 1977, Harrison 1990, McCreless 2006). According to that tradition, a successful piece follows the model of a successful spoken address in which a central argument is presented, then broken down, challenged, and proven. It is known that Bach’s duties in Leipzig included instructing students in rhetoric. Even were this not the case, as a learned musician of the European Enlightenment, he would have been acutely aware of this tradition. 8. The motion from F4-​A is properly a “chordal leap,” since it does not unfold a full triad. This text will generally treat chordal leaps as the degenerate case of arpeggiation; hence the moniker Arp2. 9. No stipulation has been made that the low-​level arpeggiating gestures of Climb must derive from a single triad, thus the label readily applies to these longer tonic-​dominant stretches.

Notes  333 10. In the interests of clarity, the present analysis keeps separate the Cascade and 3rd motives. This decision does not preclude the possibility of the two being unified at some deeper level, with both perhaps springing in the abstract from some ur-​linear-​ third. (This possibility is suggested by the close proximity and interchangeability of C and the linear 3rd, and especially by that moment in m. 21 where the 3rd grows into the C motive.) This issue, which is highly complex from both methodological and philosophical standpoints, will eventually be taken up in the book’s conclusion. 11. This generalization applies primarily to the expository areas of Classical pieces. In contrast, the transitional and developmental areas in these works exhibit more irregular phrasing. Within them, expansions, elisions, interpolations, and excisions of material frequently result in asymmetrical phrase structures. 12. This is especially true for dramatic genres such as opera, where it is well known that Mozart indicated characters’ shifting intent and mood by altering their melodic material; see David Lewin’s comments on Mozart’s Figaro (2006). Such practices led James Webster to comment that “Motivic development within a number is unquestionably one of Mozart’s most important techniques for generating coherence, precisely in the supple, unremarkable ways that dramatic music requires (and in full compatibility with the lessened importance of tonal ‘polarities’ and ‘resolutions’ compared to instrumental music)” (1990, 211). 13. As for subsequent development of the second theme, here too one can hear fainter echoes of “Leap-​then-​Leap” in mm. 37–​48 in the cellos and basses. For each station in the circle-​of-​fifths progression, their downbeat notes unfold a large descending seventh. The square patterning results in a restoration of the motto’s original rhythm and intervallic content from mm. 1–​4 (long notes arranged as paired descending leaps). 14. The material here, in terms of motives, harmony, and texture, closely resembles mm. 13–​24. In other words, the material that carried out the function of transition in the exposition is now repurposed as a retransition. 15. The upper voices, remarkably, collaborate to assemble the alternate downward E♭-​F♯ span. This is not shown in the analysis; however, readers interested in tracing it can find the start of the path at the E♭5 in m. 109 in Violin 1 and at the B♭4 in Violin 2. 16. This is not always the case, as many of Wagner’s Leitmotives took short forms, some as brief as a single sonority (i.e., the “Curse” motive from the Ring). 17. Zbikowski 2002, 54–​58, offers a sensitive account of how hearing a Leitmotive in different forms and shadings is akin to the act of remembrance. 18. The term “tradition” should be taken loosely here. Note that for all of Brahms’s professed allegiance to tradition, throughout his life he maintained a highly complex relationship with it. Peter Burkholder (1984), citing Brahms’s technique of mining harmonies and contrapuntal techniques from earlier ages to create (paradoxically) “modern” sounds, identifies him as the first truly postmodern composer. 19. The process by which a motive alters its shape over time by gradually shifting its intervallic or rhythmic content is known as developing variation. The origins of the procedure as well as its implications for motivic analysis will be further considered in later chapters.

334 Notes 20. Real sequence is generally viewed as a more literal, “mechanical” means of copying out music, in contrast with diatonic sequence in which the component intervals shift to conform to single controlling key. 21. To expand on a point made in Example 2.3, musical traditions in the West fractured starting at about the year 1900. At the same time that post-​tonal music developed, tonality persevered and continued evolving in work by composers such as Elgar, Vaughan Williams, Prokofiev, Poulenc, Britten, and Barber. This resulted in a living tradition that Daniel Harrison has fittingly dubbed “enriched tonality” (2016, 1–​5). 22. This led to important innovations notably in the domains of texture and timbre (Schoenberg’s Klangfarbenmelodie) and in a new harmonic practice that might be termed “contextual tonality.” Contextual tonality occurs when a synthetic (nontonal) entity relevant to the piece at hand—​e.g., a surface chord, scale, or collection—​is “composed out” so that its components coordinate the structure of the larger work. This phenomenon is often observed in pieces by Liszt and Bartók. 23. This view of twentieth-​century music is widely shared, and is in fact a central thesis of Straus 1990: “The late nineteenth century now appears as a period in which motivic association, a secondary and dependent determinant of structure in the classical and early romantic eras, was elevated into a central and independent organizing principle” (22). As here, Straus uses Schoenberg’s Op. 11, No. 1 to introduce readers to motivic unity; however, the motive forms he devises look very different from the ones that are prescribed by this book’s method. 24. The present analysis uncovers a different sort of unity in this work than the one afforded by more traditional motivic approaches. Specifically, aural criteria serve as the basis for parsing and bracketing musical events. This contrasts with the set-​ theory view that identifies the many overlapping [014] trichords across the voices (cf. Wittlich 1974). 25. Many minimalists, Steve Reich prominent among them, cite the Notre Dame School of polyphony (1160–​1250) as an influence on their music (Schwarz 1980, 380). 26. Later composers such as Boulez and Babbitt, cultivated styles of so-​called “total serialism,” in which the purview of the row is extended to control the order and types of events in additional domains such as rhythm, dynamics, and articulation.

Chapter 3 1. Most theorists are well versed in the general account of music theory history to follow, including its tripartite branching into musica speculativa, musica practica, and musica poetica. A fuller account is related in Christensen 2002, which sagely advises readers to treat it as a framework rather than as gospel (5). 2. The first use of the term musica poetica was by Nicolas Listenius in 1537. 3. The idea of the divine monochord stems from Robert Fludd’s 1618 treatise De musica mundana. See Gouk (2002, 229–​233) for a fuller account of Neoplatonism and to view an image of the divine monochord.

Notes  335 4. An early practitioner of analysis was Johannes Tinctoris (1435–​1511). His counterpoint treatise of 1477 reproduces numerous passages of music by close contemporaries and critiques the quality of their construction. 5. Bartel 1997 connects the rise of rhetoric with the rise of Christianity, in which “scholars and writers of the Church adopted the classical rhetorical discipline from their Roman teachers.” The practice was maintained throughout the Middle Ages by “rhetoricians focused on the art of composing letters or official documents” (65). The influence of rhetoric rapidly expanded in the Renaissance “to pervade all areas of civilization, as it had not been the case during the preceding centuries” (Kristeller 1979, 219). 6. Bartel draws a direct link from “the notion that phenomena must be terminologically identified and defined in order to be understood and taught” to the teachings of Aristotle (1997, 83). 7. The first version of Burmeister’s theory of rhetoric appeared in his 1599 Hypomnematum musicae poetica. His 1606 treatise, Musica poetica, returns to his list of figures and expands it; the latter work is the one usually cited. 8. Burmeister was not the first to observe composers employing special devices to enhance the emotional effect of their pieces. Early catalogs of figures, typically quite abbreviated, date from as early as 1559 (Palisca 1959, 156). In deploying these, composers frequently and knowingly violated the rules of strict counterpoint, allowing dissonant notes to have irregular resolutions. Mid-​sixteenth-​century musicians were well aware of the special sound and emotive effect of passages written this way, which explains their use of the alternate contemporary designation, musica reservata. 9. Burmeister’s understanding of “figure” derives from Quintilian (35–​100 c.e.), who describes it as a special, expressive form of speech that deviates from the “general, first-​kind” of speech (MGG, s.v. “Musik und Rhetoric”). 10. The term “segment,” more fully defined at the beginning of ­chapter 7, plays a central role in the theory of motivic analysis to follow, serving as the essential formal unit for viewing the structure of pieces and for establishing the content of complex motives. 11. Discussions of the pre-​Baroque and Baroque eras make frequent reference to “mannerism,” the “Doctrine of the Affections” (Affektenlehre), and “Sensitive Style” (Empfindsamkeit). The three terms are interrelated but distinct. Mannerism is the most generic of the three, referring simply to any special or ornate departure from normal style; a mannerism will likely provoke emotion but is not required by definition to do so. Affection refers to “rationalized emotional states or passions” that could be roused via external (sonic) stimulus (Buelow 2001, s.v. “Affects”). Though I do not employ the term in the text, an affect can be regarded as a specific manifestation of music-​emotive theory that may be active at the level of the phrase, as for Burmeister, or at the level of a piece, in accordance with the dominant aesthetic system of the Baroque. Empfindsamkeit refers to a style of composition that emerged later, in the mid-​eighteenth century, in which numerous, contrasting emotions are aroused by means of rapid changes in surface material. 12. Wolfgang Caspar Printz (1641–​1717) represents a lesser personage in the development of figures. His approach, codified in the three-​volume Phrynis mytileneus from 1696, is notable for reorienting figures to the purely melodic domain (Bartel 1997,

336 Notes 120–​121). Printz’s classification scheme includes larger categories of silent versus sounding events. 13. Kircher is further remarkable for being among the first to venture beyond learned counterpoint to list topics that pertain to recitative-​style melody; this occurs in Book VII of Musurgia universalis (1650). 14. Bernhard’s treatise forgoes Latin in favor of vernacular German, signaling a turn toward practical, composerly concerns (McCreless 2002, 867). Bernhard is, moreover, “the first author to explicitly apply the concept of the figures to purely instrumental music” (Bartel 1997, 114). These characteristics are symptomatic of a brave, inquisitive temperament, one that instinctively bridged both religious-​secular and German-​ Italian musical boundaries. 15. Caplin 2002 establishes a larger context for connecting poetic feet and rhyme schemes with rhetoric, citing similar examples in works by Mattheson’s precursor, Printz, and his successor, Joseph Riepel (663–​666). 16. This topic is explained in more detail later in this survey. Hinrichsen 2015, quoting Christoph von Blumröder, notes that “thematic working” had its conceptual roots in the 1700s, even though specific terms for it came later. He credits Mattheson for his role in firmly establishing elaboration as one of the primary bases of good composition. 17. These more modern styles thus saw a proliferation of figures associated with specific emotions. Awareness of this fact is critical in analysis and as such will be treated in Part II of this book. Specifically, the first Interlude of Musical Motives will touch on general principles that apply to how figures acquired and held their meaning, and how awareness of those meanings impacts analysis. 18. Harrison 1990 mines Quintilian’s writings for a fitting rhetorical term to describe a compositional “problem.” He lands upon status, “a conceptualized conflict that generates the need for a persuasive oration and determines its character. For example, the pair ‘accusation’ and ‘denial’ form a status, one that is the basis of many legal disputes” (10). 19. Ironically, where Reicha uses the word “motif,” it is to “[identify] what we would term theme,” meaning a conventional, eight-​measure event (Moreno 2000,165 n. 66). 20. According to Trippett 2013, Marx’s theory is wholly based “on principles of homology derived from Goethe’s 1790 Versuch die Metamorphose der Pflanzen zu erklären.” In a later article from 1856, Marx would go further to explain that “the motif . . . corresponds to ‘the germinal vesicle . . . the Urgestalt of everything organic—​the true primal plant or primal animal’” (2013, 111). 21. “Solche Formeln, welche den Keim und Trieb eines aus ihnen hervorwachsenden Satzes enthalten, wollen wir Motive nennen. Jede Vereinigung von zwei oder mehr Tonen kann als Motiv gelten; insolchen Motiven [  .  .  .  ] besteht der Inhalt aller Tongebilde” (Marx 1837, §7, quoted in MGG, s.v. “Thema/​Motiv”). 22. Scott Burnham is careful to note, “Despite Marx’s characterization of the motive as seed, the motive does not represent the starting point of his compositional method. He introduces it only after the presentation of his Grundformen, and there is no motivic development undertaken by the student without such a structural framework in mind from the outset” (1989, 251).

Notes  337 23. A  fuller account of this dynamic is provided in E.  T. Cone’s essay, “Schubert’s Promissory Note”; the pun in the title is very much intended (1982). 24. Writing in 1852, Lobe laments the seeming inability of German composers to craft melodies as beautiful as their French and Italian contemporaries; it is a stance that fully establishes his pedigree in the tradition of Melodielehre (Trippett 2013, 20). 25. All of the information that follows in this account of Lobe, including examples, is a paraphrase of Hooper 2017 (29–35). 26. Dahlhaus 1980 identifies a number of important trends in instrumental music composition in this era. The pieces grew in scope, with symphonies stretching to and then past the one-​hour mark. At the same time, their melodies contracted, so that the first idea might appear as a mere fragment lasting only a measure or two. The paradoxical, simultaneous exploration of large and small elements stemmed from composers’ concern for pursuing originality. Their solution was to concentrate on motivic development at the expense of presenting large, highly formulaic and repetitive melodies (40–​44). 27. “Tatsächlich spielen in der Musik die kleinssten zu engerer Einheit zusam­ mengehörigen Bildungen, die Motive, eine ganz analoge Rolle wie in der Sprache die Worte und bedingt die richtige Abgrenzung der Motive durchaus die richtige Auffassung, der Verständnis des Ausdrucks grösserer an ihnen gebildeten Entwickelungen” (Sievers 1967, 65). 28. The perpetually forward-​ tilting, upbeatness of Riemann’s theory is known as Auftaktigkeit. An excellent introduction to the Hegelian origins of this philosophy and its practical impact on Riemann’s theories of rhythm, meter, and form is given in Waldbauer 1989. 29. This preference is a byproduct of Schenker’s conceiving counterpoint and harmony as woven together. Doing so means that his entire analytic system is, in a large sense, motivic. 30. The origins and sustained influence of organicism are discussed at length in Solie 1980. 31. For generations, the organicist viewpoint also served as a basis for critical judgment. Between 1940 and 1990, it was common to see European and American critics seize on “lack of unity” as a cudgel to beat back composers and pieces they did not approve of. A fuller assessment of this dubious critical tradition is given in Auerbach 2013 (69–​75). 32. In the Preface to Schoenberg 2006, Carpenter and Neff document Schoenberg’s “steady” move “toward an understanding of the Idea as somehow standing for the wholeness of a work” (Schoenberg 2006, 18). 33. The particular expectations in different musical subcultures strongly impact an audience’s sense of what constitutes a musical work. To simplify matters, the analyses in Musical Motives will generally assume that classical artworks inhere in the scores created by their authors and that popular music artworks inhere in recordings and live performances. This is by no means a firm rule, and frequent exceptions will be made.

338 Notes 34. The extensive “Commentary” offered by Patricia Carpenter and Severine Neff, the translators and editors of Schoenberg’s Musical Idea treatise, remains the authoritative account of his theory (2006, 1–​86). In contrast to my own definitions of motive to follow in part II, which support this book’s more modest, literal, and mechanical analytic method, theirs faithfully reflect Schoenberg’s expansive view of music’s organization. Their understanding of Shape and motive, in other words, is inextricably entwined with Schoenberg’s philosophies of melody, harmony, energetics, and form. 35. Accounts of the length of a shape diverge throughout the literature. Rufer is flexible, allowing shapes to occupy a range of measures depending on tempo (1961 [1954], 28). This seems more or less consistent with Schoenberg’s practice. In the program notes to his own Four Orchestral Songs, Op. 22, for example, Schoenberg demonstrates how motives of a minor third and a second “link” to form a three-​ measure gestalt (2016, 220). 36. A mild but persistent sense of ambiguity surrounds Schoenberg’s more technical accounts of his theory. Even Carpenter and Neff, for example, are unable to fully untangle motive from feature as they explain, “The features of motive are intervals and rhythms, which can themselves be treated as motives” (Schoenberg 2006, 27–​28). 37. In commenting on the graphic shown in Example 3.12, Carl Dahlhaus explicitly contrasts Schoenberg’s atomistic approach with “the method dictated by common musical sense”(!). His aim in doing so is not to ridicule Schoenberg, but rather to defend him for seeking out a new way “to comprehend and analyse [sic] the inner unity of a work.” In this case that entails relying on a new truism, “that intervals . . . are the true substance of music” (1987, 130–​131). 38. The list of treatises and articles comprising transformational theory is extensive. The research undertaken by the authors Lewin, Cohn, Clough, Douthett, Klumpenhouwer, Harrison, and others in the late 1980s, under the heading “Neo-​ Riemannian Analysis” are recognized as seminal works in this field. For more on the early history of transformational theory and analysis, see Cohn 1998. 39. This interdependence is consistent with Schoenberg’s view of a musical work as a living organism, in which the smaller parts like sections, phrases, and motives “are activated . . . as a result of their organic membership in a living being” (2006, 104). 40. Chapter 5 offers an extended introduction to melodic reduction, characterizing it as integral to motivic analysis. Schoenberg is not well known for engaging in melodic reduction. In the context of laying out a method largely inspired by him, however, it seems only appropriate to cite his examples modeling the procedure first. 41. Burkhart 1978 establishes a definition for motivic parallelism (also known as “concealed repetition”) and provides a brief literature review of the topic in Schenker’s writings. Alegant and McLean 2001 investigates this phenomenon further, noting the significance of such cross-​level correspondence in both tonal and post-​tonal literatures. 42. The broad, stylized arrow below, imported from Schmalfeldt 2011, indicates “becoming,” a process she defines as “the special case whereby the formal function initially suggested by a musical idea . . . invites retrospective reinterpretation within the larger formal context” (9). Though Schmalfeldt’s interest in this type of “processual

Notes  339 thinking” is primarily analytical, it applies fully to historical developments as well. Indeed, Schmalfeldt establishes that her notion of becoming is ultimately rooted in Hegel’s model of historical change (Monahan 2011). 43. Goehre mentioned The Musical Idea “in essays on Schoenberg’s theoretical writings in 1973 and 1975. In 1977 Goehr translated and provided commentary on some segments from The Musical Idea manuscript in The Journal of the Arnold Schoenberg Institute” (Schoenberg 2006, xiii). 44. See Straus 1991 and Cope 2009 (99–112), for a history of set theory’s development in music. 45. The modern practice of providing a preliminary list of motives to prepare readers for upcoming musical and/​or intellectual enlightenment dates back to Wolzogen’s famous handbooks on leitmotivic content in Wagner’s Ring (Thorau 2009). 46. Dunsby and Whittall 1986, for example, begin their motivic analysis demonstration of Schoenberg’s Piano Piece Op. 19, No. 6 with the presentation of a motive table (158–​ 161). Surveying analyses from the last twenty years, one still occasionally encounters authors assigning Greek letters to motives (see Boss 1999 and Zbikowski 2002). 47. Motive, for Schenker, is a melodic pattern . . . that is repeated in the course of a musical work.” In the case of expansion, “the motive is no longer associated with its original rhythmic articulation” (Beach 2012, xvii). 48. Schenker treated the subject of rhythm extensively; however, his late works are ambivalent on whether diagrammed pitch events embody rhythm. Schenker once declared, “The fundamental structure is arrhythmic,” yet elsewhere he said, “the fundamental line signifies motion, striving towards a goal,” thereby attributing motion and temporality to it (London 2002, 703–​704). 49. It may seem that this history overlooks the work of Schoenberg’s adherents that emerged between 1950 and 1980, meaning, the books and articles by Rufer, Réti, and Carpenter, and BBC radio addresses by Hans Keller. These works enjoyed modest circulation among the academy, quietly sustaining Schoenberg’s legacy during this period. As they served mainly to clarify Schoenberg’s theory and methodology, though, they did not contribute significantly to this age’s shifting conception of motive. 50. In many contexts, the Ursatz’s broad explanatory power comes to increasingly resemble Schoenberg’s Grundgestalt. In Carl Schachter’s words, the tonic triad serving as the basis of the Ursatz is a “matrix” (cf. Schoenberg’s “complex”) “that has rhythmic properties:  it defines the beginning and end of complete and self-​contained harmonic and melodic progressions; it also provides the foundation for form and design, since motivic and thematic elements always connect (usually quite closely) to tonal structure (Schachter 1999, 136). 51. There are fascinating overlaps between the atemporal, interval-​based relationships David Lewin traces and the ambitious “chord motives” posited by Réti decades earlier. One network analysis developed in Lewin’s Generalized Musical Intervals and Transformations that ties together movements I  and III of Beethoven’s First Symphony is fully presaged in Réti’s Thematic Process: compare Lewin’s Figure 7.8 (1987, 169) with Example 3.17.

340 Notes 52. Walter Frisch has reported that Réti also corresponded with the composer in the 1910s and 1920s. At one point, commenting on Réti’s activities as advocate of new music, Schoenberg wrote to him, warmly stating, “You are a person who stands very close to my sphere of thought.” 53. The exception to this claim concerns the strict associations involving the pure intervallic sixth, marked s. In this analysis, s is a secondary element derived from motive a in the manner shown in mm. 1–​3 (staff 5). 54. Cohn 1992 treats the history of this conflict in Schenker scholarship at length and suggests a number of pathways for resolving it. 55. Enharmonicism is firmly entrenched in Schenkerian theory. There is no rule in that method against equating two motives in a piece that are spelled differently, e.g., E♭-​D-​ D♭ versus E♭-​D-​C♯. It is only the reordering of notes that is anathema, which in truth holds for most other systems of analysis as well. 56. One such blanket characterization is found in Nicholas Cook’s Guide to Musical Analysis (1987, 110). 57. This point is recognized in Schoenberg’s original formulation of the Grundgestalt, and is implicitly maintained in writings by Réti and Alan Walker. In discussing multimovement connections among Beethoven’s Piano Sonata, Op.  57 (“Appassionata”), Walker notes the plain correspondence between movements I and III with respect to the use of Neapolitan harmony. Although he does not specifically denote harmony as motivic, he calls for viewing harmonic motion as an “element” lending unity to the work (Walker 1962, 86–​88). 58. As a testament to this approach’s validity, all modern contour analysis algorithms grant special status to maxima and minima on the basis of their phenomenal impact (see Morris 1993). 59. Temperley 2013 describes the close overlap between the fields of cognitive (conceptual) modeling and computational modeling. “To call a model ‘computational,’ ” he explains, “implies . . . that it is specified in a precise, complete, and rigorous way—​ such that it could be implemented on a computer” (328). The two types of modeling have many affinities, rooted not only in approach (theorization of stepwise and network structures), but also in philosophy (the proposition that the human brain is essentially a computer). That being the case, computational modeling stands as one of the three main approaches generally understood to constitute the field of cognitive science (327). 60. A  critically important work from this last area is Lehrdahl and Jackendoff 1983, which posits a comprehensive grammar of tonal music, from the basic perception of the smallest rhythmic and pitch phonemes to the full landscape of works. While Lehrdahl and Jackendoff ’s organizational approach at the macroscopic levels is linguistic, when working closer to the surface of the music they are more inclined to explain perception in terms of basic gestalt principles. Their “well-​formedness rules” establish strict conditions for parsing meaningful pitch and/​or rhythmic shapes from long streams of music, and therefore will be cited where appropriate in ­chapter 5 on basic methodology.

Notes  341

Chapter 4 1. Strictly speaking, these configurations instantiate motives only in the most modern sense. Réti himself refers to them as cells, distinguishing them from motives in the nineteenth-​century  sense. 2. At the same time that Réti’s system is intuitive, it is not without fault. His instincts regarding the character of motives in many of his analyses are highly personal, a condition that sows seeds for confusion. In the previous example, it is odd, semantically, to ask readers to distinguish a “finishing” motive from a wholly contrasting—​but similarly named—​“concluding” motive. 3. Rationalizing pitch motive as an inherently melodic concept, Schenker 1921 [2004] outlaws one-​note pitch motives (27). 4. Rule P4’s labeling convention can technically be extended to cover arpeggiations of all kinds of chords, such as advanced tonal entities such as augmented sixth chords and chords that are common in post-​tonal music. One should employ it with extreme care in these other musics, however. The issue is that as one moves farther away from Classical tonality, it becomes increasingly difficult to distinguish scale steps from chordal leaps. For many works penned in the twentieth century that rely on chromatic chords, like C-​C♯-​E [014], it becomes well-​nigh impossible. For this reason, Arp in this study will be restricted to triads of major, minor, diminished, and augmented quality and to seventh chords of major, minor, “dominant,” and fully-​and half-​diminished qualities. 5. On the other hand, recall that analysts are not required to use the Arp designation at all when labeling these two shapes. We can continue to label Example 4.3(a) and (b) in the original way, calling them a 6th and 5th based on their boundary intervals. (Rule P6 later describes a procedure for naming hybrid motives built of two or more elided intervals.) In many cases, it may make sense to do this, such as if we want to connect these shapes to prominent motivic 5ths or 6ths appearing elsewhere in a piece. 6. Cadwallader 1988 similarly distinguishes the main body of a pitch-​based motive from tones on its fringes that change its spanning interval. Specifically, he calls the first melodic gesture of Beethoven’s Bagatelle Op. 119, No 1 on D5-​C-​B♭4-​A an “apparent fourth,” based on the terminal note participating in the next dominant harmony that unfolds in m. 2. Remarkably, after assigning a label to the motive that discounts its last note, he continues to view the apparent fourth as manifesting a parallelism with the large-​scale D5-​C-​B♭4-​A spanning mm. 1–​8. 7. It is possible to shift the alto’s motive in mm. 3–​4 over by one eighth note so that it spans B4-​G♯, but doing so does not change its 3rd nature. 8. Karpinski 2017 relies on this concept as a pedagogical tool for sight-​singing. In his method, students are taught to conceive of certain wide or difficult leaps—​for example, from scale degree 1 to scale degrees 6 or 7—​in terms of a “prefix neighbor” that connects to a more easily found structural tone such as scale degree 5 or 1. 9. These particular examples are offered more in the spirit of pedagogical demonstration than in the service of actual analysis. In a proper study of “The Great Gate of Kiev,” for example, I would likely propose a shorter rhythmic kernel than this. Specifically,

342 Notes L-​S-​S suggests itself as a possible way of unifying the first theme with the second theme introduced in mm. 30–​31, where that rhythm appears in augmentation. 10. The terminology of “foreshift” and “backshift” is taken from Ng 2006.

Chapter 5 1. Dominant methodologies include Schenkerian analysis, Lehrdahl and Jackendoff ’s time-​ span reductions (1983), and Robert Morris’s Contour Pruning Algorithm (1993). 2. The term “structural” is to be taken as neutral, signifying essential communicative and/​ or syntactic content. When it comes to subjecting poetic utterances or musical phrases to successive reductions, it often happens that the most striking bits of information—​ e.g., floral adjectives or gorgeous accented dissonances—​disappear early in the process. This phenomenon is reflected in the famous anecdote about Schoenberg’s reaction to reading an analysis by Schenker: “[But] where are my favorite notes? Ah yes, there—​the little black ones” (Epstein 1979, fn. 9). Witnessing this process is frustrating and disheartening for some. Over time, however, it generally becomes easier to untangle the aesthetically significant from the structurally significant in music. 3. There is much more that can be said about the reductions presented in the example. To start, there is the matter of the C4 missing from m. 1, which fits within the tonic harmony. Chordal leaps of this type are routinely ignored in melodic analysis. They signal a flitting away from the active melody to touch on an interior voice, in this case the presumed alto. 4. This insight, not currently appearing in the left side of Example 5.3, could be accounted for by positing an additional motive that incorporates the two structurally accented events of the passage, the starting F4 and closing G4. (The upcoming section on principles of reduction will formally fold this issue in to equal-​duration reduction.) 5. The idea of melody, then, can flexibly apply to shorter, phrase-​length gestures as well as to the melodic descent taking up an entire piece of music. The latter typically only emerges after several reductive iterations. 6. The last two criteria in his list will have less utility in the present system, which aligns more with twentieth-​century (i.e., “nontonal”) pitch-​cell practice. For what would be Epstein Point (E.P.) 4 “Degree position of pitches within a key,” we will have no reason to give special consideration to motive forms that express prominent scale degrees. E.P. 5, “Harmonic content,” will generally be irrelevant in the context of BMA. It will play a role in complex motivic analysis when other domains are grafted onto our motivic model. 7. Friedmann 1985 offers an early description of this procedure, the results of which yield a Contour Class (227). Morris 1993 refers to this ordering simply as a “normalized contour” (206). 8. Morris 1993 describes a procedure for performing this first reduction and then successively feeding the results back into the reduction machine to boil down every contour to a basic type.

Notes  343 9. These two phenomena are more formally known as metric dissonances, in which expected accent patterns are shifted via “displacement” (i.e., syncopation) or by “grouping” (i.e., cross-​rhythm, or hemiola) (Krebs 1999). Here we may also note a slight redundancy in Epstein’s discussion. His text treats dynamics and articulation separately, even though they are interdependent with syncopation and cross-​ rhythm; more specifically, these domains help create these rhythmic/​metric effects. We maintain the artificial distinction, however, because musicians effortlessly “see through” the contributing elements to perceive the metric dissonances more or less directly. 10. Temperley 1999 describes syncopation as a surface element of musical grammar that transforms a simpler “underlying structure,” much in the way that in Chomskyan linguistics a highly complex surface utterance in English can greatly transform a deeplevel, subject-​verb-​object structure (27). Much of that same article is given over to prescribing rules for understanding how music’s surface syncopations reflect a simpler beat structure that is fore-​or back-​shifted (see diagonal lines in Example 5.6). For more on the origins and role of displacement dissonance in tonal analysis, see Traut 2002. 11. The reduction reflects another of the grace notes’ functions, which is distinguishing the two voices embedded in the right hand’s melody. The soprano tones occupy the second and third eighths of each measure and compose a singable melody. The alto is expressed by the first and fourth eighth notes. 12. Carpenter recognizes this paired set of 3rds as integral to the work’s structure. She calls this the “Basic Combination,” a contrapuntal 10-​10-​10 arrangement that gives insight to the Intermezzo’s pitch-​class motivic structure (1988, 42–​47). 13. Later in ­chapter 6 when complex motivic analysis is introduced, it will be possible to view the harmonic component of a passage as motivic, thus broaching the possibility that some complex motives are more universal, occurring across separate pieces. 14. Properly speaking, mm. 92–​99 of Rossini’s melody constitute the first two parts of a three-​phrase period (Green 1979). That said, recognition of that larger form need not impinge on this selective reading of the first two segments. 15. Readers familiar with Schenkerian theory will recognize this as a manifestation of “interruption.” Without access to Schenkerian concepts such as the descending Urlinie—​the melodic entity whose descent to tonic is postponed at scale degree 2 during the half cadence—the present method cannot officially incorporate that term (Schenker [1935] 1979, 37). 16. The material that occurs between a structural dominant stopping point and a restart is recognized in numerous formal theories. Rothstein, following Koch, describes a version of this phenomenon at the phrase level that he calls a “lead-​in” (1989, 51–​ 52). Schenker calls it an “interruption fill” (Goldenberg 2012, §2). In reference to the analogous formal events at the end of sonata form development, Caplin 1998 distinguishes between the dominant arrival and a subsequent “standing on the dominant.” When the latter phenomenon occurs, “anticipatory motives derived from the . . . exposition’s main theme often appear to help prepare for the beginning of the recapitulation” (145).

344 Notes 17. Cognitive limits on higher-​level hearing are discussed in Schachter 1999, Lehrdahl and Jackendoff 1983, and Brower 1993. These limits pose no problem to musicians comfortable with the idea that analysis by nature admixes sonic and intellectual constructions. It is this blending that is key. Few musicians, for instance, are willing to traffic in hypermetric analyses so grandly abstract that they cannot even imagine how the most stretched-out events sound. 18. A  number of other pitch-​class transformations are recognized in atonal music, among them the “M” multiplier, which rescales the intervals of a note string by multiplying its intervals by a common factor. The most common application of M allows for a chromatic melody to transform into a line of fourths or fifths by multiplying all of its “1” values (half steps, as measured in 12-​tone space) by 5 or 7. 19. A few twentieth-​century musicians have attempted to solve the problem of how to invert rhythms. One common approach is to subtract all duration values—​absolute or relative (in the case of a rhythm contour)—​from a larger value. A  straightforward example of this method may be observed in the first of Milton Babbitt’s Three Compositions for Piano (Antokoletz 2014, 321). 20. To accommodate a wide range of styles, the transposition operations listed in Example 5.17 are only lightly formatted; analysts may alter them as they see fit. Rahn (1980, 40–​58), for example, uses the symbols Tx and Tpx to distinguish between pitch-​ class (pc) and pitch operations; a similar symbology using Tc could be used to specify chromatic versus diatonic content. 21. This genre designation indicates both an aesthetic stance and a mode of composition favored by Karlheinz Stockhausen and other modernists, in which “the discontinuous present is the operative mode of listening” and expectations of hierarchy, continuity, and development are all jettisoned” (Hutchinson 2016, 107). 22. The literature is rife with challenges to the organic viewpoint of music, with notable examples appearing in Street 1998, Korsyn 2003, and Chua 2004. Despite the promise of other modes of analysis, this present one abides by traditional organicism. For those wishing to explore other archetypes and interpretations of music, it will likely be possible to retain the small-​scale techniques of analysis suggested in ­chapters 4 and 5 while setting aside the upcoming material on archetypes and narrative assembly.

Interlude 1 1. This first narrative framework for describing the progress of music dates back generations. My formulation here echoes a version put forth by Heinrich Schenker in one of his earliest treaties. In Harmony, he remarks on the “The life of a motif ” as follows: “The motif is led through various situations. At one time, its melodic character is tested; at another time, harmonic peculiarity must prove its valor in unaccustomed surroundings; a third time, again, the motif is subjected to some rhythmic change: in other words, the motive lives through its fate, like a personage in a drama” (1980, 13).

Notes  345 2. A similar situation obtains in the field of biography, wherein a subject’s life is often rendered in terms of a coherent, logical arch. Relying on Camus, William Stafford explains how such a reading transforms reality—​in which “actions melt into other actions” and destiny cannot be sensed—​into art, an artificial realm where all causes and effects can be imagined as rational and knowable (1991, 228–​230). 3. To add a further wrinkle, Guck 1994 holds that all analysts, even those who mean to couch their findings in purely objective terms, tell stories about music. Narrative, then, is an unavoidable consequence of thinking about music in linguistic terms (229). 4. According to McClary 1995 (with emphasis mine), “The viability of apparently autonomous instrumental music depends” on numerous factors, including “codes of social signification such as affective vocabularies and narrative schemata” (328–​329). Agawu 1991 offers a more technical account of why the dichotomy between introversive and extroversive semiosis is “ultimately false” (23–​25). 5. Mirka 2014 locates an advanced theory of signification as far back as the writings of J.G. Sulzer (1720–​1779), who distinguishes musical signs as more “natural,” evoking passion, than purely linguistic signs which over time have become “indifferent” or “arbitrary” (26). With regard to music of the high Classical period, Elaine Sisman 2014 extends an insight from Wye J. Allanbrook to explain that “the strong connection between feelings and tone painting, as between emotion and expressive characters and topics, reflects. . . the deep mimetic roots of musical expression” (100). 6. Newcomb 1987 describes the foundational work of Vladimir Propp and Claude Lévi Strauss in the fields of narratology. Through study of a large, conventional body of literature, Propp noted patterns of structural relations. He became aware, in Victor Erlich’s words, that “the basic unit of the tale is not the character but his function” (Erlich 1981, 250, quoted in Newcomb 1987, 165). 7. The original discovery of the hero’s journey archetype is credited to Joseph Campbell’s Hero with a Thousand Faces (1949). More recent accounts of general narrative frameworks may be found in Todorov’s Introduction to Poetics (1981) and Propp’s Morphology of the Folktale (1968). 8. Markedness is a sociolinguistic term that describes a “weighted opposition,” a binary state in which one condition is regarded as more typical than the other (Hatten 1994, 34.) A modern-​day example of markedness is “male nurse,” as opposed to the unmarked—​and assumed to be female—​term, “nurse.” 9. Monahan 2013 expands and enriches the theory of agency by proposing four types of agent and by formalizing the potential hierarchical relationships among them. (This maneuver does not in any way challenge Maus 1988, which in Monahan’s opinion remains the “authoritative” treatment of the topic.) In doing so, he is able to clear up the slippage that inevitably occurs in narrative accounts of music, as authors shift their points of reference to address elements of the work itself, the fictional composer, and their own personas/​psyches. 10. The other basis for Almén’s narratives is the interplay of “topics,” which connote various musical styles by means of characteristic textures, rhythms, articulations, and pitch structures. A composer such as Mozart, for instance, might quickly progress through a series of topics across adjacent phrases: a “courtly march” might be

346 Notes supplanted by a passage of “storm and stress” followed by another of “singing style” (Ratner 1980, 9–​29). 11. The archetypes to be delineated in Musical Motives are more concerned with exclusively motivic interactions. They should be viewed as distinct from analyses that attribute drama to motives interacting with tonal space. A masterful example of that approach is Deborah Stein’s analysis of Schubert’s “Erlkönig,” in which the motives associated with the Erlking (metaphorically:  death) are shown to systematically annex regions of the song’s G minor tonality occupied by the father and the sick child (1989). 12. There are many ways to parse motives in the flowing left-​hand figuration. Rothstein 2005 prefers a shifted 4+2 grouping, in which the tenor material on E♯3, G♯, F♯, and A♯ connects. To call on a cello metaphor, the next two notes serve as a transition “across the strings,” as it were, back to the low voice on the next strong beat. Schmalfeldt 2005, in performance prefers to use a smooth wrist motion to connect the first note of each sextuplet to the rest of the upper-​register notes. My own interpretation is meant to incorporate elements from both of these readings. 13. This terminology comes from Laitz 2008, which divides both the exposition and recapitulation sections of sonata forms into First Tonal Area (FTA), transition, Second Tonal Area (STA), and closing area. This naming convention is analogous to Hepokoski and Darcy’s P, Transition, S, and C zones (2006), but has the advantage of explicitly casting the drama of the form in terms of a tonal struggle. 14. These categories are loosely based on Marx’s oppositional categories, Satz and Gang, the former being a “closed,” “well-​formed musical structure” and the latter an incomplete melodic structure that is “the very embodiment” of musical motion (Marx 1989, 249–​256). A fuller demonstration of Satz-​like and Gang-​like segment interactions in Beethoven piano sonatas, with commentary by Scott Burnham, can be found in Marx 1997, 104–​154.

Chapter 6 1. See Burkhart 1978 (159–​161), which is a gloss on Schenker 1922 (25–​48). Caplin 1998 (9–​21) and Cadwallader and Gagné 2007 (4–​12) serve in this regard, as well. The core motives identified from mm. 1–​8 in the analysis to follow are fully derivative of Schenker 1922. The findings derived from BMA in this chapter constitute a mixture of borrowed and—​where indicated—​new insights. 2. It is well documented that an early draft of this sonata featured a wholly different theme in A♭ major (see Nottebohm 1887, 564–​567). Kinderman 1995 attributes Beethoven’s decision to revise the theme to a desire to “tighten [the movement’s] thematic and harmonic relations” (32). 3. Barry Cooper traces the origin of this theme to an unpublished piano quartet by Beethoven written in 1785 (WoO 36, No. 3). In the sonata’s earliest drafts, the main theme in m. 1 begins without the pickup note, C4, and the arrival on E5 in m. 8 is followed by a rebound leap on beat 2 to C6. The subsequent changes leading to the

Notes  347 finished form, he notes, allow a closer correspondence with the main theme from movement II of the sonata (2017, 30). 4. Even at the surface level, ambiguity abounds. It is possible to parse the shape in two ways to indicate where the 3rd resides. One may define “Turn” as a hollowed-​out 3rd span from the first A♭5 to the last F with interior ornamentation; one can also view it as a linear 3rd followed by suffixes. In the present analysis, the latter reading is strongly preferred. 5. It is well known that the themes of many of Beethoven’s most significant works take the form of arpeggios and scales. What is more remarkable is that often, at a late stage within such movements, Beethoven atomizes those themes to reveal their intervallic essence. Charles Rosen believes the composer was acutely self-​aware of this procedure, which amounts to nothing less than an interrogation of the raw stuff of tonality, itself (1972, 404–​437). 6. The B♮ that appears in this line is a surface adjustment that allows for harmonic agreement between the voices as the upcoming C major V chord is tonicized. The chromaticism does not significantly impact the overall shape or even the sound of the  /​5th. 7. Having the tenor start at A♭4 alters its motivic profile in F minor. It will not do to parse it as any kind of fifth, for example one spanning A♭-​D♭ or G-​C. In the home key, it makes more sense as the 3rd, A♭4-​F elided to the 4th, F-​C. In one gesture, then, this voice makes reference both to the ascending 4th pickup that opened the work (at pitch), and the four Arp gestures that are all constructed as 3rd⊕4th. 8. The status of the \ /​ 3rd gesture here is ambiguous. It could be considered a retrograde of the 3rd \ /​gesture that began the piece or, more likely, a shape that reverses the order of the 3rd and neighbor gestures. 9. The bar line between the first two Ss indicates that the second note of the shape has been promoted to a downbeat stress; however, this effect is masked due to the distracting, weak beat accents. 10. Edward T. Cone coined the term “structural downbeat” for moments such as this. These are “points of simultaneous harmonic and rhythmic arrival,” that have the effect of “[turning whatever] precedes it into its own upbeat” (1968: 24–​25). 11. The arrow notation in this example, following Hasty 1997, illustrates how meter is created through listener expectation due to musical patterning. The third, arching arrow is dashed and breaks off to reflect the experience of listeners who expect (project) another downbeat in the middle of m. 3 but do not get it. 12. Beethoven engineers a similar effect at the beginning (mm. 1–​5) of his Piano Sonata No. 10 in G, Op. 14, No. 2. 13. It is true that some clarification of this metric ambiguity emerged in mm. 9–​12 and 66–​69, yet it is more effective here because of the tight correspondence with mm. 1–​4 in pitch. The harmonic context is also clarified, with clear dominant-​tonic motions coinciding with the arrival of the motive’s last note on E♮6. 14. The appearance of this dissonant chord at the retransition, though somewhat unexpected, makes sense in light of the main theme’s pitch material. The prominent B♮s and A♭s resonate with and prepare the upcoming motivic contrapuntal gesture of

348 Notes mm. 58–​59. As the main theme appears, each of these two notes will finally resolve correctly to C and G, dissolving the tension held at the previous fermata.

Interlude 2 1. See Auerbach 2008 for demonstration of a nonliteral Focal Point event coordinating the structure of Brahms’s First Rhapsody, Op. 79, No. 1. See Korsyn 2003 for discussion of a related phenomenon occurring in the realm of form, in which listeners may hear one or more phrase expansions without “the prototype” phrase ever being “explicitly stated” (93). 2. There is a long tradition of using analysis to investigate late-​ arrival climactic moments, of the type that E. T. Cone calls “epiphanies” (1987, 246–​248) This compositional trope is most often found in late Romantic works. James Hepokoski describes a closely related phenomenon: a “breakthrough” moment, he writes, is” characterized as “a seemingly new (although normally motivically related) event in or at the close of the ‘development space’ [that] radically redefines the character and course of the movement” (1993, 6). 3. Cone explains that, in such cases, our consciousness unfolds in a “double trajectory” (1977, 558). Note that the two levels of Cone’s trajectory correspond to the two-​level hierarchy implicit in Example 6.5.2(b). 4. This is not to say that analysts’ choice of template necessarily signals their level of knowledge or experience with a work. Though the Accretion template tends to make itself available in the later stages of study, an analyst always retains the ability to “hear forward.” In the end, then, it will come down to personal choice.

Chapter 7 1. It bears mentioning that the sample BMA analyses in c­ hapter 6 did take care to address music’s textural complexity by plumbing all of the voices for motives. In doing so, we already achieved one important advance over traditional motivic approaches that focus too closely on melodic events (to the exclusion of all others). This step forward, though, does not change the fact that all shapes identified within that broader texture remain essentially monophonic. A musical segment in BMA can thus be reasonably understood to be a container housing one or maybe two one-​dimensional motives. 2. An important exception in this regard is Hans Keller’s Functional Analysis (FA), a non-​notational analytic technique for demonstrating musical associations via pedagogical recomposition. (Keller’s method is described in detail by O’Hara 2020.) Written in score format, FAs were intended for performance in between a work’s movements. A number of these analyses were, in fact, broadcast on the BBC, mostly between 1957 and 1963. The gradual transformations modeled by FA closely resemble developing variation. The critical distinction is that the “conception of

Notes  349 thematic process” is synchronic rather than linear. As such, O’Hara schematizes the potential connections among entities as a “network of equal motive forms” connected by arrows signaling forward and backward relationships in time (2019, 21). 3. This definition, which traces its origins to Joachim Burmeister, accords with that given by Joseph Riepel, who is often considered the first modern authority on form. Riepel’s basic phrase (Absatz), for example, is defined as that which “contain[s]‌only as much as is absolutely necessary for it to be understood and felt as an independent section of a whole” (London 1990, 516). 4. Philosophers since the time of Zeno have grappled with establishing parameters of a momentary “now.” Cognitive science at the turn of the twentieth century developed the modern concept of the “specious present,” so called because “the notion of present, of the ‘now’, is completely absent from the description of the world in physical terms” (Rovelli, 1995). Over the course of the twentieth century, numerous spans have been proposed for the “psychological present,” ranging from approximately one to eight seconds. 5. Network representations are ideal for modeling concepts and/​or sensations that blend two or more domains. This, in large part explains their rise in popularity in music theory over the past three decades. Network models figure prominently in transformational theory. Swain 2002 applies them to investigate harmonic rhythm, which, according to the author, results from the interaction of surface rhythms, triad identity, and chordal inversion. Networks further serve as the basis for Robert Gjerdingen’s musical schemata, small compositional formulas that are codefined by their literal musical content—​pitches, scale degrees, harmony—​and their syntactic and topical/​rhetorical function (2007). 6. This slight “lopsidedness” is a central characteristic of the theme. A full analysis of the movement would note how this aspect contributes to the surprise, elided “bang” that occurs eight measures later, launching the transition section. It would also note the theme’s continually shifting metric setting throughout the development, with imitative fragments appearing in both off-​beat and on-​beat orientations. 7. Musically marked events, such as minor key scale degrees and sonorities appearing in major contexts, are generally good candidates for serving as Special Effects. Not all Special Effects have the quality of being marked, but many do (Hatten 1994). 8. See Reynolds 2003 for an exhaustive and imaginative treatment of this topic. The author catalogs a rich panoply of allusion practices, ranging from the hidden quotation of motives (literal or transformed) from other composers’ works to the use of established ciphers (“naming”) to signal specific meaning to other musicians. His Motives for Allusion engages extensively in technical analysis; despite this, motivic analysis remains the medium rather than the message. As such, Reynolds 2003 serves more as a model for interrogating meaning experienced at the intersection of many works as opposed to the specific narrative content of individual works. 9. Taking inspiration from the theories of Rameau, Hugo Riemann developed these categories as the syntactic elements of a full-​fledged system theorizing harmonic progression. His system remains in common use in Europe. In the United States, the harmonic function labels T, D, and PD (adopted from “SD: subdominant”) are

350 Notes commonly employed as a supplement to Roman numerals by helping to document, for example, how a Classical phrase conventionally progresses from a Tonic state (where I is often fleshed out by voice-​leading sonorities) through a Pre-​Dominant state (ii or IV), to a cadence involving either arrival on the Dominant or to a new tonic via Dominant-​Tonic motion. 10. The latter of these typically is used to track pitch and pitch-​class events, though contours may be posited for other aspects of music, such as articulation, rhythm, dynamics, and so forth. 11. In the process of establishing the model for complex motives, it would have been eminently possible to exchange the location of counterpoint and harmony, in effect rendering the former a Primary domain and the latter a Derivative one. 12. Harmony is derivative of pitch, as well, but to a lesser extent in that one identifies chord roots on the basis of information given in the voices. Treating Harmony as an independent entity is a compromise made in the face of an unsolvable dilemma. 13. The operative word, “tasteful,” is critical to maintaining balance in this more adventurous style of analysis. Whenever an unconventional interpretation is considered, the analyst should pause to reassess. He should be vigilant for any moment at which he feels his approach to a reading might appear at all outlandish; that is the moment it should be abandoned. 14. Schoenberg 1985, Clough 1979 and 1994, and Straus 1990 all set precedents for applying set theory analysis to works of previous eras. More recently, Dmitri Tymoczko has argued that triadic, functional harmony, an eighteenth-​century development, manifests strongly, albeit in incipient form, in the music of Palestrina (2015). 15. See Mailman 2015, which employs David Lewin’s binary-​ state GIS in a similar manner as here. The author explains the GIS as essentially “a vector of on/​off switches” that applied to each cell “can either ‘reverse’ (make opposite, flip, invert) the current state of something (with a digit 1) or leave the state of something as is (with a digit 0) (2015, 235). 16. The segmentation given in Example 7.5 adheres to Lehrdahl and Jackendoff ’s “well-​ formedness” principles for musical groups. Such principles promote cohesion and continuity by requiring, among other things, that groups be composed of “contiguous events,” that a full piece counts as a group, and that, in any case that a larger group contains smaller ones, that it is “exhaustively partitioned” by them (1983, 37–​38). 17. On the basis of the sustained F♯ bass pedal, one can argue that mm. 17–​24 exhibit no significant tonal motion and therefore constitute one segment. Alternatively, it is possible to say that smaller surface harmonic motions are present within mm. 17–​20 and mm. 21–​24, allowing each to stand as a viable segment. 18. The present demonstration concentrates on Complex assembly and not CMA in full. For discussion of the issues that impact Focal Point selection, readers should consult the next section of this chapter. 19. The present suggestion runs counter to Schoenberg, who explicitly recognizes “motives of the accompaniment” in his theory (2016, 60).

Notes  351 20. Brahms incorporated Romany elements in his music at all stages of his development. His interest in folk music in general and Hungarian music specifically—​the latter of which developed out of his early friendship with violinist Eduard Reményi—​is detailed in Jan Swafford’s biography of the composer (1999, 55–​62). 21. Readers will note that a few note heads, most prominently in the bass, are “unmoored” with respect to motivic arrow labels. These serve as guide tones to orient readers as they audiate the Map. These notes are mute with respect to actual motivic meaning and can thus be ignored, or erased, if preferred. 22. There is no way to justify this weighting scheme over others in absolute terms. A 50–​ 50 division of weight between Primary and Secondary domain groups is not inherently superior to any others such as 60–​40, 75–​25, or 98–​2. It is born out of a desire for simplicity. A straightforward averaging of domain groups is preferable to a scaled weighting scheme that would further complicate the method by introducing other multiplicative factors. 23. Readers may wonder, if Focal Point selection is meant to occur early, then why delay this topic until now? It is because in the earlier context of rehearsing the basics of CMA Narrative assembly, it was necessary to have each process run more or less autonomously. To invite uncertainty into that demonstration would have distracted from its purpose. And nothing is more uncertain than leaving open the question of which segment should serve as the Focal Point!

Chapter 8 1. A number of sources, notably among them Citron 1988 and Aichele 2018, describe the powerful societal forces in music reception that have led to Chaminade’s marginalization as a “mere” salon composer. 2. Chaminade’s heavy reliance on the subdominant is consistent with a trend described by Notley 2005 and Harrison 1994, in which later Romantic composers substituted IV for V as a new pole opposing the tonic realm. The new prominence of subdominant harmony manifested at multiple structural levels, from cadence all the way up to primary tonal areas. 3. The decision to allow a single key to persist for a work’s entirety is unusual. The exaggerated monotonality calls to mind Chaminade’s Piano Sonata, Op.  21, in which the exposition of the first movement never escapes the orbit of the C minor tonic. In seeking a gendered interpretation for this “subversive” compositional gesture—​ which is to say:  how the music suggests feminine origins or attributes—​Marcia Citron alights on the metaphor that “a major aspect of desire is being denied [an expected event or pattern]” (1993, 148–​152). 4. The voice is rendered in MacinTalk, a technology developed by Apple in 1984 that is still used today in many text-​to-​speech applications. The title of the song makes reference to the character of Marvin the Paranoid Android, a morose robot from Douglas Adams’s Hitchhiker’s Guide to the Galaxy universe.

352 Notes 5. All published analyses of “Paranoid Android” essentially agree on its main themes and its fatalistic narrative. According to Rusch 2013, the song “depicts a socially alienated and anxiety-​ridden persona” living in a capitalistic society in which “Power (‘When I am king’) and materialism . . . generate self-​importance (‘Why don’t you remember my name?’). There, a “plea to be cleansed . . . is met with a cynicism that God may be passive, leaving the persona no escape from Pandemonium” (§2.1). Letts 2010, in tracing the reception history of OK Computer, fleshes out this consensus with quotations of Nadine Hubbs, James Doheny, Allan F. Moore, and Anwar Ibrahim and Mac Randall (28–​32). 6. The full quotation is as follows: “Just a joke, a laugh, getting wasted together over a couple of evenings and putting some different pieces together” (Jabba 1998). 7. As expected, the imagery in the finished music video aligns with the text, particularly in terms of the setting and themes; e.g., a bar full of repugnant folk, among them an obese, aggressive administrator wearing a suit. This close correspondence is highly remarkably, however, in light of a claim by Carlsson that he completed work on the video using the instrumental soundtrack alone, with no knowledge of the lyrics (Footman 2007, 160). 8. Sears 2011 analyzes the A section of “Paranoid Android” only; this is done for the purpose of comparing the results obtained through waveform analysis of the recording with those yielded through traditional formal/​harmonic analysis. In contrast to Rusch and Osborn, Sears selects G minor as the tonic of A, even as he notes the “destabilizing” role of E natural over this chord in the chorus (2011, 7). 9. At this tempo, the six-​measure phrases seem normative. If one transcribes such that q = 200, as Rusch does, these same phrases seem to shift against the underlying hypermeter (2013, §2.5). 10. Where previous six-​measure segments functioned in two-​bar hypermeter, this one changes the feel to three-​bar hypermeter. The harmonic and metric domains work in tandem to disorient listeners, as the former suspends all sense of progression and the other trips up listeners by tugging on the hypermetrical rug on which they are standing. 11. This has less to do with the mere juxtaposition of human and digital noise; popular music has routinely, since the 1970s New Wave movement, paired human-​acoustic utterances with computer-​and waveform sound elements. The blending, rather, must purposefully invoke the topic. 12. “In the early nineteenth century,” Charles Rosen explains, “madness had its attractions as well as its terrors.” Specifically, the condition was tied to the notion of inspiration: “Madness, for the Romantic artist, was more than a breakdown of rational thought; it was an alternative which promised not only different insights but also a different logic” (1995, 646–​647). Further glosses on this topic appear in Stein and Spillman 1996 and Cone 1982. 13. This moment is strongly reminiscent of one from the Beatles’ “Day in the Life” from their Sgt. Pepper album. At 2:49, following the words, “And somebody spoke and I went into a dream,” the music switches on echo distortion, and a disembodied voice sighs a high-​pitched “Aaah.” To note further parallels with “Paranoid Android,” “A

Notes  353 Day in the Life,” was assembled out of separate compositions by John Lennon and Paul McCartney, and centers on issues of anxiety and identity. 14. For “Paranoid Android,” the question of whether drugs are involved is moot. For “A Day in the Life,” George Martin confirmed that the lyrics, “having a smoke” refers to members of the Beatles sneaking out of the recording area from time to time to smoke marijuana (Badman 2000). 15. Fuller details about the show’s history, from genesis to legacy, is provided in Flinn 1989 and Mandelbaum 1990. 16. The fortieth anniversary recording of A Chorus Line includes as a bonus track the early version of “At the Ballet” that Hamlisch screened for Michael Bennett. The close correspondence between this piano sketch and the final scored work is uncanny. The texts are identical, and their forms differ only in that the final version omits the second chorus before the last “ballet” climax section. As a result, many of the primary motives of this analysis can be seen as present from the beginning, among them the hopeful 2nd, the fourths and oscillating neighbor figures and Threefold Repetition. The linear 3rd, too, is prominent in the early version in both descending and ascending forms, though notably falls silent in the place where eventually Maggie will sing it as a bridge to the Climax area. 17. This moment stands as the embodiment of Michael Bennett’s philosophy that, “by nature,” dance “is the essence of the Broadway musical” (Stempel 2010, 589).

Chapter 9 1. Eighteenth-​century fugal treatises routinely recommended to composers that they design a three-​or four-​voice polyphonic passage, and then use it to generate multiple segments (Marpurg 1970). Schubert and Neidhöfer’s Baroque Counterpoint, a modern stylistic compositional treatise, explicitly draws on this same paradigm (2006). 2. Harrison 1997 offers a detailed account of “Good Vibrations” that relates its idiosyncratic tonal and formal structure to its composition from spliced studio fragments. The section I refer to as chorus is in his analysis called an extended refrain. 3. The verses, as a group, oppose the choruses, but remain organically related to them. While exhibiting similar grooves and harmonic rhythm, the verses create their subtle contrast by substituting a new texture and new harmonies—​A and G chords that produce a sense of dominant/​subdominant alternation. 4. Gjerdingen’s outside reference points for schemata are rooted in the fields of philosophy and psychology. To explain the concept of schema, Gjerdingen expressly invokes cognitive categories such as prototypes and exemplars (2007, 10). Following from this, his formal model for that entity, like my own formulation of the Complex, takes the form of a network. 5. Gjerdingen’s concentration on Galant style informs his resistance to grand, organic theories of music. He notes a hierarchy in that style, consisting of parts,

354 Notes phrases, sections, movements, etc. Critically, there is no firm, syntactic framework: “Replacing a D with a C♯ in a small melodic figure would not cause the whole musical house to collapse, nor would replacing [one schema with another]” (2007, 425). Other comments made on the same page effectively communicate Gjerdingen’s disdain for nineteenth-​century metaphysics, specifically the “self-​inflicted” problem of determining a work’s unity (2007, 425). 6. Kandinsky’s thoughts on circles in general resonate well with nontraditional modes of organization, potentially overlapping with developments in advanced mathematics that track relationships simultaneously on four or more separate axes: “The importance of circles . . . prefigures the dominant role they would play in many subsequent works, culminating in his cosmic and harmonious image Several Circles. ‘The circle,’ claimed Kandinsky, ‘is the synthesis of the greatest oppositions. It combines the concentric and the eccentric in a single form and in equilibrium. Of the three primary forms, it points most clearly to the fourth dimension’ ” (Spector 1994, 157). 7. An overview and history of similarity relations can be found in Schuijer 2008 (130–​ 178). While the algorithms he describes were designed more for network-​style and (Forte-​ian) “nexus”-set analysis, there is nothing to prevent them from being adapted to diatonic collections and tonal musics. For a complementary approach to the topic rooted in cognitive science, see Hanninen 2004; her investigation of similarity (with applications for analysis) is based on the mind’s tendency to identify musical events in terms of porous categories. 8. See Cambouropoulos 2006 and Lartillot 2004 for accounts of the technical complexities of programming computers to return meaningful motivic findings from lengthy strings of musical data.

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Discography The Beatles. 1967. “A Day in the Life.” Parlophone CDP7464422. The Beach Boys. 1966. “Good Vibrations.” Capitol 5676. The Bee Gees. 1977. “Stayin’ Alive.” Capitol Music Group. Radiohead. 1997. OK Computer. Capitol Records. Rolling Stones. 2002 [1965]. “(I Can’t Get No) Satisfaction” (remaster) ABKCO Music. Franklin, Aretha. 1967. “Respect.” Rhino Atlantic. Hamlisch, Marvin and Kleban, 2015 Edward. A Chorus Line 40th Anniversary Celebration. Masterworks Broadway. Jepsen, Carly Rae. 2012. “Call Me Maybe.” School Boy/​Interscope Records. The Knack. 1979. “My Sharona.” Capitol Records. Outkast, with André 3000. 2003. “Hey Ya!” Arista 82876 561002. Queen, with David Bowie. 1981. “Under Pressure.” EMI 5250.

Index Note: An e following a page number indicates a musical example, figure, or chart abruptio figure, 59 abstraction, 12, 53, 72–​73, 137, 208 in art, 16–​17, 17e abuse of analysis, 8–​10, 317, 329n6 Accretion narrative templates (in CMA analysis), 208–​12, 322 overlap with Synthesis narrative, 211–​12,  215 CMA–​2 (Synthesis/​Dissolution variant), 212, 212e, 215, 218 CMA–​2< (Synthesis), 212, 212e, 218 Focal Point in, 248 information flow in, 208–​12, 209e, 242 rondo and, 214 Add six chord (+6), 279, 284–​85, 286 affect in Baroque music, 56, 62, 67, 335n11 in Classical music, 62 Agawu, Kofi, 94, 312, 331n17, 345n4 agency of motive, 20–​21, 22, 165–​66, 190, 345n9 personification and, 168–​69, 170, 172–​74, 260, 290–​91, 344n1 Aichele, Michele, 351n1 Alegant, Brian, 338n41 Alexander, Christopher, The Nature of Order, 17–​18,  330n15 Allanbrook, Wye J., 345n5 allusion. See embodiment/​allusion domain Almén, Byron, 169, 170, 345–​46n10 amateur listeners and musicians, 19, 22–​23, 62, 76, 312–​13,  327–​28 ambiguity in analysis, 12, 107, 109, 116, 154, 157, 186, 188e, 324 developing variation and, 324–​26 harmonic,  200–​34 metric, 200–​201, 347n13 tonal, 278 ambivalence,  277–​78 anacrusis, 113, 137, 200–​201 analysis of self, 3, 211, 325 analytic error, 89–​92, 146–​47 style and harmonic claims, 232

analytic extravagance, 314–​15 analytic freedom/​flexibility, 87, 93–​94, 102, 220,  322–​24 analyst’s proclivities and, 210–​11 in CMA analysis, 233, 240 ancient Greece, 56–​57 André 3000, 319–​20 Anson-​Cartwright, Mark, “Chord as Motive,” 85 ante, upping the, 33, 192 anxiety in “At the Ballet,” 301, 301e, 303 in “Paranoid Android,” 277, 290–​91 archetypes, narrative, 130, 165–​81, 322. See also Non-​Engagement narrative archetype (BMA–​2°); Propagation narrative archetype (BMA–​1); Synthesis narrative archetype (BMA–​2•); Triumph narrative archetype BMA,  169–​81 CMA, 205–​18,  238–​39 complementation-​based, 170, 171–​72, 205, 211 conflict-​based, 170–​71, 174, 176–​81, 205, 211 summary chart, 216, 217e, 218 arch motive, 318e, 319 Aristotle, 57, 335n6 arpeggiating motive, 32–​33, 106, 108, 113, 332nn8–​9, 341nn4–​5 in Beethoven’s Piano Sonata Op. 2, No. 1, 183–​84, 185, 186e, 193, 194–​95 in Chaminade’s “L’Ondine,” 271 in composite motive, 115–​17 internal placement of prefix figures, 117–​18 nomenclature for, 110–​11, 111e arpeggiation, 87 as texture attribute, 224, 273, 275 arrows used in analysis, 155–​61, 221 coupling (register), 236 dashed, 155, 157, 161, 210, 236, 243, 245, 247, 282, 347n11 dotted, 155–​56, 236, 247 double-​barbed, 155, 159, 160, 245

368 Index arrows used in analysis (cont.) single-​barbed, 155, 159, 243, 245 transformational,  241–​42 art, nonrepresentative, 322, 323e, 324, 354n6 art history, motifs in, 14, 15e–​16e,  16–​18 articulation domain, 5 in complex motivic analysis (CMA), 101, 223e, 224, 227e, 237 formatting conventions of, 227e attack points, 120, 121 “At the Ballet,” by Marvin Hamlisch, 296–​310 “aspiration,” 303, 304, 310 content and drama in, 304, 306–​7, 310 “Crisis” section, 298, 304, 306–​7, 308e Denouement section, 298, 304, 307, 310 “epiphany” (“upturned glance”), 300, 301e, 302, 303, 304, 310 list of motives with narrative associations, 305e Threefold Repetition, 300, 301e, 303, 304, 307, 309e attributes, 81 binary formatting of, 233, 251, 253, 284 in cognitive theory, 97–​98, 99, 99e concept of motive and, 10, 85–​87, 101 Gestalt principles of, 3, 10 improvised (partial) values, 273 mapping, 240–​43, 245 specifying, 234–​35,  237–​38 spreadsheet representation, 252e, 258e, 274e tally of, 239, 251, 252e, 253, 257, 273 valuing, 97–​99, 170–​71, 221–​22, 249–​51, 257, 271, 273, 285, 286–​87 audiation, 149, 222–​23 audibility, motivic analysis and, 102, 105,  130–​34 Auerbach, Brent, 86, 348n1 augmentation, 153, 154e, 160e augmented sixth chord, 314 Auner, Joseph, 325 awkwardness,  48–​49 Babbitt, Milton, 51, 82, 334n26 Three Compositions for Piano, 344n19 Bach, J. C., 39 Bach, Johann Sebastian Fugue in B, Well-​Tempered Clavier, Book I, 116e, 117 Fugue in B-​flat minor, Well-​Tempered Clavier, Book II, 70 Fugue in C-​sharp minor, Well-​Tempered Clavier, Book I, 318

Fugue in E, Well-​Tempered Clavier, Book II, 318 Fugue in G-​sharp minor, Well-​Tempered Clavier, Book I, 316, 316e, 317 Gigue from Fourth English Suite, 32e, 32–​33, 33e, 49 Partita No. 4, BWV 828, 138, 138e Prelude in B-​flat minor, Well-​Tempered Clavier, Book II, 70e “Bach” motive, 226 “Backbeat” motive, 282, 282e, 286, 294–​95, 295e back-​relatedness, 161,  209–​10 backshift, 127, 342n10, 343n10 balance, compositional, 39, 42, 127, 201, 225 Barber, Samuel, 334n21 barline notation, 125–​27, 126e Baroque period, 27 constituent style traits, 29e, 30 motives in, 32–​39, 167 motive theory in, 55, 58–​61, 100 Bartel, Dietrich, 59, 62, 335nn5–​6 Bartók, Béla, 334n22 Concerto for Orchestra, 232 basic motivic analysis (BMA), 101, 129–​63 of “At the Ballet,” by Marvin Hamlisch, 296–​310 distinguishing elements from Schoenbergian analysis, 129 domains considered in, 101, 219 minimum competency needed for, 129 narrative archetypes, 130, 205, 216, 217e narrative restrictions, 129–​30, 205 pitch and pitch-​class exemplars, 183–​95 preliminary narrative strategies, 161–​63 principles for linking motives, 150–​61 Propagation narrative template for, 163, 205 rhythm exemplars, 195–​207 rules in context of full method, 261e shortcomings of, 219 Basic Shape. See Grundgestalt Beach Boys, the, “Good Vibrations,” 319–​20,  353n2 Beatles, the “A Day in the Life,” 352–​53nn13–​14 “Yellow Submarine,” 72 Bee Gees, the, “Stayin’ Alive,” 320 Beethoven, Ludwig van atomization (intervallic view of tonality), 347n5 Bagatelle, Op. 119, No. 1, 92–​93, 112, 112e, 341n6 Mattheson’s influence on, 60

Index  369 motivic saturation in music of, 46 Piano Concerto No. 4, 46 Piano Sonata No. 1 in F minor, Op. 2, No. 1, 183–​207, 188e, 189e, 190e–​93e, 196e–​97e, 202e Piano Sonata No. 3 in C, Op. 2, No. 3, 66, 75e, 78e, 78–​79, 105, 147, 147e, 177e, 177–​81,  180e Piano Sonata No. 5 in C minor, Op. 10, No. 1, 87, 88e, 89, 93, 105–​6, 106e Piano Sonata No. 7 in D, Op. 10, No. 3, 157–​61, 157e–​61e Piano Sonata No. 8 in C minor (Pathétique), Op. 13, 8, 9e,  106–​7 Piano Sonata No. 10 in G, Op. 14, No. 2, 139, 347n12 Piano Sonata No. 13 in F minor (Appassionata), Op. 57, 46, 340n57 Piano Sonata No. 14 in C-​sharp minor, Op. 27, No. 2, 95, 156 Piano Sonata No. 16 in G, Op. 31, No. 1, 66 Piano Sonata No. 24 in F-​sharp, Op. 78, 144–​45,  145e String Quartet in B-​flat, Op. 18, No. 6, 170, 171e String Quartet in F, Op. 18, No. 1, 46 Symphony No. 1, 89–​90, 90e Symphony No. 3 (“Eroica”), 93, 94e Symphony No. 5, 13e, 14, 18, 18e, 20, 90e, 90–​91, 98–​99, 99e, 115 Symphony No. 6 (“Pastoral”), 166 Bennett, Michael, 297, 353nn16–​17 Bent, Ian, 67, 70 Berg, Alban, 50 Four Songs, Op. 2, 51 Berlioz, Hector, Symphonie Fantastique, 46 Bernhard, Christoph, 59, 336n14 Berry, Wallace, Structural Functions in Music, 253 binary forms, 143, 146, 148 rounded, 146–​47, 148, 150, 245, 262 binary representation, 233, 238, 249, 251, 284, 350n15 Bloom, Harold, 331n18 blues, 26, 312 Blumröder, Christoph von, 336n16 BMA–​1. See Propagation narrative template BMA–​2+. See Triumph narrative archetype BMA–​2°. See Non-​Engagement narrative archetype BMA–​2•. See Synthesis narrative archetype borrowing, modal. See mixture (modal)

Boss, Jack, 92, 93 Boulez, Pierre, 334n26 boundary (bounding) interval of motive, 82, 108, 109, 110, 113, 115, 271 Bowie, David, 319 Boyle, Matthew, 321–​22 Brahms, Johannes, 54 Intermezzo in A, Op. 76, No. 6, 140e, 141 Intermezzo in A minor, Op. 118, No. 1, 48e,  48–​49 Rhapsody No. 1, Op. 79, No. 1, 348n1(1) Romany musical elements in works of, 351n22 String Quartet in A minor, Op. 51, No. 2, 76e, 76–​77, 91, 105 Symphony No. 3, 79, 81 tradition and, 333n18 use of motives, 46–​47 Waltz in B minor, Op. 39, No. 11, 235–​38, 236e, 237e, 240–​61, 244e, 246e bridging intermovement gaps (attacca),  144–​45 Britten, Benjamin, 334n21 Brower, Candace, 344n17 bubblegum music, 319 Burkhart, Charles, 338n41, 346n1 Burkholder, Peter, 333n18 Burmeister, Joachim, 349n3 Hypomnematum musicae poeticae, 335n7 Musica poetica, 56, 58–​59, 60, 335nn7–​9 Burnham, Scott, 336n22, 346n14 Burns, Gary, 319 cadence, 219 in Burmeister’s conception of fugue, 58 in Classical period, 39, 219 complex motive boundaries and, 222 in contour reduction, 134 in harmonic domain, 230 “stock,” 31 structural pitches and, 95, 134 cadenza, 147, 180 Cadwallader, Allen, 92–​93, 341n6, 346n1 caesura, 143 “Call Me Maybe” (Jepson), 319 Campbell, Joseph, Hero with a Thousand Faces, 345n7 canon (body of works), 57 canon (imitative technique), 195, 199, 231, 243, 245 Caplin, William, 336n15, 343n16, 346n1 Carlsson, Magnus, 277, 352n7 Carpenter, Patricia, 72, 87, 101, 337n32, 338n34, 338n36, 339n49, 343n12 “Cascade” motive, 35–​39, 333n10

370 Index category (mental network), 97–​99 as analog to motive, 223 changeability and porousness of, 98 causality, 12, 17–​18 chaining (self-​replication), 32, 66, 155, 180 Chaminade, Cécile “L’Ondine,” Op. 101, 267–​76 Piano Sonata, Op. 21, 351n3 Chopin, Frédéric, 46 Nocturne in F-​sharp, Op. 15, No. 2, 136–​37, 137e Prelude in C minor, Op. 28, No. 20, 170 Prelude in F-​sharp, Op. 28, No. 13, 174, 175e Waltz in A minor, Op. 34, No. 2, 112, 112e chordal leap, 332n8. See also arpeggiating motive Christensen, Thomas, 334n1 chromaticism, 47, 48–​50 chromatic motive, 109 Chua, Daniel, 344n22 Cinnamon, Howard, 85 circle of fifths, 143, 190e, 192e–​93e, 247, 333n13 circular reasoning, 255–​57, 326 Citron, Marcia, 351n1, 351n3 Classical period, 27, 28 motives in, 39–​45, 54, 167, 333nn11–​12 motive theory in, 55, 61–​65 style traits, 29e, 30, 195 Climax figure, 58, 58e “Climb” motive, 31, 49, 332n9 Clough, John, 338n38, 350n14 CMA–​1. See Propagation narrative templates (in CMA analysis) CMA–​2. See Accretion narrative templates (in CMA analysis) CMA–​3. See Cyclic narrative templates (in CMA analysis) CMA Narrative assembling multiple, 257, 259–​61 for Brahms’s Waltz in B minor, 248–​55 constructing,  248–​55 Focal Point quantified in, 249–​51, 273 graphical representation of, 253–​54, 254e, 259e, 267, 274e, 289e interpretation of, 254–​55, 259–​61, 287 multiple readings, 257 numerical essence of, 251 as paired complement with CMA Map, 238–​40,  247–​48 quantitative analysis, 221, 249–​53, 257, 263, 267, 273, 274e, 275 for Radiohead’s “Paranoid Android,” 280, 287–​93 recasting and revising, 255–​61, 262

relation to BMA, 238 role in CMA, 239 tally of motivic complex elements, 251, 252e, 253, 257, 258e, 263, 267, 274e, 288e coda, 44–​45, 180–​81, 186, 189–​90, 200, 214, 269 cognitive theory, 96–​99, 340n59, 344n17, 349n4 coherence, 4, 8, 14. See also unity Cohn, Richard, 84, 107, 338n38, 340n54 Colonel Bogey March, 8, 9e comedy archetype, 173, 260–​61 Common-​Practice music, 32, 48, 69, 156, 168, 170, 219, 229, 230–​31, 312, 332n3, 332nn5–​6. See also Baroque period; Classical period; Romantic period communication among musicians, 102, 105–​6, 327–​28 of musical meaning, 19 complexity (as aesthetic virtue), 79–​80 complex motive, 223e assembly,  235–​38 concept of, 211–​12 concerns about working with, 230–​35 formalizing,  221–​35 harmonic root motion in, 222 network structure of, 223–​24, 238 scope of, 222 standard content and modes of representation, 227e theorizing content of, 226–​30 complex motivic analysis (CMA), 101, 219–​63. See also Organic Map; CMA Narrative abbreviated readings, 261, 271–​73 advantages of, 225 basic motivic analysis (BMA) compared with,  219–​21 of Brahms’s Waltz in B minor, 240–​61 of Chaminade’s “L’Ondine,” 267–​76 CMA Narrative, 238–​40, 248–​55 developing variation and, 324–​25 domains considered in, 101, 219–​21 flowchart for, 240e fugue and, 318 minimizing redundancy, 234–​35 motivic flexibility in, 101 multiple readings, 255–​57 narrative archetypes, 205–​18, 238–​39 Organic Map, 238–​48 philosophy of, 225 principles for linking motives, 150–​61 procedures for carrying out, 239 provisional, 257 of Radiohead’s “Paranoid Android,” 276–​96 rationale for, 219–​21

Index  371 rules for, 261e segmentation in, 233, 234–​36, 267, 268, 271, 279–​80, 292,  321–​22 “composing out,” 85, 133, 178, 234, 334n22 composite motive, 247 nomenclature for, 116e pitch, 115–​17, 243, 247 rhythmic, 123, 125, 295 Synthesis narrative and, 176 compositional premise, 28, 39, 59, 157, 232, 243 compositional “problem” or status, 42–​43, 63, 66, 272, 336n18 compositional strategy, 7–​8, 32–​33, 35–​39, 46–​53,  192 composition-​centric vs. analytic-​centric thinking, 325 computer-​aided analysis, 96, 311, 326, 354n8 computer voice (in “Paranoid Android”), 277, 285, 291, 295–​96, 296e, 351n3 conceptual modeling, 17–​18, 96–​99, 330n15 Cone, Edward T., 144, 210, 337n23, 347n10, 348nn2–​3,  352n12 consonance, 57 contour analysis, 135–​36, 225, 340n58, 342nn7–​8 changing definitions of, 135 as domain in complex motivic analysis (CMA), 224–​25, 227e, 229 formatting conventions of, 227e points of (corner notes), 94, 95 contour reduction, 134, 135–​37 Cook, Nicholas, Guide to Musical Analysis, 340n56 Cooper, Barry, 346n3 corner notes. See contour cosmology,  56–​57 counterpoint motivic migration in, 35–​38 reduction on basis of, 131 requirements for, 331n2 style and, 28 counterpoint domain in complex motivic analysis (CMA), 219–​21, 223e, 224–​25, 227e, 229, 238 formatting conventions of, 227e coupling, 169 cyclic form, 176 Cyclic narrative templates (in CMA analysis), 212–​16, 276–​96,  322 CMA–​3, 212–​16, 214e, 218 CMA–​3↑ (Modified Cyclic), 215, 216e, 218,  267–​76 Focal Points in, 248, 254–​55

rondo form and, 213, 214, 215 sonata form and, 214–​15 verse-​chorus form and, 213 Dahlhaus, Carl, 47, 337n26, 338n37 Dallapiccola, Luigi, Quaderno Musicale di Annilibera, 226 dance, power of, 297, 307, 353n17 “Day in the Life, A,” by the Beatles, 352–​53nn13–​14 Degeorge, Gérard, 330n13 derivation, 77, 83, 91, 105, 231 derivative domains, 224, 229 dessin, 55, 64–​65 developing variation, 73–​74, 77, 324–​26, 333n19, 348–​49n2 development section. See sonata form diatonicism, 48, 99, 108–​9 digression (rounded binary form), 146e, 146–​ 47, 148, 235, 240, 245, 247, 254, 255, 260 diminution, 92, 153, 154e, 158, 160e directed distance, 152 discrete (+) joining pitch motives, 115–​17 rhythmic motives, 123 displacement dissonance. See metric dissonance dispositio, 57, 59 Dissolution type (CMA–​1>). See Propagation narrative templates (in CMA analysis) dissonance, harmonic, 28, 50, 317 dissonance, metric. See metric dissonance distortion, 276, 277 disunity, 278, 321 divided durations, 123, 123e, 128e “Divine Monochord,” 57, 334n3 Doctrine of the Affections, 335n11 Doheny, James, 296 domains, musical. See also articulation domain; contour domain; counterpoint domain; dynamics domain; embodiment/​allusion domain; harmony domain; orchestration/​ texture/​timbre domain; pitch domain; rhythm domain; special effects domain in basic motivic analysis (BMA), 129 binary representation of, 233–​35 in complex motivic analysis (CMA), 101, 206, 219–​21, 222, 249–​51, 257, 273, 282–​87 contour applied to, 135 feature and, 74–​76 interdependence of, 79, 94 motivic identity on basis of, 5 dominant (D). See harmonic function labels double fugue, 59, 176 double neighbor figures, 111, 112

372 Index double-​tonic complex, 278 drama motives’ conveyance of, 21, 165, 172–​73 protagonist in, 168–​69 text/​music associations in, 18, 331n17 duality, 201, 280 Dunsby, Jonathan, 69, 339n46 duration scaling, 152–​53, 153e, 154e, 233 duration types (S-​M-​L), 120, 121e Dvořák, Antonin Symphony No. 9, 176 dynamics domain in complex motivic analysis (CMA), 101, 219–​20, 223e, 224, 227e,  237–​38 defined, 226 formatting conventions of, 227e efficiency, 133, 229, 233 Eitan, Zohar, 330n9 electronic music, 280, 319 Elgar, Edward, 334n21 elided (⊕) joining pitch motives, 115–​17 rhythmic motives, 123 Ellington, Duke, “Take the A Train,” 72 elocution, 59 embodiment/​allusion domain, 349n8 in complex motivic analysis (CMA), 227e, 233 defined, 226, 228 formatting conventions of, 227e in Radiohead “Paranoid Android,” 285, 286, 293 emotion ancient Greek views on, 56–​57 awkwardness in performance, 48–​49 in eighteenth-​century music, 62, 345n5 encoding, 31 figures associated with, 336n17 musica poetica and, 56 Narrative Curve and, 213 real sequence and, 47–​48 as requirement for motive, 3, 10–​14, 16, 25, 166, 315 tone painting and, 31 Empfindsamkeit, 62, 335n11 empiricism, 78 energy, musical, 3, 11, 79, 163 intervallic cell as generator of, 65 motive as source of, 69–​70, 181, 329n7 radiating from Focal Point, 18 “wind-​up” return and, 147–​48

enharmonicism, 108, 306, 340n55 enriched tonality, 50, 334n21 constituent style traits, 29e Epstein, David, 243, 343n9 Beyond Orpheus, 93–​96, 100, 134–​41 Epstein Point (E.P.) 1, 134, 135–​36 Epstein Point (E.P.) 2, 134 Epstein Point (E.P.) 3, 134, 136–​37 equal duration reduction (EDR), 132, 132e approach of, 131 compared with tonal reduction, 131–​34 contour reduction, 134, 135–​37 efficiency of, 133–​34 Epstein’s Beyond Orpheus as model for,  134–​41 form analysis and, 143–​48 patterning in, 134, 136–​37, 142–​43, 149 rhythmic and metric salience as criterion, 134,  137–​41 rules for larger musical spans, 141–​50 “windows,” 139, 194 Erlich, Victor, 345n6 escape tone, 286, 303 expert vs. non-​expert analysis, 19–​20, 22–​23 exposition. See sonata form extramusical associations, 226, 228 extroversive practice, 167–​68, 345n4 family as theme in Hamlisch “At the Ballet,” 297–​310 fa-​sol-​do motive, 316, 317 “fate” motive, 326 feature (characteristic), 73, 73e motive distinguished from, 74–​76, 80, 338n36 terminological collapse with motive, 80–​87 “feature motive,” 81, 84–​85, 86 feedback (electronic), 277, 280 figure, musical in Baroque music, 55, 58–​59, 60, 100, 335–​36n12,  336n14 Burmeister’s conception of, 335nn8–​9 in Classical music, 60, 63 early catalogs of, 335n8 figure, rhetorical, 57–​59 film music Leitmotive in, 330n16 text/​music associations in, 18 First Tonal Area (FTA) (sonata form), 174, 176, 196, 200, 346n13 flourish (motive), 247, 257 Fludd, Robert, De Musica Mundana, 334n3 Focal Point, 162, 242e, 243, 244e, 246e, 247 broadened scope in CMA, 205–​8, 218

Index  373 CMA Narrative Rule, 248 in Cyclic narrative, 254–​55 deduction of, 206–​8 establishment of identity/​location, 162–​63, 205, 212, 235, 240, 248, 255–​57, 267, 272, 279, 280, 285–​86, 318 located outside of piece, 208 quantification of, 249–​51 recasting, 257 segments’ degrees of relatedness to, 253–​54 sub-​elements of, 248, 250 fonts used in labeling motives, 109, 125 foreshadowing, 208–​12. See also back-​relating foreshift, 127, 342n10, 343n10 Forkel, J. N., 63 formalization of analysis, 10, 20, 82–​84, 100–​102, 129, 150, 324–​26 formal training in music analysis, 234 form analysis, 143–​48 boundaries, 143–​45, 272 in complex motivic analysis (CMA), 219–​21, 240–​41, 269, 270e Forte, Allen, 69 “Motivic Design and Structural Levels in the First Movement of Brahms’s String Quartet in C Minor,” 82–​84, 85 “New Approaches to the Linear Analysis of Music,” 85 The Structure of Atonal Music,  82–​83 fragmentation, 69, 155–​58, 161, 161e Franklin, Aretha, 319–​20 Friedmann, Michael, 342n7 Frisch, Walter, 340n52 Brahms and the Principle of Developing Variation, 91 Frye, Northrop, 173, 260 Fuga realis figure, 59 fugue state, 291–​92 fugue subject, 315, 317–​18 “full reset,” 144, 145–​46 functional harmony. See harmony, functional Gagné, David, 346n1 Galant music, 26, 321–​22, 353–​54n5 Galuppi, Baldassare, 39 Gang, 66, 67e, 346n14 gap-​filling motives, 40–​41, 43, 45 Garnham, Alison, 87 Gedanke. See Idea (Idee or Gedanke) generic content, 157, 189, 194, 197, 235–​37, 255 Gestalt principles of perception, 3–​4, 10–​12, 14, 19, 340n60 gesture studies, 167

Gjerdingen, Robert, Music in the Galant Style, 320–​21, 329n3, 349n5, 353–​54nn4–​5 glissando, 123, 226 Gluck, Christoph, “Che fiero momento” from Orfeo ed Euridice, 118, 118e Goehr, Alexander, 80, 339n43 Goethe, Johann Wolfgang von, Versuch die Metamorphose der Pflanzen zu erklären, 336n20 “Good Vibrations,” by the Beach Boys, 319–​20,  353n2 grace notes, 140e, 141, 247, 273, 343n11 grammar, study of, 20, 340n60 Granot, Roni, 330n9 Greenwood, Colin, 276, 277 Gregorian chant, 30–​31 grouping dissonance. See metric dissonance Grube, Ernst, 330n14 Grundgestalt (Basic Shape), 72–​73, 73e, 77, 87, 88e, 89, 93, 206, 210, 339n50, 340n57 Guck, Marion, 345n3 Guido of Arezzo, 56 guitar lick. See hook, musical hairpin dynamic, 161–​62, 237–​38 half cadence (HC), 39, 113, 133, 147, 186, 232, 279, 283, 343n15 Hamlisch, Marvin, “At the Ballet,” 296–​310 Handel, George Frideric Concerto Grosso, Op. 6, No. 1, 33–​39, 34e, 36e–​38e Concerto Grosso, Op. 6, No. 4, 315, 316e Hanninen, Dora A., 354n7 Hansen, Howard, 82 Hanslick, Eduard, 79, 329n1 harmonic function labels (T, PD, D), 71, 228, 234, 349–​50n9 harmonic motive (Riemann), 71 harmonic sequence, 49, 142–​43, 190e, 192e–​93e, 334n20 harmonic syntax, 27–​28, 79, 131, 230, 284 harmony, functional, 27–​28, 30, 32–​33, 332nn5–​6 harmony domain, 5 chromatic techniques, 47, 48–​50 in complex motivic analysis (CMA), 219–​20, 223e, 224, 227e, 237 as constituent style trait, 30 formatting conventions of, 227e meaning in music supplied by, 79 reduction,  233–​34 tonal progressions, 141, 349–​50n9 unified and conflicting content, 230–​32

374 Index Harrison, Daniel, 334n21, 336n18, 338n38, 351n2, 353n2 Harriss, Ernest, 60 hash mark notation, 121–​23, 194 Hasty, Christopher, 347n11 Hatten, Robert, 30–​31, 167, 168, 331n18 Haydn, Franz Joseph Mattheson’s influence on, 60 Piano Sonata in D, Hob. XVI:37, 146e,  146–​47 Piano Sonata in E-​flat, Hob. XVI:52, 230–​31 Piano Sonata No. 31 in E, Hob. XVI:31, 5–​6,  6e Piano Sonata No. 36 in C-​sharp minor, Hob. XVI:36, 113, 114e Symphony No. 45 (“Farewell”), 208 Symphony No. 103, 219, 220e, 223 Symphony No. 104, 68e,  68–​69 “head” event, 242 Hegel, Georg Wilhelm Friedrich, 329n1, 339n42 Helmholtz, Hermann von, 329n1, 330n8 hemiola (grouping dissonance), 127, 343n9 Hepokoski, James, 348n2 hermeneutic analysis, 19, 326 “Hey Ya” (André 3000 with OutKast), 319–​20 hierarchy in counterpoint, 331n2 in BMA and CMA, 209e, 210, 241 of form, 64, 68, 143, 240–​41, 353n5 in Organic Map, 241 in Schenker’s theory, 93, 133 in Schoenberg’s theory, 72–​73, 73e, 78, 80–​81, 93, 98 Hilse, Walter, 59 Hinrichsen, Hans-​Joachim, 336n16 Holst, Gustav, 54 The Planets, 49e, 49–​50, 50e, 51 hook, musical, 42–​43, 315, 318–​20 hook notation (prefixes/​suffixes), 113 Hooper, Jason, 64 Huron, David, 84 Hutchinson, Mark, 344n21 hypermeter, 141, 352n10 Idea (Idee or Gedanke), 72, 73e Schoenberg’s concept of, 73e, 80 idée fixe, 46 identity (in “Paranoid Android”) as Allusion attribute, 285–​86, 293 computer, 296 human, 277, 296 split (fractured), 277, 285, 291–​92, 296 identity relation. See motivic (shape) identity

imagination, music and, 3–​4, 11, 19, 21, 97–​98, 149, 169, 174, 201, 228 imperfect authentic cadence (IAC), 146e incomplete neighbor tone, 117, 118e information theory, 331n1 narrative flow and, 162–​63 style and, 25–​27 initiating event (Focal Point), 162, 163, 166, 170, 206 intensity curve. See Narrative Curve interdependence of domains, 79, 94 interpretation in CMA, 221, 240, 253–​55, 259–​61, 273,  287–​93 intervallic cells, 47, 55, 66, 68, 107, 341n1 intervallic disposition of motives, 109 interval-​preserving operations, 77, 101, 151, 153, 154e, 155, 156 interversion, 89, 93 introversive practice, 167–​68, 345n4 intuition in motivic analysis, 91, 95, 102, 154e,  155–​57 inventio, 57, 59, 63 inversion. See mirror inversion inversus, 159 irony/​satire archetype, 173 “I Won’t Grow Up” (Peter Pan), 113, 114e Jabba (Jason Davis), 276 Jackendoff, Ray, 133, 242, 340n60, 342n1, 344n17, 350n16 “jack of all trades”, 311–​14 Jagger, Mick, 318 Jakobsen, Roman, 167–​68 jazz, 27, 54, 232, 284, 331n17 Jepson, Carly Rae, “Call Me Maybe,” 319 “Jetsons” theme, 117, 118e Joplin, Scott, “The Entertainer,” 113, 114e Kandinsky, Wassily, 322, 354n6 Little Accents, 323e, 324 Several Circles, 322, 324 Karpinski, Gary, 341n8 Keller, Hans, 22, 87, 339n49, 348–​49n2 Kerman, Joseph, 170 Kielian-​Gilbert, Marianne, 77 Kinderman, William, 346n2 Kircher, Athanasius, Musurgia universalis, 59, 336n13 Klangfarbenmelodie, 334n22 Knack, the, “My Sharona,” 320 Koch, Heinrich Christian, 63, 66, 343n16 Korsyn, Kevin, 329n6, 344n22, 348n1 Kramer, Lawrence, 331n18

Index  375 Krebs, Harald, 343n9 Kristeller, Paul, 335n5 Kurth, Ernst, 79 labeling. See nomenclature, universal Laitz, Steven, 330n12, 346n13 “lament” figure, 58, 167, 280 Lassus, Orlando, In me transierunt, 59, 60 leaping motive, 40–​45, 48–​49, 109, 110 Leeman, Pierre, March of the Belgian Paratroopers, 131–​34, 135 Lehrdahl, Fred, 133, 242, 340n60, 342n1, 344n17, 350n16 Leitmotive, 46, 47–​48, 330n16, 333nn16–​17,  339n45 Léonin, 31 Lester, Joel, 60, 62, 63 Letts, Marianne, 352n5 Lévi-​Strauss, Claude, 345n6 Levitan, Daniel, 330n10 Lewin, David, 226, 333n12, 338n38, 350n15 Generalized Musical Intervals and Transformations, 339n51 linear motive, 108, 109–​10 in Beethoven’s Piano Sonata Op. 2, No. 1, 184, 185–​87, 188e, 189, 190 in composite motives, 115–​17 line graph. See Narrative Curve linguistics, reduction in, 130–​31 listening experience. See also imagination, musical forward vs. backward trajectories, 208–​12 in-​time, 205, 219 Listenius, Nicolas, 334n2 Liszka, J. J., 173, 260 Liszt, Franz, 334n22 use of motives, 46, 47–​48 literary theory, 168–​69, 173, 253, 322 Lobe, Johann Christian, Catechism of Composition, 67–​69, 337nn24–​25 Local Points, 206, 207, 207e, 208, 209e, 210, 239, 241, 242–​43, 244e, 245, 246e, 247, 254 logic. See coherence MacinTalk, 351n4 Mahler, Gustav Symphony No. 5, 163 use of motives, 47–​48 Mailman, Joshua, 350n15 mannerism, 335n11 “Mannheim Rocket,” 194 markedness, 168, 226, 345n8, 349n7 Marshak, Boris I., 330n14

Marvin the Paranoid Android, 351n4 Marx, Adolf Bernhard, 181, 336n20, 336n22, 346n14 Die Lehre von der musikalischen Komposition, 65–​66, 67e, 68, 76 mathematic symbology Forte’s use of, 83 present study’s use of, 115 Schoenberg’s use of, 76–​77, 105, 339n46 Mattheson, Johann, 59–​61, 66, 336n16 The Complete Capellmeister, 60, 61e Maus, Fred, 345n9 “Music as Drama,” 168–​69 maximal and minimal values (contour), 94–​95, 135–​36, 142, 340n58 McClary, Susan, 331n18, 345n4 McCreless, Patrick, 63 McLean, Donald, 338n41 mechanistic view of music, 77–​79 Medieval period, 28, 334n25 constituent style traits, 29e music theory in, 56 stock formulas in chant, 30–​31 melodic blockage, 177, 179, 190 melodic reduction. See reduction, melodic melodic sequence, 142, 179 Melodielehre,  61–​69 melody-​only analysis, shortcomings of,  89–​92 memorability requirement for motive, 7, 8, 315 definition of musical present (“now”), 222–​23,  349n4 stock formulas and, 30–​31, 39 Mendelssohn, Felix, 46 metaphor, 21, 57, 149, 161–​62, 166, 168, 213, 331n2 metric dissonance, 137–​39, 141, 343n9 displacement (syncopation type), 125–​26, 137–​39, 141, 343n9 grouping (hemiola/​phase type), 126–​27, 136–​37, 137e, 141, 343n9 Meyer, Leonard, Music, the Arts and Ideas,  25–​26 minimalism, motives in, 53, 334n25 minutiae, challenges of, 162 Mirka, Danuta, 345n5 mirror inversion, 60, 61e, 77, 82, 101, 151, 151e, 154, 159, 159e, 233 mixture (modal), 49, 183, 275 “M” multiplier, 344n18 Modernism, constituent style traits of, 29e modes, 30–​31, 57, 332n4 moment form, 329–​30n7, 344n21

376 Index Monahan, Seth, 345n9 monophony, 163 mora figure, 59 Moreno, Jairo, 62e, 63, 64, 65, 66, 336n19 Morris, Robert, 342n1, 342nn7–​8 motif (in art), 14, 15e–​16e,  16–​18 motion requirement for motive, 3, 10–​14, 66, 100, 166, 315, 329n1, 329n3, 329n7 motive. See also harmonic motive; pitch and pitch-​class motives; rhythmic motives agency of, 20–​21, 22, 165–​66, 168–​69, 170, 172–​73, 190, 260, 290–​91, 344n1, 345n9 alteration of, 101 in Baroque period, 32–​39, 167 boundary-​crossing of, 143–​45, 148 boundary interval of, 82 central role in music, 3–​10 chordal, 84, 100 chronological survey of use in Western art music,  30–​54 in Classical period, 39–​45, 54, 167, 333nn11–​12 as cognitive category, 98–​99 cultural history of, 167 emotion requirement of, 3, 10–​14, 16, 166, 315 essence of, 7 feature distinguished from, 74–​76, 80, 338n36 fugue subjects and, 315–​18 hook as, 315, 318–​20 interval quality in, 330n11 judgment of potential, 314–​24 legal definition of, 21 limitations on, 46 Lobe’s definition of, 67–​68 in Medieval period, 30–​31 memorability requirement for, 7, 8, 315 in minimalist music, 53 monophonic, 5 motion requirement of, 3–​5, 10–​14, 66, 100, 166, 315, 329n1, 329n3, 329n7 oversaturation,  7–​8 performance implications of (see performance implications) polyphonic, 5, 318 (see also complex motivic analysis [CMA]) in post-​tonal music, 50–​53, 54 preferred length for, 100 principles for linking, 150–​61 as protagonist, 168–​69, 173, 174, 255, 259–​60 prototype form of, 34–​35, 117

in Renaissance period, 31 Riemann’s definition of, 70–​71, 329n3 role of, 149–​50 in Romantic period, 45–​50, 54 Schenker’s definition of, 339n47 Schoenberg’s conception of, 4–​6, 73 scope of, 148, 149, 150 single-​line (see basic motivic analysis [BMA]) size limitations of, 149 as style element of music, 25–​30 terminological collapse with feature,  80–​87 themes assembled from, 12, 18, 65, 66, 200–​201,  315–​16 transformations of, 34, 41–​42, 69, 82, 89–​90, 154–​56, 221, 233 twelve-​tone row and, 51, 53, 54 twentieth-​century concept of, 80–​87 universality of, 22 universal nomenclature for pitch and rhythm,  105–​28 working definition of, 4–​6 motivic analysis as discipline accessibility of, 22–​23, 312–​13 advantages of, 313–​14 in Baroque period, 55, 58–​61, 100 “boiling away”, 56, 81, 85–​86, 99 in Classical period, 55, 61–​65 commonalities with schema theory, 321 comparative analyses, 105–​6 in context, 311–​14 dramatic readings, 36–​39 drawbacks of, 311–​12 future promise of, 324–​28 history of theoretical approaches, 55–​102, 334n1 as “jack of all trades,” 311–​14 late nineteenth century, 55, 69–​80 limitations of, 149–​50, 324–​25 Lobe’s influence on, 68–​69 Mattheson’s influence on, 60 pre-​1600 approaches to, 56–​57 present-​day techniques, 87–​99, 100 resuscitation of, 22, 102 in Romantic period, 55, 64–​69, 100 Schenkerian analysis and, 92–​96 Schoenberg’s influence on, 4–​6 Schoenberg’s methods, 55–​56, 71–​81 skepticism about, 8 in supporting role, 7 motivic combination, 12, 18, 67, 176, 200–​201, 315–​16

Index  377 “motivic debt,” 66 motivic function, 186–​87, 198 motivic identity, 34–​35 motivic interaction, 187, 198 “game of pairs,” 189, 192, 199–​201, 203–​4 motivic parallelism, 79, 81, 101, 338n41 motivic (shape) identity, 14, 46, 143, 150–​161, 283, 320, 341n6 motivic working (motivische Arbeit),  68–​69 motto motive as, 42–​43, 51, 90–​91, 118, 157, 157e,  159–​60 in Renaissance masses, 31 Mozart, Wolfgang Amadeus Hunt Quartet, 64e, 65 motivic development techniques of, 333n12 Piano Quartet in G minor, K. 478, 125 Piano Sonata in F, K. 280, 5, 6e Piano Sonata in F, K. 332, 139–​40, 140e, 142e,  142–​43 String Quartet in C, K. 465, 73–​74, 74e Symphony No. 25 in G minor, 40–​45, 40e, 41e–​42e, 44e, 45e multivalence, 80, 219–​20, 225 musical space motion through, 11, 39–​45, 306–​10, 331n22 motivic migration in, 35–​38 motivic saturation of, 14, 46–​50 repetition of motives stretching, 40–​42 musical topics, 59, 345–​46n10 musica poetica, 56, 57, 58–​59, 334nn1–​2 musica practica, 56, 334n1 musica speculativa, 334n1 music cognition. See cognitive theory musicianship in analysis, 7 “musician’s phrase,” 222 Musique concrète, 232, 277 Mussorgsky, Modest, “Great Gate of Kiev” from Pictures at an Exhibition, 122e “My Sharona,” by The Knack, 320 mythology, 168, 173 Narrative basic principles, 168–​69 BMA archetypes, 165–​81 CMA archetypes, 205–​18, 238–​39 contradictory readings, 181, 259–​61 dramatic genres, 173, 260 Focal Point in, 162–​63, 248 gauging fitness of, 262 in instrumental music, 166–​67, 331n17 role in motivic analysis, 165

theoretical justification for framing motivic analyses as, 165–​69 theory, 21, 165–​69 Narrative Curve graphical representation of, 215e, 248, 253–​54, 259e, 267, 289e interpretation of 254–​55, 260, 273–​76,  287–​93 in literary theory, 213 in motivic analysis, 210, 213, 253–​54, 254e, 255, 257, 259, 262, 273, 274e, 275, 287, 289e, 291, 292 multiple representations of, 257 Narrative Rules BMA, 163, 169, 261e CMA, 248, 256, 261e narrative trajectory, 173, 208, 210, 248 Nattiez, Jean-​Jacques,  166–​67 Neff, Severine, 337n32, 338n34, 338n36 Neidhöfer, Christoph, 353n1 neighbor motion, 111–​13, 117, 301, 303 nesting. See recursion (nesting) network, 19 complex motive as, 223–​24, 238 mental,  97–​99 models, 349n5 Newcomb, Anthony, 167, 345n6 New German School of composition, 46, 47–​48 Ng, Samuel, 342n10 nicknames for motive, 115 nodes in BMA, 162, 166 in CMA, 208, 210, 213, 238–​39, 241, 242e Noëma figure, 59 noise, 280, 352n11 “noise” (analytic), 236–​37 nomenclature, universal, 20, 102, 105–​28 historical approaches to, 76–​77, 87, 89, 105–​7 ornaments in, 117–​19 for pitch and pitch-​class motives, 108–​19, 228 for rhythmic motives, 119–​28, 228 Non-​Engagement narrative archetype (BMA–​2°), 171–​72, 174, 176, 205, 211, 216 nonstructural tones, 136, 139–​41, 194 Notley, Margaret, 351n2 objectivity, 19, 83, 167, 251, 345n3 O’Hara, William, 348–​49n2 “onset interval,” 152 opera, text/​music associations in, 18, 166, 333n12 “orange patch,” 178

378 Index orchestration/​texture/​timbre domain,  5 in complex motivic analysis (CMA), 101, 219–​20, 223e, 224, 227e, 238 excluded from basic motivic analysis (BMA), 129 formatting conventions of, 227e in post-​tonal music, 51 in Radiohead “Paranoid Android,” 286 organicism, 337nn30–​32. See also unity challenges to, 344n22 computer-​aided analysis of, 326 as dominant force in Western music, 66, 312 Focal Point and, 162–​63 in “Paranoid Android,” 294 in Schenkerian analysis, 72, 149 in Schoenbergian analysis, 338n39 two-​dimensional representation of, 241 Organic Map (CMA), 238–​48 for Brahms’s Waltz in B minor, 242–​48, 244e, 246e construction of, 239, 240–​48 drawbacks of, 247 graphical representation of, 241–​42, 242e multiple readings, 257 as paired complement with CMA Narrative, 238–​40,  247–​48 relation to BMA, 238 visual essence of, 251 organum, 31 originality, compositional, 47, 337n26 ornamentation, 60 as domain in complex motivic analysis (CMA), 219–​21, 226, 233, 238, 286 excluded from basic motivic analysis (BMA), 129, 141 formatting conventions of, 227e metrically accented tones, 134, 139–​41 in Radiohead “Paranoid Android,” 286–​87 of stock diatonic gestures, 117–​19 Osborn, Brad, 278, 352n8 OutKast,  319–​20 Palestrina, Giovanni Pierluigi da, 350n14 Palisca, Claude, 59, 335n8 paranoia,  290–​94 “Paranoid Android,” by Radiohead, 276–​96 additive origins of, 276 analysis of, 278–​96 data interpretation and narrative, 287–​93 Focal Point of, 279, 280, 285–​86 form of, 279–​80, 281e protagonist in, 276–​77 spoken title as rhythm motive, 294–​96

Parry, Hubert, 69 passacaglia, 278, 279, 280, 282, 283, 285, 292 passing tones, 60, 130, 136 Pathopoeia figure, 59 patterning, 134, 136–​37, 142–​43, 149 pedal point, 230, 231, 245 perception, music, 96–​99 Gestalt principles, 3–​4, 10–​12, 14, 19 limits of, 149 perfect authentic cadence (PAC), 268 performance implications, 221, 253, 259, 346n12 hand-​crossing,  48–​49 motivic identification and, 195, 200 period (Renaissance segment of music), 58, 59 period (two-​phrase form unit), 39, 64, 65e, 66,  146–​47 Pérotin, 31 personification of motive, 168–​69, 170, 172–​73, 344n1 of non-​living things, 21–​22 petit dessin, 65, 68, 76 “Petrushka” chord, 233 phase (metric). See metric dissonance phenomenal accent, 125 phrase, 5, 40, 55, 64, 77 division into segments, 63, 143 Riepel’s study of, 62–​63 physicality, 228 Pinter, Charles C., 82 pitch and pitch-​class motives acting independently from rhythmic motives, 5 arpeggiating nomenclature, 110–​11 in basic motivic analysis (BMA),  129–​63 BMA of Beethoven’s Piano Sonata Op. 2, No. 1, 183–​95 in complex motivic analysis (CMA), 223e, 224, 227e,  235–​36 directional indication, 109 in Fortean analysis, 84 intervallic disposition, 109 interval measurements, 108–​9 limitation on scope of, 84, 108–​9 operations employed in motivic analysis, 150–​52,  154e ornamentation of stock diatonic gestures,  117–​19 phrase boundary-​crossing of, 143–​45, 148 rules for labeling, 108–​19

Index  379 sample analysis, 157–​59 in Schenkerian analysis, 84 single-​note, prohibition on, 4, 10, 108,  341n3 summary label for, 115 unidirectional motives, 109–​11 pitch bends, 283, 285, 287, 320 pitch cells. See intervallic cells pitch class. See also pitch and pitch-​class motives directionality of, 109 equivalence, 82 motives, 100–​101 in set theory, 51, 53, 54, 77, 84–​86 transposition involving, 151 pitch domain, 155. See also pitch and pitch-​class  motive plagal cadence, 174, 268, 273 Plato, 57 Plomp, Reiner, 330n8 plot. See Narrative. See also drama poetic meter, 60 Poetics, 56, 59–​60 points of contour. See maximal and minimal values polyphony, 53, 56, 91–​92, 101, 256, 318 popular music constituent style traits, 29e motivic analysis in, 26, 276–​96,  318–​20 Porter, Yves, 330n13 post modern music, 26, 232 post-​tonal  music constituent style traits, 29e miniatures and song forms in, 50–​51 motives in, 50–​53, 54 Poulenc, Francis, 334n21 pragmatism, 210, 222, 256, 280 pre-​dominant (PD). See harmonic function labels prefix figures for pitch motives, 113–​15, 117–​19 for rhythmic motives, 121–​22, 122e Preliminary Rules of motivic analysis. See Rules for motivic analysis premise. See compositional premise print technology, 57 Printz, Wolfgang Caspar, Phrynis mytileneus, 335–​36n12,  336n15 program music, 28, 30, 166 nineteenth-​century, 46, 268 Prokofiev, Sergei, 334n21 proof, mathematical, 78

Propagation narrative archetype (BMA–​1), 163, 169e, 169–​71, 187, 194–​95, 203, 205, 208, 211, 216, 219, 322 multiple-​motive, 170, 171–​73, 205 Propagation narrative archetypes (CMA), 205–​8, 206e, 211, 215, 216, 218 Dissolution type (CMA–1​>), 207e, 208, 212, 215, 248, 255 Focal Point in, 248 information flow in, 208–​12, 209e,  241–​42 limitations of, 220 for multisection works, 206–​7, 207e Propositions (theoretical). See Rules for motivic analysis Propp, Vladimir, 345nn6–​7 protagonist in dramatic genres, 173 motive as, 168–​69, 173, 174, 255, 259–​60 in “Paranoid Android,” 276–​77, 290–​94 prototypes, 34, 63, 97–​98 provisional analysis (scouting), 247, 257 psychology of music, 96–​99 public engagement with analysis, 22, 312–​13 Purcell, Henry, “When I Am Laid in Earth” from Dido and Aeneas, 167 “purple patch,” 178 push (rhythmic), 282 quantitative analysis as element of CMA Narrative construction, 221, 239, 249–​53, 256–​57, 263, 267, 273 spreadsheet representation, 251, 252e, 253, 258e subjectivity of, 251 tally, 251, 252e, 253, 257, 258e, 263, 267, 274e, 288e unity calculation, 249–​51 quasi-​tonal shapes, 48–​49,  133–​34 Queen, “Under Pressure,” 319 Quintilian, 335n9, 336n18 radio addresses, 22, 71, 81, 87, 339n49 Radiohead, “Paranoid Android,” 276–​96 Rahn, John, 344n20 Rameau, Jean-​Philippe, Treatise on Harmony, 332n6, 349n9 Rasch, Rudolf, 330n8 real sequence, 47–​48, 48e, 334n20 recapitulation. See sonata form recomposition, 180, 215 rectus, 159 recursion (nesting), 79, 141, 143–​44, 199–​200, 313. See also motivic parallelism

380 Index reduction, harmonic, 233–​34 reduction, melodic maximal and minimal values in, 135–​36, 142 motives discovered under, 18, 101, 111 musical complexity and, 79–​80 nonstructural tones in, 135, 136, 139–​41 pruning, 111, 131 role in present study, 100 in Schenkerian analysis, 92, 95 in Schoenberg’s analyses, 78e, 78–​79, 100, 338n40 reduction, principles of, 130–​50, 243. See also reduction, melodic; reduction, rhythmic comparison of EDR and tonal approaches,  131–​34 Epstein’s Beyond Orpheus and, 134–​41 equal duration reduction method (EDR) (auditory salience method), 130–​41 higher-​order, 142, 143, 243 introducing non-experts to, 313 invisibility resulting in certain methods of, 134 linguistic analogy, 130–​31 repeatability of, 131 rooted in auditory salience, 130–​34 rules for (see Rules for motivic analysis) stages of, 130–​33 syntax-based,  131–​34 tone extraction, 20, 92, 112, 129, 137, 139, 142–​43, 148, 311 reduction, rhythmic, 100, 122 redundancy (analytic), 234–​35 redundancy (compositional), 25–​26 register, 149 swaps, 141, 159 Reich, Steve, 334n25 Reicha, Anton, 64e, 64–​65, 66, 68, 76, 107, 336n19 relatedness, 155, 218, 322. See also unity degree of, 233, 253, 273, 275 Reményi, Eduard, 351n22 Renaissance period, 27 constituent style traits, 29e cosmological views in, 57 motives in, 31 repetition, 119, 154 “Respect” (performed by Aretha Franklin),  319–​20 rest notation (-​), 120–​21 Réti, Rudolph, 69, 87, 93, 100, 339n49, 339–​40nn51–​52, 340n57, 341nn1–​2 descriptive labeling system, 106–​7

The Thematic Process in Music, 89–​91, 95, 339n51 retransition. See sonata form retrograde, 77, 82, 89, 151, 152e in rhythm operations, 153–​54, 154e types of, 154e retrograde inversion, 82, 152, 152e reversion. See retrograde Reynolds, Christopher, Motives for Allusion, 349n8 rhetoric, 57–​59, 60, 61–​62, 63, 67, 130, 144, 332n7, 335n5, 335nn7–​8 rhetorical motive, 300, 302–​3, 307, 309e rhythm and blues, 26 rhythm domain, 5. See also rhythmic motives BMA focused on, 129 in concert with pitch domain, 5 duration scaling in, 101 and equal duration reduction (EDR), 134, 137–​41 metric or displacement dissonance in, 125, 126, 127, 137–​41, 343n9 as primary domain, 119 in Radiohead “Paranoid Android,” 282, 294–​96 rhythmes, 64 rhythmic emphasis, 125 rhythmic motives acting independently from pitch motives, 5 angled hashmark conventions, 121–​23, 194 barline notation, 125–​27, 126e in basic motivic analysis (BMA), 129–​63 BMA of Beethoven’s Piano Sonata Op. 2, No. 1, 195–​207 in complex motivic analysis (CMA), 223e, 224, 227e,  236–​37 composite, 123 consistency of, 119 divided durations, 123, 123e duration as prime importance in labeling,  120–​21 extended rules, 125–​28 identity of, 152–​54 inversion of, 344n19 operations employed in motivic analysis, 152–​54,  154e prefix and suffix conventions, 121–​22 rules for labeling, 119–​28 sample analysis, 159–​60 in Schenkerian analysis, 84, 339n48 summary chart of nomenclature, 128e summary label for, 123–​25, 124e

Index  381 treatment of rests, 120 Ricci, Adam, 107 Riemann, Hugo, 79, 234, 337n28, 349–​50n9 Catechism of Composition,  70–​71 motive defined by, 329n3 rigor in motivic analysis, 92–​94, 102, 129, 324, 325 Riepel, Joseph, 62–​63, 66, 336n15, 349n3 Rink, John, 253 Riordan, James, 319 “roll” attribute, 226, 257, 259 Rolling Stones, the, “Satisfaction,” 315, 318–​19 romance archetype, 173 Roman numerals, 228, 234, 350n9 Romantic period constituent style traits, 29e, 30 formalist composers, 46–​47, 48–​49 motives in, 45–​50, 54 motive theory in, 55, 64–​69, 100 New German School, 46 rondo forms, 143, 146, 148 Accretive narrative and, 214 Cyclic narrative and, 213, 214 Non-​Engagement narrative and, 174 Rosen, Charles, 8–​10, 49, 317, 347n5,  352n12 Rossini, Gioachino, Barber of Seville Overture, 143–​44, 144e, 343n14 rotational form, 269, 273, 274e, 292, 298 Rothgeb, John, 91, 92 Rothstein, William, 343n16, 346n12 rounded binary form, 146–​47, 148, 150, 245, 262 “rounding,” 145–​48, 146e, 257 Rovelli, C., 349n4 Rowell, L., 329n1 Rufer, Josef, 87, 91, 106, 338n35, 339n49 Rules for motivic analysis BMA Narrative Rule, 163, 169, 261e CMA Map Rule, 241, 261e Global Rules of motivic analysis, 261e, 262 Proposition 1 of motive theory, 10 Proposition 2 of motive theory, 10, 165–66, 315 Proposition 3 of motive theory, 25 Reduction Rule 1 (RR1), 136 Reduction Rule 2 (RR2), 141 Reduction Rule 3 (RR3), 148–​50 Rule 1 of Motivic Analysis, 150, 261e Rule 2 of Motivic Analysis, 162, 261e Rule CMA1, 222–​23, 230, 261e Rule CMA2, 239, 261e Rule P1, 108

Rule P2, 108–​10 Rule P3, 109–​10 Rule P4Arp, 110–​11, 341n4 Corollary 1 (for Rule P4Arp), 110 Rule P4Neighbor, 111–​13 Rule P5, 113–​15 Rule P6, 115–​17, 341n5 Rule R1, 119 Rule R2, 120 Rule R3, 121–​22 Rule R4, 121–​23 Rule R5, 123–​25 Rule R6, 123–​25 Rule R7, 125 summary chart, 261e Rusch, René, 278–​79, 352n5, 352nn8–​9 salience, 93, 95. See also equal duration reduction (EDR) higher-​order,  142 reduction method rooted in auditory, 130–​34 Saint-Saëns, Camille, 47 “Satisfacti “Satisfaction,” by the Rolling Stones, 315,  318–​19 on,” by the Rolling Stones, 315, 318–​19 saturation, motivic, 39–​45 in Romantic music, 46–​50 Satz, 55, 66, 67e, 346n14 Satzlehre,  64–​65 scatter plot, 213, 214e Schachter, Carl, 339n50, 344n17 Scheibe, J. A., 63 schema theory, 320–​22, 353–​54nn4–​5 Schenker, Heinrich concept of motive, 69, 71, 329n1, 339n47 Harmony, 344n1 motivic parallelism and, 79 prohibition on one-​note pitch motives, 341n3 treatment of rhythm, 339n47 Schenkerian analysis, 84–​85, 326–​27, 337n29, 342n1 expertise/​training required, 22 goal of, 149 internal conflict of motive and system, 92, 340n54 “interruption” in, 343nn15–​16 reconciliation with Schoenbergian analysis,  92–​96 reduction method in, 131–​34 theories compared with Schoenbergian analysis, 85 Schmalfeldt, Janet, 167, 338–​39n42, 346n12

382 Index Schoenberg, Arnold. See also Schoenbergian analysis as composer and critic, 55, 71 conception of motive, 4–​6, 73, 81, 149 concept of developing variation, 73–​74, 77, 324–​26,  333n19 evolution of theoretical concepts, 81 Four Orchestral Songs, Op. 22, 338n35 The Fundamentals of Musical Composition, 5, 78–​79,  81 Harmonielehre,  80–​81 hierarchy of formal terms, 72–​73, 73e Klangfarbenmelodie, 334n22 location of Grundgestalt in analyses, 210 mathematical symbology used by, 76–​77,  105 melodic reduction technique, 78–​79 Models for Beginners in Composition, 80 motive-​based analysis of music, 55–​56, 69, 71–​81,  107 The Musical Idea, 74–​76, 80, 81, 338n34 “O Alter Duft” from Pierrot Lunaire, 208 Piano Piece Op. 19, No. 6, 339n46 Pierrot Lunaire, 51 predictions concerning legacy, 324–​25 radio talks, 22, 71, 81 Style and Idea, 81, 350n14 Suite for Piano, Op. 50, 50 theories compared with Schenker, 92 Three Piano Pieces, Op. 11, No. 1, 51, 52e, 85, 86e, 334n23 view of musical work as living organism, 72, 338n39 Schoenbergian analysis basic motivic analysis compared with, 129 complex motive and, 221–​22 in dialog with Schenkerian analysis, 92–​96 fragmentation in, 156 methodological adherents to, 87–​92 set-​theory analysis influenced by, 84 theories compared with Schenkerian analysis, 85 Schubert, Franz, 46 “Erlkonig,” 18, 346n11 “Neugierige,” 119, 119e String Quartet No. 9 in G minor, 230, 231e, 233 Unfinished Symphony, 163 Schubert, Peter, 353n1 Schuijer, Michiel, 354n7 Schumann, Robert and Brahms (chess), 278

“Sphynxes” from Carnaval, 315 Symphony No. 4, 137 scope of motive. See motive Sears, David, 352n8 Second Tonal Area (sonata form), 42, 159, 174, 176, 183–​84, 206, 346n13 Second Viennese School, 50–​53 Segment Burmeister’s period compared with, 58 complex motive length and, 222–​25 in complex motivic analysis, 235–​63, 335n10 in Schenkerian analysis, 92–​93 tallying of, 251, 252e, 253 segmentation (parsing) in Burmeister’s Lassus analysis, 60 in CMA, 231e, 233, 234, 235, 236e, 242, 267, 268, 271, 279–​80, 292, 321, 322e, 350n16 exhaustive (Lehrdahl and Jackendoff), 242 and harmonic motives, 233 in Rufer’s analyses, 89 in set theory, 84 sensed connection, 155–​57, 160–​61, 236, 243 Sensitive style. See Empfindsamkeit serialism total, 334n26 twelve-​tone, 51, 53, 54, 77 Sessions, Roger, 329n1 set-​theory analysis, 78, 82, 84–​85, 326 applied to previous eras, 350n14 expertise/​training required, 22 motive and, 85–​87, 100–​101 shadowing (voices), 236, 238 shape (gestalt), 4–​5, 10–​12, 14, 19–​20, 73e, 74–​76, 75e,  94–​95 Sharpe, Robert, 9 Sherrill, Paul, 321–​22 sigh figure, 58, 167, 228 silence, 144 similarity relations, 325, 354n7 Sims, Eleanor, 330n14 Sisman, Elaine, 345n5 slash notation, 111–​14 Smetana, Bedrich, The Moldau, 166 Smith, Charles, 314 social order, 173, 260 solfege, 56 sonata form, 146, 148 conflict-​based narratives in, 174, 176 development, 148, 176, 177–​80 exposition, 148

Index  383 Laitz’s division (into FTA, transition, STA, Closing), 346n13 motivic activity in, 40–​45 narrative in, 167 recapitulation, 146, 148, 180, 181 retransition,  147–​48 transition, 149 Sousa, John Philip, 12e Liberty Bell March, 12 Spaeth, Sigmund, 329n6 special effects domain in complex motivic analysis (CMA), 227e, 238, 257 defined, 226 formatting conventions of, 227e Spector, Nancy, 354n6 Spillman, Robert, 352n12 split consciousness on rehearing music, 210 Stafford, William, 345n2 static, 277 status. See compositional “problem” or status “Stayin’ Alive,” by the Bee Gees, 320 Stein, Deborah, 346n11, 352n12 stock formulas, 25, 26, 30–​31 Stockhausen, Karlheinz, 344n21 Kontakte, 329–​30n7 storytelling, musical, 130, 166, 168, 173. See also Narrative Straus, Joseph, Remaking the Past, 85–​86, 331n18, 334n23 Strauss, Richard Till Eulenspiegels Lustige Streiche, 126e,  126–​27 use of motives, 47–​48 Stravinsky, Igor, The Rite of Spring, 98 Street, Alan, 344n22 structural accent, 133–​36, 143, 234, 242 style constituent traits, 27–​28, 29e, 30, 195 contextual analysis and, 91–​92 harmonic claims and aesthetic premises, 232 life cycle of, 25–​27 periods, 27 role of motives in, 25–​30 violation of, 232 subdominant. See harmonic function labels (pre-​dominant) sub-​elements of motives, 73, 115, 170, 206, 233,  248–​50 subjectivity, 19 in analysis, 7, 232, 251–​52 in eighteenth-​century music, 62 in harmonic analysis, 231–​32

subliminality, 277 suffix figures for pitch motives, 113–​15, 117–​19 for rhythmic motives, 121–​22, 122e Sulzer, J. G., 345n5 summary label for pitch motives, 115 for rhythmic motives, 123–​25, 124e surface motive, 40, 129, 134 Swafford, Jan, 351n20 Swain, Joseph, 349n5 symmetry, 35, 64, 153, 181 synchronic vs. diachronic, 210, 241–​42 syncopation (displacement dissonance), 125, 126, 137–​39, 156, 343nn9–​10 submetrical, 282 syntax. See harmonic syntax Synthesis narrative archetype (BMA–​2•), 172, 176, 205, 211–​12, 216 Synthesis narrative archetype (in CMA analysis). See Accretion narrative templates “Table of Motives”, 83, 83e, 339n45 tactus, 70 tally. See quantitative analysis Tchaikovsky, Pyotr, 312 Symphony No. 4, 163 Temperley, David, 340n59, 343n10 tension correlated with CMA Narrative, 254, 287, 290. See also Narrative Curve ternary form, 27, 143, 322, 324 Non-​Engagement narrative and, 174 texture domain. See orchestration/​texture/​ timbre domain thematic transformation, 46 thematic working (thematische Arbeit), 61, 63, 336n16 theme in contour reduction, 134 motives’ role in assembling, 12, 18, 65, 66, 200–​201,  315–​16 originality of, 47 in sonata form, 87, 88e,  89–​91 Thuringus, Joachim, Opusculum bipartitum, 59 “Till” motive, 126–​27 timbre domain. See orchestration/​texture/​ timbre domain “time-​span reduction” method, 242, 342n1 Tinctoris, Johannes, 335n4 Todd, R. Larry, 85 Todorov, Tzvetan, Introduction to Poetics, 345n7

384 Index tonal reduction. See Schenkerian analysis tone painting. See word (or tone) painting tonic (T). See harmonic function labels Tovey, D. F., 79, 178, 183 tragedy archetype, 173 trajectory, dramatic, 47, 275 transformation analytic,  8–​9 arrow representation, 162, 205, 210, 241–​42 motivic, 34, 41–​42, 69, 82, 89–​90, 154–​56, 221, 233 transformational theory, 78, 86, 349n5 transgression, 173, 260 transition. See sonata form transparency in analysis, 251, 262 transposition, 77, 101, 150–​51, 151e, 158e, 158–​59, 233, 344n20 types of, 154e Traut, Donald, 320 trill, 226, 233 Trippett, David, 336n20 “Tristan chord,” 226 tritone shape, 283, 286–​87 Triumph narrative archetype (BMA–​2+), 172, 177–​81, 205, 211, 216, 296–​310 “Turn” motive, in Beethoven’s Piano Sonata Op. 2, No. 1, 183–​84, 185, 186e, 193, 194 twelve-​bar blues, 26 twelve-​tone music. See serialism, twelve-​tone “two-​dimensional” structure of music, 85, 232, 241 Tymoczko, Dmitri, 332n5, 350n14 “Under Pressure,” by Queen, 319 unequal subdivision (rhythm), 123 unidirectional motive, 108, 109–​11, 117 unity aesthetic, 46 analytical explanation of, 72, 87, 137, 170, 313, 334n23, 338n37, 340n57 analytic taste and, 337n31 calculating,  250–​51 fluctuations in, 218 graphical representation of, 214e–​16e, 239, 254e, 259e, 274e, 289e relative values of, 213, 249–​51, 250e, 290 twelve-​tone row and, 51, 53, 54 underlying, 8, 40–​45

valuing, 213, 249–​51, 250e, 287, 290, 292, 334n24 Western chauvinism and, 72 “upturned glance” (epiphany) motive, 300, 301e, 302, 303, 304, 310 Ursatz, 84, 85, 92, 339n50 variation. See developing variation Vaughan Williams, Ralph, 334n21 vector, 153, 225, 229, 350n15 Verdi, Giuseppe, “Stride la vampa!” from Il Trovatore, 137, 138e verse-​chorus form, 213 verse-​refrain form, 26 voice swap, 157 voicing in instrumental music, 185, 187, 189–​90, 235–​36, 348n1(2) Von Békésy, Georg, 330n8 Wagner, Richard, 85 Parsifal, 48e Tristan und Isolde, Prelude, 115 use of motives, 46, 47–​48, 330n16, 333nn16–​17, 339n45 “wail” motive, 317, 318 Walker, Alan, 72, 87, 340n57 water sprite representation, 268 Webern, Anton, 50 Webster, James, 333n12 weighting of domains, 229, 249–​51, 252e, 257, 273, 287, 351n22 role in CMA, 229, 351n22 strategies of, 249–​50 Whittall, Arnold, 339n46 “wind-​up” return,  147–​48 Wolzogen, Hans, 339n45 word (or tone) painting, 31, 59, 345n5 Wyn Jones, David, 60 Yearsley, David, 39 Yorke, Thom, 285 Zbikowski, Lawrence, 170–​71, 223, 333n17 Conceptualizing Music, 97–​99, 101 Zeno, 349n4 zig-​zag motive, 40–​45, 108 Zuckerkandl, Victor, 329n1