Conceptualizing Music: Cognitive Structure, Theory, and Analysis (Ams Studies in Music Series) 9780195140231, 0195140230

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Conceptualizing Music: Cognitive Structure, Theory, and Analysis

Lawrence M. Zbikowski

OXFORD UNIVERSITY PRESS

CONCEPTUALIZING MUSIC

AMS Studies in Music Lawrence F. Bernstein, General Editor Editorial Board Joseph Auner Scott Bur nham Richard Crawford Walter Fr isch, Chair Sarah Fuller Robert Judd Janet Levy Jessie Ann Owens Kerala Snyder Judith Tick Gary Tomlinson

Q CONCEPTUALIZING MUSIC Cognitive Structure, Theory, and Analysis

Lawrence M. Zbikowski

1 2002

3 Oxford New York Auckland Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi São Paulo Shanghai Singapore Taipei Tokyo Toronto

Copyright © 2002 by Oxford University Press, Inc. Published by Oxford University Press, Inc. 198 Madison Avenue, New York, New York 10016 www.oup.com Oxford is a registered trademark of Oxford University Press 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, electronic, mechanical, photocopying, recording, or otherwise, without the pr ior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Zbikowski, Lawrence Michael. Conceptualizing music : cognitive structure, theory, and analysis / Lawrence M. Zbikowski. p. cm. — (AMS studies in music) Includes bibliographical references (p. ) and index. ISBN 0-19-514023-0 1. Musical perception. 2. Musical analysis. 3. Cognition. I. Title. II. Series. ML3838 .Z25 2002 781'.11— dc21 2001058756

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dem andenken meiner Mutter: Anneliese Margerite Zbikowski, 1926 –1999

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preface

n picking up a book with the title Conceptualizing Music: Cognitive Structure, Theory, and Analysis, one might reasonably assume that it deals with music cognition and how our knowledge of that discipline can be applied to music theory and analysis. This book does not do that, or at least not in a simple way. To begin, it does not have much to say about the fairly large body of research usually placed under the rubric “music cognition.” This work, having been developed out of music psychology and infor med by recent research in the brain sciences and mind sciences, proceeds by carefully crafted exper iments, which are subjected to closely argued statistical and logical analysis. As practiced by such eminent and able researchers as Carol Krumhansl, John Sloboda, and David Huron, the study of music cognition has told us much about how humans process sonic and musical infor mation. But this book proceeds in a somewhat different way. Drawing on the same body of research from the brain sciences and mind sciences that shaped studies in music cognition, it explores how basic cognitive capacities are specified for understanding music. The project takes inspiration from recent work in linguistics and rhetor ic by researchers like Ronald Langacker, Gilles Fauconnier, Mark Turner, and George Lakoff, and it is based on the assumption that musical understanding relies not on specialized capacities unique to the processing of patterned sound but on the specialized use of general capacities that humans use to structure their understanding of the everyday world. The methodology, in consequence, relies not on exper imental design and data analysis but on using a broad and quite extensive body of research to inter pret recurrent tropes of musical understanding. These tropes involve such things as the importance to musical understanding of relatively small and compact musical phenomena like “motives,” “themes,” and “chords”; the use of terms grounded in nonmusical domains — terms like “space” and “depth”— to character ize musical events; and the reliance on patter ns of logical inference to reason about music. The result of this investigation is a theoretical perspective on musical organization, but one rather different from what usually counts as “music theory.” To make sense of this claim requires a bit of explanation about the intellectual context of music theory, for music theory is, within the rolling seas of humanistic studies, a

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p re fac e rather strange fish. Put bluntly, it is clear that much of what music theory does, as a discipline, does not count as any sort of theory in moder n scholarship. This is exemplified by each of the two distinct but related and intertwined strands that make up contemporary music theory. One strand is occupied with pedagogy, the other with speculative and highly systematic approaches to musical organization. Music theor y, as it is presented in the classroom, is most often engaged with a careful and often relentless explication of what, for want of a better ter m, we can call musical grammar. Consider the following, from Edward Aldwell and Carl Schachter’s Harmony and Voice Leading: Like VII⁶,V ⁴₃ has 2 as its bass.V ⁴₃, in fact, resembles VII6 so closely that they are almost interchangeable chords. The bass of V ⁴₃ is a more neutral tone than that of V ⁶₅ (or, as you will see,V ⁴₂) and can move convincingly either to 1 or to 3. Consequently,V ⁴₃, like VII⁶, forms a natural connection between I and I⁶ and appears very frequently as a passing chord within an extended tonic.1

The prose and ter minology are impressively dense. But one should not be misled into thinking that the authors are concer ned only with abstruse compositional techniques, for immediately after this excer pt Aldwell and Schachter refer to a passage from an impromptu by Franz Schubert that illustrates the niceties of voice leading with which they are concer ned. Their assumption is that the reader is familiar with the music and counts it as typical, and it is this familiar ity that provides a phenomenological anchor for what might appear to be rather thick jargon. If you know Schubert’s impromptu, or (better yet) can summon it in your sonic imagination when reading the example in score, Aldwell and Schachter’s point about the harmonization of the second scale-step in the bass is not just clear but even obvious. At the heart of pedagogical music theor y are familiar or typical examples of music, the mysteries of which are revealed by a music theor ist (or theor ists) eager to share the secrets and wonder of this music with others. As elegant and persuasive as this approach might seem, it is, within our cur rent cultural climate, more than a little unrealistic: music by Schubert and his contemporar ies is often unfamiliar to the students who read Aldwell and Schachter’s text (or any of a number of similar texts) and is not typical of the music that resonates through these students’ digitized and hypercommercialized environments. That this should be so is often regarded as symptomatic of an illness of the late twentieth centur y, an illness that leads to an insufficient engagement with the g reat traditions of Western culture. For Classical music (as it is so styled), the antidote is music theory. Music theory, with its careful explication of the musical grammar of Mozart and Beethoven and Schubert, thus becomes the last redoubt against the dissolution of Western culture represented by a dwindling interest in the music of eighteenth- and nineteenth-centur y Europe. If, for a moment, we step back from Aldwell and Schachter’s text and generalize its intent beyond the specific repertoire relative to which it is framed, we might be able to avoid this rather sanctimonious stance.We could argue that music is a highly complex and idiosyncratic mode of human communication and that having a knowl1. Edward Aldwell and Carl Schachter, Harmony and Voice Leading, 2nd ed. (San Diego: Harcourt Brace Jovanovich, 1989), 112.

p re fac e edge of the grammar of this mode of communication is essential to its deeper appreciation, no matter what for m music might take. The argument is a familiar one to me, not the least because I often find myself making it. And yet, something rings hollow. The grammar that music theor y teaches is unavoidably tied to the repertoire to which it refers, and just how this is generalized to apply to other repertoires is not immediately apparent: I know of no theory text that explains how the grammar of Schubert’s musical discourse is manifested in the music of, say, John Coltrane or Pr ince. Given its isolation from contemporary culture, the music theory of the classroom appears to be little more than a ghost that haunts the echoing halls of a crumbling cultural empire. The second strand of music theory partakes of the systematic quality inherent in grammars but generalizes it away from natural language and toward a free-standing intellectual construct. As an example of this sort of theory, consider the following brief passage from David Lewin’s analysis of a section of the opening of Claude Debussy’s piano prelude Reflets dans l’eau. In this excer pt, X, Y, and Z represent specific collections of musical notes, RI refers to the compound operations retrograde and inversion, RICH is a function that effects ser ial transfor mations, and T refers to transposition: In measure 10 the music of measure 9 is repeated and extended. The crescendo recurs. In the melody the repetition gives rise to a rotated for m of Z1, marked “rot Z1” on figure 10.10. Rot Z1 is Bb-Ab-F-Eb; it embeds ser ially the or iginal for m of Y, Ab-FEb, and precedes this Y by its overlapping inverse-RI-chained for m Bb-Ab-F. (Bb-AbF is RICH–1(Ab-F-Eb).) This relationship is more or less inherent in the der ivations of X,Y, T(X), their repetitions, and Z1.2

It is, of course, something of a challenge to evaluate this passage in isolation. Not only is it just one part of a larger analysis, but also it comes late in a book occupied with various and sundry applications of formal algebra and mathematical mapping theory to music. Nonetheless, what should be clear is that more than familiar ity with Debussy’s prelude is required to make sense of Lewin’s inter pretation of the passage. The reader must also be familiar with a style of abstract thought that is bound to appear cabalistic to the uninitiated, one in which the transfor mation of musical entities is at least as important as the entities themselves. For some, the inaccessibility of this mode of thought is one of its char ms. For others, it is proof of the hermeticism and ir relevance of music theory. Before continuing, I should make clear that I have deep respect for the theor ists whose work I have cited. I use this work in my teaching and continue to be intr igued and stimulated by it. I also want to emphasize that these excer pts by no means reflect all that there is to music theory. I take them as representative of two strands of thought that are replicated and woven together in all sorts of different ways to create the texture of contemporar y theoretical practice.What is important for my purposes here is that the practice of contemporary music theory is not like that of contemporary cultural or social theory. Instead of probing the cultural or histor ical 2. David Lewin, Generalized Musical Intervals and Transformations (New Haven, Conn.:Yale University Press, 1987), 234.

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p re fac e context for musical utterances, or the complex networks of social interaction that give rise to musical behavior, music theory continues to focus on details of musical discourse with an obsessiveness that is both maddening and quixotic to cultural and social theor ists. Given the impressive traditions of music theory and their influence on my own thought, I cannot guarantee that what I offer here is a great improvement on this situation. One of the things I want to do in the chapters that follow, however, is to develop a somewhat different view of music theory— one that sees music theory as a response to a problem. The problem is that of musical understanding: how it is that we can make sense of sequences of nonlinguistic patter ned sound, that we can do so with amazing rapidity, and that (often as not) we can return to these or similar sound sequences and find continued reward. I will argue that our understanding of music relies on a play of concepts and conceptual structures that emerges from training basic cognitive capacities on musical phenomena and that music theory and music analysis der ive from this play. This mode of inquiry is not one common in the discipline of music theor y, despite its similar ities to work done by Leonard B. Meyer, Eugene Nar mour, and Robert Gjerdingen. It does, however, share features with the approach to music evident in Susan McClary’s recent Conventional Wisdom. That this should be so reveals a debt on my part, for it was Professor McClar y who first suggested that I read Mark Johnson’s The Body in the Mind back in the late 1980s, and this had a profound effect on my research. In her book, McClary explores the cultural and histor ical forces that have shaped genres like opera and the blues and compositional practices like tonality. My focus is on a somewhat different set of forces: those that shape the way humans think. It seems inevitable that these forces are in some sort of grand, if ill-defined, dialogue with cultural and histor ical agencies: it is, after all, human cognitive processes and human culture and histor y about which we are talking. That cultural and social theor y have turned a deaf ear to this dialogue is not surprising: cognitive theory has had little room for and less patience with culture, and the detail of its investigative method is no match for the epic sweep of high theoretical practice at its best. And yet it seems we must, at some point, come to ter ms with cognitive structure, for if we do not develop an understanding of how cognitive processes shape the basic mater ials of thought, we risk accepting these mater ials as things g iven by nature, just as culture and histor y— and music, for that matter — were once assumed to be given by nature. A glimpse of the problem can be seen in McClary’s compelling analysis of Robert Johnson’s 1936 “Cross Road Blues.” McClary contrasts Johnson’s blues with those of Bessie Smith, noting that the influence of Johnson’s music on white British blues players of the 1960s was due in part to a misconception: the Br itish musicians believed that the idiosyncrasies of Johnson’s blues style represented “authentic” blues practice. Describing the unique sound of Johnson’s “Cross Road Blues,” McClary writes, An affect of dread and entrapment pervades this tune — partly the result of his strangulated, falsetto vocals and his uncanny replication of that timbre on the guitar. Moreover, Johnson’s percussive guitar pulse, which locks in at the eighth-note level, allows almost no sensual movement: even though Johnson’s singing constantly strains

p re fac e against that beat, the listener’s body is regulated by those short, aggressively articulated units. The guitar thus seems to represent simultaneously both oppressive outside forces and a desperate subjectivity fighting vainly for escape.3

I have no quar rel with McClar y’s analysis — indeed, in this short passage, she has captured a number of the essential features of Johnson’s performance style. The difficulty comes with the ultimate justification for the affect produced by the song. Why do Johnson’s vocals and guitar work yield dread and entrapment rather than joyful anticipation and a feeling of liberation? Clearly, the rhythmic framework is important, but why is it that the r igidity of Johnson’s beat constrains us rather than providing a secure foundation from which we can coolly regard his plaint? These are not easy questions, all the more so because of the relatively unique character of Johnson’s recording when compared with other blues recordings of the per iod, and because hear ing “Cross Road Blues” as something other than a moving, haunting song is to misunderstand it rather thoroughly. Cultural, social, and histor ical context cannot, by themselves, explain the or igin of our affective response to the song, for our broad agreement on the effect of Johnson’s music transcends these implements of high theory (even if they have a profound influence on what we do with “Cross Road Blues” once we have heard it). I propose that explor ing the way cognitive structure infor ms our understanding of music gives us a way to account for the source of our broad agreement on the affect that pervades Johnson’s blues and can help us understand better the ways culture, society, and history reshape musical practice. Again, the way I want to accomplish this is by reconceptualizing what it means to theor ize about music. This can be done by approaching music theor y from the perspective provided by recent work in cognitive science. My intellectual guideposts include not only the wealth of work done in the mind sciences and the brain sciences but also contemporar y and histor ical ways of theorizing about music. These theor ies of music — now with “theory” understood in somewhat more traditional ter ms — capture important aspects of how it is we structure our understanding of music. At their best, they represent a technical and systematic articulation of an accord on what matters in music that is similar in kind, if not ter minology, to our accord on how Robert Johnson’s blues move us: we agree on how music is put together and we agree on what music means because both are structured by basic cognitive processes through which we organize our understanding of the world. And so music theor y— this rather strange fish in the seas of humanistic scholarship— may yet tell us some quite interesting things about the cultural and social construction of music. Understanding the way music theory instantiates cognitive processes will also help explain its continuing value. It will offer such help whether that theor y be prosaic — as within the classroom or within cr itical discourse (since even the most radical of cultural or sociological theor ists inevitably makes recourse to basic music-theoretical constructs) — or poetic, as with the elusive and allusive constructs of abstract theory. 3. Susan McClary, Conventional Wisdom: The Content of Musical Form (Berkeley: University of California Press, 2000), 51.

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p re fac e As should be apparent from the preceding, my intent here is to address not only music theor ists but also musicologists and ethnomusicologists who find the challenges of theorizing about music intr iguing.What follows will also be of interest to those with either a professional or avocational interest in cognitive science, for music presents a number of interesting problems for cognitive processing, not the least of which are its embeddedness in culture and the demands it places on realtime processing. In entertaining the thought of such an audience, however, I should briefly clar ify a distinction I draw between sound and music and the cognitive abilities related to each, which is based on three suppositions. First, not all sound is music. Second, an account of how humans process sound is not the same thing as how they understand music. Third, phenomena relevant to musical understanding exist at a conceptual level— that is, at a level of cognitive activity at least potentially accessible to conscious thought. I should emphasize that I regard the conceptual level as occupying only a small part of our total cognitive activity, and I am not at all opposed to efforts by music psychologists and others who try to explain how structures at the preconceptual level connect with and motivate structures on the conceptual level. For me, however, it is at the conceptual level that I find the most profoundly interesting questions, for concepts are the tools that allow us to construct the complex notions essential to musical understanding. From this perspective, conceptualizing music is fundamental to inquir ies about music, whether those be from the perspective of music cognition, or ethnomusicology, or musicology, or theory.

acknowledgments

n the course of writing this book I enjoyed the assistance of many people, all of whom improved the product immeasurably. Among the many colleagues who read drafts of material or responded to presentations I have given, are the following: Kofi Agawu, Holly Aksnes, Jeanne Bamberger, Larry Barsalou, Philip Bohlman, Candace Brower, Scott Bur nham, Clif Callender, Thomas Chr istensen, Martin Clayton, Rick Cohn, Nick Cook, Arnie Cox, Bob Gjerdingen, Robert Hatten, Bob Holzer, Brian Hyer, Rich Janda, Carol Krumhansl, the late Jim McCawley, Marc Perlman, Anne Robertson, John Rothgeb, Janna Saslaw, Martin Stokes, and Mark Turner. Their comments, suggestions, and quer ies helped me strengthen and reformulate my arguments. Ben Brinner, Gilles Fauconnier, Douglas Hofstadter, Travis Jackson, Bobby Short, Sumarsam, and Susan Youens were generous in their response to questions I posed to them and provided me with infor mation and insight I simply could not have gained elsewhere. Students in my classes and seminars at the University of Chicago listened to many of the ideas presented in this book, to which they responded with questions, challenges, and comments. Although it would be impractical to acknowledge all of them here, they contributed immensely to the shape those ideas have taken in this book. Deborah Gillaspie of the Chicago Jazz Archive and Regenstein Library patiently endured my requests for obscure recordings and was indispensable in helping me find mater ials that I needed. The musical examples were expertly prepared by Jürgen Selk of Music Graphics Inter national. Philipp Goedicke and Heinr ich Jaeger helped me with the translation of difficult passages in Ger man, and my brother Gene Zbikowski assisted in decipher ing some of the more recalcitrant clauses in Rameau’s and Proust’s French. José António Martins and Aron Topielski served as my research assistants, ably tracking things down, organizing my sprawling files, and getting to know the photocopier, perhaps better than they wanted to. Maribeth Payne, when she served as Executive Editor for Music at Oxford University Press, listened to my ideas for the book (at least once at the r isk of missing her train) and then provided valuable encouragement and assistance in the process of turning a proposal into a final manuscript. Institutional support came through a yearlong fellowship at the Franke Institute

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ac k nowle dg m e nt s for the Humanities (for merly the Chicago Humanities Institute) at the University of Chicago and from the Department of Music of the University of Chicago. The latter provided not only a home for my research but financial support as well. Some of the recordings discussed in chapter 5 were made available by the Archives for Traditional Music in Bloomington, Indiana, and by the Bowling Green Sound Recordings Archives, Bowling Green, Ohio. Finally, production of this book was facilitated by subventions from two scholarly societies. The Society for Music Theor y provided a subvention to defray the costs of producing the musical examples, and the result of this assistance can be seen in the number and appearance of the examples I was able to include. The Publications Committee of the American Musicological Society was equally enthusiastic about the book and ag reed to include it in its ser ies, AMS Studies in Music. This decision not only made the book more affordable but also gave me an excellent and endlessly patient editor in Lawrence Ber nstein. My family — Vicky Long, Anna Katia, and Andrei Nicolai — had to put up with sharing me with this project, and I am afraid they got the short end of the deal more than once.Without their support, understanding, and uncr itical companionship, this book would have been much the poorer. My musical examples generally adhere to the readings of the following editions: the new Beethoven Werke; the Johannes Brahms Sämtliche Werke; the Neue Mozart Ausgabe; Casimir i’s edition of the works of Palestr ina; the Neue Schubert Ausgabe; Clara Schumann’s edition of the Lieder of Robert Schumann; the new Richard Wagner: Sämtliche Werke (in conjunction with the C. F. Peter’s score of Tristan); and the Collected Works of Giaches Wert for Corpus mensurabilis musicae. Some indications of editor ial intiative in those editions — generally with respect to dynamic markings added on the basis of parallel readings — have been realized tacitly in my examples for the sake of clarity of appearance. The setting of Bernhard Klein’s “Trockne Blumen” was prepared from the 1822 edition by E. H. G. Christiani in Berlin. When dealing with histor ical sources wr itten in languages other than English, I have generally followed one of two practices. Where there is no translation of the work, or where I think existing translations are not wholly satisfactory, I provide my own translation, with the or iginal in a footnote.Where satisfactory translations exist, I use these and do not include the or iginal in the footnote. In a few cases, I have thought readers might like to make reference to both the or iginal and a translation and consequently have included citations for both in the footnotes. Some of the mater ial that follows has been previously published elsewhere and is used here by kind per mission of the journals in which it or iginally appeared. This material includes the following: “Conceptual Models and Cross-Domain Mapping: New Perspectives on Theor ies of Music and Hierarchy,” Journal of Music Theory 41/2 (© 1997, Journal of Music Theory); “Musical Coherence, Motive, and Categorization,” Music Perception 17/1 (© 1999 by The Regents of the University of California); and “The Blossoms of ‘Trockne Blumen’: Music and Text in the Early Nineteenth Century,” Music Analysis 18/3 (© 1999, Blackwell Publishers, Ltd.).

contents

Introduction: Conceptualizing Music 3

part i. aspects of cognitive structure 1. Categorization

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2. Cross-Domain Mapping 63 3. Conceptual Models and Theor ies

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part ii. analysis and theory 4. Categor ization, Compositional Strategy, and Musical Syntax 137 5. Cultural Knowledge and Musical Ontology

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6.Words, Music, and Song: The Nineteenth-Century Lied 243 7. Competing Models of Music: Theories of Musical Form and Hierarchy 287 Conclusion: Cognitive Structure, Theory, and Analysis Bibliography 335 Index 353

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CONCEPTUALIZING MUSIC

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introduction

Q conceptualizing music

arly in the opening volume of A la recherche du temps perdu, Marcel Proust presents the first of a number of memorable accounts of listening to music. He describes Charles Swann’s initial encounter with the andante of Vinteuil’s sonata for violin and piano:

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Doubtless the notes which we hear at such moments tend, according to their pitch and volume, to spread out before our eyes over surfaces of varying dimensions, to trace arabesques, to give us the sensation of breadth or tenuity, stability or capr ice. But the notes themselves have vanished before these sensations have developed sufficiently to escape submersion under those which the succeeding or even simultaneous notes have already begun to awaken in us. And this impression would continue to envelop in its liquidity, its ceaseless overlapping, the motifs which from time to time emerge, barely discernible, to plunge again and disappear and drown, recognized only by the particular kind of pleasure which they instill, impossible to descr ibe, to recollect, to name, ineffable— did not our memor y, like a laborer who toils at the laying down of firm foundations beneath the tumult of the waves, by fashioning for us facsimiles of those fugitive phrases, enable us to compare and to contrast them with those that follow. And so, scarcely had the exquisite sensation which Swann had exper ienced died away, before his memory had furnished him with an immediate transcr ipt, sketchy, it is true, and provisional, which he had been able to glance at while the piece continued, so that, when the same impression suddenly returned, it was no longer impossible to grasp.1

What Proust summons in this lyr ical, enchanted vignette is the awakening and initial consolidation of musical understanding. Swann’s first impressions of Vinteuil’s sonata are vague and unfor med, his mind simultaneously struggling with and savoring the ineffability of the music. But then, with the aid of memory, patterns emerge. Although these are incomplete and subject to revision, they offer him a way to make sense of the music, even as it continues to play. Conceptualizing Music provides an exploration of the process of musical under1. Marcel Proust, Swann’s Way (vol. 1 of Remembrance of Things Past), trans. C. K. Scott Moncr ieff and Terence Kilmartin (New York: Vintage Books, 1981), 227.

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i nt roduc t i on standing — that is, the process through which those liquid impressions spoken of by Proust are transfor med into structures that make it possible to grasp music. In what follows, I argue that Swann’s— or anyone’s— understanding of music draws on the same cognitive processes that humans use to organize their understanding of the world as a whole. Confronted with musical sound, these processes create musical concepts, the things that enabled Swann to gain a g rasp of the music. The act of conceptualizing music is the beg inning of a whole chain of cognitive events that allow us to theor ize about music and to analyze the things that populate our aural past, present, and future. The notion that Swann’s musings might give rise to musical concepts demands some further consideration. Concepts are often thought of as highly stable cognitive structures of considerable complexity, a view hardly commensurate with the ephemera attended to or produced by Swann. Recent work in the brain sciences and the mind sciences, however, has changed how we view concepts. There are now persuasive arguments that concepts are quite fluid, that they are not ir revocably wedded to words or to concrete representations, and that they are not even unique to our species.2 In consequence, the provisional replicas of musical phrases that make it possible for Swann to secure a foothold in the unfamiliar ter rain of Vinteuil’s sonata need not automatically be excluded from the conceptual domain. In fact, they are very much like the concepts we use to structure our understanding of the everyday world. This same work in the brain sciences and the mind sciences suggests a way to account for the apparent simplicity and immediacy of musical understanding, which seems incommensurate with the complexity of musical structure. For instance, the sonata by the fictional Vinteuil is intended to be a relatively complex contemporary work that has captured the fancy of the musical elite of the Paris salons. Nonetheless, Swann, whose connoisseurship does not extend to music, is able to gain a grasp of the work almost immediately. That he is able to do so is not simply novelistic license but is, in fact, thoroughly plausible: almost everyone has had the exper ience of listening to an unusual composition or exotic repertoire and being able to make something of it. This possibility has suggested to some a latent musicality in humans comparable to the sort of competence for language proposed by Noam Chomsky.3 Competencies of this sort raise as many questions as they answer, however, particularly where cultural entities such as music are concer ned. It seems more promising to follow the path of researchers who have rejected linguistic competence as a given 2. See, for instance, Douglas R. Hofstadter and the Fluid Analogies Research Group, Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought (New York: Basic Books, 1995), chaps. 5– 6, 8– 10; Gerald M. Edelman, The Remembered Present: A Biological Theory of Consciousness (New York: Basic Books, 1989), chap. 8; and Donald R. Griffin, Animal Minds (Chicago: University of Chicago Press, 1992), chap. 6. 3. The notion of musical competence has generated a range of commentar y and scholarship. See John Blacking, “Music, Culture, and Experience,” in Music, Culture, and Experience: Selected Papers of John Blacking, ed. Reginald Byron, with a foreword by Bruno Nettl (Chicago: University of Chicago Press, 1995), 228 – 31, on musical competence and culture; Steven Pinker, How the Mind Works (New York: W.W. Norton, 1997), 528 – 38, on musical competence and its relation to other competencies; and Allan Keiler, “The Origins of Schenker’s Thought: How Man Is Musical,” Journal of Music Theory 33 (1989): 273 – 98, on a nineteenth-century conception of musical faculties akin to musical competence.

conc e p tual i z i ng mu s i c and who have set about explor ing the cognitive foundations of language.4 Their task has been to discover what processes are basic to human cognition and then to determine how they are specified for language. For my part, I would like to explore how some of these same general cognitive processes are specified for music. By this means I hope to account for the apparent ease and real rapidity with which we can conceptualize a highly complex, completely unfamiliar music on our first encounter, without having to postulate the faculty of musical competence. At a bit more of a remove, but no less important for a complete account of cognitive processing, is the way concepts come to be organized into the more extended cognitive structures with which our thought is usually occupied. This is where theories come into play, for theor ies are the cognitive tools that guide the way we reason about the things we exper ience. At first, this might seem to be a rather specialized use of the notion of “theory,” for the theory with which much current literature is occupied — within and without music scholarship— is hardly the stuff of everyday exper ience. Recent research has countered this view of theory by demonstrating that the elegant and abstract theor ies of science have much in common with the tools for reasoning used by very young children.5 Theories are the basic means by which we make our exper ience coherent and guide further action. The rough-andready transcr ipt that guides Swann’s listening thus has something in common with the more fully articulated and systematic structures we usually associate with the idea of “music theory.” That music theory might have alliances with everyday thought processes is a provocative claim. On the one hand, music theory often manifests itself as a relentlessly practical discipline: a codification of the scales, chords, and grammatical rules proper to a highly circumscr ibed portion of musical discourse, assembled with the intent of rendering music comprehensible to those who would become musically literate. On the other hand, music theory can reach into the far cor ners of abstraction to embrace complicated mathematical concepts or the arcane symbologies of voice-leading graphs, as any reader of the Journal of Music Theory, Music Theory Spectrum, or Music Analysis will quickly discover. Nonetheless, I want to argue that music theory, in all its diverse forms, reflects the same basic processes that guide our understanding of the everyday world. Theorizing about music is an activity specialized only in its domain, not in the cognitive processes it involves. What might these cognitive processes be, and how would they manifest themselves? To answer these questions, let us begin at a beginning, with two theor ies of 4. For general introductions to some of the working assumptions of cognitive linguists, see George Lakoff, “The Invariance Hypothesis: Is Abstract Reason Based on Image-Schemas?” Cognitive Linguistics 1 (1990): 39– 74; and Michael Tomasello, “Introduction: A Cognitive-Functional Perspective on Language Structure,” in The New Psychology of Language: Cognitive and Functional Approaches to Language Structure, ed. Michael Tomasello (Mahwah, N.J.: Erlbaum Associates, 1998), vii–xxiii. In the field of cognitive linguistics, Ron Langacker’s work is particularly notable for its thoroughness and its systematic approach. See Langacker, Theoretical Prerequisites, and Descriptive Application, vols. 1 and 2, respectively, of Foundations of Cognitive Grammar (Stanford, Calif.: Stanford University Press, 1987, 1992); idem, Grammar and Conceptualization (Berlin: Mouton de Gruyter, 2000). 5. See Alison Gopnik and Andrew N. Meltzoff, Words, Thoughts, and Theories (Cambridge, Mass.: MIT Press, 1997); and Alison Gopnik, Andrew N. Meltzoff, and Patricia K. Kuhl, The Scientist in the Crib: Minds, Brains, and How Children Learn (New York:William Morrow, 1999).

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i nt roduc t i on music from Greek antiquity. These theor ies, and the music to which they refer, are so unfamiliar that even many who make music theory the focus of their research have only passing knowledge of what they involve. But there is an advantage in this unfamiliar ity, for the disor ienting effect it can have also serves to loosen our notions about what a theory of music, or a theoretical construct, should be. Despite connections with music theory as it was practiced in Europe and (to a lesser extent) in the Arabic world, Greek music theory of antiquity is the theory of an alien society. Nonetheless, this theory was a beginning — one of the starting points for accounts of musical organization in the Western tradition. We can discern within it, therefore, the theor ists of antiquity grappling with basic constructs equivalent to, if still different from, the sort of constructs taught in beginning music theory classes today. Both aspects will allow us to see the role basic cognitive structures play in our understanding of music.

ancient music theory and modern cognitive science Those who wrote on Greek musical practice in antiquity concer ned themselves with a wide variety of topics, including the place of music in society, musical aesthetics, the construction and nature of musical instruments, and the organization of pitch mater ials. Specific discussions of pitch mater ials— the usual topic of disquisitions more directly or iented to music theory— centered around the set of pitch relationships that has come to be called the Greater Perfect System.6 As shown in figure I.1, this consisted of a set of four tetrachords (hypaton, meson, diezeugmenon, and hyperbolaion), which, together with one additional note (called Proslambanomenos), provided the framework for a two-octave system of pitches basic to Greek music. The end points of the tetrachords (the notes Hypate hypaton, Hypate meson, Mese, and so on), together with Proslambanomenos, were regarded as stable, unmovable pitches. There was, however, no fixed standard for tuning — the note-names given in figure I.1 are simply for the pur poses of illustration.Within the boundar ies marked by each tetrachord were two other pitches, whose placement varied according to which of three different genera was understood to be in play. (In the tetrachord hypaton, for instance, the variable notes above Hypate hypaton were Parhypate hypaton and Lichanos hypaton.) The diatonic genus located the movable pitches in a manner analogous to moder n diatonic scales (for instance, given the reference pitches on fig. I.1, Parhypate hypaton in the diatonic genus would be equivalent to F3, and Lichanos hypaton would be equivalent to G3), but the chromatic and enharmonic genera situated the pitches in ways that have no comfortable analogue in modern scale construction. The result was a system in which the placement of movable pitches could vary widely and in which intervals between successive pitches could be smaller than a half step and larger than a whole step. 6. For a more detailed discussion of the Greater Perfect System and its place in Greek theor y of antiquity, see Andrew Barker, ed. and trans., introduction to Harmonic and Acoustic Theory (vol. 2 of Greek Musical Writings), Cambridge Readings in the Literature of Music (Cambr idge: Cambridge University Press, 1989), 12– 13. For a more general overview of Greek music theor y and a thorough discussion of the sources, see Thomas J. Mathiesen, Apollo’s Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages (Lincoln: University of Nebraska Press, 2000), part 4.

conc e p tual i z i ng mu s i c C5

Nete hyperbolaion Tetrachord hyperbolaion

G4

Nete diezeugmenon Tetrachord diezeugmenon

D4

Paramese

C4

Mese Tetrachord meson

G3

Hypate meson Tetrachord hypaton

figure I.1

D3

Hypate hypaton

C3

Proslambanomenos

Diagram of the Greater Perfect System of Greek music theory

There were two main theoretical approaches to presenting the elements of the Greater Perfect System. The Pythagorean approach der ives from a metaphysics associated with Pythagoras of Samos, who lived during the sixth centur y b.c. Its hallmarks are a persistent interest in number and the deployment of numer ical conceptions in cosmological contexts. In contrast to this, the Aristoxenian approach, associated with the Peripatetic school of the fourth century b.c., places little reliance on number, trusting instead in observation and reason as the means to knowledge about music.

Pythagoras and the Blacksmiths Nicomachus of Gerasa, a mathematician and har monist wr iting around the beginning of the second century a.d., described Pythagoras’s discovery of the basic pr inciples of music theory as follows: He [Pythagoras] was plunged one day in thought and intense reasoning, to see if he could devise some instrumental aid for the hear ing which would be consistent and not prone to er ror, in the way that sight is assisted by the compasses, the measur ing rod and the dioptra, and touch by the balance and by the devising of measures; and happening by some heaven-sent chance to walk by a blacksmith’s workshop, he heard the hammers beating iron on the anvil and giving out sounds fully concordant in combination with one another, with the exception of one pairing; and he recognized among them the consonance of the octave and those of the fifth and the fourth. He noticed that what lay between the fourth and the fifth was itself discordant, but was essential in filling out the greater of these intervals. Overjoyed at the way his project had come, with god’s help, to fulfillment, he ran into the smithy, and through a great variety of experiments he discovered that what stood in direct relation to the difference in the

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i nt roduc t i on sound was the weight of the hammers, not the force of the str ikers or the shapes of the hammer-heads or the alteration of the iron which was being beaten. He weighed them accurately, and took away for his own use pieces of metal exactly equal in weight to the hammers.7

Nicomachus continues the story by descr ibing how Pythagoras used the weights to conduct further exper iments. After suspending the weights from identical str ings, Pythagoras plucked pairs of strings and discovered the same concords as he had heard produced by the blacksmiths. He further discovered that the interval of an octave was produced by weights in a 2:1 ratio, that of the fifth by weights in a 3:2 ratio, and that of the fourth by weights in a 4:3 ratio, as shown in figure I.2a. The one discordant interval— that of a second sounded by the middle two weights — was the product of a 9:8 ratio. Additional exper imentation showed that the smallest weight sounded a fourth, with the next to smallest weight (8:6 ⬅ 4:3) and a fifth with the next to largest (9:6 ⬅ 3:2; see fig. I.2b). The octave could thus be viewed as the product of either a fourth plus a fifth (12:9:6; fig. I.2c) or of a fifth plus a fourth (12:8:6; fig. I.2d). According to Nicomachus, Pythagoras also discovered that these ratios held constant throughout the musical domain. It made no difference whether the constituent notes of the intervals were produced through string tension, string division, beating on pots, or blowing on tubes — the relationships between these notes always reduced to the self-same ratios.8 The Pythagorean view of music outlined by Nicomachus assumes that music has its origins in the natural world and that the natural world has a basic (if often unseen) order that can be expressed through number. It is thus important to Nicomachus’s story that the r inging of the hammers is accidental and not contr ived: their harmony has everything to do with the inherent order of the world and almost nothing to do with the blacksmiths. It is also significant that the concordant intervals are immediately apparent to Pythagoras and that he can discer n them even amid the discordant clang of the major second. Not only is the basis of musical order natural, but also it is manifest to all who have ears to hear. The association of these intervals with the pounding hammers provides the computational tool for 7. Nicomachus, Enchiridion, in Barker, Greek Musical Writings, 2: 256– 57. The dioptra was a rod that was used for the indirect measurement of the height of tall objects. 8. Nicomachus, Enchiridion, 258. It should be noted that Nicomachus’s story is a complete fiction. There is no evidence whatsoever that Pythagoras ever conducted any empirical research on the acoustic origins of harmonic relationships, with or without blacksmiths. Perhaps more important, the ratios described by Nicomachus simply do not work. To sound the intervals descr ibed in the story, the values of the weights must be squared— that is, the weights must be in the ratio 4:1 to produce the octave, 9:4 to produce the fifth, and 16:9 to produce the fourth. The ratios given by Nicomachus only work when used to segment a str ing into different sounding lengths. One-half the length of a str ing will sound an octave with the entire length of the string; two-thirds the length of the str ing will sound a fifth with the entire length of the str ing; and three-fourths the length of a str ing will sound a fourth with the entire length of the str ing. The importance of Nicomachus’s story lies in its influence: in the for m Boethius gave it in the sixth century, it became the standard account of basic Pythagorean principles for the Middle Ages and Renaissance; see Ancius Manlius Severinus Boethius, Fundamentals of Music, ed. Claude V. Palisca, trans. Calvin Bower, Music Theory Translation Ser ies (New Haven, Conn.:Yale University Press, 1989), 17– 19. A somewhat different perspective on Nichomachus’s story can be found in Mathiesen, Apollo’s Lyre, 399.

conc e p tual i z i ng mu s i c a.

12

9

8

6

8

6

4:3 3:2 2:1

b.

12

9

4:3 3:2 2:1

c.

12

9 3:2

4:3

d.

12

6

8 3:2

figure I.2

6

4:3

Ratios of the octave, fifth, and fourth from Pythagorean legend

which Pythagoras had searched, for it allowed him to translate the constituent notes of the har monic intervals into magnitudes — that is, into number.9 These numbers then provide further proof of the order of nature, for the ratios of the concordant intervals (the octave, fifth, and fourth) are all simple (1:2, 2:3, and 3:4), while the ratio of the discordant second is relatively complex (8:9). Finally, the numbers involved in the ratios of the concords—1, 2, 3, and 4— were also those of the tetraktys of the decad, which Pythagoreans regarded as the “fount and root of everflowing nature.”10 The account of musical organization presented by the story of Pythagoras and the blacksmiths is a model of concision. At its core are but three intervals: the octave, fourth, and fifth. The notes that make up these intervals are assigned magnitudes, the cor respondence of which yields numerical ratios. These ratios come to stand for the intervals — the ratio 1:2 is the octave— and can also be used to describe relationships between them, leading to a precise account of the composi9. The notion of a computational tool I employ here derives from the work of Edwin Hutchins, especially that presented in the second chapter of his Cognition in the Wild (Cambridge, Mass.: MIT Press, 1995). Hutchins proposes that various of the navigational tools used by seafarers are in fact computational tools in that they facilitate computation by transfor ming analog information into digital infor mation. This is exactly what the hammers did for Pythagoras: they transfor med the analog information of sound into the digital infor mation of hammer weights (with an inter mediary stage occupied by the computational tool of a scale for measur ing the weights). 10. Barker, Greek Musical Writings, 2: 30. A tetraktys is any coordinated group of four items; those of the tetraktys of the decad sum to 10, which is the basis of the base-10 number ser ies used by the Greeks.

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i nt roduc t i on tion of intervals. The interval between the Mese and Proslambanomenos of figure I.1 is an octave, a 1:2 ratio. This octave is made up of a fourth (from Mese to Hypate meson, a 3:4 ratio) and a fifth (from Hypate meson to Proslambanomenos, a 2:3 ratio). The fifth is in tur n made up of a fourth (from Hypate meson to Hypate hypaton, another 3:4 ratio) and a tone (from Hypate hypaton to Proslambanomenos, an 8:9 ratio). With these components in place, a Pythagorean theor ist could descr ibe, through number, relationships between any of the fixed notes of the Greater Perfect System and eventually character ize the relationships that obtained among the movable notes of the various genera. The order of the cosmos, which was for Pythagoreans the order of number, thus found sounding expression in the domain of music.

Aristoxenus and Aristotelianism Although the Pythagorean perspective on musical order was an influential one — for instance, it infor med Plato’s and Aristotle’s writings on music — it was not the only one available to antiquity. The alter native offered by Aristoxenus in his Elementa harmonica (most likely written toward the end of the fourth century b.c.) starts with a definition of the science of harmonics: It is to be understood as the science which deals with all melody, and inquires how the voice naturally places intervals as it is tensed and relaxed. For we assert that the voice has a natural way of moving, and does not place intervals haphazardly.We try to give these matters demonstrations which confor m to the appearances, not in the manner of our predecessors, some of whom used arguments quite extraneous to the subject, dismissing perception as inaccurate and inventing theoretical explanations, and saying that it is in ratios of numbers and relative speeds that the high and the low come about. Their accounts are altogether extraneous, and totally in conflict with the appearances. Others delivered oracular utterances on individual topics, without giving explanations of demonstrations, and without even properly enumerating the perceptual data. We, on the other hand, try to adopt initial pr inciples which are all evident to anyone exper ienced in music, and to demonstrate what follows from them.11

This account of harmonics reveals Aristoxenus to be in conflict not only with the Pythagoreans (the unnamed antagonists who dismiss perception and explain pitch relations through ratios) but also with earlier har monic theor ists whose empir ical work he found deficient because they did not explain their methods of proof or properly descr ibe their observations. Aristoxenus’s alter native was to apply Aristotle’s intellectual method to music more rigorously than did Aristotle himself .12 This entailed restricting the account of music to ter ms and concepts that could properly be said to belong to the domain of music. It excluded descr iptions that made recourse to ratios (which are in the domain of number) or to theor ies about the propagation of physical sound (which 11. Aristoxenus, Elementa harmonica, in Harmonic and Acoustic Theory (vol. 2 of Greek Musical Writings), ed. and trans. Andrew Barker, Cambridge Readings in the Literature of Music (Cambr idge: Cambridge University Press, 1989), 149 – 50. 12. For commentar y on Aristoxenus’s approach, see Barker, Greek Musical Writings, 2: 66– 69, 119.

conc e p tual i z i ng mu s i c are in the domain of physics). Once the definition of these basic musical concepts was accomplished, an explanation of the entire domain of music could then follow. Aristoxenus’s demonstration proceeds in three steps. First, he identifies two forms of vocal motion, the continuous and the intervallic. In the continuous for m, which is associated with speech, the voice appears to traverse space without stopping, until the point of silence. In the intervallic for m, which is associated with singing, the voice appears to stand still at specific points, and then pass over some interval of space before coming to rest at another point.13 The various pitches upon which the voice pauses when singing constitute musical notes; the spaces between these notes are musical intervals. Aristoxenus’s second step is to draw distinctions among the various musical intervals. The first distinction is made with regard to magnitude, which reflects the amount of space between the two notes of the interval. That such a space exists is inferred from the difference between the two pitches that adjoin the interval; the size of the space can be reckoned in ter ms of how many other notes could be put inside it.14 The second distinction is made with regard to concord and discord. Aristoxenus identifies the concordant intervals as the fourth, fifth, and octave (and their octave duplications). These are the only concordant intervals he accepts as determined by the intr insic nature of melody — all other intervals are by definition discordant.15 The final step toward assembling the basic definitions and pr inciples of harmonics is the der ivation and division of the tone. Aristoxenus defines the tone as the difference between the first two concords (the fourth and the fifth) and explains that it can be divided in half (yielding the semitone), in thirds (yielding the least chromatic diesis), or in fourths (yielding the least enhar monic diesis, which is the smallest interval recognized as melodic).16 These distinctions allow him to locate various notes within the tetrachords of the different genera and thereby to specify the scalar structure of each. With these steps, Aristoxenus lays out the basic mater ials for his account of musical organization. Singing involves a specific way of using the voice that creates musical notes and musical intervals. Intervals can be distinguished according to size and whether they are concordant or discordant. Concordant intervals — the fourth, fifth, and octave— are accepted as axiomatic to melody and thus representative of the basic mater ials from which the various intervals of the Greater Perfect System can be developed.

13. Aristoxenus, Elementa harmonica, 133. 14. Aristoxenus, Elementa harmonica, 136. 15. Aristoxenus, Elementa harmonica, 139. Aristoxenus further distinguishes between composite and incomposite intervals (p. 137); however, this distinction is not necessary for a basic understanding of his theory. 16. Aristoxenus, Elementa harmonica, 140. The different dieses apply to the three genera mentioned above: the half-tone is used in the diatonic genus; the third-tone is used in the chromatic genus; and the fourth-tone is used in the enhar monic genus. For further discussion of Aristoxenus’s Elementa harmonica, see Mathiesen, Apollo’s Lyre, 319– 34.

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i nt roduc t i on Greek Theory and Cognitive Structure As mentioned, the music theor ies of Pythagoras and Aristoxenus belong to a world remote from our own. Not only did these theor ists have to grapple with the most basic of principles, but also the music they would descr ibe is a microtonal one that is primarily concer ned with the successive notes of melody rather than the simultaneous notes of harmony. Despite this — or perhaps because of it— Pythagorean and Aristoxenian accounts of musical organization give us a glimpse into how theories are formed and, more important, the cognitive processes that are basic to these theories. In particular, three cognitive processes can be seen at work: categorization, cross-domain mapping, and the use of conceptual models.

categorization

Our ability to categor ize things is a cognitive process so basic and so pervasive that it can easily escape our notice.Were you to lift your eyes from this book and survey your sur roundings, you might well see chairs, lamps, tables, and other books; were you outside, you might see trees, birds, clouds, cars, and bicycles. If you considered the other things that populate your day, you might think of friends and family members, facial expressions and gestures, actions and activities. Your recognition of these things reflects the categor ies through which we structure our thought: to recognize a book is to identify it as a member of the category book; to recognize a tree is to identify it as a member of the category tree. Categorization occurs in all sensor y modalities and throughout the range of mental activities: we categor ize smells and sounds, thoughts and emotions, skin sensations and physical movement. Categor ies are not just basic to thought; they also give insight into our thought processes. At one time it was thought that categor ies reflected the structure of the real world, but recent research has shown that the categor ies humans use are shaped by their interactions with their environments. Our reasons for developing and employing a given category are part and parcel of the category itself: categor ies are not only not given by nature, but also they are subject to change and modification as our thought unfolds. Two categor ies basic to Pythagorean and Aristoxenian music theory are those for consonant or dissonant intervals. Consonant intervals (such as the octave, fifth, and fourth) are fundamental to the conceptualization of Greek music: they mark the stable pitches of the Greater Perfect System and are the source of derivation for all further intervals, both consonant and dissonant. The process of categor ization is also exhaustive: any interval that can be conceived belongs to one of these two categories. This is not to say, however, that consonant and dissonant intervals are given by nature in any simple way, Pythagoras and the blacksmiths notwithstanding.17 As one 17. I should note here that psychoacousticians distinguish between musical consonance, which is a cultural construct framed relative to a particular set of musical practices, and sensory consonance, which is a consequence of how sound waves are processed by the hear ing mechanism (which involves the cochlea and the auditory cortex). Sensory consonance is thus a fairly straightforward product of nature. Although musical consonance has its basis in sensory consonance, there is some freedom in how the sensory data are inter preted.

conc e p tual i z i ng mu s i c example, consider the way Aristoxenians and Pythagoreans classified the interval of an octave plus a fourth. Aristoxenians considered the interval a consonance, since it was simply the combination of two smaller consonances. Pythagoreans, in contrast, classified intervals according to the numer ical ratio for med by their constituent pitches. As explained by the anonymous (and thoroughly Pythagorean) author of the Sectio canonis (fourth century b.c.), consonant intervals are those whose ratios are either multiple (of the for m [mn]:n) or epimor ic (of the for m [n + 1]:n). Dissonant intervals are those whose ratios are epimer ic (of the for m [n + m]:n, where m is greater than 1 and neither equal to nor a multiple of n).18 Because the octave plus a fourth had the epimer ic ratio 8:3, it was regarded as a dissonance. Another example of how categor ies shape our understanding of phenomena is provided by Greek theor ists’ treatment of thirds and sixths. Although thirds and sixths sound fairly consonant, they were nonetheless categor ized as discords. Two factors bear on this classification. First, forming thirds and sixths requires using the movable pitches of the Greater Perfect System — at best, a third or a sixth will involve only one of the stable pitches bounding the constituent tetrachords of the system. Thirds and sixths were intervals that necessar ily varied in size, and so they were placed among the dissonances. Second, in the classification of intervals Greek theory followed a tradition of dichotomous categor ies: there was concord, discord, and nothing else. By contrast, neither of these factors played a part in the music theory of early India. Indian music theor ists were consequently free to focus on the qualitative aspect of intervals rather than on their cor respondence with the fixed notes of a tuning system and to construe intervallic relationships as concordant, discordant, or neutral.19 These two examples show that while the categor ies for consonant and dissonant intervals may be basic to Pythagorean and Aristoxenian theor y, just how they are defined reflects the context and goals of categorization: consonance and dissonance are not naturally occur ring properties, but ways of constructing an understanding of musical organization. Of course, there are numerous other categor ies important for Pythagorean and Aristoxenian music theor y, including those for pitches, intervals, and numer ical ratios. These categor ies and others are basic to the sort of systematic account of musical phenomena provided by these theor ies — indeed, it is simply not possible to have a theory of music, or of anything else, without first having categor ies.

cross-domain mapping

Cross-domain mapping is a process through which we structure our understanding of one domain (which is typically unfamiliar or abstract) in ter ms of another (which is most often familiar and concrete). For example, one way to think about the elusive concepts of electr ical conductance is in terms of a hydraulic model: flipping the light switch tur ns on the juice, and elec-

18. Sectio canonis, in Harmonic and Acoustic Theory (vol. 2 of Greek Musical Writings), ed. Andrew Barker, Cambridge Readings in the Literature of Music (Cambr idge: Cambridge University Press, 1989), 193. 19. Lewis Rowell, Music and Musical Thought in Early India, Chicago Studies in Ethnomusicology (Chicago: University of Chicago Press, 1992), 157 – 60.

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i nt roduc t i on trical cur rent flows to the light bulb to light the room. By this means we take what we know about a fairly concrete and familiar source domain — the flow of water and other liquids — and map it onto a rather abstract and unfamiliar target domain: that of electr icity. As a wealth of research on analogy and metaphor has shown, the process of mapping structure from one domain to another is basic to human understanding. One place cross-domain mapping is evident is in the Pythagorean and Aristoxenian construal of interval. Because musical pitches are ephemeral and virtually intangible, relationships between pitches — musical intervals — represent something of a challenge to understanding. One way to meet this challenge is to map structure from the physical world onto music, a process evident in Nicomachus’s story of Pythagoras and the blacksmiths. Pythagoras hears harmonious sounds, traces their origins to the blacksmiths’ hammers, and then proceeds to conduct various experiments using weights equivalent to those of the hammers. These exper iments lead, among other things, to a highly pragmatic objectification of musical pitch, as pitches are translated into physical objects that can be weighed, studied, and preserved. By performing a mapping from the concrete physical domain proper to the blacksmiths’ hammers onto the domain of musical sound, Nicomachus’s story allows us to structure the latter domain in ter ms of the for mer. Of course, musical notes are not physical objects that can be weighed, studied, and preserved— they remain ephemeral and virtually intangible. Nonetheless, we are so accustomed to the mapping between concrete physical objects and musical sound that we sometimes have to be reminded that notes are not endur ing physical objects. Aristoxenus’s construal of musical interval involves a slightly different mapping. As we have seen, according to Aristoxenus, when the voice moves intervallically, it appears to stand still at a given place (a musical pitch) and then pass over an interval of space (a musical interval) before coming to rest at another place (another musical pitch). Underlying this account is a mapping from the familiar domain of two-dimensional space onto that of music. This mapping allows us to apply the methodology of measur ing space to music. The difference between two linear measures yields a third measure; similarly, the difference between the intervals of a fifth and a fourth yields the interval of a tone. Since linear measures can be easily divided into equal halves or thirds or fourths, the musical tone can be similarly divided, something impossible from the Pythagorean perspective. On closer inspection, the Pythagorean and Aristoxenian construals of interval are indeed incommensurate. From the Pythagorean perspective, pitches are physical objects, and an interval descr ibes the relationship between these objects. From the Aristoxenian perspective, pitches are breadthless points that simply mark out an expanse of two-dimensional space, and an interval is the expanse itself. Each mapping gives an account of interval, but each leads to a different conceptualization of musical structure. This point can be generalized for music theory as a whole: mapping structure from a nonmusical domain onto music is a way of creating musical structure, and different mappings will lead to different accounts of musical structure.

conce ptual mode ls

Both categor ization and cross-domain mapping provide the basis for fundamental ontological assertions about musical mater ials: this

conc e p tual i z i ng mu s i c interval is a consonance; the pitches of an octave are physical objects. They can also lead to conditional statements: if the interval is an octave, then it is a consonance; if a pitch is an object, then its properties are measurable. Propositions like this are basic to conceptual models, which act as guides to reasoning and inference. In their simplest for m, conceptual models consist of concepts in specified relationships, which pertain to a specific domain of knowledge. For an example of a conceptual model, let us return to the classification of consonant and dissonant intervals presented in the Sectio canonis, according to which all consonant intervals have either multiple or epimor ic ratios, and all dissonant intervals have epimer ic ratios. This classificator y system relies on a conceptual model that organizes concepts related to interval, concord, discord, and the three classes of ratios. The simple patter n of inference that follows from this model is that if an interval has a multiple or an epimor ic ratio, it is a concord; if it has an epimer ic ratio, it is a discord. Integral to this model are the products of categor ization and cross-domain mapping. Two types of categories are involved in the model: those pertaining to music (the categor ies of concord and discord) and those pertaining to number (the multiple, epimoric, and epimer ic ratios). Cross-domain mapping cor relates the two types of categor ies by construing musical interval as a relationship between two objects (namely, musical pitches) to which magnitudes (in the for m of numbers) can be assigned. Specific classes of ratios can then be used to distinguish between the musical categor ies. The robustness of this particular conceptual model is reflected in the debate over the status of the octave plus a fourth that continued into the Middle Ages. In the second centur y a.d., Ptolemy showed the speciousness of the cor relation of concord with multiple or epimor ic ratios and argued for a classification of intervals based on empir ical evaluation and the postulate that a concord added to a concord produces a concord.20 Although Ptolemy still used ratios to descr ibe various intervals, they were no longer part of the conceptual model through which intervals were classified into concords and discords. In the sixth century, Boethius presented both the Pythagorean and Ptolemaic models but took no position on which he preferred.21 After Boethius, when an author wished to invoke the author ity of the Pythagorean approach, the Pythagorean model of intervallic classification was cited; when an author wished for a more empirically satisfying classification, the Ptolemaic model was used.22 Conceptual models provide the first level of organization for concepts. They are too limited and localized, however, to provide the comprehensiveness we expect from theor ies of music. Theories achieve this comprehensiveness by integrating 20. Ptolemy, Harmonics, in Harmonic and Acoustic Theory (vol. 2 of Greek Musical Writings), ed. Andrew Barker, Cambridge Readings in the Literature of Music (Cambr idge: Cambridge University Press, 1989), 286– 90. 21. Boethius, Fundamentals of Music, 81– 82, 169. 22. For a discussion of these modes of reasoning, see C. André Barbera, “The Consonant Eleventh and the Expansion of the Musical Tetractys: A Study of Ancient Pythagoreanism,” Journal of Music Theory 28 (1984): 191– 223. Barbera’s treatment of Aurelian’s Musica disciplina on p. 210 is especially illuminating.

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i nt roduc t i on clusters of conceptual models. And as we shall see in the following chapters, conceptual models also play a role in categor ization and cross-domain mapping. There, as in theor ies, they provide guides for reasoning and inference about specific and circumscr ibed domains of knowledge.

cognitive processes and music theory Much has been left out of this discussion of theories of music from Greek antiquity, with respect to both the theories themselves and the cognitive processes behind them. To be sure, these theories are of a different order than Swann’s musings on Vinteuil’s sonata. Nonetheless, the cognitive processes we have seen at work in Pythagorean and Aristoxenian theory are the same processes through which we organize our understanding of the world as a whole. Just how this occurs— how categor ization, cross-domain mapping, and the use of conceptual models shape our theor ies of music and guide our analyses of musical works — is the subject of the remainder of this book.

overview I have divided the chapters that follow into two parts. In the first, I present a detailed overview of research on the three cognitive processes highlighted in this introduction. This overview is itself framed around specific musical topics, such as motivic transfor mation, text painting, and the ways in which we structure our understanding of a specific musical domain. The research that has been done in cognitive science over the past three decades has been extensive and far ranging, and one of the jobs of this portion of the book is to br ing this work to bear on basic issues of musical understanding. Another objective is to show in some detail how these processes relate to one another and how they form the bedrock for our thought about music. The second part of the book moves from this foundation to analytical studies of specific musical issues. These issues include relationships between categor ization and musical syntax, the problem of musical ontology, textmusic relations, and conceptions of musical for m and musical hierarchy. Chapter 1 begins the overview of research in cognitive science with a close look at processes of categorization. For centur ies, writers in the West regarded categor ies as fixed and immutable, and any variation in categor ization was taken as evidence of the failure of the human intellect to deal with the structure of the real world. It took the pioneer ing work of Eleanor Rosch and others in the 1970s to show that category structure was not as simple as first believed. In particular, some levels of categorization are preferred over others, and some members of a category are regarded as better representing the categor y than others (a phenomenon known as graded membership). The key to how this research can be applied to music is provided by the musical motive (or, as Proust would have it, the motif ). Motives are generally reckoned to be one of the basic building blocks of musical works, but they are also a bit slippery: the “same” motive typically assumes a number of diverse shapes over the course of a work. Thinking of a motive as a cognitive categor y makes it possible to account for its identity, as well as its diversity, and reveals how aspects of categorization are embodied by musical mater ials. These preliminary applications of categorization to

conc e p tual i z i ng mu s i c music also show ways musical mater ials can be organized over the course of a work and offer an explanation of how it is possible to have musical concepts that are independent of language. If categor ization can be said to be the source of musical concepts, cross-domain mapping is the means by which these concepts are placed in cor relation with others. Chapter 2 examines the process of cross-domain mapping in some detail, beginning with the work of cognitive linguists who, in the 1980s, proposed that metaphor was a basic structure of understanding. This proposal gained added weight when it was shown that metaphor ical projection (which is one way to accomplish crossdomain mappings) was a general process not restricted to linguistic expressions but grounded in embodied exper ience. One example of cross-domain mapping that involves music in a rather immediate way is the technique of text painting, a compositional device that aims to represent in music specific images summoned by the text of a vocal work. Text painting provides a point of departure for the exploration of how cross-domain mapping is manifested in our understanding of music, as it leads to an extension of crossdomain mapping called conceptual blending. In a conceptual blend, elements from two cor related domains are projected into a third, giving rise to a r ich set of possibilities for the imag ination. As I show in the latter part of chapter 2, text painting can lead to such blends, as can program music. Chapter 3, which focuses on conceptual models and theor ies, gets to the heart of the perspective on cognition developed in part I. My point of departure is research by Jeanne Bamberger on children’s representations of musical structure. In my analysis of Bamberger’s study of one specific eight-year-old boy, I show the part played by categor ization and cross-domain mapping in the conceptual models used by this boy to come to ter ms with a musical environment. I also show how these models are combined to for m a theor y of music and how this theor y changes in response to changes in the task at hand. This close-up glimpse of the structure and role of conceptual models and theor ies leads, in the middle of the chapter, to a more generalized character ization of these knowledge structures, which I connect with work on similar structures in artificial intelligence, cognitive anthropology, ethnomusicology, and developmental psychology. In the latter part of the chapter, I return to music theory and explore the role of conceptual models and theor ies (that is, theories framed relative to a cognitive perspective) in analyses by Jean-Philippe Rameau and Heinr ich Schenker, two of the best-known music theor ists of the last three hundred years. Although the features of cognitive structure discussed in part I might seem to be relatively detailed, in truth all are associated with relatively high-level cognitive processes. My reason for focusing on this level is quite simple: it allows me to engage in issues of immediate and occasionally central importance to music scholarship and to do so in a way that connects with extensive research in cognitive psychology and cognitive linguistics. Part II explores this possibility in g reater depth by considering various problems of musical understanding from the perspective on cognitive structure and music theory developed in part I. In chapter 4, I turn to the matter of how musical mater ials are organized within a work — more properly, the problem of musical syntax and, by extension, musical

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i nt roduc t i on semiotics. Although semioticians are usually quick to grant that music has a syntax, they are more doubtful about whether its semantic level has any depth. By taking a close look at how composers make use of categor ies of musical events — in this case, the way Mozart and Beethoven use motives in the opening movements of three str ing quartets — I am able to provide insight into how musical mater ials are organized in the service of musical discourse, as well as how features of this organization contr ibute to meaning construction as a whole. In chapter 5, I confront a somewhat larger problem — one that may seem ir redeemably abstract: the problem of what counts as a work of music. I view this problem, usually called the problem of musical ontology, as one of cultural knowledge and try to show that, as opposed to being hopelessly recondite, the problem is of immediate importance for understanding music. By approaching the entire work of music as a categor y— a category that includes all the scores, performances, representations, and such that are said to be “of ” the piece — I develop a model for the cultural knowledge upon which judgments about musical ontology are made. Determinations of what counts as an instance of a particular musical work are thus one of the ways members of a musical community construct and negotiate their identity. My examples for this chapter are two songs taken from the traditions of popular music and jazz: “I Got Rhythm” and “Bye Bye Blackbird.” The latter offers an intr iguing case of how the cultural knowledge relative to which deter minations of musical ontology are made can become complicated when implicated in the layered discourse structures Mikhail Bakhtin called “double-voiced discourse,” and which were extended to African American culture through Henry Louis Gates Jr.’s notion of “Signifyin(g).” Chapter 6 returns to the analysis of individual musical works by pursuing one of the entailments of text painting noted in chapter 2: under certain circumstances, combinations of words and music, through the process of conceptual blending, create worlds for the imagination well beyond those that spr ing from words or music alone.Where only a few fairly circumscr ibed instances of text-music relations were considered in chapter 2, here research on conceptual blending is applied to the whole of five Lieder from the nineteenth centur y. These analyses offer a way to flesh out the theory of conceptual blending as it applies to music and provide a further perspective on musical syntax. In these songs, we see words and music combining to create r ich domains in which the imagination can play, as well as discover how musical syntax shapes our understandings of the words themselves. The final analytical chapter (chap. 7) turns to music theory itself, specifically to the theor ies of musical for m and hierarchy that go back to the eighteenth and early nineteenth centur ies. Accounts of the for m a musical work takes, or of how its elements relate to one another, are basic to theor izing about music— indeed, we can see these emerging in the course of M. Swann’s ruminations on Vinteuil’s sonata — but at times it seems that theorists are talking about quite different things. For instance, there are two common ways to talk about musical for m: the first approaches for m as der iving from the assembly of relatively static building blocks that are combined to create the finished work; the second approaches for m as an emergent property of the work, which becomes manifest only as the music unfolds over time. The first approach yields a view of musical for m that is quite static, the second a view rather

conc e p tual i z i ng mu s i c more dynamic. Using the analytical framework provided by cross-domain mapping, I discuss the source of these two models for musical for m, as well as two models for musical hierarchy, and explore some of the ways these models interacted over the course of the history of music theory. In the conclusion I return to M. Swann and to his final encounter with Vinteuil’s sonata after a year in which it became thoroughly intertwined with his love affair with Odette, the courtesan with whom he had become acquainted around the same time he first encountered the andante. This will provide a frame for a review of the points made in the preceding chapters and an instrumentality for drawing conclusions from the whole.

cognitive structure, theory, and analysis A central claim of this book is that through developing an appreciation of how aspects of cognitive structure shape our understanding of music we can better appreciate the active role of theories of music in that understanding. A further claim is that our analyses of musical phenomena — from the most mundane and localized of accounts to the most abstract and comprehensive— similarly reflect cognitive structure, in that every analysis is based on some sort of theory of music. Musical analyses are in truth dialogues, and not just dialogues between the analyst and an imagined audience: musical analyses are also dialogues between the analyst and some body of theoretical knowledge. Analysis rarely, if ever, simply cor roborates a theory: analysis pulls theor y and pushes it, extending and chang ing theory just as it also extends and changes our understanding of musical phenomena. The analyses I present throughout this book are no different, except that they engage cognitive theory as well as music theor y. The intent of the analyses is to show how our understanding of particular musical phenomena can be character ized in terms of specific cognitive processes and structures and thereby connect that understanding to research in cognitive science as a whole. The analyses are not intended as definitive statements about how we can account for such understanding; they are intended to be the initiation of a dialogue with cognitive theory, a dialogue whose purpose is to expand our knowledge of both music and cognition. Analysis is thus a central concer n of what follows, but, unlike cognitive structure or theor y, I have not treated it as a central topic for investigation. Instead, analysis will be a fundamental tool to explore both and to provide new insight into the conceptual worlds wrought by musical sound.

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aspects of cognitive structure

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chapter one

Q categorization

n the opening eleven measures of the prelude to Richard Wagner’s Tristan und Isolde there are three successive statements of a melodic motive that foreshadows, and then later accompanies, the tragic arc of the opera. Three times this motive emerges from silence, swells through the cellos and English hor n, and then sinks back into the stillness from which it came. After the third statement, the motive disappears, then reappears a few long minutes later near the end of the prelude. Here it is stated first in the cellos and violas (and completed by the oboes and bassoons), then in the English hor n, and finally in the bass clar inet. After the last of these, the prelude dissolves into the first scene of the opera. All of these statements are shown in example 1.1. Although our first inclination is to treat these various statements as somehow the same — that is, all can be regarded as “statements of the opening motive from Wagner’s Tristan und Isolde”— there are actually notable differences among them. There is, of course, the change in the instrumentation used for the statements at the end of the prelude, which contrasts with the distinctive timbral stamp put on the motive in the opening measures. There is a similar diversity in the pitches through which successive statements are given voice, since versions of the motive begin on either A3 (or Ab3), B3 (or B2), or D4. Although there are significant similar ities in the rhythmic figuration used for the various statements, there is no patter n of duration and accentuation common to all. And there are also somewhat smaller variations: the first statement begins with a minor sixth instead of the major sixth used by the others, and the fourth is the only one shaped by both a diminuendo and a rallentando. Despite their differences, these seven melodic fragments sound similar enough to one another to be regarded as functionally equivalent. Such equivalence was important to Wagner’s compositional style, for it provided the mater ial foundation for works uninter rupted by conventional for ms. By recalling specific motives at crucial points within his musical and dramatic discourse Wagner was able to create a sense of shape and unity that seemed inevitable without being predictable. By the time of Tristan, however, such motives were no longer simple building blocks to be assembled and per muted but had become infinitely malleable constructs. Carl Dahlhaus, recognizing both the structural importance and mutability of these

I

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aspe c t s of cog n i t ive st ruc ture Statements of the opening motive from Richard Wagner’s Tristan und

example 1.1 Isolde, Prelude

Vnc. 1

Eng. Hn.

1.

Vnc. 5

Eng. Hn.

2. cresc.

8

dim.

Eng. Hn.

Vnc.

3. cresc.

85

Vnc., Vla.

Ob., Bn.

4. dim. 88

Vnc., Vla.

Ob.

5. Eng. Hn. 101

6.

Bs. Cl. 104 7. più

motives within the opera, likened them to woven threads that surface only to divide and then disappear from sight.1 To understand this music— to make sense of the sonic texture Wagner weaves— requires being able to assimilate these various musical phrases into a single cognitive construct and then recall that construct, often after an hour or more of Wagnerian effusion. Understanding Wagner — or most music, for that matter — requires being able to think in ter ms of categor ies of musical events. In this chapter, I explore what recent research into categor ization can tell us about this process. First, however, I develop a slightly clearer picture of two basic aspects of understanding music, which will provide the g roundwork for applying research on categor ization to situations of the sort presented by the opening of Tristan. I do this by reviewing a theory of musical motive developed by one of the many students of Wagner. Not that Wag1. Carl Dahlhaus, Richard Wagner’s Music Dramas, trans. Mary Whitall (Cambr idge: Cambridge University Press, 1979), 63.

cate g ori zat i on ner ever actually taught composition. But the influence of his music was enor mous, and many lessons were taken away from his operas. Among these were lessons on compositional technique absorbed, refined, and retransmitted — in both treatise and score— by Arnold Schoenberg.

musical coherence and motive Schoenberg thought of himself first and foremost as a Brahmsian, but, under the influence of Alexander von Zemlinsky, he also found a passion for Wagner. Schoenberg noted that his early works showed the influence of both masters: “In my Verklärte Nacht the thematic construction is based on Wagner ian ‘model and sequence’ above a roving harmony on the one hand, and on Brahms’s technique of developing variation — as I call it — on the other.”2 Wagner was also known for his harmonic innovation, although Schoenberg took pains in one of his late essays to show that Brahms’s harmonies were every bit as “progressive” as Wagner’s.3 Nonetheless, it was Wagner’s harmonic language that was perceived as posing the most for midable challenge to composers of the late nineteenth century, for the free treatment of dissonance integral to this language loosened prevailing conceptions of tonal organization and called into question the “laws of tonality” that had for merly held sway. From Schoenberg’s perspective,Wagner’s music presented few dangers for tonality. As Schoenberg had argued in his Harmonielehre of 1911, tonality had its or igins in acoustic phenomena.4 But shaping music in confor mance with acoustic phenomena was not all there was to musical composition: composition also required insight into how the human mind worked. In an essay that attempted to sort out some of the problems raised by the “emancipation of the dissonance” Schoenberg wrote: Tonality’s origin is found — and rightly so — in the laws of sound. But there are other laws that music obeys, apart from these and the laws that result from the combination of time and sound: namely, those governing the working of our minds. This latter forces us to find a particular kind of layout for those elements that make for cohesion — and to make them come to the fore, often enough and with enough plasticity— so that in the small amount of time granted us by the flow of the events, we can recognize the [musical] figures, grasp the way they hang together, and comprehend their meaning.5

In Schoenberg’s view, the laws governing the workings of our minds require the composer to wr ite in such a way that listeners can quickly recognize musical figures and the way they cohere. The listener, upon grasping this coherence, will then be able to comprehend the work. Key to musical coherence and comprehension were musical motives. According 2. Arnold Schoenberg, “My Evolution (1949),” in Style and Idea: Selected Writings of Arnold Schoenberg, ed. Leonard Stein, trans. Leo Black (New York: St. Martins Press, 1975), 80. 3. Arnold Schoenberg, “Brahms the Progressive (1947),” in Style and Idea, 398– 441. 4. Arnold Schoenberg, Harmonielehre (Leipzig:Verlagseigentum der Universal-Edition, 1911); trans. as Theory of Harmony by Roy E. Carter (Berkeley: University of California Press, 1978), 23– 25. 5. Arnold Schoenberg, “Opinion or Insight? (1926),” in Style and Idea, 259.

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aspe c t s of cog n i t ive st ruc ture to Schoenberg, comprehension starts with recognition, and recognition starts with basic musical figures — that is, motives: “Motive is at any one time the smallest part of a piece or section of a piece that, despite change and variation, is recognizable as present throughout.”6 More specifically, motives consist of intervals and rhythmic patterns combined to produce a shape or contour that, once recognized, can be easily remembered.7 A particularly str iking illustration of Schoenberg’s concept of motive is provided by his analysis of a subordinate theme from the first movement of Brahms’s Sextet in Bb major, Op. 18 (1860), shown in example 1.2.8 As Patricia Car penter and Severine Neff have noted, rhythm is central to Schoenberg’s concept of motive.9 This centrality is clearly evident in his analysis of the Brahms sextet. Each family of motives is distinguished by a specific rhythmic patter n: all of the a motives use a qdeΩç pattern; and all of the b motives use a qdeq pattern. (Both patter ns, of course, contribute to the marvelous waltz-like feel of the theme.) Contour also serves to distinguish the two families, although here some variation among the different motive forms can be noted. Motives a1, a2, and a4 all preserve the basic contour of motive a: the second note of the motive is lower than the first note, and the last note of the motive is higher than the first note. Motive a3 preserves only a portion of the contour of a: although the second note of the motive is lower than the first, so is the last note. In a similar fashion, motives b1 and b3 preserve the basic contour of motive b (the second note is lower than the first note, and the third note is lower than the second), while b2 preserves only a portion of the contour of b (the second note is lower than the first note, but the third note is higher than the second). As this example shows, Schoenberg’s concept of motive is broad and dynamic: a family of motives can be distinguished simply by rhythmic figure or contour; motive forms can be various and need have only some of their features in common. This conception is rather different from, for example, Heinrich Schenker’s or Rudolph example 1.2 mm. 84– 93

Schoenberg’s analysis of the Brahms Sextet, Op. 18, first movement,

85

89

a2

a

a1

b

b2

b3

a3

b1

a4

6. Arnold Schoenberg, The Musical Idea and the Logic, Technique, and Art of Its Presentation, ed. and trans. Patricia Car penter and Severine Neff (New York: Columbia University Press, 1995), 169. 7. Arnold Schoenberg, Fundamentals of Musical Composition, ed. Gerald Strang and Leonard Stein (London: Faber and Faber, 1967), 8. 8. Schoenberg, “Brahms the Progressive,” 417. 9. See the commentary in their edition of Schoenberg’s The Musical Idea and the Logic, Technique, and Art of Its Presentation, 27– 29.

cate g ori zat i on Réti’s concept of motive. Both Schenker and Réti regard specific intervallic relationships as constituent of motive; rhythm and contour are regarded as secondar y aspects of motivic organization.10 The difference between Schenker’s or Réti’s conception of motive and that of Schoenberg lies with Schoenberg’s notion of coherence and the role it plays in making music comprehensible. Coherence comes about when the various parts that make up a musical entity are connected in such a way that those parts similar to other entities become prominent. The work is most comprehensible to the listener when the ar rangement of these parts is such that their relationship to each other and to the whole is manifest.11 Thus there is no need to restrict the distinguishing features of a family of motives to specific intervallic relationships, nor is there a need to require that all motive forms share exactly the same features. All that is required of motive is recognizability and a potential for connection to other motive forms. This potential for connection contr ibutes to coherence, which is, in turn, the basis for comprehensibility. According to Schoenberg, then, the process of comprehension starts with recognizable bits (motives) that are easily remembered. Motives hang together not simply because their constituent parts are connected to one another but because these connections emphasize similar ities to other motives. Coherence thus reflects properties shared by collections of motives; it is not, properly speaking, a property of any one individual motive. Motive forms are of necessity variable, for differences between forms reveal most clearly what is typical of the collection of motives as a whole. And, although attention to coherence is important to the composer who wishes to craft a convincing work, the apprehension of coherence is essential to the listener who would make sense of that work. Many composers, working in the long shadow cast by Ludwig van Beethoven across the nineteenth century, relied on musical motives to make their works coherent. As Edward Cone has noted, the use of thematic transfor mation as a unifying device became increasingly important for composers of the later nineteenth century, composers whose lengthy movements often embraced stylistic extremes of tempo, meter, texture, and mood.12 However, the prevalence of the device also poses problems for the listener, for it is often difficult to sort out relationships among various motivic entities. Consider the relationship of derivation, in which later motive forms are derived from earlier motive forms; thus motive b3 in example 1.2 is said to be der ived from motive b. As straightforward as this might appear, tracing der ivational relationships is rarely a simple task: motive b can itself be understood to be derived from one of the motives prevalent in the preliminary subordinate theme heard starting in m. 61 of Brahms’s sextet (shown in ex. 1.3), which has the same rhythmic patter n but the reverse contour. Could b3 then be regarded as der ived directly from this earlier motive form, or is it still to be regarded as der ived from b? Schubert’s Wanderer Fantasie, Op. 15 of 1822 presents an even more complicated 10. Heinrich Schenker, Der freie Satz, Neue musikalische Theor ien und Phantasien, 3 (Vienna: Universal-Edition A.G., 1935); Rudolph Réti, The Thematic Process in Music (New York: Macmillan, 1951). I discuss histor ical construals of motive below in the first part of chap. 7. 11. Arnold Schoenberg, Coherence, Counterpoint, Instrumentation, Instruction in Form, ed. Severine Neff, trans. Severine Neff and Charlotte M. Cross (Lincoln: University of Nebraska Press, 1994), 20 – 23. 12. Edward T. Cone, “On Der ivation: Syntax and Rhetor ic,” Music Analysis 6 (1987): 238.

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aspe c t s of cog n i t ive st ruc ture example 1.3 61

Johannes Brahms, Sextet, Op. 18, first movement, mm. 61– 64 in tempo

dolce

dolce

dolce pizz.

dolce pizz.

situation. The work is based on an ar ietta from Schubert’s 1816 cantata “Der Wanderer,” Op. 4/1, D. 489, which is quoted in the work’s second movement Adagio; the relevant passage from the cantata appears in example 1.4a. If we have the ar ietta in mind, we can hear the motivic mater ial of the first movement as der ived from the ar ietta and then presented instrumentally in the subsequent Adagio (the motive from the first movement is labeled c in ex. 1.4b; its use in the Adagio is demonstrated in ex. 1.4c).13 The temporal order of the process of derivation is thus reversed: c is heard as der ived from c1. If we are coming to the work fresh, we will most likely hear the Adagio as der ived from the first movement: c1 is thus der ived from c. Finally, if we know the ar ietta but have temporar ily forgotten it, its reprise in the Adagio, anticipated by the “derived” motives of the first movement, can be a moment of great rhetor ical impact: the pianistic musings of the first movement have summoned forth the ar ietta that now stands before us. It would seem that, as Cone argued, hearing relationships among motive forms is an ineluctably subjective affair. Following his argument still further, how we hear these relationships is important to how we respond to a work, for, as Schubert’s fantasy suggests, it infor ms our understanding of musical rhetor ic. The most dramatic case occurs in a work in which there are multiple der ivations of motivic mater ial. In the course of such a work we can lose our sense of how motive forms are connected, until the composer — often unexpectedly — reveals how the mater ials relate to one another by bringing them into rapprochement. The rhetor ical aim of this sort of compositional strategy is what Cone calls “epiphany,” and, when successful, 13. While the annotations in ex. 1.4 focus on the distinctive rhythmic figure common to each of the excerpts, it is worth noting that each passage also features a move to the dominant.

cate g ori zat i on example 1.4 Franz Schubert, (a) “Der Wanderer,” Op. 4 No. 1, D. 489, mm. 23– 26; (b) Wandererfantasie, D. 760, mm. 1– 3; (c) Wandererfantasie, mm. 189– 90 a

23

3

Die Son

ne dünkt mich hier so

3

kalt, die Blü

te welk, das Le

ben alt,

b 1 Allegro con fuoco ma non troppo

c c 189

Adagio

c1

it can compel the listener to realize a previously unsuspected — or at most unconfirmed — relationship among diverse motives.14 Put another way, the strategy that leads to epiphany compels the listener to realize aspects of musical coherence that become evident only over the course of time. Motives and motivic relationships are important for both the coherence and the rhetor ic of music, but understanding the part they play in musical understanding poses some unique challenges. If the recognition of motives is central to the process of comprehending music, it must occur very rapidly. This rapidity has led some to argue for cognitive modules dedicated to the processing of such basic musical materials.15 The theory of cognitive modular ity, an adaptation of faculty psychology first proposed by the philosopher Jerry Fodor, bears some resemblance to the notion of competence discussed br iefly in my introduction.16 The coherence of musical 14. Cone, “On Derivation,” 246. 15. See, for example, David Temperley, “Motivic Perception and Modular ity,” Music Perception 13 (1995): 141– 69; and Eugene Nar mour, The Analysis and Cognition of Basic Melodic Structures: The Implication-Realization Model (Chicago: University of Chicago Press, 1990). 16. Jerry A. Fodor, The Modularity of Mind: An Essay on Faculty Psychology (Cambridge, Mass.: MIT Press, 1983). According to the theor y Fodor proposed in The Modularity of Mind, cognitive structure is organized into modules dedicated to specific processing tasks. There are thus modules for such things

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aspe c t s of cog n i t ive st ruc ture materials, however, is an emergent property that is less well explained from a modular perspective since it involves the active compar ison and evaluation of a number of motive forms. One model that can r ise to these challenges is offered by recent research into categor ization, which has demonstrated that categor ization is both extremely rapid and evaluative. From the perspective provided by this research, the coherence of music reflects our ability to group musical events into categor ies: the a and b motives of example 1.2 each constitutes a cognitive categor y, with five members in one category (a, a1, a2, a3, and a4) and four in the other (b, b1, b2, and b3). To descr ibe the “laws of the mind” that Schoenberg noted — laws that force the composer to arrange musical elements so that they cohere— is to descr ibe the process of categorization. In what follows, I shall review research on processes of categor ization and show how it can be used to account for the role of motive as a starting place for higher-level cognitive processes and for relationships among diverse motive forms.

processes of categorization For the most part, the categor ies through which we structure our understanding of the world are not cause for a great deal of reflection. To all appearances, these categories are simply givens. A book is a book, a tree is a tree, and any equivocal cases are just a matter of insufficient knowledge. This commonsense view of categorization was the predominant view in philosophy and psychology at least since the time of Plato: categories, because they were constitutive of knowledge, were regarded as stable and universal. It was only in the 1950s that the adequacy of this view began to be called into question, most notably by Ludwig Wittgenstein in his Philosophical Investigations. There, in the midst of a discussion of language games, Wittgenstein paused to consider the category of “game” itself and found that category structure was far more complicated than it first appeared.17 Research carried out in the 1960s and 1970s showed that numerous aspects of the way humans categor ize could not be reconciled with the traditional view of categorization, and by the 1980s a new view of categorization had begun to develop. The categor ies through which humans organize their understanding of the world came to be seen as ways of having knowledge, rather than as reflecting what could be known. The research crucial to developing this new view of categor ization focused on two topics. The first concer ns the relationship between the process of categorization and the taxonomic structures to which it gives r ise. The second concer ns the

as vision, hearing, language processing, and, presumably, the identification of musical motives. Fodor has since made arguments against modular ity; see his recent The Mind Doesn’t Work That Way (Cambridge, Mass.: MIT Press, 2000). 17. Ludwig Wittgenstein, Philosophical Investigations, trans. G. E. M. Anscombe (New York: Macmillan, 1953), 31– 32. For summar ies of the recent history of research into categor ization, see Eleanor Rosch, “Categor ization,” in Encyclopedia of Human Behavior, ed.V. S. Ramachandran (San Diego: Academic Press, 1994), 1: 513 – 23; and George Lakoff, Women, Fire, and Dangerous Things: What Categories Reveal about the Mind (Chicago: University of Chicago Press, 1987), chap. 2.

cate g ori zat i on internal structure of categor ies— that is, how members of a category relate to one another. Most of the categor ies we use in daily life can be organized into hierarchically arranged taxonomies. The cat prowling around my feet is a calico cat, a housecat, a feline, a mammal, and a living organism. The levels in taxonomies of this sort are related by inclusion: feline includes all of the different sorts of housecats, a category that includes all of the different sorts of calico cats, a category that includes my particular cat. In categor izing things, it seems logical to work from the top of the hierarchy down, moving from the most abstract level to the most concrete. I note first that the thing before me is a living organism, and as I increase my level of discrimination determine exactly what sort of organism it is. In actually categor izing things in the world around us, however, we start neither at the most specific level (“the cat prowling around my feet”) nor at the most general (living organism) but at a level in between; this level has come to be called the basic level. Research on the basic level tells us where, for practical pur poses, the process of categorization begins. The first section that follows reviews research on the basic level and shows how it supports Schoenberg’s contention that musical comprehension begins at the level of the motive. It is similarly a commonplace to regard each level of a taxonomy as having clear, fixed boundar ies: a creature either is or is not a housecat. Categories are thus unchanging anchors of understanding, their structure immutable and constant. The categories we actually use in daily life, however, cannot be so neatly character ized. These categor ies have a somewhat more complicated structure: membership is by degrees; category boundar ies are relatively fluid and often hazy; and category structure can change over time. In these cases, the process of categorization is a highly dynamic one, requiring that we evaluate potential categor y members relative to existing categor y members which, together, define a standard of typicality. Categories with a variable membership are thus said to show typicality effects. The second section that follows reviews research on categor ies that illustrate typicality effects and shows how it can be used to model the coherence and variability of motive forms basic to Schoenberg’s theory of motive.

Basic-Level Categor ization

the basic leve l

The psychologist Roger Brown was perhaps the first to note that the categor ies we most frequently employ are not at the lowest level of a taxonomy (and concer ned with individuals), nor are they at the highest level (and concer ned with broad classes); instead, they are in the middle of a taxonomy, at a level of maximum utility.18 For instance, we typically call the thing in our purse or pocket a dime, even though we might also call it money or a metal object (names at the superordinate level of the taxonomy), or my favorite 1956 dime (which would be at the subordinate level of the taxonomy).

18. Roger Brown, “How Shall a Thing Be Called?” Psychological Review 65 (1958): 14– 21; idem, Social Psychology (New York: Free Press, 1965), 319– 21.

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aspe c t s of cog n i t ive st ruc ture table 1.1. Sample Taxonomies Showing the Basic Level Superordinate

Basic Level

Subordinates

Musical instrument

Guitar

Folk guitar Classical guitar Grand piano Upright piano Delicious apple Mackintosh apple Freestone peach Cling peach Kitchen table Dining room table Floor lamp Desk lamp

Piano Fruit

Apple Peach

Furniture

Table Lamp

Adapted from Eleanor Rosch et al., “Basic Objects in Natural Categor ies,” Cognitive Psychology 8 (1976): 388.

Subsequent research into ethnobotanical systems of classification by Brent Berlin and his associates supported the importance of mid-level classification and gave empirical evidence that this level is psychologically basic: at this level, people name things more readily, languages have simpler names, categories have greater cultural significance, things are remembered more readily, and things are perceived holistically.19 Research directed specifically at mid-level classification was car ried out by Eleanor Rosch and her associates in the early 1970s. In their report, this level was named the basic level, a term which has been generally adopted in the literature on categor ization.20 Examples of sample taxonomies showing the basic level are given in Table 1.1. Rosch and her associates suggested that two contrasting pr inciples influence the taxonomic level at which people prefer to categor ize.21 The first is the efficiency principle, according to which people prefer to minimize the number of categor ies they 19. Brent Berlin, “Speculations on the Growth of Ethnobotanical Nomenclature,” Language in Society 1 (1972): 51– 86; idem, “Ethnobotanical Classification,” in Cognition and Categorization, ed. Eleanor Rosch and Barbara B. Lloyd (Hillsdale, N.J.: Erlbaum Associates, 1978), 9– 26; Brent Berlin, Dennis E. Breedlove, and Peter H. Raven, Principles of Tzeltal Plant Classification: An Introduction to the Botanical Ethnography of a Mayan-Speaking People of Chiapas (New York: Academic Press, 1974). 20. Eleanor Rosch, Carolyn B. Mervis,Wayne D. Gray, David M. Johnson, and Penny Boyes-Braem, “Basic Objects in Natural Categor ies,” Cognitive Psychology 8 (1976): 382 – 439. 21. This inter pretation of Rosch’s work is drawn from Lawrence W. Barsalou, Cognitive Psychology: An Overview for Cognitive Scientists (Hillsdale, N.J.: Erlbaum Associates, 1992), 181– 84. See also Rosch et al., “Basic Objects in Natural Categor ies”; Eleanor Rosch, “Principles of Categorization,” in Cognition and Categorization, ed. Eleanor Rosch and Barbara B. Lloyd (Hillsdale, N.J.: Erlbaum Associates, 1978), 27– 48; Carolyn B. Mervis and Eleanor Rosch, “Categor ization of Natural Objects,” Annual Review of Psychology 32 (1981): 89– 115; and Mary E. Lassaline, Edward J.Wisniewski, and Douglas L. Medin, “Basic Levels in Artificial and Natural Categor ies: Are All Basic Levels Created Equal?” in Percepts, Concepts, and Categories: The Representation and Processing of Information, ed. Barbara Bur ns, Advances in Psychology, 93 (Amsterdam: North-Holland, 1992), 327 – 78.

cate g ori zat i on must consider in making a categor ization. For instance, if you were concer ned with things in my house, categor izing at the level of musical instrument would yield the most efficient categor y, since the number of contrasting categor ies at this level (such as furniture and fruit) is significantly less than at the next level (guitar, piano, apple, peach, table, lamp). The second pr inciple is the informativeness principle, according to which people tend to maximize the infor mativeness of their categor izations. Since the most infor mation about any entity is found at the most specific level of a taxonomy, you would use grand piano to categor ize the thing sitting in the living room. Rosch and her associates proposed that the inter mediate level of a taxonomy (in this case, piano) optimizes both efficiency and infor mativeness and is thus the preferred level for basic categor izations. A number of empirical operations converge at the basic level. The basic level is the highest level whose members have similar and recognizable shapes; it is also the most abstract level for which a single mental image can be formed for the category. The basic level is also the highest level at which a person uses similar motor actions for interacting with categor y members. The basic level is psychologically basic: it is the level at which subjects are fastest at identifying category members, the level with the most commonly used labels for categor y members, the first level named and understood by children, the first level to enter the lexicon of a language, and the level with the shortest pr imary lexemes.22 In her initial work, Rosch assumed that the basic level depended on bundles of perceived-world attr ibutes that for med natural discontinuities and that such attr ibutes were inherent in the real world. She later came to doubt this assumption, and subsequent research has shown that the basic level is variable. It depends on cultural context and level of expertise and on whether one is dealing with categor ies that occur naturally, as humans interact with their environments, or with categor ies created for exper imental ends.23 Other research has indicated that the basic level is strongly deter mined by the ways in which humans interact with their environment and that it is highly dependent on the way humans perceive the spatial configuration of physical parts.24 In all cases, however, Roger Brown’s fundamental insight has held up: the preferred categor ization for most of the things we encounter occupies a maximally useful level in the middle of a taxonomy. 22. Rosch et al., “Basic Objects in Natural Categor ies”; Eleanor Rosch, “Human Categor ization,” in Studies in Cross-Cultural Psychology, vol. 1, ed. Neil Warren (London: Academic Press, 1977), 1– 49; Barbara Tversky and Kathleen Hemenway, “Objects, Parts, and Categories,” Journal of Experimental Psychology: General 113 (1984): 169 – 93. 23. On Rosch’s reservations about the objectivity of the basic level, see Rosch, “Principles of Categorization”; on the relationship between expertise and the basic level, see James W. Tanaka and Marjor ie Taylor, “Object Categor ies and Expertise: Is the Basic Level in the Eye of the Beholder?” Cognitive Psychology 23 (1991): 457 – 82; on the contrast between natural and artificial categor ies in this context, see Lassaline et al., “Basic Levels in Artificial and Natural Categor ies.” 24. On relationships between the basic level and the environment, see Barbara Tversky and Kathleen Hemenway, “Categor ies of Environmental Scenes,” Cognitive Psychology 15 (1983): 121– 49; on the basic level and humans’ interactions with physical objects, see Tversky and Hemenway, “Objects, Parts, and Categor ies”; Irving Bieder man, “Recognition-by-Components: A Theor y of Human Image Understanding,” Psychological Review 94 (1987): 115 – 47; and Lawrence W. Barsalou, “Deriving Categories to Achieve Goals,” Psychology of Learning and Motivation: Advances in Research and Theory 27 (1991): 1– 64.

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34

aspe c t s of cog n i t ive st ruc ture

the basic level and musical motives In a close analogue to what are, perhaps, the most distinctive features of basic-level categor ies, Schoenberg’s theory of musical coherence begins not with individual musical events or with four- or eight-measure phrases, but at a level somewhere in between. Although the motive is the smallest recognizable part of a musical work, it is in fact made up of still smaller parts— namely, its constituent pitches, intervals, and durations. The cognitive salience of the motive thus mir rors that of the basic level: in both cases, the focus is on the whole rather than on the parts. Each of Schoenberg’s families of motives has a distinctive “shape” or contour that allows us to distinguish it from other motives. Similarly, the basic level is the highest taxonomic level at which category members have similarly perceived overall shapes and the highest level at which a single mental image can reflect the entire categor y. Finally, motive recognition is not something given directly by perception and can change with expertise: what counts as a motive, just as what counts as the basic level, is not immutable. To illustrate cor respondences between a musical motive and a basic-level category, let us consider the opening of Beethoven’s Fifth Symphony, given in example 1.5. The passage is a familiar one, and it illustrates important matters of musical organization that we will later explore in Wagner’s Tristan.25 To the extent that we hear a “motive” in these opening gestures, we hear a figure that compr ises four notes. The motive has a distinctive “shape” or contour that allows us to distinguish it from other motives (although such are in rather short supply in this particular example). Lastly, there is a certain minimal level of expertise involved in picking out mm. 1– 2 and its ilk as “the motive.” One can easily imag ine an alter nate hear ing that would take mm. 1– 2 and mm. 3– 4 as the main thematic mater ial for this section; the ensuing music would then represent a sort of fragmentation of this thematic mater ial, rather than successive statements of various for ms of the motive.26 summary

Research on basic-level categor ies provides support for Schoenberg’s proposal that musical comprehension beg ins at the motivic level, for such a level maximizes both efficiency and infor mativeness. In addition, there appear to be a number of correlations between musical motives and basic-level categor ies. Both are concer ned with wholes, rather than the parts of these wholes; shape (whether as visual property or auditory analogue) is important to both; and both are subject to the influence of expertise. Finally, while entities such as “motives” may be basic to the process of comprehending music, they are actually relatively high-level cognitive constructs (as are basic-level categor ies). Although such constructs are fundamental to reason (and may even represent an important starting point for conscious 25. That a passage from Beethoven might be used to shed light on Wagner’s compositional strategies is not accidental, for Beethoven’s compositional style had a profound influence on Wagner. For discussion, see Klaus Kropfinger, Wagner and Beethoven: Richard Wagner’s Reception of Beethoven, trans. Peter Palmer (Cambr idge: Cambridge University Press, 1991); and Thomas S. Grey, Wagner’s Musical Prose: Texts and Contexts (Cambridge: Cambridge University Press, 1995). 26. It is worth noting, however, the role of the fermatas in suggesting that mm. 1– 2 are one entity and mm. 3– 4 another, since these add time for the listener to process the musical infor mation presented by Beethoven. This additional time may also play a role in what is considered the most “typical” form of the motive, a topic explored in greater depth later in this chapter.

example 1.5 Ludwig van Beethoven, Symphony No. 5 in C Minor, Op. 67, first movement, mm. 1– 38 1

Allegro con brio ( = 108)

Flutes

Oboes

a2 Clarinets in B

Bassoons

Horns in E

Trumpets in C

Timpani in C, G

Allegro con brio ( = 108) Violin I

Violin II

Viola

Cello

Bass

(continued)

36

aspe c t s of cog n i t ive st ruc ture example 1.5

(continued)

7

a2

reasoning processes), they are the product of myriad other still more-basic processes that operate below the level of consciousness.

Typicality Effects

graded structure and a typology of categories

As noted, the variability of motive forms was important to Schoenberg’s notion of musical coherence, for this variability tended to emphasize how motive forms were similar to

cate g ori zat i on example 1.5

(continued)

14

cresc.

cresc.

cresc.

cresc.

cresc.

cresc.

cresc.

cresc.

cresc.

cresc.

cresc.

cresc.

(continued)

one another. Research on categor ization has demonstrated an analogous structure for numerous categor ies. Membership in these categor ies is not fixed but is instead graded through a dynamic process in which the attr ibutes of potential category members are compared with the attr ibutes most typically found within the category. As an example of such a graded structure, consider the category bird. Experimental rankings show that subjects view robins and sparrows as the best examples of birds, with

37

38

aspe c t s of cog n i t ive st ruc ture example 1.5

(continued)

20

owls and eagles lower down in the rankings, and ostriches, emus, and penguins among the worst examples.27 All are considered members of the category bird, but some better represent the category than others. Consequently, category structure is graded according to typicality: category members range from the most typical to the least typ27. Eleanor Rosch, “On the Inter nal Structure of Perceptual and Semantic Categor ies,” in Cognitive Development and the Acquisition of Language, ed. Timothy E. Moore (New York: Academic Press, 1973), 111– 44; idem, “Cognitive Representations of Semantic Categor ies,” Journal of Experimental Psychology: General 104 (1975): 192 – 233.

cate g ori zat i on example 1.5

(continued)

27

(continued)

ical, with the former securely inside the bounds of the category (robins and sparrows) and the latter in danger of being excluded from the category (emus and penguins). Graded membership has been shown to be pervasive among what are conventionally called natural categories, so named based on their emergence from the interaction of humans with their natural environments.28 For the sake of clarity, and 28. On the pervasiveness of natural categor ies, see Lawrence W. Barsalou, “The Instability of Graded Structure: Implications for the Nature of Concepts,” in Concepts and Conceptual Development: Ecological and Intellectual Factors in Categorization, ed. Ulric Neisser (Cambr idge: Cambridge University Press, 1987), 102. On the ter m “natural” applied to certain categor ies, see Barsalou, Cognitive Psychology, chap. 2.

39

40

aspe c t s of cog n i t ive st ruc ture example 1.5

(continued)

33

cresc.

cresc.

cresc.

cresc.

cresc.

cresc.

cresc.

to avoid certain of the associations summoned by the ter m “natural,” I call this sort of category a Type 1 category. Type 1 categor ies stand in contrast to categor ies in which membership is based on individually necessar y and jointly sufficient conditions, such that the members of category x must have features y and z, and if something has features y and z it is a member of category x. Because the conception of categories of this latter sort is often traced backed to the work of Aristotle, such categor ies have been called clas-

cate g ori zat i on sical categories; because the structure of these categor ies is not typically an analog representation of the natural world, such categor ies have also been called artificial.29 I call this sort of category a Type 2 category. Most evidence indicates that Type 2 categories simply represent a specialized for m of Type 1 categor ies— take a Type 1 category, specify limits for the categor y through the imposition of necessar y and sufficient conditions for category membership, and you create a Type 2 category.30

prototype effects and frame structure

Eleanor Rosch and Carolyn Mervis, in their pioneer ing work on Type 1 categor ies, suggested that such categories were organized around a stable cognitive construct called a prototype, which encapsulated the statistically most-prevalent features of members of the category and against which potential category members were compared.31 Type 1 categories were thus said to exhibit “prototype effects.” It is clear, however, that the prototype offers more structure than simply a record of the attr ibutes cor related with a particular category: although wings and beak are both highly cor related with bird, we know that wings are used for locomotion and beaks are used for eating. Relationships between attr ibutes, as well as the values assigned these attr ibutes, are thus important to the function of the prototype. As a way of captur ing the relational structure inherent in most categor ies, Lawrence Barsalou proposed using the notion of a frame, as developed in artificial intelligence research, to represent category structure.32 As Barsalou has shown, the 29. On classical or artificial categor ies, see Edward E. Smith and Douglas L. Medin, Categories and Concepts (Cambridge, Mass.: Harvard University Press, 1981), chap. 1; Sharon Lee Armstrong, Lila R. Gleitman, and Henry Gleitman, “What Some Concepts Might Not Be,” Cognition 13 (1983): 263 – 308; Lila R. Gleitman, Sharon Lee Armstrong, and Henry Gleitman, “On Doubting the Concept ‘Concept’,” in New Trends in Conceptual Representation: Challenges to Piaget’s Theory?, ed. Ellin Kofsky Scholnick (Hillsdale, N.J.: Erlbaum Associates, 1983), 87– 110; Lakoff, Women, Fire, and Dangerous Things, chap. 2; Barsalou, Cognitive Psychology, chap. 2. 30. Although the typology of categories I introduce here places a burden on those familiar with the traditional labels, it has two advantages. First, it avoids the complications caused if “natural” is inter preted as “given by nature”; while Type 1 categor ies result from humans’ interactions with their environment, they are not given by that environment in any simple way. Second, the typology classifies categor ies on the basis of their internal structure. This is especially useful when consider ing research on categor ization, since “artificial” categor ies (such as things to pack in a small suitcase, as discussed by Barsalou in his “Deriving Categories to Achieve Goals”) often have the same basic structure as do “natural” categories (such as bird). 31. Eleanor Rosch and Carolyn B. Mervis, “Family Resemblances,” Cognitive Psychology 7 (1975): 573 – 605. See also James Hampton, “Prototype Models of Concept Representation,” in Categories and Concepts: Theoretical Views and Inductive Analysis, ed. Iven van Mechelen, James Hampton, Ryszard S. Michalski, and Peter Theuns, Cognitive Science Ser ies (London: Academic Press, 1993), 67– 95. 32. Barsalou, Cognitive Psychology, chap. 7; idem, “Frames, Concepts, and Conceptual Fields,” in Frames, Fields, and Contrasts: New Essays in Semantic and Lexical Organization, ed. Adrienne Lehrer and Eva Feder Kittay (Hillsdale, N.J.: Erlbaum Associates, 1992), 21– 74; idem, “Flexibility, Structure, and Linguistic Vagary in Concepts: Manifestations of a Compositional System of Perceptual Symbols,” in Theories of Memory, ed. A. F. Collins, S. E. Gathercole, M. A. Conway, and P. E. Morris (Hillsdale, N.J.: Erlbaum Associates, 1993), 29– 101. The exploration and implementation of frame structures in work on artificial intelligence is demonstrated in Marvin Minsky, “A Framework for Representing Knowledge,” in The Psychology of Computer Vision, ed. Patrick Henry Winston (New York: McGraw-Hill, 1975), 211– 77; Marvin Minsky, The Society of Mind (New York: Simon and Schuster, 1985); and Douglas B. Lenat and R. V. Guha, Building Large

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42

aspe c t s of cog n i t ive st ruc ture attributes

values

individuals

large

size medium

color

small

*

brown

*

wren

white

cardinal red green

Bird

chirps

sound

* chicken

clucks sings squawks flies *

parrot

locomotion runs

figure 1.1 A partial frame for the category bird (asterisks indicate the values of the prototype that are stored in memory)

basic structure of a Type 1 category can be conceived of as a relational network made up of relatively abstract attr ibutes, to which concrete values are assigned by each individual. For the categor y bird, for example, attributes might include size, color, sound, and locomotion, as shown in figure 1.1. For the attr ibute size, values might include large, medium, and small. Each member of the categor y exemplifies specific values for each of the attr ibutes: a wren is small, brown, chirps, and flies; a chicken is large, white, clucks, and (for the most part) runs. Of course, individuals with none of the attr ibutes of the category would be excluded from it. Prototype effects ar ise from the compar ison of the values represented by individuals with the values of the prototype for the categor y that are stored in memory (indicated with aster isks in fig. 1.1). If the values of the prototype for bird were small, brown, chirps, and flies, then a wren would be most typical of the category, a male cardinal (small, red, sings, flies) would be somewhat less typical, and a chicken (large, white, clucks, runs) would be least typical.

applications to music

Returning to the opening of the Fifth Symphony, we can see that, as suggested by Schoenberg’s account of motive, there are a

Knowledge-Based Systems: Representation and Inference in the Cyc Project (Reading, Mass.: Addison Wesley, 1989).

cate g ori zat i on number of different for ms that Beethoven’s motive takes in the first thirty-seven measures of the movement, and these vary with respect to contour, dynamics, and orchestration. Approached from the perspective of categorization, each motive form can be viewed as a member of the categor y motive forms from the opening of Beethoven’s Fifth Symphony.33 Attributes of this category might include things such as orchestration, dynamic, and melodic profile. In the following discussion, I show how these three attr ibutes could play a part in deter mining membership in the category motive forms from the opening of Beethoven’s Fifth Symphony; however, I should emphasize that, for present pur poses, what is of concer n is less the specific attr ibutes and more the model of categor ization they illustrate. To character ize melodic profile, it is useful to account for intervallic relationships among motive forms in ter ms of diatonic intervals. That is, within the diatonic context of the movement, the descending third from G4 to Eb4 can be reckoned to be equivalent to the descending third from F4 to D4, even though the for mer is major and the latter is minor. Here I represent a descending third with –3, an ascending third with +3, and a unison with a u.With this in mind, the attr ibute-values for the first two statements of the motive would be tutti, fortissimo, and u, u, –3. Although rhythmic profile is an equally important attr ibute of the category, it is not as useful for distinguishing among the various motive forms found in the opening measures shown in example 1.5. All the motive forms found there would assign the same value to this attr ibute: short, short, short, long (where short is equivalent to an eighth note and long varies between a quarter note and three tied half notes). In consequence, the attr ibute rhythmic profile is relatively transparent in the opening of the symphony, as is the attr ibute played by instruments; both will be omitted from the following account of category structure. Figure 1.2 presents a frame diag ram for the categor y motive forms from the opening of Beethoven’s Fifth Symphony; it shows the values that thirteen instances of the motive assign to the attr ibutes orchestration, dynamic, and diatonic melodic profile. The result is a rather dense diag ram (owing in part to the number of individuals categorized), which gives an intr iguing and rather counter intuitive picture of what is most typical of the various motive forms gathered there. Based on the evidence provided by these individuals, the most typical for m of the motive would assign the values solo, piano, and u, u, –3 to the relevant attr ibutes. Although the last value is what we might expect, the first two are not: it is difficult to think of Beethoven’s theme as anything other than tutti and fortissimo. Were we to take into account a further fifteen instances of the motive, the profile 33. What follows is by no means the first attempt to use research on categor ization to model variation among musical elements; notable are the studies of Robert L.Welker,“Abstraction of Themes from Melodic Variations,” Journal of Experimental Psychology: Human Perception and Performance 8 (1982): 435 – 47; and Lucy Pollard-Gott, “Emergence of Thematic Concepts in Repeated Listening to Music,” Cognitive Psychology 15 (1983): 66– 94. The following extends this work by taking advantage of research done since the early 1980s and by endeavoring to give a more thorough account of the process of categor izing musical events. Mention should also be made of Robert O. Gjerdingen’s discussion of typicality in A Classic Turn of Phrase: Music and the Psychology of Convention, Studies in the Cr iticism and Theor y of Music (Philadelphia: University of Pennsylvania Press, 1988), 93– 94, which anticipates many of the points made here.

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44

aspe c t s of cog n i t ive st ruc ture attributes

values

individuals mm. 1-2

tutti

orchestration

solo ensemble

mm. 3-5

mm. 6-7

mm. 7-8

f, ff mm. 8-9

dynamic

cresc. mm. 10-11

piano mm. 11-12

mm. 12-13

u, -2, -2 mm. 14-15

u, u, -2

diatonic melodic profile

mm. 15-16

u, u, -3 mm. 16-17

u, u, -4 mm. 17-18

u, +2, +2 mm. 18-19

figure 1.2 Diagram of the category structure for the category motive forms from the opening of Beethoven’s Fifth Symphony, mm. 1– 21

of typicality would be skewed even further away from what we might expect (this is shown in fig. 1.3, where the frame diagram has been rearranged somewhat in the interests of legibility). The difference between the evidence provided by figures 1.2 and 1.3 and our usual recollection of how Beethoven’s theme sounds is due in part to a limitation of frame diagrams: they are essentially statistical representations of the most common values assigned attr ibutes by individuals. They may not represent the most important attribute values for a given category, however.

beyond the prototype: conceptual models Recent empir ical work on categor ization has shown that category structure is even more variable than had been assumed by the researchers who first proposed the prototype theory of category structure.34 In most Type 1 categor ies, some attr ibutes are more important to categor y structure than others. As a result, some of the statistically most prevalent features of members of a category may be disregarded in for mulating the 34. Armstrong et al., “What Some Concepts Might Not Be”; Gleitman et al., “On Doubting the Concept ‘Concept’ ”; Barsalou, “The Instability of Graded Structure”; Lawrence W. Barsalou, “Intraconcept Similar ity and Its Implications for Interconcept Similar ity,” in Similarity and Analogical Reasoning, ed. S.Vosniadou and A. Ortony (Cambr idge: Cambridge University Press, 1989), 76– 121.

cate g ori zat i on mm. 1-2

mm. 3-5

tutti

mm. 25-26

solo

mm. 26-27

ensemble mm. 27-28

mm. 6-7

mm. 7-8

f, ff

mm. 28-29

cresc. mm. 29-30

mm. 8-9

piano mm. 30-31

mm. 10-11

mm. 11-12

u, -2, -2

mm. 31-32

u, u, -2 mm. 32-33

mm. 12-13

u, u, -3 mm. 14-15

mm. 15-16

u, u, -4

mm. 33-34 (vln. I)

u, u, u,

mm. 33-34 (vln. II, vla.)

u, +2, +2 mm. 16-17

mm. 34-35

u, u, +4 mm. 35-36 (vln. I)

mm. 17-18

u, -3, +2 mm. 18-19

mm. 22-24

u, +3, u

mm. 35-36 (vln. II, vla.)

+4, u, u

mm. 36-37

figure 1.3 Diagram of the category structure for the category motive forms from the opening of Beethoven’s Fifth Symphony, mm. 1– 37

prototype. For example, attributes such as natural environment and means of locomotion have a strong influence on how we categor ize whales, leading us to disregard such taxonomic attr ibutes as mode of respiration and means of reproduction. In consequence, a whale seems closer to a prototypical fish than to a prototypical mammal, despite its proper Linnean categor ization.35 Research has also shown that judgments of typicality change over time, even when no new individuals are categor ized. It appears that, rather than constituting a stable cognitive entity, the prototype for a category is actually fluid and variable and it changes with the circumstances of categorization. An alter native view of category structure suggests that categor ies are organized around conceptual models. In brief, conceptual models consist of concepts in specified relationships; each model pertains to a specific domain of knowledge. Such models are central to reasoning and inference, and they will be discussed in g reater detail in chapter 3; in what follows, the emphasis is on the role conceptual models play in categorization, rather than on the structure of such models. With regard to catego35. For a discussion of some of the factors involved in this particular categor ization, see John Dupré, “Are Whales Fish?” in Folkbiology, ed. Douglas L. Medin and Scott Atran (Cambr idge, Mass.: MIT Press, 1999), 461– 76.

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aspe c t s of cog n i t ive st ruc ture rization, the primary function of the conceptual model is to supply a guide for reasoning about accepted and potential members of the category. This is accomplished through a simplified representation of category structure that incor porates knowledge about what values are most typical for a select group of attributes for the given category. These attr ibutes are selected according to the goals of categor ization, which are themselves infor med by more global conceptual models applicable to a broad range of categorization tasks.36 The conceptual model for a g iven category thus reflects infor mation of the sort summar ized in frame diagrams but conditioned by knowledge about the overall goals of categor ization. As a means of developing a preliminary understanding of the concepts and relationships constituent of a conceptual model for a category, let us return once more to the opening of Beethoven’s symphony and consider a conceptual model for the category motive forms from the opening of Beethoven’s Fifth Symphony. The model, diagrammed in figure 1.4, consists of four correlated conceptual elements, character ized as the things necessary for a melodic fragment to count as an instance of the motive: • • • •

the rhythmic patter n Ω≈ç « h a statement by the full orchestra a fortissimo dynamic an intervallic patter n consisting of three repeated notes followed by a descending diatonic third37

These elements g ive priority to select attr ibutes of the motive (rhythmic patter n, orchestration, dynamics, and intervallic profile) and assign default values to these attributes — that is, they define what counts as a “typical” member of the category. This network of attributes and values then provides a guide for categor izing the various versions of the motive that occur in the opening measures. Accordingly, versions of the motive such as those of mm. 1– 2 and mm. 22– 24 (which instantiate all aspects of the conceptual model) would be judged most typical of the category; motive forms such as those of mm. 6– 7 and mm. 29– 30 (which instantiate only two aspects of the conceptual model) would be less typical; and motive forms such as those of mm. 7– 8 and mm. 35– 36 (which instantiate only the rhythmic aspect of the conceptual model) would be least typical of the category. What, then, of the evidence provided by figure 1.3? That is, what can one make of the lack of correlation between the conceptual model and the individual category members, since most of these would be reckoned to be less typical members according to the conceptual model for the categor y? The answer to this question requires delving a bit deeper into the way conceptual models both reflect and shape our understanding of music. 36. Barsalou, “Deriving Categor ies to Achieve Goals”; Lawrence W. Barsalou, Wenchi Yeh, Barbara J. Luka, Karen L. Olseth, Kelly S. Mix, and Ling-Ling Wu, “Concepts and Meaning,” in Chicago Linguistics Society 29: Papers from the Parasession on the Correspondence of Conceptual, Semantic, and Grammatical Representations, ed. Kathar ine Beals, Gina Cooke, David Kathman, Sotaro Kita, Karl-Er ik McCullough, and David Testen (Chicago: University of Chicago, Chicago Linguistics Society, 1993), 23– 61. 37. I should emphasize that the conceptual models I descr ibe here are by no means the simplest elements of conceptual structure. Each conceptual cluster of the present model, for instance, could be represented by a still smaller conceptual model cor relating the concepts that make up the cluster.

cate g ori zat i on qqq h

rhythmic pattern

stated with full orchestra motive forms from the opening of Beethoven’s Fifth Symphony stated at fortissimo dynamic

u, u, -3 intervallic pattern

figure 1.4 Conceptual model for the category motive forms from the opening of Beethoven’s Fifth Symphony

The conceptual model shown in figure 1.4 gives undeniable priority to the statements of the motive that open the movement. The preference given the first statements of musical mater ials we encounter is not absolute — there are, of course, works in which the pr incipal mater ials emerge only gradually — but it does reflect the fact that we must process musical mater ials in time and that it is often the case that significance accrues to the first events in any psychological process. Note that Beethoven departs from his opening mater ials only gradually; in particular, divergences from the intervallic patter n of the motive (the aspect of the typicality shown by fig. 1.3 that best matches the proposed conceptual model) occur somewhat later in the opening measures and cor relate with the compositional strateg ies of development and transition.38 The initial statements of the motive thus represent anchor points for the process of elaboration that Beethoven undertakes: the variations evident in figure 1.3 are variations on the musical mater ials summar ized in the conceptual model of figure 1.4. The conceptual model of figure 1.4 is also infor med by our ideas about musical themes: that is, such themes should be strongly and clearly stated at pr ivileged points within a movement (such as the beg inning of the movement or after a change of key or tempo), after which they may be modified or embellished in confor mance with compositional strategies. Our local model for the motive of Beethoven’s symphony is thus shaped by a global model of what constitutes an appropriate musical theme. Such global models are developed through abstraction from any number of local models, and, perhaps more important, they are taken from the broader base of knowledge that constitutes culture.39 For instance, in the case of Beethoven’s symphony, the relevant global model for a musical theme reflects the influence of nineteenth-century German and Austrian musical culture and, in particular, the efforts 38. Relationships between processes of categor ization and compositional strategy are developed more fully in chap. 4. 39. This perspective on culture is explored more fully in chaps. 3 and 5.

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aspe c t s of cog n i t ive st ruc ture of the nineteenth-centur y critic and theor ist A. B. Marx and others to come to terms with Beethoven’s compositional style.40 Our global model of what counts as a theme (which applies to any number of works by any number of composers) is thus in rapport with the local models through which we organize our understanding of specific musical works. Without a global model, it can be difficult to decide what aspects of a phenomenon are relevant for categorization. Without local models, there is no way to anchor global models to specific phenomena. It should be emphasized that the conceptual model sketched here and diagrammed in figure 1.4 represents limited features of a network of interrelated propositions that might be used to guide reasoning about how motive forms in the opening of Beethoven’s symphony relate to one another. The model does not represent, in a simple way, what someone “has in mind” when confronting this music. The simplicity of the model (which reflects in part the global models relative to which it is framed) contr ibutes to its efficiency. It is specific enough to allow for clear distinctions between the motive of the opening measures and other thematic mater ials in the symphony (such as the new theme that enters in m. 63). It is general enough, however, to accommodate the wide range of different for ms the opening motive takes. The model also reflects our intuition that there is just one main form of the opening motive, despite evidence to the contrary. Intuitions such as this contribute to the plausibility of Type 2 categor ies, with their cr isp boundar ies and clear definitions. Features of the conceptual model for a g iven categor y will often be transfor med into the necessar y and sufficient conditions character istic of Type 2 categor ies: take a Type 1 category and specify limits for it by regarding the constituent elements of the conceptual model relative to which it is structured as necessary and sufficient conditions for category membership, and you create a Type 2 category. In descr iptions of music, this process yields “textbook” definitions of the sort that often lead to considerable debate among music theor ists. Although such debates appear to be about music, they are in fact about how to define the categories through which we organize our understanding of music.

summary: typicality effects and musical motive

Categories that show typicality effects offer a way to model both the coherence and the variability of motive forms basic to Schoenberg’s theory of motive. The property of coherence is analogous to the shared attr ibutes of category members— that is, our 40. Marx’s is perhaps the most important nineteenth-century voice within the tradition of analyzing the thematic aspects of Beethoven’s music. Although Marx did not restrict himself to a definition of “theme” as such, preferring a broader and more organic account of musical organization, he did offer the notion of the Satz. Formed from motives, the Satz is a complete self-sufficient musical idea and represents the first coherent unit of musical organization. See Adolph Ber nhard Marx, Musical Form in the Age of Beethoven: Selected Writings on Theory and Method, ed. and trans. Scott G. Burnham, Cambridge Studies in Music Theor y and Analysis, 12 (Cambridge: Cambridge University Press, 1997), 68. The Satz is roughly comparable to Schoenberg’s notion of a Grundgestalt, as discussed in Schoenberg, The Musical Idea, 169. It is no accident, of course, that Marx’s formal theor ies reflect his efforts to make explicit Beethoven’s compositional strategies. That is, to the extent that our notion of what constitutes a theme resonates with Marx’s definition, that notion is infor med by works such as the Fifth Symphony. Further discussion of Marx’s notion of a motive is taken up in chap. 7.

cate g ori zat i on sense that a collection of things coheres as a categor y reflects the attr ibutes shared by those things. The variability Schoenberg noted is analogous to the variation among members of a Type 1 category. Just as certain motive forms are taken as the source for the der ivation of further motive forms, so certain category members will be regarded as more typical of the category than others. While typicality effects reflect, to a certain extent, statistical invariances among the attr ibute-values demonstrated by category members, they are also a function of the goals of categor ization. These goals shape the category’s conceptual model, which represents what is regarded as most typical of the category and which also provides a guide for reasoning and inference about potential category members. An important difference between collections of musical motives and cognitive categories is that the for mer must be processed under the temporal constraints of musical perfor mance. Under most circumstances, these constraints will infor m the conceptual model for a categor y of motive forms, with priority given to those forms that occur early in a work. As the example of Schubert’s Wanderer Fantasie suggests, however, other factors may cause our concept of what constitutes the central motive of a work to change as the piece unfolds.

categorization and wagnerian leitmotiven Wagner’s Leidensmotiv Approaching the seven statements of the opening motive from Tristan und Isolde given in example 1.1 as a cognitive categor y offers a way to explain why it is that we consider them “the same” even when they are manifestly different, and it gives some insight into their role as a point of entry into Wagner’s sonic fantasy. Knowing something about the structure of cognitive categor ies also gives us a way to glimpse features of Wagner’s compositional strategy, which both exploits and challenges our ability to categor ize. Before we explore the motive as a category, let us first situate the motive in its original context. As shown in example 1.6, the motive is accompanied by harmonies (provided by the clar inets and bassoons) and a r ising chromatic line in the oboes. Hans von Wolzogen, in his classification of the motives from Tristan und Isolde (which he referred to as Leitmotiven), called the main motive the Leidensmotiv (the suffer ing motive) and the r ising chromatic line the Sehnsuchtsmotiv, or the yearning motive.41 The har mony on the downbeat of m. 2 is traditionally known as the “Tristan chord.” As Carl Dahlhaus has noted, all of these elements are intertwined to such an extent that taking any one of them out of context distorts the whole.42 Nonetheless, it is the

41. Hans von Wolzogen, Thematischer Leitfaden durch die Musik zu Richard Wagner’s Tristan und Isolde: Nebste einem Vorworte über den Sagenstoff des Wagner’schen Dramas (Leipzig: Feodor Reinboth, 1890), 15. This work was also published in an English edition as Guide through the Musical Motives of Richard Wagner’s Tristan and Isolde: With a Preface on the Legend and the Poem of Wagner’s Drama (Leipzig: Feodor Reinboth, 1889). 42. Dahlhaus, Richard Wagner’s Music Dramas, 63.

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50

aspe c t s of cog n i t ive st ruc ture example 1.6

Opening motivic group from Richard Wagner’s Tristan und Isolde 1

changes to the Leidensmotiv that are the most noticeable (not the least because it is the first sounding element of the ensemble), and so in the following I will focus on it, with the understanding that it is but one part— if a rather prominent one — of a larger whole.43 With these thoughts in mind, let me propose that the categor y statements of the Leidensmotiv is organized around a conceptual model consisting in two cor related elements, character ized as the things necessar y for a melodic fragment to count as an instance of the motive: • an ascending sixth, followed by three descending half-steps • the rhythmic patter n Z e«qd q e«qd e44

, ,

Again, this model is greatly simplified, for in addition to ignor ing the mater ials that invariably accompany the Leidensmotiv, nothing is said of dynamics or orchestration, and the notion of a “motive” or “theme” is simply assumed (as part of the global model that frames this local model). The model is sufficient, however, to distinguish the Leidensmotiv from other motivic mater ials in Wagner’s music drama and to evaluate the typicality of different versions that appear over the course of the work. Turning to the versions of the motive given in example 1.1 we can note the following range of typicality: statements 1, 2, 6, and 7 are in complete confor mance with the model (they are typical of the category), but statements 3, 4, and 5 confor m rather less well (they are less typical of the category).Viewed from the perspective of compositional strategy,Wagner begins with two thoroughly typical members of the category and then follows them with a markedly less-typical member that adds a note and changes the rhythmic profile. After a considerable span of music, he returns to the motive, but again in a less than typical for m— indeed, the two temporally compressed versions of mm. 85– 90 enact the sense of reminiscence they are meant to evoke by presenting to our ears a distillation of the most salient aspects of 43. Robert P. Morgan has recently offered an analysis of the Tristan Prelude which focuses more on harmonic structure than on the appearance of motive forms and which offers an intr iguing alter native to what I present in the following. See Morgan, “Circular Form in the Tristan Prelude,” Journal of the American Musicological Society 53 (2000): 69– 103. A selection of analyses of the Prelude spanning the twentieth century can be found in Robert Bailey, ed., Prelude and Transfiguration from Tristan and Isolde (New York:W.W. Norton, 1985). 44. The actual duration of the concluding note of the motive is variable; in all cases, however, its duration is of moderate length relative to that of the other notes that make up the motive.

cate g ori zat i on the motive. Ten measures further (beginning in m. 100) there are two final appearances of the motive before the curtain goes up, each a thoroughly typical for m. Wagner’s compositional strategy thus falls into three stages. In the first stage (associated with statements 1 and 2), he establishes the motive. In the second stage (associated with statements 3, 4, and 5), he presents less typical for ms of the motive; these are cor related with a larger set of “developmental” strategies, with which the central portion of the Prelude is concer ned. Finally, in the third stage (associated with statements 6 and 7), he returns to more typical for ms of the motive, preparatory to concluding the Prelude and beginning the music drama proper.45 Two things emerge from this initial sketch. First, in the different versions of the Leidensmotiv that appear in the Prelude, we have a category that develops over time. Because categor ization is an active response to the environment, it always has a temporal dimension: a comparative categor ization of birds, for instance, demands that we evaluate each in turn.With music the temporal aspect is slightly more prominent, since musical entities are thoroughly ephemeral: not only must we evaluate each musical entity in tur n, but also this evaluation is practically the only evidence that the entities ever existed at all. Wagner is clearly conscious of the way the Leidensmotiv functions through time and uses it to g ive shape to the Prelude as a whole. Second, the view of Wagner’s compositional strategy der ived from comparing the versions of the motive in the Prelude, fascinating as it might be, is also misleading: the sort of circularity that it suggests is fundamentally at odds with his goal of perpetually progressive music. By looking at further instances of the Leidensmotiv over the course of Tristan und Isolde we can develop our understanding of both of these things and refine our inter pretation of Wagner’s treatment of the motive in the Prelude.

The Leidensmotiv and Musical Syntax The Leidensmotiv is prominent at five moments in Tristan und Isolde: in act 1, scene 2, mm. 26– 33 (p. 36; see ex. 1.7a) and scene 5, mm. 439– 41, 456– 58, and 468 – 72 (pp. 175 – 78; ex. 1.7b); in act 2, scene 3, mm. 260 – 78 (p. 448; ex. 1.7c); and in act 3, scene 2, mm. 93– 107 (pp. 594 – 96; ex. 1.7d) and scene 3 (near the conclusion of the opera), mm. 153 – 57 (p. 630; ex. 1.7e).46 In each case, there are three entr ies of the motive, beginning (as did those in the opening of the Prelude) on A (or, in the case of the first entry in act 3, scene 2, Ab), B, and D. Each group departs from the conceptual model proposed above in various ways. The versions of act 1, scene 2 have one less pitch (and, of course, one less interval) than the model and a different rhythmic profile. Those of act 1, scene 5 have a different rhythmic profile. In act 2, scene 3, the versions of the motive are quite close

45. This syntactic patter n is analogous to the Beg inning–Middle–End paradigm discussed by Kofi Agawu, but here it is expressed purely in ter ms of categor ies, rather than in ter ms of tonal organization. See Victor Kofi Agawu, Playing with Signs: A Semiotic Interpretation of Classical Music (Princeton, N.J.: Princeton University Press, 1991), chap. 2. 46. Measure numbers are given by scene; page numbers refer to the Dover reprint of the C. F. Peters 1911 edition of the score: Richard Wagner, Tristan und Isolde (New York: Dover Publications, 1973).

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aspe c t s of cog n i t ive st ruc ture to the model, but the first two have extended endings, while those of act 3, scene 2 have an altered rhythmic profile, so that their overall duration is greatly expanded. Finally, the versions of the motive in act 3, scene 3 are greatly compressed (as are those of act 1, scene 2). Within each group, however, the versions of the motive are relatively consistent (with the exception of those of act 1, scene 5, about which more in a moment), although the last statement (beginning on D) is always a bit different from the preceding two. This consistency suggests that each g roup of three statements of the Leidensmotiv forms a syntactic unit, which represents its own local standard of typicality. These units are themselves members of a superordinate category (to which we could give some sort of cumbersome name like successions of the Leidensmotiv beginning on A/Ab, B, and D) whose members span almost the entirety of Wagner’s music drama.47 For the most par t, the statements that make up these syntactic units are conjunct, and, although they may stretch across a number of measures, the connection between the successive statements is quite obvious. The one exception comes with the three statements of act 1, scene 5, which occur at a climactic moment in the drama. Tristan has just dr unk what he believes is a death potion. Isolde wrests the cup from him, sings “Verräther, ich tr ink’ sie dir!” (“Betrayer! I dr ink to you!”), and then empties what remains in the cup. Unbeknownst to either, the draught they have consumed will lead not to death but will instead cause them to fall even more deeply in love. The melody for Isolde’s unintentionally ironical “Ich tr ink’ sie dir!” is the version of the Leidensmotiv that begins example 1.7b. For the fifteen measures of music that follow, the stage directions read: “She drinks, then throws the cup away. Both [Tristan and Isolde], seized with awe, in the greatest excitement but motionless, look fixedly into each other’s eyes, in which the expression of defiance of death soon gives way to the glow of love.” The cellos then enter with the second statement of the Leidensmotiv, beginning on B. Further stage directions follow, to accompany another ten measures of music: “Trembling seizes them: they clutch convulsively at their breasts and pass their hands over their foreheads.” Unison cellos and violas then br ing in the last statement of the Leidensmotiv, beginning on D. In this instance, what draws the three versions of the motive together into a single categor y is not so much their similar ity to one another (although this is still quite audible) or their temporal proximity, but the way Wagner pr ivileges them within his musical discourse. Not only is there nothing else to compete with them at the moment of their appearance, but also their par ticipation in this pivotal moment suggests that they are autonomous agents within the drama itself . We should, if but briefly, consider the notion of syntax developed in the preceding paragraphs. First, the basic idea of syntax that I employ here is what Webster’s calls “a connected or orderly system.” I flesh out this idea further in chapter 4; for now, it is enough to say that this appears to be how at least some music theor ists 47. Robert P. Morgan has also pointed out that each successive phrase within these units takes up the same notes outlined in the top voice of the preceding one, making it seem that each phrase emerges from the one just before; see Morgan, “Circular Form in the Tristan Prelude,” 95, 102.

example 1.7 Statements of the Leidensmotiv from Richard Wagner’s Tristan und Isolde: (a) act 1, scene 2, mm. 26– 33 (Richard Wagner: Sämtliche Werke [WSM], vol. 8, part 1, mm. 313 – 20); (b) act 1, scene 5, mm. 439 – 41, 456 – 58, 468 – 72 (WSM; vol. 8, part 1, mm. 1754 – 56); (c) act 2, scene 3, mm. 260 – 78 (WSM, vol. 8, part 2, mm. 1890 – 1908); (d) act 3, scene 2, mm. 93– 107 (WSM, vol. 8, part 3, mm. 1301– 15; (e) act 3, scene 3, mm. 153– 57 (WSM, vol. 8, part 3, mm. 1581– 85) a 26

Eng. Hn.

cresc.

meno b 439

Isolde: 468

456

Ich trink

sie

Vnc.

dir! Eng. Hn.

Vnc., Vla. sehr ausdrucksvoll

c 260

Eng. Hn.

più 266

273

espress. d 93

Hns., Bns.

Hns., Bs. Cl.

ausdrucksvoll 101

Eng. Hn., Bs. Cl., Hns.

ausdrucksvoll e 153

Vnc.

dim.

Vla.

Vn. II

3

poco cresc.

dim.

54

aspe c t s of cog n i t ive st ruc ture construe the notion.48 Second, the structural integrity of the syntax associated with the Leidensmotiv emerges only over time. Although all of its elements are present from the opening moments of Wagner’s music drama, confir mation of the syntax must wait until well into the opera. Third, this syntax is specific to Tristan und Isolde. Not only would we expect a different motive to be used for another work, but this motive would almost certainly be deployed in different ways. Musical syntax, at least with regard to this example, is thus created over time and is idiosyncratic to one particular composition. Finally, semantic value may become associated with syntactic structure, something evident in Wagner’s manipulation of the three statements of the motive in the climactic moment that occurs in act 1, scene 5. By disrupting or modifying his musical syntax, Wagner can create a type of meaning that is thoroughly — and exclusively— musical.

Syntactic Structure and Compositional Strategy As a general type, the category statements of the Leidensmotiv has a temporal span coextensive with that of Tristan und Isolde. More specifically,Wagner carefully articulates the category over the course of the drama, with the motive appear ing in syntactic units of three successive statements so that, with each entry of the motive on A (or Ab), we expect to hear two further entr ies, replicating the patter n set in the opening measures. Wagner relies on this expectation in act 1, scene 5 to underline both the tragedy and passion of Tristan’s and Isolde’s love. From this perspective, the further appearances of the Leidensmotiv in the Prelude after the initial three seem somewhat anomalous, for here they are only in pairs: statements on B and D in mm. 85– 90, and on Ab and B in mm. 100 – 106. But Wagner is playing a deep, even subliminal, game: buried beneath the overheated music in mm. 80 – 83 are three rhythmically displaced versions of the Leidensmotiv, all beginning on Ab (as shown in ex. 1.8). Although little more than wraiths appear ing in the midst of a fury of motives, these statements have their continuation — indeed, their consequence — in the entrances on B and D in the measures that follow. This hidden syntactic unit implies that the next round of statements, which start with the entrances on Ab and B in mm. 100 – 106, should be followed by one additional entrance of the Leidensmotiv on D.Wagner withholds the third statement, however, and instead calls for the curtain to go up: in response to our anticipation of a third statement of the motive, Wagner gives us an entire opera.49 The shadowy appearances of the Leidensmotiv in mm. 80 – 83 of the Prelude and the somewhat less-typical versions that follow in mm. 85– 90 suggest that Wag48. Cone, in “On Der ivation,” pairs the organizational system of syntax with the expressive tools of rhetor ic. As another example of this sort of approach, Robert P. Morgan, in a recent essay, describes tonality as compr ising “not only the abstract collections of diatonic pitches (plus their chromatic alterations), which have significant symmetr ical properties of their own, but various asymmetr ical syntactical functions, harmonic and linear, that transfor m these collections into a full-fledged compositional language” (Morgan, “Symmetr ical Form and Common-Practice Tonality,” Music Theory Spectrum 20 [1998]: 2, emphasis added). 49. Morgan points out that the har monic syntax for these final statements is also incomplete; see “Circular Form in the Tristan Prelude,” 83.

example 1.8 Statements of the Leidensmotiv from Richard Wagner’s Tristan und Isolde, Prelude, mm. 80 – 83 zu 3.

80 Fl.

3

Hb. 3

Kl.A. 3

E.H. 3

1. F. 2.

espress.

più

espress.

più

F. Hr.

3.

E. 4. E. 1. 2.

Fg.

3.

più Bk1.A. espress.

1. Tr.F. 1. 2.

Ps.

3.

Btb.

Pk. cresc.

1.V. più

3

3

3

3 3

3

3

3

3

3

2.V. più Br. più espress. Vc. più Kb. più

(continued)

example 1.8 (continued) 82

zu 8.

Fl.

3

Hb. 3

Kl.A. 3

E.H. 3

F.

F. Hr. E.

E. 1. 2.

Fg.

3.

Bk1.A. 1.

1. 2. zus.

Tr.F. più 1. 2.

Ps.

più 3. più

Btb.

Pk.

3

1.V. 3

3

3

3

3

3

3

3

3 3

3

2.V.

Br.

Vc. trem. Kb.

cate g ori zat i on ner is both playing with and relying on our capacity to remember the motive (a capacity directly related to our ability to categor ize it). But what Wagner wants is not the sort of recognition that calls attention to itself , distracting us from the flow of his drama as we become aware of its artifice, but something much more subtle. In consequence, the motive undergoes continual change, as the different versions collected in example 1.7 show, the only constant being the opening sixth and descending half steps. (Contrary to Schoenberg’s concept of a motive— admittedly developed with reference to Brahms — rhythmic figuration is only weakly linked to the identity of the Leidensmotiv within the opera.) At the same time, the repetitions of the motive proper to each syntactic unit — which set up local, if ephemeral, standards for typicality — give each unit the illusion of stability and thus of properly representing the Leidensmotiv.What results is a syntax that is in constant transfor mation. Further proof of Wagner’s attention to musical memory can be seen in the relative atypicality of two of the rare isolated statements of the Leidensmotiv within Tristan und Isolde. One such statement occurs in the third scene of act 1. Isolde, recounting to Brangäne how her wrath against Tristan was tur ned to pity in her first encounter with him, sings “Er sah’ mir in die Augen. Seines Elendes jammerte mich!— Das Schwert— ich ließ es fallen!” (“He looked into my eyes. His anguish touched my heart! The sword— I let it fall!”). As shown in example 1.9a, the middle phrase is sung to a modified version of the Leidensmotiv. This statement begins, unlike any other, on G4, and the chromatic passage that leads away from the E5 extends to four descending half-steps. And, relatively early in the long dialogue with Tristan that makes up scene 2 of act 2, Isolde sings “Wie schmerzte tief die Wunde!” (“How deeply the wound smarted”), again using a less-typical version of the Leidensmotiv (as shown in ex. 1.9b). The statement is doubled and or namented by the strings, and its chromatic descent continues unhindered through six half steps. Both of these atypical appearances of the Leidensmotiv— atypical in their for m relative to the conceptual model of the motive, and atypical in their isolation — function as remembrances of the motive rather than statements of it. Carl Dahlhaus, in compar ing the treatment of themes in the first movement of Anton Br uckner’s Sixth Symphony to Brahms’s method of developing variation, noted Bruckner’s use of a similar strategy.When Bruckner returns to a theme, the example 1.9 Isolated statements of the Leidensmotiv from Richard Wagner’s Tristan und Isolde: (a) act 1, scene 3, mm. 135– 38 (Richard Wagner: Sämtliche Werke [WSM], vol. 8, part 1, mm. 672– 75); (b) act 2, scene 2, mm. 341– 43 (WSM, vol. 8, part 2, mm. 886– 88) a 135

Isolde: b

Isolde: wie

Sei nes E

len

des

jam

mer te

mich

341

schmerz

te

tief

die

Wun

de!

57

58

aspe c t s of cog n i t ive st ruc ture correspondence with the or iginal version is often only approximate. Dahlhaus comments, That the one version is able to substitute for the other means, aesthetically, that instead of developing variation, where each variant represents . . . a consequence of the preceding one and a prerequisite for the next one, Bruckner makes use of an analytically elusive but clearly perceivable similar ity by association, which makes the later version seem like a wr itten-out memor y of the earlier one. The logic of discourse, as conceived by Brahms, gives way to a system of approximate cor respondences.50

The preceding analysis of transfor mations to the Leidensmotiv suggests that a more apt compar ison would have juxtaposed Bruckner to Wagner rather than to Brahms, for it is “written-out memor ies” such as those shown in example 1.9 that contribute much to the power of Wagner’s music dramas: we respond to such memories not with our intellect but in a way that seems far more intuitive and thus far more deeply felt. Wagner, of course, could have had no explicit knowledge of how humans structure their understanding through categor ization, since empir ical evidence for this cognitive process did not begin to accumulate until a hundred years after the 1865 premiere of Tristan und Isolde. And yet Wagner almost assuredly had an implicit understanding of what Schoenberg called “the laws that govern the working of our minds.” Wagner’s music shows that he knew how to lay out his musical mater ials— to make them come to the fore, often enough and with enough plasticity — so that his listeners could comprehend their meaning. His music also shows that he knew how to challenge this ability, to modify the structure of categor ies of musical materials so that these same mater ials seemed new, or to have an entirely different ontological status (changing from a theme into a remembrance of a theme). An account of the way Wagner transfor med the Leidensmotiv cannot exhaust his inexhaustible music, but it can give a glimpse into the processes through which we come to understand his music, as well as the way Wagner’s compositional strateg ies both exploit and challenge that understanding.

categorization and conceptualizing music Schoenberg’s theory of motive, shaped by his understanding of the constraints on musical composition imposed by human cognitive processing (his “laws of the mind”), offers insight into how we organize our understanding of music in ter ms of categories of musical events. Motives were, for Schoenberg, where musical recognition started, and the coherence of musical motives was what made musical comprehension possible. As we have seen, these two functions are replicated in cognitive categor ies. Our preferred level of categor ization is at a level in the middle of a taxonomy— the basic level— which, like the motive, strikes a compromise between efficiency and infor mativeness. The categor ies we use most often in everyday life 50. Carl Dahlhaus, Nineteenth-Century Music, trans. J. Bradford Robinson (Berkeley: University of California Press, 1989), 273.

cate g ori zat i on are not defined in ter ms of individually necessary and jointly sufficient conditions. Instead, they have variable membership: some members are more typical of the category than others, and membership in the category is graded rather than an all-ornothing affair. Musical motives show a similar amount of variation, and it is through developing a notion of what they have in common — a conceptual model for what is typical of the category— that we begin to comprehend the musical organization of works like those that fascinated Schoenberg. As the analysis of Wagner’s use of the Leidensmotiv shows, Schoenberg’s conception of a motive is not adequate for all circumstances (especially in its reliance on rhythmic figuration), nor are composers always content to establish a single model for a motive and stick with it. Indeed, they may vary it constantly (as did Wagner in the case of the Leidensmotiv), or they may combine the models for different motive forms in any number of ways (as Cone’s work on the problem of motivic der ivation shows). Although focusing on motives offers a place to start, it is on the more general notion of a musical category— free as it is from associations with Beethoven’s compositional process, fascinating as that is — that I want to focus. While a collection of assorted motive forms is a good example of a musical categor y, categor ies can be much more various and structured around whatever set of musical relationships seems best to account for what is salient about a particular repertoire. The relevant units may be harmonic (as in a chaconne), involve a repeated bass patter n (as in a passacaglia), or combine the two (as in the linear cadential patter ns that Susan McClary has shown provide a structural framework for music of the sixteenth century);51 music of the twentieth centur y suggests an even greater number of possibilities. And music (construed as patter ned sound) may be just one of a number of contributing factors: one could also envision musical categor ies infor med by the text being set (of particular importance for liturgical music) or the affect that is to be summoned (a concer n for some types of dramatic music). In all cases, the choice and structure of the relevant musical categor ies will be guided by the global conceptual models relative to which the local models for each category are framed. My proposal, then, is that categories are where our conceptualization of music starts. If to think is to think in terms of categories, then to think of music is to think in terms of musical categories.Viewed this way, categories constitute an analogue— or perhaps replacement — for the notion of a group as it has been developed by Fred Lerdahl and Ray Jackendoff. For Lerdahl and Jackendoff, musical understanding begins with the process of segmenting a musical work into contiguous sequences of pitch-events, drum beats, or the like.52 Each such segment constitutes a group, and groups are arranged into a strict hierarchy that ultimately yields the entire work of music.53 Musical categories 51. Susan McClary, Conventional Wisdom: The Content of Musical Form (Berkeley: University of California Press, 2000), 14– 16. 52. Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, Mass.: MIT Press, 1983); the process of grouping is descr ibed on p. 13; the definition of a group is given on p. 37. 53. By “strict hierarchy,” I mean a hierarchy in which the boundar y points at each superordinate level confor m to boundar y points at the level immediately subordinate. Lerdahl and Jackendoff define this sort of organization as “hierarchical”; see Lerdahl and Jackendoff, A Generative Theory of Tonal Music, 13, 37. Conceptions of hierarchy as they are applied to music are discussed in greater detail in the latter part of chap. 7.

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aspe c t s of cog n i t ive st ruc ture can absorb many of the functions of groups — specifically, the role of the group as the first level of organization for musical phenomena — but do not require absolute contiguity or str ict hierarchical organization. As a result, a theory of musical categor ies can easily account for the multiple strands of polyphonic music in a way that grouping theory cannot. Each of the overlapping entr ies of a work in canon, for instance, could be regarded as a member of a category; this sort of analysis is simply impossible with grouping theory, since overlaps between groups are not per mitted. If categories are where our conceptualization of music starts, they must be closely linked to concepts themselves. At the r isk of some confusion, I would like to go further and suggest that musical categor ies are concepts. Now, to attempt any definition of a concept is to (at least potentially) embroil myself in a long-standing debate within philosophy and cognitive science.54 To skirt this debate, I concentrate on a definition of “concept” that reflects recent work in the mind sciences and the brain sciences, and that can be applied to music. Although I think this definition can inform the larger debate on “concept,” I shall leave the substance of the debate for another time. The definition of “concept” I develop here is influenced by the work of Gerald Edelman, who has been interested in developing a biological approach to consciousness. Edelman’s definition of a concept is developed as a descr iption of the capacities necessar y for the control of complex interactions between an organism and its environment: An animal capable of concepts is able to identify a particular thing or action and control its future behavior on the basis of that identification in a more or less general way. It must act as if it could make judgments based on recognition of category membership or integrate “particulars” into “universals.” This recognition rests not just on perceptual categor ization (although a concept may have a highly sensory content) but, to some degree, must also be relational. It can connect one perceptual categor ization to another even in the absence of the stimuli that tr iggered these categor izations.55

Thus to have concepts involves not only the process of categor ization but also recognizing relationships between categor ies.56 What is also important is that having concepts is a capacity that is not limited to humans, a point also made by Donald Griffin.57 Concepts are thus not necessar ily tied to language. 54. For a recent and stimulating sally in this debate, see Jerry A. Fodor, Concepts: Where Cognitive Science Went Wrong (Oxford: Clarendon Press, 1998). 55. Gerald M. Edelman, The Remembered Present: A Biological Theory of Consciousness (New York: Basic Books, 1989), 141. 56. Other works that either make a strong connection between categor ies and concepts or assert their equivalence include James Hampton and Danièle Dubois, “Psychological Models of Concepts,” in Categories and Concepts: Theoretical Views and Inductive Analysis, ed. Iven van Mechelen, James Hampton, Ryszard S. Michalski, and Peter Theuns, Cognitive Science Ser ies (London: Academic Press, 1993), 11– 33; Barsalou, “Flexibility, Structure, and Linguistic Vagary in Concepts”; Barsalou et al., “Concepts and Meaning”; Smith and Medin, Categories and Concepts; and Gregory L. Murphy and Douglas L. Medin, “The Role of Theories in Conceptual Coherence,” Psychological Review 92 (1985): 289 – 316. 57. Donald R. Griffin, Animal Minds (Chicago: University of Chicago Press, 1992), chap. 6. A similar approach can be seen in the work of Douglas Hofstadter and his associates, which has resulted in a number of computer programs that deal with relatively compact bundles of information they call “concepts”; see Hofstadter and the Fluid Analogies Research Group, Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought (New York: Basic Books, 1995).

cate g ori zat i on With this perspective in mind, let me propose that a musical concept has three character istics. First, it is a product of the process of categor ization. A musical category, then, is quite literally where our conceptualization of music begins. Second, a musical concept is an essential part of the means through which we guide present and future actions. These actions thus constitute a sort of indirect evidence for a cognitive structure almost as ephemeral as music itself. Third, a musical concept can be related to other concepts, including concepts associated with bodily states (both physical and emotional), perceptual categor ies (including sound, which, after all, is not necessar ily music), and linguistic constructs. From the perspective provided by this definition, language — in the sense of natural language — is not required in order to have musical concepts. I have, of course, used language to character ize musical categor ies, as well as the conceptual models around which musical categor ies are organized. But we could imagine a listener — perhaps a particularly astute listener, but perhaps one no more skilled than Proust’s M. Swann — who develops a musical category without recourse to language.While language is still nearly indispensable for communicating features of musical concepts and for developing such concepts in r icher contexts, it is not required.58 The notion of concepts independent of language is more than a little provocative, and with consequences that extend beyond music and the general debate on “concept” noted above. Where some authors have excluded music from the conceptual realm (because, by their definition, concepts require language),59 music can join dance, the visual arts, and any of the other nonlinguistic modes of human expression as a properly conceptual activity. This perspective on musical understanding also offers a new way to think about musical syntax. Music theory has traditionally (if not explicitly) character ized syntax in ter ms of relationships between categor ies of musical objects or events. For instance, a perfect authentic cadence, as it is usually defined, consists (in part) of a dominant chord followed by a tonic chord, with bass motion from 5 to 1, and with the soprano concluding an octave above the bass. The definition involves categor ies like scale step (5 and 1), harmonic function (dominant and tonic), voice (bass and soprano), and interval (the octave). Members of these categor ies, when placed in specific relationships (succession and “above”), produce a component of musical syntax (the perfect authentic cadence).60 Musical syntax can also be conceived of 58. The idea that language was not required for musical analysis was one of the ideas behind Hans Keller’s wordless analyses. See Keller, “Wordless Functional Analysis no. 1: Mozart, K. 421,” The Score and I.M.A. Magazine 22 (1958): 56– 64; idem, “The Musical Analysis of Music,” in Essays on Music, ed. Christopher Wintle (Cambr idge: Cambridge University Press, 1994), 126 – 28; idem, “Functional Analysis no. 9a: Mozart’s Piano Sonata in A Minor, K. 310,” in Essays on Music, ed. Christopher Wintle (Cambridge: Cambridge University Press, 1994), 129 – 38. 59. Ray Jackendoff, Consciousness and the Computational Mind (Cambridge, Mass.: MIT Press, 1987); Mark DeBellis, Music and Conceptualization (Cambridge: Cambridge University Press, 1995). 60. It is worth noting that Type 2 categor ies are chiefly involved in this definition: within a given context, something either is or is not an example of 5; something either is or is not a dominant chord; and so on. Such categor ies are typical of the sorts of taxonomies established by formal music theor y. However, note that at least one categor y (for voice) is less explicitly defined and functions more like a Type 1 category. For instance, the soprano is, by convention, the highest sounding voice within a multivoice texture, but in instrumental works it may actually sound well below the range of human sopranos (and thus be a somewhat atypical example of a soprano voice).

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aspe c t s of cog n i t ive st ruc ture as an emergent property of sequences of musical events. Wagner’s treatment of the Leidensmotiv offers one example of this, but the same can be said of most of the musical works that interest us: it is through the development of local levels of syntax that musical works become distinctive, and it is the multivalence of this syntax that makes repeated listening to the same work a rewarding exper ience. Of course, syntactic structure that is shared between musical works is also important, and in most music there is a dialogue between the two analogous to the dialogue between the local and global models relative to which musical categor ies are framed.61 Elaborating this approach to musical syntax is the main goal of chapter 4. There we will see how composers rely on syntactic conventions to provide a framework for the development of more local patter ns of syntax specific to individual works. Before we can more fully investigate the role musical concepts play in understanding and the way musical syntax comes about, we need to consider two important issues. First, there is the issue of how relationships between concepts are established. This will be taken up in chapter 2, which explores how conceptual domains such as music and language are cor related through the process of cross-domain mapping. This process allows structure from one conceptual domain to be brought to bear on another and for relationships among concepts to be established. Second, there is the issue of where conceptual models come from and how they are used to guide reasoning. Chapter 3 shows how concepts and conceptual relationships are combined into conceptual models and how conceptual models are connected together to create theor ies of music.

61. My perspective on musical syntax owes a debt to Eugene Nar mour’s construal of musical style. Narmour distinguishes between intraopus style (which is specific to a g iven work) and extraopus style (which can be seen across a number of works). See Narmour, The Analysis and Cognition of Basic Melodic Structures; and idem, The Analysis and Cognition of Melodic Complexity: The Implication-Realization Model (Chicago: University of Chicago Press, 1992).

chapter two

Q cross-domain mapping

bout a quarter of the way through the Credo of his Pope Marcellus Mass (printed 1567), Giovanni Pierluigi da Palestrina indulges in a marvelous bit of text painting with telling effect. The text Palestr ina sets here is “Qui propter nos homines et propter nostram salutem descendit de cælis” (“Who for us men, and for our salvation, came down from heaven”). As shown in example 2.1, with the first statement of the word “descendit,” each voice begins a scalar descent. Christ’s descent from heaven is thus represented with a cascading fall through musical space, a ser ies of overlapping movements “down” the musical scale. Palestrina’s text painting is a str iking embodiment of the conventional construal of pitch as “high” and “low.” This way of thinking about pitch relations has a venerable tradition. Its basic elements can be seen in Aristoxenus’s descr iption of pitch relations in ter ms of two-dimensional space, which was discussed in the introduction to this volume. Pitches are understood as points in space, and musical intervals are reckoned in ter ms of distances between these points. However, the spatial or ientation crucial to Palestr ina’s text painting — the cor relation of the “up” and “down” of physical space with specific pitch relations, such that a musical scale can “descend”— was seldom used in Greek music theory. As Andrew Barker has noted, the standard Greek for what would now be called “high-pitched” is oxys, which meant “sharp,” “pointed,” or “keen-edged”; its musical opposite was barys, which meant “heavy” (but not, in opposition to oxys, “blunt”).1 Just when “up” and “down” consistently came to be cor related with musical pitch is unclear, but the linkage was in place at least by the beginning of the tenth century, a good six hundred years before Palestrina wrote his Mass. From around the tenth century, thus, musicians in the West began writing about and depicting pitch in ter ms of “high” and “low,” mapping structural relations from the domain of vertically or iented, two-dimensional space onto the domain of music. Perhaps more remarkable than the long tradition of construing pitch relations in terms of “up” and “down” are the ready reminders of how arbitrary a construal it is.

A

1. Andrew Barker, ed., Harmonic and Acoustic Theory (vol. 2 of Greek Musical Writings), Cambridge Readings in the Literature of Music (Cambr idge: Cambridge University Press, 1989), 69, n. 2.

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aspe c t s of cog n i t ive st ruc ture example 2.1 mm. 53– 58

Giovanni Pierluigi da Palestrina, Credo of the Pope Marcellus Mass,

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Cantus tem

de

scén

dit

de cæ

lis.

Altus de scén dit de cæ

lis, de scén

dit

de cæ

lis.

Tenor I tem

de

scén dit de

cæ

lis.

Tenor II de

scén

dit de cæ

lis.

de scén

dit de cæ

lis.

de scén dit de

cæ

lis.

dit de cæ

lis.

Bassus I

Bassus II tem

de scén

Consider, for instance, “up” and “down” on the piano: how can D4 be “above” C4 on the piano when they are both on the same hor izontal plane? Think of playing the two notes on the cello — to play the “higher” D4, we have to move our left hand “down,” so that it is closer to the ground. In fact, there are countless reminders of the artificiality of describing pitch in ter ms of “high” and “low.” And yet Palestr ina’s text painting seems anything but arbitrary— there seems to be an aptness to his portrayal of the descent from heaven that goes beyond mere traditions of depiction. In this chapter, I explore the function of cross-domain mappings of the sort that underlie this small bit of text painting in the Credo of the Pope Marcellus Mass. Cross-domain mapping plays two important roles in musical understanding: first, it provides a way to connect musical concepts with concepts from other domains, including those associated with language; second, it provides a way to ground our descriptions of elusive musical phenomena in concepts der ived from everyday experience. Both of these contr ibute to the establishment of relationships between concepts, relationships that are fundamental to the prospect of theorizing about music. In the first section that follows, I provide an introduction to the theor y of cross-domain mapping as it has been developed in recent work by cognitive linguists and others. This introduction provides a framework for explaining what makes mappings possible and why some mappings are more effective than others. Cross-domain mapping also makes it possible to cor relate the musical domain with others, such as the domain of physical space or of gesture. Under certain circumstances, such cor relations provide the basis for r ich worlds of the imagination.

c ro s s - doma i n map p i ng Correlating musical pitches with vertically or iented, two-dimensional space, for instance, leads quite naturally to an imag inary world in which pitches become things that move through space: the successive notes of a scale g radually descend and ascend; in other passages, some notes leap, while still others fall. Within this imaginary world, each traversal of space has a specific and unmistakable sound — that is, descent sounds one way, ascent another. And this is not something limited to text painting of the sort demonstrated by Palestrina, as any number of cartoon soundtracks confir m. Never mind that actual traversals of space sound nothing like those of the hyperkinetic Roadrunner or the hapless Wile E. Coyote; if the cor relation between the domains is properly established, elements from each will blend together to create novel relationships and elements. In the second section that follows, I descr ibe the process that leads to this sort of blending and show the role conceptual blending plays in text painting and program music.

an introduction to cross-domain mapping Cross-Domain Mapping and Metaphor The theory of cross-domain mapping is a product of a generalized approach to linguistic metaphor first taken by George Lakoff and Mark Johnson in 1980. Perhaps the most common conception of metaphor is of a literary device, a manifestation of the figural use of language to create colorful if imprecise images. Lakoff and Johnson accumulated a substantial body of evidence demonstrating that metaphor was not simply a manifestation of literary creativity but was, in fact, pervasive in everyday discourse.2 As an example, consider the way up and down are used to characterize emotions, consciousness, and health: emotions I’m feeling up. My spir its rose. I’m feeling down. I fell into a depression. My spirits sank. consciousness Get up. I’m up already. He rises early in the mor ning. He fell asleep. health He’s at the peak of health. She’s in top shape. He came down with the flu. Each character ization suggests not a literal representation of the spatial domain implied by the or ientation up–down but, instead, uses our knowledge of physical space to structure our understanding of emotions, consciousness, or health. Based on evidence provided by a large number of similar examples of the 2. George Lakoff and Mark Johnson, Metaphors We Live By (Chicago: University of Chicago Press, 1980). Their work has recently been extended in Lakoff and Johnson, Philosophy in the Flesh: The Embodied Mind and Its Challenge to Western Thought (New York: Basic Books, 1999).

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aspe c t s of cog n i t ive st ruc ture appearance of metaphor ical constructions in everyday discourse, Lakoff and Johnson proposed that metaphor was a basic structure of understanding through which we conceptualize one domain (the target domain, which is typically unfamiliar or abstract) in ter ms of another (the source domain, which is most often familiar and concrete). Further study has provided a wealth of empirical evidence for this proposal and contr ibuted to the development of the field of cognitive linguistics.3 Fundamental to the theor y of metaphor that sprang from Lakoff and Johnson’s work is a distinction between conceptual metaphors and linguistic metaphors. A conceptual metaphor is a cognitive mapping between two different domains; a linguistic metaphor is an expression of such a mapping through language. For instance, the conceptual metaphor state of being is orientation in vertical space maps relationships in physical space onto mental and physical states.4 The cross-domain mapping wrought by this conceptual metaphor then gives rise to innumerable linguistic expressions. Some of these expressions are commonplace, such as “Maxwell seems a bit down today.” Others summon a r ich imagistic world, such as that of John Keats’s “Ode to a Nightingale”: My heart aches, and a drowsy numbness pains My sense, as though of hemlock I had drunk, Or emptied some dull opiate to the drains One minute past, and Lethe-wards had sunk.

Here the descent to the mythical r iver gives a physical cor relate to the narcotic state of the nar rator: the act of sinking is mapped onto a melancholy emotional state. Thus the same conceptual metaphor (state of being is orientation in vertical space) is behind both linguistic metaphors, one commonplace (“Maxwell seems a bit down today”), the other poetic. With respect to music, the “high” and “low” used to descr ibe pitches reflect the conceptual metaphor pitch relationships are relationships in vertical space. This metaphor maps spatial or ientations such as up–down onto the pitch continuum. The mapping yields a system of metaphors replete with possibilities for describing musical pitch. We can speak in ter ms of pitch contour (meaning successions of pitches, which are located at different places in pitch-space), gesture (mean3. For a review of the empir ical evidence supporting metaphor as a basic cognitive process, see Raymond W. Gibbs, Jr., The Poetics of Mind: Figurative Thought, Language, and Understanding (Cambridge: Cambridge University Press, 1994). For discussion of the link between the study of metaphor as a cognitive process and the central concer ns of cognitive linguistics, see George Lakoff, “The Invariance Hypothesis: Is Abstract Reason Based on Image-Schemas?” Cognitive Linguistics 1 (1990): 39– 51. 4. By convention, conceptual metaphors are represented in capital letters. Thus love is a journey designates a conceptual metaphor of general application, and “Love is a journey” a specific linguistic expression based on that metaphor. The conceptual metaphor state of being is orientation in vertical space is a variant of the states are locations conceptual metaphor discussed by George Lakoff and Mark Turner in More Than Cool Reason: A Field Guide to Poetic Metaphor (Chicago: University of Chicago Press, 1989). On cross-domain mapping as a general phenomenon, see Lakoff and Turner, More Than Cool Reason, 4; George Lakoff, “The Contemporar y Theory of Metaphor,” in Metaphor and Thought, 2nd ed., ed. Andrew Ortony (Cambridge: Cambridge University Press, 1993), 202– 51; Gibbs, The Poetics of Mind; and Gilles Fauconnier, Mappings in Thought and Language (Cambridge: Cambridge University Press, 1997).

c ro s s - doma i n map p i ng ing successions of pitches with a specific directionality and contour), and musical space (meaning a three- or four-dimensional extension of the basic two-dimensional mapping).5 This system is g iven graphic representation in traditional musical notation: notes that are the result of more rapid vibrations of the sounding medium are placed higher on the page than notes that result from less rapid vibrations (with the exception of sharps and flats). The two-dimensional space of the musical page thus cor relates with the spatial or ientation ascr ibed to pitch.6 The systematic quality that results from mapping spatial or ientations onto the pitch continuum thus leads to an entire vocabulary for descr ibing relationships among pitches that provides a r ich set of possibilities for furthering our conceptualization of music. As common as conceiving of pitches as “high” or “low” seems, not all cultures describe pitch relationships in purely spatial ter ms. As I noted here, Greek theor ists of antiquity used oxys (“sharp” or “pointed”) and barys (“heavy”) to character ize pitches. And traversing histor ical distance is not the only way to discover alter native conceptualizations of pitch relations. Consider three examples in which it is culture, rather than time, that creates distance: 1. Steven Feld’s research has shown that the Kaluli of Papua New Guinea describe melodic intervals with the same ter ms they use to character ize features of waterfalls. For instance, in Kaluli sa means “waterfall,” and a mogan is a still or lightly swirling waterpool; sa-mogan is the flow of a waterfall into a level waterpool beneath it. Sa-mogan is also used to descr ibe a melodic line that descends to a repeated note, the contour of which replicates that of a waterfall flowing into a pool. In contrast, there are no specific names for ascending intervals, which nonetheless do occur in Kaluli song.7 Behind this account of musical intervals is the conceptual metaphor pitch relationships are waterfall characteristics, which provides the basis for a r ich set of descriptive terms that capture some aspects of melody but not others. 2. In Bali and Java pitches are conceived not as “high” and “low” but as “small” and “large.”8 Here the conceptual metaphor is pitch relationships are relationships of physical size, a mapping that accurately 5. For further discussion of mappings between the spatial and pitch domains, see Arnie Walter Cox, “The Metaphor ic Logic of Musical Motion and Space” (Ph.D. diss., University of Oregon, 1999). 6. It is worth noting that the spatial domain of the musical page is itself metaphor ical, since the way the page is or iented in physical space — that is, whether it is propped on a music stand or lying flat on a table, turned right side up or upside down — does not change what we regard as the top and bottom of the page. Two factors, each independent of the actual or ientation of the page in physical space, help establish the spatial domain of the page: the conventional or ientation of the symbols on the page (either “rightside up” or “upside down”) and the relative distance of the symbols on the page from the reader. Rightside up symbols that are farthest from the reader are at the “top” of the page; rightside up symbols that are nearest the reader are at the “bottom” of the page. 7. Steven Feld, “Flow Like a Waterfall: The Metaphors of Kaluli Musical Theory,” Yearbook for Traditional Music 13 (1981): 30 – 31. 8. Personal communication from Benjamin Br inner, 8 July 1997. See also Wim van Zanten, “The Tone Mater ial of the Kacapi in Tembang Sunda in West Java,” Ethnomusicology 30 (1986): 85.

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aspe c t s of cog n i t ive st ruc ture reflects the nor ms of acoustic production: small things typically vibrate more rapidly than large things. This acoustic fact is represented throughout the numerous parts of the gamelan, the collection of instruments central to the musical practice of Bali and Java. 3. The Suyá of the Amazon basin do not have an extensive vocabulary for describing pitch relationships. When they are descr ibed, however, it is in terms of age: pitches are conceived not as “high” and “low” but as “young” and “old.” The conceptual metaphor that guides this mapping is pitch relationships are age relationships, which accurately reflects the Suyá’s beliefs that the pitch of the voice becomes deeper with age.9 With each of these conceptions of pitch relationships it is easy to focus on what they lack rather than what they offer. That is, it is natural (if not quite excusable) to reckon difference in somewhat chauvinistic terms: that the Kaluli do not have terms to describe ascending intervals, where we do; that the way pitch relationships are characterized in Bali and Java does not transfer into graphic representations with the same ease as do “high” and “low.” It has to be remembered, however, that mapping “high” and “low” onto music has its own limitations: “high” and “low” cannot reflect the subtle play of flowing water, nor do they provide much of an explanation for how acoustic features correlate with pitch relationships. Such differences show that each mapping between domains makes some conceptualizations possible, while it disables others.

Image Schema Theory The variety of conceptual metaphors used to character ize pitch relations leads to the question of the ultimate g rounding of the process of cross-domain mapping. Even if we grant that we understand a target domain (such as pitch relationships) in ter ms of a source domain (such as or ientation in vertical space), how is it that we understand the source domain in the first place? Mark Johnson answered this question by proposing that meaning was grounded in repeated patter ns of bodily experience.10 These patter ns give rise to what Johnson called image schemata, which provide the basis for the concepts and relationships essential to metaphor. An image schema is a dynamic cognitive construct that functions somewhat like the abstract structure of an image and thereby connects together a vast range of different experiences that manifest this same recurring structure.11 Image schemata are by no means exclusively visual — the idea of an image is simply a way of captur ing the organization infer red from patter ns in behavior and concept for mation. As one example of an image schema, consider the verticality schema, which might be summar ized by a diagram of the sort given in figure 2.1.We grasp this structure repeatedly in thousands of perceptions and activities that we exper ience every day. Typical of these are the exper iences of perceiving a tree, our felt sense of standing upr ight, the activity of climbing stairs, forming a mental image of a flagpole, and 9. Anthony Seeger, Why Suyá Sing: A Musical Anthropology of an Amazonian People (Cambridge: Cambridge University Press, 1987), 100 – 02. 10. Mark Johnson, The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason (Chicago: University of Chicago Press, 1987). 11. Johnson, The Body in the Mind, 2.

c ro s s - doma i n map p i ng

figure 2.1 Diagram of the verticality schema

watching the level of water rise in the bathtub. The verticality schema is the abstract structure of the verticality experiences, images, and perceptions. Our concept of verticality is based on this schema, and this concept is in turn invoked by the various conceptual metaphors that use vertical space as a source domain through which to structure such target domains as emotions, consciousness, health, and musical pitch. By definition, image schemata are preconceptual: they are not concepts, but they provide the fundamental structure upon which concepts are based. In consequence, it is important to emphasize that any diagram used to illustrate an image schema is intended to represent the key structural features and inter nal relations of the schema; it is not meant to summon a r ich image or mental picture that we somehow have “in mind” and use actively to structure our thought. More directly, whatever actually occupies our thoughts is not, by definition, an image schema. We can conceive of image schemata, just as we can conceive of any of a number of nonconceptual or preconceptual cognitive processes. We can also note general patter ns in the way concepts are structured, which can be attr ibuted to image schemata. However, there are, by definition, no “image-schema concepts.” The relationship between the verticality schema and our character ization of musical pitch with reference to the spatial or ientation up–down is fairly immediate: when we make low sounds, our chest resonates; when we make high sounds, our chest no longer resonates in the same way, and the source of the sound seems located nearer our head. The “up” and “down” of musical pitch thus cor relate with the spatial “up” and “down”— the vertical or ientation — of our bodies. The verticality schema offers a straightforward way to explain why we character ize musical pitch in ter ms of high and low even when the actual spatial or ientation of the means through which we produce pitches either does not reinforce the characterization or runs directly counter to it. At present, the image schema remains largely a theoretical construct.Work across a variety of fields, however, has made strong arguments for the importance of such a construct, including that by Leonard Talmy in linguistics, Gerald Edelman in neuroscience, David McNeill in psychology, and Raymond W. Gibbs Jr. and Herbert L. Colston in psycholinguistics.12 Recently, Lawrence Barsalou and his associates have 12. Leonard Talmy, Concept Structuring Systems (vol. 1 of Toward a Cognitive Semantics) (Cambr idge, Mass.: MIT Press, 2000), 409 – 70; Gerald M. Edelman, The Remembered Present: A Biological Theory of Consciousness (New York: Basic Books, 1989), chap. 8; David McNeill, Hand and Mind: What Gestures Reveal about Thought (Chicago: University of Chicago Press, 1992); Raymond W. Gibbs, Jr., and Herbert L. Colston, “The Cognitive Psychological Reality of Image Schemas and Their Transformations,” Cognitive Linguistics 6 (1995): 347 – 78.

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aspe c t s of cog n i t ive st ruc ture developed a comprehensive theory of mental representation based on perceptual symbols (which are analogical structures similar to image schemata) and have begun to provide empir ical work to support the theory.13 Antonio Damasio, working from a neurophysiological perspective, has made compelling arguments for the importance of the body to consciousness and thought.14 Although research on image schemata and similar structures is still preliminary, it is also highly promising and offers some of the best prospects for solving some of the problems of the relationship between mind and body that have dogged cognitive research throughout this century.

The Invariance Pr inciple The theory of image schemata provides a way to explain how conceptual metaphors are grounded. It does not, by itself, explain why some conceptual metaphors seem intuitively better than others. For instance, the conceptual metaphor pitches are fruit could provide the grounding for such expressions as “You must play the first note more like an apple, the second more like a banana.” Although such mappings are possible, they are certainly not common. Pitches and fruits just do not seem to be a good match. To account for why some metaphor ical mappings are more effective than others, George Lakoff and Mark Turner proposed that such mappings are not about the imposition of the structure of the source domain on the target domain, but are instead about the establishment of correspondences between the two domains. These cor respondences are not haphazard, but instead preserve the image-schematic structure latent in each domain. Lakoff and Turner for malized this perspective with the Invariance Pr inciple, which Turner states as follows: “In metaphor ic mapping, for those components of the source and target domains deter mined to be involved in the mapping, preserve the image-schematic structure of the target, and import as much image-schematic structure from the source as is consistent with that preservation.”15 According to the Invariance Pr inciple, mapping the spatial or ientation 13. Lawrence W. Barsalou,Wenchi Yeh, Barbara J. Luka, Karen L. Olseth, Kelly S. Mix, and Ling-Ling Wu, “Concepts and Meaning,” in Chicago Linguistics Society 29: Papers from the Parasession on the Correspondence of Conceptual, Semantic, and Grammatical Representations, ed. Kathar ine Beals, Gina Cooke, David Kathman, Sotaro Kita, Karl-Er ik McCullough, and David Testen (Chicago: University of Chicago, Chicago Linguistics Society, 1993), 23– 61; Lawrence W. Barsalou, Karen Olseth Solomon, and Ling-Ling Wu, “Perceptual Simulation in Conceptual Tasks,” in Cultural, Psychological, and Typological Issues in Cognitive Linguistics: Selected Papers of the Bi-Annual ICLA Meeting in Albuquerque, July 1995, ed. Masako K. Hiraga, Chris Sinha, and Sher man Wilcox (Amsterdam: John Benjamins, 1999), 209– 28; Lawrence W. Barsalou, “Perceptual Symbol Systems,” Behavioral and Brain Sciences 22 (1999): 577 – 609. 14. Antonio R. Damasio, The Feeling of What Happens: Body and Emotion in the Making of Consciousness (New York: Harcourt Brace, 1999), chaps. 5 and 6. 15. Mark Turner, “Aspects of the Invariance Hypothesis,” Cognitive Linguistics 1 (1990): 254. For additional wr itings on the Invariance Pr inciple (which at first was called the Invariance Hypothesis), see Lakoff, “The Invariance Hypothesis”; Mark Turner, “An Image-Schematic Constraint on Metaphor,” in Conceptualizations and Mental Processing in Language, ed. Richard A. Geiger and Brygida Rudzka-Ostyn, Cognitive Linguistics Research, 3 (Berlin: Mouton de Gruyter, 1993), 291– 306; and Mark Turner, The Literary Mind (New York: Oxford University Press, 1996), chap. 3. A preliminary discussion of a similar sort of topographical invariance, with applications to music, can

c ro s s - doma i n map p i ng up– down onto pitch works because of correspondences between the image-schematic structure of components of the spatial and acoustical domains. Both space and the frequency spectrum are continua that can be divided into discontinuous elements. In the spatial domain, division of the continuum results in points; in the acoustic domain, it results in pitches. Mapping up–down onto pitch allows us to import the concrete relationships through which we understand physical space into the domain of music and thereby provide a coherent account of relationships between musical pitches. Mapping various fruits onto musical pitches works less well because fruit does not (in any ordinary way) constitute a continuum. To employ this mapping is to highlight instead both the discontinuity among musical pitches and how they are unlike one another (an emphasis on difference suggested by the idiomatic phrase “like apples and oranges”).

Cross-Domain Mapping and Conceptual Models According to cur rent theory, cross-domain mappings are grounded in repeated patterns of embodied exper ience called image schemata. These schemata provide the basic structure employed in the mappings: the verticality schema is thus fundamental to our understanding of two- or three-dimensional spaces as having directionality and of musical pitch as “high” and “low.” Image schemata also constrain the possibilities for mapping between two domains, a constraint reflected in the Invariance Pr inciple. Because the verticality schema can be applied to both the spatial and the musical domains, we can use our understanding of the for mer to structure our understanding of the latter. It remains to be explained why one mapping would be preferred over another — why, for instance, we tend to descr ibe pitch relations in ter ms of “high” and “low” rather than “small” and “large.” On the f ace of it, both of these mappings are equally viable. Both draw on aspects of our embodied exper ience: on the one hand, countless exper iences with the seeming or igin of our own voices; on the other hand, countless exper iences with the sounds g iven out by physical objects in the world around us. Both mappings allow us to descr ibe musical pitches as elements within a continuum. And each mapping can be easily understood from the perspective provided by the other. For instance, in Camille Saint-Saëns’s Le Carnaval des animaux, the music for the elephant is played by the contrabass (large is low), that for the birds by the flute (small is high).16 Although musicians educated in the West sense the novelty of the mapping, they can nonetheless understand it perfectly well. In a similar f ashion, musicians from Bali and Java, when confronted with Western conventions for notation, have few if any problems translating “small” and “large” into “high” and “low.”17

be found in Peter Gärdenfors, “Semantics, Conceptual Spaces, and the Dimensions of Music,” in Essays on the Philosophy of Music, ed.Veikko Rantala, Lewis Rowell, and Eero Tarasti, Acta Philosophica Fennica, 43 (Helsinki: Philosophical Society of Finland, 1988), 9– 27. 16. Camille Saint-Saëns, Le Carnaval des animaux: Grande fantasie zoologique, ed. Felix Aprahamian (Zurich: Eulenberg, 1974): “L’éléphant” (no. 5), p. 11, “Volière” (no. 10), pp. 23– 27. 17. Personal communication from Sumarsam, 10 April 1998.

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aspe c t s of cog n i t ive st ruc ture The reason we prefer one mapping over another has to do with the global conceptual models we absorb from culture and that supply crucial support for the preferred mapping.18 In the West, the descr iption of pitch relations in ter ms of “up” and “down” arose around the same time musicians began to develop ways of notating polyphonic compositions. These notational systems often relied, either directly or indirectly, on the physical placement of symbols on the page.19 The attr ibution of “high” and “low” to musical pitches is thus cor related with a system of notation that permitted both the visualization and the preservation of musical works. In turn, this notation relied on a global model that made three important assumptions: first, pitches could be regarded as objects that were independent of the sound source that produced them; second, graphical symbols could be used to represent these pitchobjects; and third, the surface on which these symbols appeared was analogous to physical space. In Bali and Java, the perfor mance of music was associated with the rich palette of instruments through which the music was effected. Thus the attr ibution of “small” and “large” to pitches cor related with character istics of the musical instruments intr insic to musical perfor mance. The conception of musical pitches as physical objects relies on a global model that does not, at some fundamental level, disassociate a pitch from the sound source that produces it.20 As noted earlier, the character ization of pitch relations can be infor med by mappings other than “high” and “low” and “small” and “large.” In each case, the basic mapping relies on embodied knowledge and on the cor relation of the musical domain with a more concrete domain. The specific mapping chosen within a tradition of discourse about music reflects not so much absolute musical structure as it does the broader cultural practice within which music and its understanding are embedded: mappings reflect the conceptual models that are important to culture. The cross-domain mappings employed by any theory of music are thus more than simple cur iosities — they are actually key to understanding music as a r ich cultural product that both constructs and is constructed by cultural exper ience.

18. These models and the relationship between global and local models will be discussed in greater detail in the next chapter. 19. With regard to an indirect reliance on physical placement, it was often a part of the pedagogy of daseian notation (developed in the ninth century, apparently with an eye toward accommodating the needs of organum at the fourth) to place “high” notes higher on the page, even though no such discr imination was required by the notation (since it relied str ictly on a limited repertoire of letter-like symbols to indicate different pitches). See Musica et Scolica enchiriadis una cum aliquibus tratatulis adiunctis, ed. Hans Schmid, Veröffentlichungen der Musikhistor ischen Kommission, Bayerische Akademie der Wissenschaften, 3 (Munich: Verlag der Bayerische Akademie der Wissenschaften, 1981); and the Musica enchiriadis and Scolica enchiriadis, ed. Claude V. Palisca, trans. Raymond Er ickson, Music Theory Translation Series (New Haven, Conn.: Yale University Press, 1995). These treatises are cur rently thought to have been wr itten no later than the tenth centur y and possibly as early as the middle of the ninth. For further discussion of the histor y of this notational convention, see Mar ie-Elisabeth Duchez, “La Représentation spatio-verticale du caractère musical grave-aigu et l’élaboration de la notion de hauteur de son dans la conscience musicale occidentale,” Acta musicologica 51 (1979): 54– 73. 20. It should be observed that a disassociation of pitch from sound does not obviate an imageschematic basis for understanding pitch relations. It only bears witness to a reification of pitch after its initial conceptualization.

c ro s s - doma i n map p i ng Cross-Domain Mapping, Music, and Music Theory

pale strina’s text painting

The theory of cross-domain mapping outlined in the preceding discussion provides a relatively simple way to account for the effectiveness of Palestr ina’s text painting. According to this theor y, we use the verticality schema, the product of countless bodily exper iences, to give physical space an “up” and a “down” analogous to the “up” and “down” of our bodies. This orientation is then mapped on to a metaphor ical musical space made up of pitches and the relations (or distances) between them. Pitches that result from more rapid vibrations of the sounding medium are regarded as “higher” than pitches that result from less rapid vibrations of the sounding medium. As each of the voices in Palestrina’s six-part texture takes up the word “descendit,” it begins to “descend” through musical space. The notion of descent summoned by the text is thus given sounding image by a specific ser ies of musical events. Of course, we could also hear (through the ears of a Javanese musician) the pitches growing larger, or hear (through the ears of the Suyá) the pitches g rowing older, or hear (through the ears of a Greek theor ist) the pitches g rowing heavier. Distinct from these ways of hearing, Palestrina’s text painting relies on a conceptual model that character izes pitches as objects in two-dimensional, vertically or iented space, in which “up” and “down” describe specific pitch relations. This model is strongly associated with the conventions of musical notation as developed in the West: as pitches get “lower” in sound, they are also wr itten “lower” on the musical staff. There is an additional reason why Palestrina’s text painting is as convincing as it is, however. The image of descent created by Palestrina relies on more than just the general notion of descent, which could have been evoked in a variety of ways: by a downward leap of a single interval; by a short sequence that alter nated descending thirds with ascending seconds; or through having each voice enter in tur n, beginning with the highest voice and ending with the lowest. The scalar descent chosen by Palestr ina, however, provides a str iking analogue for the descent of our bodies through physical space (when this descent is unaided by artificial means). Such a descent involves a lessening of potential energy and a continuous action in one direction, articulated by the regular transfer of weight from one leg to another.21

21. Most of us find descent — especially scalar descent — well represented by the thought of walking down a staircase, but I think it could be argued that walking down a hillside works as well. The reason is that it is not so much the neat, two-dimensional image of stairs that is operative but the regular transfer of weight from one leg to another. Indirect evidence is provided by a striking anecdote related by John Hockenberry, from a time when he was a reporter for National Public Radio. In order to get to a group of Kurdish refugees on a remote edge of Iraqi Kurdistan dur ing the after math of the 1991 Gulf War, Hockenberry, a paraplegic since 1976, had to abandon his wheelchair temporar ily and r ide on a donkey. He comments on the effect of becoming reacquainted with a non-wheeled mode of transportation through the rhythm of the donkey’s gait: “It was walking, that feeling of groping and climbing and floating on stilts that I had not felt for fifteen years. I had long ago grown to love my own wheels and their special physical grace, and so this clumsy leg walk was not something I missed until the sensation came rushing back through my body from the shoulders of a donkey.” Hockenberry, Moving Violations: War Zones, Wheelchairs, and Declarations of Independence (New York: Hyperion, 1995), 2– 3.

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aspe c t s of cog n i t ive st ruc ture The act of singing a descending scale cor relates well with the basic structure of this event: the relaxation many singers feel as they sing a descending scale matches the lessening of potential energy; the temporary pauses on each note of the scale match the regular transfer of weight, which articulates a physical descent. The text painting of “descendit” is thus supported by our embodied knowledge of descent, as well as by the conventions of ascribing “high” and “low” to musical pitches. In its exploitation and enr ichment of a mapping between the domains of physical space and music, Palestr ina’s text painting also gives us a glimpse into a process of meaning construction. Conventionally, text painting is understood to operate through a crude sort of mimesis: physical descents are represented by musical descents. By contrast, I have argued that hear ing a succession of musical events as a descent is an act that is thoroughly mediated.22 What mimesis there is is highly conditioned by the choice of cross-domain mappings through which discourse about music is structured; in turn, these mappings reflect the global models of a given cultural perspective and histor ical moment. Palestr ina’s text painting is not just woven into this web of meaning construction; it also spins its own threads. Some result from specific features of physical descents summoned by the passage, some from the point within the larger musical and dramatic discourse at which this str iking moment occurs, and some from the sonic attr ibutes that get mapped back onto the notion of physical descent. The meaning constructed is not, in the final analysis, simple or direct but multivalent and contingent, and it reflects the r ich set of correspondences activated by mapping between the two domains.

cross-domain mapping and music theory

Because it provides a way to br ing an integrated system of terms and structural relations to bear on problems of musical understanding, cross-domain mapping plays an important part in theor ies of music. Indeed, every theory of musical organization employs crossdomain mappings of one sort or another. Often, the appeal of such mappings is strong, and the mappings seem intuitively correct (much as “high” and “low” seem intuitively cor rect for the character ization of pitch relations). Further investigation, however, reveals that these mappings are every bit as mediated as those that are less systematically developed. Rudolf Louis and Ludwig Thuille’s character ization of tonality in their Harmonielehre provides a case in point. The relevant passage, which appears at the beginning of the first chapter, runs as follows: The unity within the diversity of all har mony is ensured through the law of tonality. This asserts that any succession of harmonies can become musically understandable only when each (independently appear ing) chord is perceived to be in a specific relationship of dependence with respect to the principal chord that underlies the entire harmonic context. Both melodic and har monic succession require a center, a point of repose, around which everything twists and tur ns. For melodic relationships, this stationary middle point is the tonic note, the Tone, whose central place in the scheme of the scale is made manifest by the melodic motions that we direct away from tonic and 22. This same argument, mutatis mutandis, applies to McClary’s analysis of Robert Johnson’s blues mentioned above in the preface.

c ro s s - doma i n map p i ng then back toward it again. The same role of a fixed middle point and resting place that, within melodic unity, falls to the tonic note, is played, with respect to har mony, by the tonic chord: the consonant triad that has the tonic note as its root.23

The view set forth by this character ization is that musical organization is analogous to that of the physical world. Music consequently obeys laws that are independent of human beings —“tonality” is, as it were, a natural force.24 Musical understanding relies on apprehending the har monic dependencies that reflect these immutable laws. The focal point of these dependencies is the center of the system — either the tonic note or the tonic chord— which acts as both a center of gravity and an axis of symmetry.25 To support this perspective, Louis and Thuille appeal to the empir ical evidence provided by actual melodic and har monic progressions, which they believe show that every properly constructed melody tur ns around a single tonic note, and that every properly constructed har monic progression tur ns around a single tonic chord. Louis and Thuille’s character ization of tonality does a marvelous job of capturing the compelling coherence wrought by well-composed tonal music. Given the evidence of ethnographic and histor ical studies of musical cultures, however, the idea that Western European tonality is a naturally occur ring force seems doubtful, as would be the notion of a science aimed at discovering the laws behind this force. Also implicit in Louis and Thuille’s theory is the concept that tonality exists apart from musical syntax: successions of musical events do not g ive rise to the law of tonality but serve only to provide evidence of its existence. According to this perspective, successions of musical events that do not provide evidence of tonal relations cannot be understood as music. Of course, such a view places rather profound restrictions on what counts as music. Theorizing about music requires that we bring order, even if of a tenuous sort, to an ephemeral and often intang ible domain. Cross-domain mapping aids this process by bringing systems of relationships to bear on the musical domain and by 23. “Die Einheit in der Mannigfaltigkeit aller Har monie wird gewährleistet durch das Gesetz der Tonalität. Dieses sagt aus, daß irgendwelche Folgen von Har monien nur dann musikalisch verständlich wirken können, wenn jeder (selbständig auftretende) Accord in einem bestimmten Verhältnis der Abhängigkeit von einem dem ganzen har monischen Zusammenhang zug runde liegenden Hauptaccord aufgefaßt wird.Wie die melodische Folge, so bedarf auch die Accordfolge eines Centrums, eines ruhenden Pols, um den sich alles ‘dreht und wendet.’ Für die melodischen Beziehungen ist dieser feststehende Mittlepunct die Tonica, der Ton, dessen centrale Stellung im Schema der Tonleiter dadurch zum Ausdruck gebracht wird, daß wir deren melodische Bewegung von ihm ausgehen und zu ihm wieder zurückkehren lassen. Dieselbe Rolle eines fixen Mittle- und Ruhepuncts, die innerhalb der melodischen Einheit der Tonica zufällt, spielt in harmonischer Hinsicht der Tonica-Accord: der consonierende Dreiklang, der Tonica zum Grundton hat.” Rudolf Louis and Ludwig Thuille, Harmonielehre, 7th ed. (Stuttgart: Carl Grüninger Nachf. Ernst Klett, 1920), 7. 24. I should point out that Louis and Thuille are not concer ned with tonality as it might be broadly defined, but with tonality as it is represented in Wester n European music of the eighteenth and nineteenth centur ies. This is made all the more clear by their character ization of tonality in har monic ter ms, something that has limited applicability to a fairly wide range of music cur rently recognized as tonal. 25. In the pages that follow this excer pt, Louis and Thuille explore in greater detail the idea that tonic is at the center of a symmetr ical scheme of pitches and har monies. See Louis and Thuille, Harmonielehre, 8– 10.

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aspe c t s of cog n i t ive st ruc ture correlating r ich, if at times complicated, images with essential musical concepts. Such mappings are a way to both structure our understanding and extend it — indeed, much work in music theory is devoted to explor ing the ramifications of these mappings. Nonetheless, each mapping reflects the cultural values and imperatives relative to which it is framed, not the verities of absolute musical structure. Tonality is not, in a simple way, a centr ic and symmetr ical system, any more than it is a reflection of logic (as Hugo Riemann would have it), psychological energetics (as Ernst Kurth would have it), or gravity (as Arnold Schoenberg would have it).26 Instead, tonality is a way of understanding musical organization. The cross-domain mappings through which notions such as tonality are articulated are not simply essential to theor ies of music; in fact, they constitute what counts as music in the first place.

Summary Cross-domain mapping is a general cognitive process through which we structure an unfamiliar or abstract domain in ter ms of one more familiar or concrete. Crossdomain mapping plays two important roles in musical understanding. First, it provides a way to connect musical concepts with concepts from other domains. As we saw here, pitch relations within the domain of music have been connected with concepts associated with vertical space, waterfalls, physical size, and human aging. Each such mapping made possible systematic accounts of the ways pitches related to one another. Second, cross-domain mapping allows us to g round our descr iptions of elusive musical phenomena in concepts der ived from everyday exper ience, since the structural relations basic to cross-domain mapping have their source in repeated patterns of bodily exper ience — that is, in image schemata. As we have seen, the mappings we use to structure our discourse about music are not accidental but reflect two constraints. One constraint is the Invariance Pr inciple, which proposes that the best cross-domain mappings are those that preserve as much of the image-schematic structure of both target and source domains as possible. The other constraint is provided by the global conceptual models relative to which cross-domain mappings are framed. Taken together, these constraints suggest that cross-domain mappings not only provide a way to structure our understanding of music but also shape our ideas about what we include under the rubric “music.” For an element to count as musical, it must be able to serve as a target for the cross-domain mappings that guide our discourse about music. Because cross-domain mapping offers a way to connect what are often elusive musical concepts with concepts from more concrete domains, and because these connections give rise to integrated systems of terms and relations, cross-domain mapping is essential to our theor izing about music. Indeed, as we shall see in the 26. Hugo Riemann, Musikalische Logik: Hauptzüge der physiologischen und psychologischen Begründung unseres Musiksystems (Leipzig: C. F. Kahnt, 1874); Ernst Kurth, Die Voraussetzungen der theoretischen Harmonik und der tonalen Darstellungssysteme (Bern: Akademische Buchhandlungen von Max Dreschel, 1913); Arnold Schoenberg, Harmonielehre (Leipzig:Verlagseigentum der Universal-Edition, 1911); trans. as Theory of Harmony, by Roy E. Carter (Berkeley: University of Califor nia Press, 1978).

c ro s s - doma i n map p i ng next chapter, the concepts der ived from processes of categor ization and the relations created by cross-domain mapping provide the basic mater ials for music theory.

conceptual blending Palestrina’s text painting relies on our understanding of pitches as “high” and “low” and on our exper iences with physical descents down staircases, slopes, and hillsides to create a vivid aural representation of the text. However, the imaginary world summoned by Palestr ina also extends beyond the immediate bounds of text and music. Using the basic cor relation between text and music as a point of departure, we can enter an imag inary domain in which the pitches to which “descendit” is sung become objects descending through musical space.Within this domain, every physical descent is accompanied by sounds that result from a smooth transition from very rapid to less rapid vibrations of the sounding medium. This extension of Palestr ina’s imaginarium cannot be predicted simply from linking the domain of text with the domain of music. It results instead from blending elements and events from these two domains to create a new one with its own structures and relations, a domain populated by such things as pitch-objects and the sound of descent. It must be admitted that an imaginary domain populated with pitch-objects moving through musical space is a somewhat rarefied one. Even so, the process of conceptual blending through which it comes about is itself exceedingly common. For instance, concepts about humans and concepts about animals are often brought together in children’s stor ies to produce talking animals. Such creatures are powerful devices in storytelling, for they offer nar rative possibilities beyond those offered by characters with only human or animal attr ibutes. In a like fashion, the combination of musical concepts with those from other domains creates possibilities for meaning construction that reach far beyond those of music alone. As an introduction to a methodology for explor ing such conceptual blends in greater detail, let us turn to one of the talking animals from recent literature and discover what he can tell us about the process behind the imaginary world summoned by Palestr ina’s text painting.

Talking Animals and Conceptual Integration Networks The Old Grey Donkey, Eeyore, stood by himself in a thistly cor ner of the forest, his front feet well apart, his head on one side, and thought about things. Sometimes he thought sadly to himself , “Why?” and sometimes he thought, “Wherefore?” and sometimes he thought, “Inasmuch as which?”— and sometimes he didn’t quite know what he was thinking about. So when Winnie-the-Pooh came stumping along, Eeyore was very glad to be able to stop thinking for a while, in order to say “How do you do?” in a gloomy manner to him.27

Thus A. A. Milne introduces a new character into the stor ies he crafted for his son, in this case a character built around a stuffed toy donkey Christopher Robin had 27. A. A. Milne, The World of Pooh: The Complete Winnie-the-Pooh and the House at Pooh Corner, illustrated by E. H. Shepard (New York: E. P. Dutton, 1957), 45– 46.

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aspe c t s of cog n i t ive st ruc ture received as a Chr istmas present. Eeyore is, unquestionably, a donkey, fond of thistles and content to stay outside in all sorts of weather. But Eeyore is also endowed with human character istics: he is able to talk, to be perversely gloomy, to work his own convoluted chains of logic, and, on occasion, to be capable of exquisite irony. In fact, Eeyore is a blend of some of the concepts associated with donkeys and with humans. In order to study conceptual blends such as that represented by Eeyore, the rhetor ician Mark Turner and the linguist Gilles Fauconnier developed the notion of conceptual integration networks (CINs).28 Each CIN consists of at least four circumscr ibed and transitor y domains called mental spaces. Mental spaces temporar ily recruit structure from more-gener ic conceptual domains in response to immediate circumstances and are constantly modified as our thought unfolds.29 For instance, Milne’s sketch of Eeyore sets up two closely related mental spaces. The first is that of the Old Grey Donkey— solitary, graceless, and phlegmatic. The second is that of a somewhat morose and plodding intellect, tangled in its own thoughts and happy enough to leave them behind at the first opportunity for social interaction. Aspects of these two spaces are combined in a third space, producing the character of Eeyore. Turner and Fauconnier use CINs to for malize the relationships between the mental spaces involved in a conceptual blend, to specify what aspects of the input spaces are imported into the blend, and to descr ibe the emergent structure that results from the process of conceptual blending. The CIN for the conceptual blend used by Milne is diagrammed in figure 2.2. Its network involves four interconnected mental spaces, which are shown as circles. Central to the network are two cor related input spaces, the “donkey” space and the “human” space. The solid double-headed ar row linking these two spaces indicates 28. Research on conceptual blending and conceptual integ ration networks is discussed in Gilles Fauconnier and Mark Turner,“Conceptual Projection and Middle Spaces,” UCSD Department of Cognitive Science Technical Report 9401 (San Diego: University of Califor nia, San Diego, 1994); idem, “Blending as a Central Process of Grammar,” in Conceptual Structure, Discourse, and Language [based on papers presented at the First Conceptual Structure, Discourse and Language Conference, San Diego, 1995], ed. Adele E. Goldberg (Stanford, Calif.: Center for the Study of Language and Infor mation, 1996), 113– 30; idem, “Principles of Conceptual Integration,” in Discourse and Cognition: Bridging the Gap: [Second] Conceptual Structure, Discourse, and Language Conference, Buffalo, 1996, ed. Jean-Pier re Koenig (Stanford, Calif.: Center for the Study of Language and Infor mation, 1998), 269 – 83; idem, “Conceptual Integration Networks,” Cognitive Science 22 (1998): 133 – 87; Mark Turner and Gilles Fauconnier, “Conceptual Integration and Formal Expression,” Metaphor and Symbolic Activity 10 (1995): 183 – 204; idem, “Conceptual Integration in Counterfactuals,” in Conceptual Structure, Discourse, and Language, II, ed. JeanPierre Koenig (Stanford: Center for the Study of Language and Infor mation, 1998), 285– 96; Turner, The Literary Mind; Fauconnier, Mappings in Thought and Language; Seana Coulson, Semantic Leaps: Frame-Shifting and Conceptual Blending in Meaning Construction (Cambridge: Cambridge University Press, 2001), 115 – 202. The most comprehensive study of conceptual blending as of this writing is Gilles Fauconnier and Mark Turner, The Way We Think: Conceptual Blending and the Mind’s Hidden Complexities (New York: Basic Books, 2002). 29. The theor y of mental spaces is developed in Gilles Fauconnier, Mental Spaces: Aspects of Meaning Construction in Natural Language, 2nd ed., with a foreword by George Lakoff and Eve Sweetser (Cambridge: Cambridge University Press, 1994); Fauconnier, Mappings in Thought and Language; Gilles Fauconnier and Eve Sweetser, eds., Spaces, Worlds, and Grammar (Chicago: University of Chicago Press, 1996); see also Turner, The Literary Mind.

c ro s s - doma i n map p i ng

Generic space • mapping between beings and beings, traits and traits

Input space

Input space Donkey space • donkey • slow-moving • eats thistles, stays outside in all sorts of weather • four legs, hooves

Human space • person • gloomy disposition • embraces discomfort as natural state • can think and talk

Eeyore space • talking donkey • gloomy, plodding character • clumsy, ill-at-ease

Blended space

figure 2.2 Conceptual integration network (CIN) for the anthropomorphic blend used for A. A. Milne’s Eeyore

that elements within them serve as structural cor relates: person is correlated with donkey, and gloomy disposition is correlated with slow-moving. Guiding the process of mapping between these domains is the generic space, which defines the core crossspace mapping and basic topography for the CIN.30 Throughout this network, beings are mapped onto beings, and character traits onto character traits. Guided by the conceptual framework provided by the gener ic space, structure from each of the input spaces is projected into the fourth space, called the blend, which results in the anthropomorphic character of Eeyore. The mapping is only partial, however, reflecting the limitations imposed by the gener ic space. Since the gener ic space does not map between physical character istics, we do not expect Eeyore to be of human appearance or to be human-sized.31 The dashed ar rows linking the gener ic space to the input spaces, and the input spaces to the blended space, indicate the directions in which structure is projected: 30. The topography of a domain consists of the elements that populate the domain and the relations that hold between them. By definition, all of the domains in a CIN must have a unifor m topography, which is represented in its abstract for m by the gener ic space. The requirement of uniform topography within the cor relational structure of a CIN can be seen as another manifestation of the Invariance Pr inciple discussed earlier in this chapter. 31. Inasmuch as a number of the characters in Milne’s stor ies or iginated as stuffed toys, they are easy to imagine as rather diminutive in size; in fact, this is how they are rendered in E. H. Shepard’s illustrations. In his text, Milne is relatively silent on this matter, although various contextual clues suggest that the “animals” with which he deals are of the stuffed variety.

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aspe c t s of cog n i t ive st ruc ture from the gener ic space to the input spaces, and from the input spaces to the blended space. The arrows are double-headed because, under certain circumstances, structure may also be projected from the blended space back into the input spaces, and from the input spaces back into the gener ic space. The idea of anthropomorphic animals that emerges in the blended space may thus influence the way we think about “regular” animals, leading us to talk to them and act toward them as though they had human character istics. Similarly, our exper iences with actual animals and people give life to the abstractions of the gener ic space. The double-headed ar rows also serve as a reminder of the limitation of all of the diagrams of CINs I shall use: mental spaces are dynamic structures, as are the CINs that are built from them. Thus figure 2.2 represents a sort of analytical snapshot of this particular network, framed with the intent of capturing its essential features, but making no claim to exhausting the possibilities for descr iption. Hints about how the CIN and its spaces may develop can be gleaned from the diagram, but a full account would require a ser ies of such snapshots. Although the diag ram given in figure 2.2 is standard in the literature on mental spaces, it can lead to two misunderstandings. First, since the blend is at the bottom of the diagram, it gives the impression that concepts precipitate down into the blend. Second, the function of the gener ic space can be a bit confusing, since it does not seem to be directly involved in the blend. In the interests of clarifying these points I offer figure 2.3, which represents the essential components of a four-space CIN in a slightly different for mat. Here the gener ic space is properly represented as both the backg round and the foundation for the entire network. The two input spaces are concrete representations of the abstract str ucture represented by the gener ic space, and the conceptual blend is a fur ther projection from these. An important aspect of the topography of CINs is the basic logic established by the gener ic space. For the CIN of figure 2.2, the assumption is that beings visibly manifest their character traits. Old donkeys are slow-moving and balky; morose humans are given to gloomy pronouncements on the state of the world; and Eeyore talks and acts like the clumsy, gloomy character he is. The topography of the network also guides three operations — composition, completion, and elaboration — that produce emergent structure unique to the blend. Composition puts together elements from the input spaces to create new entities in the blended space, yielding the character of Eeyore: although donkeys cannot actually think and talk, and humans do not have four legs or hooves, Eeyore has all these traits. Completion extends the image suggested by the initial mapping from the input spaces, drawing on our backg round knowledge of the circumstances summoned by the CIN. For instance, we know that gloomy characters expect the worst of situations. Eeyore can thus be relied on for solemn pronouncements of impending disaster on even the sunniest of days, to greet each calamity as confir mation of his estimation of the world, and to eat his thistles with little sign of relish. Elaboration is a more extensive operation than completion is; it develops the structure of the blended space by building on the pr inciples and logic evinced by the blend. In effect, the input spaces decrease in importance and the focus is directed toward the rich imaginary possibilities of the blended space. At this point, we can start to wr ite

c ro s s - doma i n map p i ng Blended space

Input spaces

Generic space

figure 2.3

Alternative representation of a four-space CIN

our own stor ies about the Old Grey Donkey.Were we to place Eeyore aloft in an airplane, we could be sure he would profess no enjoyment of the view but would instead focus on the various aeronautical catastrophes that, from his perspective, were almost certainly imminent. Given Eeyore’s clumsiness and the awkwardness of his hooves, we would be much less likely to imagine him flying the plane, leaving this to the more dexterous animals or to Chr istopher Robin. Although the conceptual blend that yields anthropomorphic animals is important to Milne’s story, it is not the only blend in evidence. Because Eeyore originated as a stuffed animal, he retains some of the character istics of the species. Accordingly, in the story in which he is introduced, he loses his tail only to have it recovered by Winnie-the-Pooh and nailed back on by Christopher Robin, a sequence of events unlikely were he based solely on real donkeys. This points to yet another conceptual blend, in which one of the input spaces is structured around stuffed, rather than real, animals (and one that I shall not pursue in the present discussion). A. A. Milne’s Eeyore and most of the other characters from the Winnie-the-Pooh stories provide clear examples of conceptual blending. As indicated, however, the process of blending is not restricted to children’s stor ies. On the one hand, conceptual blending is also common in everyday discourse. Witness statements such as “The car is being stubbor n today— I just can’t get her to start,” which blends concepts related to the physical properties of inanimate objects and those related to the behavior of humans. On the other hand, conceptual blending also has its place in literature. Consider Proust’s descr iption of one feature of the spr ingtime walks along the “Méséglise way” in Combray: We would leave town by the road which ran along the white fence of M. Swann’s park. Before reaching it we would be met on our way by the scent of his lilac-trees, come out to welcome strangers. From amid the fresh little green hearts of their foliage they raised inquisitively over the fence of the park their plumes of white or mauve

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aspe c t s of cog n i t ive st ruc ture blossoms, which glowed, even in the shade, with the sunlight in which they had bathed.32

Here Proust blends features of the lilac trees with actions of which only animals or humans are capable, thus creating a memorable image that perfectly captures the intense sensual engagement prompted by spring. Conceptual blending is a pervasive and often transparent cognitive process. A given situation or story may involve any number of conceptual blends, as the character of Eeyore— constructed from the attr ibutes of both stuffed and real animals — shows. Each such blend can be descr ibed through a conceptual integ ration network, which per mits a systematic descr iption of specific features of the blend. Finally, the CIN associated with the character of Eeyore can be used to explain why the Old Grey Donkey has some, but not all, of the features of humans, and why we can easily imagine him taking part in some activities but not in others.

Conceptual Blends and Text Painting In the conceptual blends just discussed, the input spaces for each CIN were summoned by language. As Fauconnier has noted, however, mental spaces are very general and are constructed for many cognitive purposes; language is but one way to prompt the constr uction of a mental space.33 Under cer tain circumstances, music can also prompt space construction. In the case of Palestrina’s text painting, the mental space is relatively circumscr ibed and focuses on an orderly progression of pitches that lead resolutely toward a cadence. This space is in cor respondence with that set up by the text, which focuses on Chr ist’s movement from the heavenly to the mundane and the lessening of potential energy associated with physical descents. Correlations between the musical and textual spaces involved in Palestr ina’s text painting set up the CIN shown in figure 2.4. The gener ic space for the CIN is structured around the notion of elements that are in directed relations conceived with respect to a teleological framework.Within the network, motions through physical and musical space are directed motions. As with the conceptual blend associated with the character of Eeyore, the emergent structure of the blended space can be descr ibed in terms of the operations of composition, completion, and elaboration. Composition puts musical pitches together with the act of descent to yield pitch-objects that descend. Composition also associates descent with a specific sound, which actual descents may or may not produce. Completing this image, we might infer that the lower the pitch, the closer it is to the ground and to the mundane.We could also infer that, since descent can be given a sound, ascent can also be given a sound. Palestr ina in fact confir ms the latter inference in mm. 92– 93 of the 32. Marcel Proust, Swann’s Way (vol. 1 of Remembrance of Things Past), trans. C. K. Scott Moncr ieff and Terence Kilmartin (New York: Vintage Books, 1981), 147 – 48. Further blends in Proust are discussed in Turner, The Literary Mind, 91– 92, 120 – 23; see also my concluding chapter. 33. Personal communication from Gilles Fauconnier, 8 September 1998. This perspective is also represented, somewhat less explicitly, in Fauconnier and Turner, “Conceptual Integration Networks”; and Fauconnier, Mappings in Thought and Language.

c ro s s - doma i n map p i ng

CIN for Palestrina’s text painting

figure 2.4

Credo, when, as shown in example 2.2, he sets “ascendit” with steadily r ising pitches. Elaborating the blend, we might imagine pitch-objects doing all sorts of things, not just ascending and descending. Something like this is behind Louis and Thuille’s character ization of tonality as a system of forces operating on pitches distributed throughout the field of musical space. The extension of the conceptual blend suggested by mm. 92– 93 of the Credo example 2.2 mm. 92– 94

Giovanni Pierluigi da Palestrina, Credo of the Pope Marcellus Mass,

92

Et

a

scén

dit

in

cæ

lum

Et

a

scén

dit

in

cæ

lum

Et

a

scén

dit

in

cæ

lum,

Et

a

scén

dit

in

cæ

lum

se

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aspe c t s of cog n i t ive st ruc ture notwithstanding, Palestr ina’s text painting is a relatively isolated instance of meaning construction involving music and language. Indeed, text painting is usually regarded as a clearly circumscr ibed compositional technique, most often restricted to a single word or image. Under certain circumstances, however, music and language can combine to create rather more extended possibilities for meaning construction, as is shown by an instance of text painting in Giaches de Wert’s seven-part madrigal “Tirsi morir volea,” first printed in 1581. The text for Wert’s madrigal is from a poem by Giovanni Battista Guar ini that is probably the most popular madr igal text of the late sixteenth century. It recounts a sexual encounter between a shepherd and a nymph.34 The passage relevant to discussion here appears in example 2.3; the text for the entire poem, with the verses that appear in example 2.3 underlined, is as follows: tirsi morir volea

thyrsis wished to die

Tirsi mor ir volea, Gli occhi mirando di colei ch’ adora, Quand’ella, che di lui non men ardea, Li disse: “Ahimè, ben mio, Deh non mor ir ancora Che teco bramo di mor ir anch’ io.”

Thyrsis wished to die, gazing at the eyes of his beloved, when she, whose ardor equaled his, said: “Alas, my love, do not die yet, since I long to die with thee.”

Frenò Tirsi il desio, Ch’ebbe di pur sua vita allor finire, E sentea morte, e non potea mor ire; E mentre il guardo suo fisso tenea Ne’ begli occhi divini, E’ l nettar amoroso indi bevea, La bella Ninfa sua, che già vicini

Thyrsis curbed the desire, which by then had almost ended his life: he felt death near, yet could not die; and while he kept his gaze fixed upon those eyes divine, and drank from thence the nectar of love, his pretty Nymph, who felt

Sentea i messi d’Amore, Disse con occhi languid’ e tremanti: “Mori, cor mio, ch’io moro.” Cui r ispose il Pastore: “Ed io, mia vita, moro.” Così mor iro i fortunati amanti, Di morte sì soave e sì gradita, Che per anco mor ir tornaro in vita.

Love’s heralds near, said with languishing and trembling looks: “Die my heart, for I die.” At which the Shepherd replied: “And I, my life, die.” Thus the happy lovers died a death so sweet and pleasant, that in order to die again, they returned to life.

The text painting beg ins in mm. 31– 32 when the word “tremanti” is set to a written-out or nament (a tr ill or gruppo) in all parts. “Tremanti” (“trembling”) sets up a mental space focused on an intense and partially involuntary physical reaction to stress that produces repeated oscillating motions. The written-out or nament sets up a mental space focused on the rapid alter nation of a “minor chord” with Eb3 in the lowest voice, and a “major chord” with FS4 in the highest (which creates an 34. The context for Guar ini’s poem and Wert’s setting of it have been discussed by Laura Macy in “Speaking of Sex: Metaphor and Performance in the Italian Madrigal,” Journal of Musicology 14 (1996): 1– 34.

Giaches de Wert, “Tirsi morir volea,” mm. 28– 39

example 2.3 28 C

6

7

A

ci

ni

Sen tea i mes

si d’a mo

re,

Dis

se

con oc

chi

5

ci

ni

Sen tea i mes

si d’a mo

re,

Dis

se

con oc

chi

ci

ni

Sen tea i mes

si d’a mo

re,

Dis

se

con oc

chi

ci

ni

Sen tea i mes

si d’a mo

re,

Dis

se

con oc

chi

T

B

31

Mo

ri, cor mio,

ch’io mo ro,

Mo

ri, cor mio,

ch’io mo ro,

Mo

ri, cor mio,

ch’io mo ro,

lan

guid’ e

tre

man

ti:

Cui

lan

guid’ e

tre

man

ti:

lan

guid’ e

tre

man

ti:

Cui

lan

guid’ e

tre

man

ti:

Cui

Cui

(continued)

example 2.3

(continued)

34

Mo

ri, cor mio, ch’io mo ro,

Mo

ri, cor mio, ch’io mo ro,

Mo

ri, cor mio, ch’io mo ro,

ris pos’ il Pa sto

re:

Ed io, mia vi ta, mo ro,

Ed io, mia

ris pos’ il Pa sto

re:

Ed io, mia vi ta, mo ro,

Ed io, mia

ris pos’ il Pa sto

re:

Ed io, mia vi ta, mo ro,

Ed io, mia

ris pos’ il Pa sto

re:

Ed io, mia vi ta, mo ro,

Ed io, mia

37

Mo

ri, cor mio, ch’io

Mo

ri, cor mio,

Mo

ri, cor mio,

mo

ro.

Co sì mo rir

no i

Co sì mo rir

no i

ch’io mo ro.

Co sì mo rir

no i

ch’io mo ro.

vi ta mo ro,

Ed io,

mia vi ta, mo ro.

Co sì mo rir

no i

vi ta mo ro,

Ed io,

mia vi ta, mo ro.

Co sì mo rir

no i

vi ta mo ro,

Ed io, mia

ta, mo ro.

Co sì mo rir

no i

vi ta mo ro,

Ed io,

mia vi ta, mo ro.

Co sì mo rir

no i

vi

c ro s s - doma i n map p i ng

Generic space • changes in disposition represent motion

Music space • written out trill in all parts (cross relation, alternation of major and minor triads)

Text space • “tremanti” (“trembling”) intense and partially involuntary physical reaction to stress

Blended space • pitches summon motion • sound-of-trembling

figure 2.5

CIN for mm. 31– 32 of Wert’s “Tirsi morir volea”

augmented-second cross-relation).35 Similar ities between these spaces suggest correlations between their elements: each chord in the musical space cor relates with an end-point of the physical motion summoned by the textual space, and the intensity of the physical reaction cor relates with the rapid alter nation of major and minor chords and the cross-relation between the outer voices. It is the cor relations between these spaces that set up the CIN shown in figure 2.5. The gener ic space for the CIN is structured around the idea that changes of disposition represent motion.36 Physical trembling of the sort summoned by “tremanti” is one instantiation of this notion, and the rapid alter nation of musical materials is another. Once again, the emergent structure of the blend can be descr ibed in terms of the operations of composition, completion, and elaboration. Composition combines musical pitches with specific features of trembling, so that the pitches summon a sense of physical motion even though the sound-source producing them remains relatively fixed: the singers of Wert’s madrigal need not actually tremble when they sing “tremanti.” Composition also suggests that trembling has a sound, 35. At the time Wert’s madrigal appeared, terms such as “minor chord” and “major chord” were not conventionally used to descr ibe simultaneous sonor ities. Writers on music dur ing the per iod preferred to descr ibe sonor ities in ter ms of their intervallic makeup. In the present context, this more accurate terminology is just a bit unwieldy, and I have consequently used somewhat more familiar and concise modern ter ms. I trust their anachronistic application here will not prove unduly confusing. 36. This is analogous to the phi phenomenon noted by Gestalt psychologists. See Kurt Koffka, Principles of Gestalt Psychology (London: Routledge and Kegan Paul, 1935), 179.

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aspe c t s of cog n i t ive st ruc ture even though most actual trembling is done in relative silence. If we complete the pattern suggested by the basic mapping, we can infer that once the physical action stops the sound will stop. Finally, through elaboration we can imagine that successions of restricted groups of pitch mater ials could depict intense physical actions more complex than trembling, perhaps even extending to the interaction of physical bodies. Although the elaboration of a blended space is often left to our imagination, at times it may be explicitly developed. This is indeed what Wert does in the measures immediately following the setting of “tremanti.” Here are some of the salient features of the music of mm.33 – 38: • Starting with the pickup to m.33, the women’s and men’s voices engage in a rapid alter nation of entrances. • The beginnings and endings of the entrances are elided, so that the singing is seamless. • The spacing between entrances is gradually compressed, culminating in the joining of men’s and women’s voices in mm.37 – 38; in fact, this is the first time in the madr igal that the two vocal groups sing together. • The setting is almost entirely homophonic within each group of voices. • The har monic mater ial is highly restricted, consisting almost entirely of triadic sonor ities built on G, D, and F. • In m. 38, the music breaks off, and there is a half measure of silence. The alter nation of restricted groups of pitch mater ial, the charged interaction of the vocal groups, the sudden breaking off of the voices in m.38, and the context provided by the blend produced by the text painting of “tremanti”— all summon an image of intense physical activity followed by a sudden suspension of that activity. It is an image that gives sounding representation to the sort of death — sexual orgasm — about which the poem obsesses. This image also offers a way to ground the double entendre exploited by Guarini, built on the paradoxical connection between life at its most intense and death. Both sexual climax and death are marked by sharp, nearly immediate contrasts: orgasm followed by quiescence; the clamor of life followed by the silence of death. Wert’s music, building from the common g round shared by sexual climax and death, breathes life into a play of words that, by this point in the sixteenth century, had become a rather common commonplace.37 It is important to emphasize that not all combinations of text and music will yield rewarding conceptual blends. For a blend to occur, there not only needs to be some cor relation between two domains, but the domains must also have a unifor m topography. In some cases — certain strophic songs, for instance — the cor relation between text and music is simply too general to generate a compelling blend. In 37. My inter pretation of connections between sexual climax and death is somewhat different from that offered by Laura Macy. Noting that early physiological accounts saw both sex and death as an emission of spirit, Macy writes that “this link is surely at the bottom of the metaphor ic use of the word death to mean sexual climax” (“Speaking of Sex,” 5).While I would not want to deny the importance of this connection, my argument is that commonalities between the larger physiological processes of both orgasm and death could also serve to ground the metaphor and that Wert’s music provides a musical analogue for these.

c ro s s - doma i n map p i ng other cases — formulaic songs composed for opera or reflecting the more commercial side of popular music — the cor relation between text and music may be so tenuous as to be virtually nonexistent. Also important are the conceptual models that inform the inter pretation of the cor relation between the input spaces for a blend. A careful listener who is nonetheless unaware of the context of Palestr ina’s music, for example, will almost certainly realize that something is going on in the passage cited in example 2.1 but may interpret the music as “sad” or “losing energy.” If conceptual models associated with the act of descent, or with this particular portion of the Mass, are not activated, the listener may get no farther than this. Similarly,Wert’s climactic moment, for a listener who does not understand the text (either for lack of knowledge of Italian or out of innocence of the double entendre), may simply be heard as “exciting.” In both cases, the conceptual blends will remain latent: potential but not actualized opportunities for the construction of meaning. As Wert’s madrigal suggests, conceptual blends involving text and music may be relatively extended. Chapter 6 will consider such blends in greater depth, showing how they develop over the course of entire songs, how the same text set to new music can give rise to two very different songs, and how music alone can elaborate a blend first set up by text and music.

Conceptual Blending and Program Music In theory, conceptual blends may involve mental spaces associated with any domain of thought. Musical domains could thus be cor related not only with domains associated with language but also with physical gesture or color.38 In the following, I would like to consider the conceptual blends that occur when instrumental music is associated with an extra-musical program. Although such programs are almost always invoked through language, the connection between the musical and linguistic domains is much looser, and the concepts that emerge from the blend are somewhat more variable. The generality of such blends also allows them to cover greater expanses of music — in the example with which I am concer ned here, an entire symphony. Ludwig van Beethoven’s Symphony No. 6 in F major, Op. 68 (“Pastorale”) is among the most well-known of instrumental works with which extra-musical programs have been associated. In the case of the Sixth Symphony, this association was aided by the descr iptive titles Beethoven gave individual movements (such as 38. The correlations I refer to here are between the conceptual domains associated with music and with colors or gestures; this fits with my notion of concepts as not necessar ily linguistic. However, I am not thinking of synaesthesia, where stimuli applied to one of the five senses produces responses in one or more of the other senses as well; I view this phenomenon as functionally automatic and thus not involving concepts. Synaesthesia between music and color is common enough to have warranted relatively extensive research, and no end of commentar y. See, for instance, Lawrence E. Marks, The Unity of the Senses: Interrelations among the Modalities (New York: Academic Press, 1978); Wilson Lyle, “Colour and Music: An Introduction,” Music Review 43 (1982): 261– 64; Michael Hurte, Musik, Bild, Bewegung: Theorie und Praxis auditiv-visueller Konvergenzen (Bonn:Verlag für systematische Musikwissenschaft, 1982); and Jonathan W. Bernard, “Messiaen’s Synaesthesia: The Cor respondence between Color and Sound Structure in His Music,” Music Perception 4 (1986): 41– 68.

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aspe c t s of cog n i t ive st ruc ture “Scene by the Brook”). As Richard Will has pointed out, the programmatic aspects of the Sixth Symphony created difficulties for those who sought to give an account of the work, for the simplistic representation of natural sounds seemed in conflict with the received wisdom that Beethoven’s music referred to nothing outside itself.39 Symptomatic of this uneasiness with Beethoven’s program was Donald Francis Tovey’s outr ight rejection of any link between such natural sounds and the music of the Sixth Symphony. Tovey writes, “In the whole symphony there is not a note of which the musical value would be altered if cuckoos and nightingales, and country folk, and thunder and lightning, and the howling and whistling of the wind, were things that had never been named by any man, either in connection with music or with anything else.”40 With the cor relation between the domain of nature and the domain of music sundered, Tovey paves the way to approach the work as “a perfect classical symphony” and to claim for it a place in the pantheon of Beethoven’s works. Nevertheless, Tovey’s analysis of the symphony seems to speak of something other than absolute music. Describing an important moment in the slow movement, he writes, The deep shadow of this remote key of G flat becomes still deeper as C flat, which, changing enhar monically to B natural, swoops round to our or iginal key B flat. At the outset of this wonderful passage the theme was that of the first subject with the murmur of the brook becoming articulately melodious in the clar inet and the bassoon. At the moment when the melody gathers itself up into a sustained phrase and makes its enhar monic modulation, there comes a phenomenon full of deep meaning. From this point nothing is left of the melody but sustained notes and bird-song tr ills; the whole of the rest of the return to the main key is harmonic and rhythmic. In this as everywhere else the movement remains true to type, a perfect expression of the happiness in relaxation.41

Here we have key areas that swoop, clarinets and bassoons that are articulate, and melodies capable of independent motion, all within a movement that expresses the happiness there is to be found in relaxation. At first glance, Tovey’s prose seems to retain the very correlation between the domains of music and nature that he had earlier rejected, and to develop a conceptual blend based on this cor relation. Still present are the murmur of the brook, the bird-song tr ills of melody, and the general atmosphere of the pastoral, all wedded to Beethoven’s music. Closer consideration, however, shows that the cor relation of music and nature cannot explain the structural attr ibutes of the imaginative domain summoned by Tovey. Although nature includes living beings, music does not; at best, music compr ises sounds that occur within a temporal framework. The independent agency implied by Tovey, evident in the articulate and goal-directed entities he imagines, also seems somewhat out of step with the commonplace view of 39. Richard Will, “Time, Morality, and Humanity in Beethoven’s Pastoral Symphony,” Journal of the American Musicological Society 50 (1997): 271– 329. 40. Donald Francis Tovey, Symphonies (vol. 1 of Essays in Musical Analysis) (London: Oxford University Press, 1935), 45. 41. Tovey, Essays in Musical Analysis, 1: 51. The reference is to mm. 78– 85 of the slow movement.

c ro s s - doma i n map p i ng nature as a domain in which events are guided not so much by individual volition as by larger forces working from without. In short, it is one thing to link elements of nature and musical sounds to create a domain in which the cuckoo sings with the timbre of the clar inet and the sound of a brook is summoned by undulating patterns in the str ings. It is rather another to animate musical sounds and to endow them with their own volition. As it tur ns out, Tovey’s inter pretation does not rely on a simple cor relation between music and nature. Instead, Tovey activates a much larger network of mental spaces to produce his inter pretation. Central to this network is one of the most common of conceptual blends, that of anthropomorphism (which played an important role in the blend that produced A. A. Milne’s Eeyore). The basic cor relation that underlies this blend can be seen in statements like “The car is being stubbor n today — I just can’t get her to start.” In this mapping, the domain of inanimate objects is structured by the human domain; more specifically, human being is mapped onto car, and a volitional state proper to humans (stubbornness) is mapped onto the mechanical state of the car (not-starting).42 A blend that exploits this mapping might then attribute additional volitional or emotive states to the vehicle (“I think the car wants to stay home,” “She’s mad because I haven’t changed her oil”), or extend into the nonvehicular domain (“I don’t think the toaster likes me, it keeps burning the bread”). In its most abstract for m, this blend involves two input spaces, as shown in the CIN of figure 2.6. One recruits structure from the human domain, the other from some non-human domain. The cor relation of these two spaces gives r ise to the blended space of anthropomorphism, whose emergent structure reflects the counter part correlations of the input spaces. Within this space, non-human entities become endowed with the character istics and intellects of humans while retaining many of the features that make them distinct from humans. An anthropomorphic car may be stubbor n and sullen, but it will also be able to stay outside year round (even though it may not “like” to do so). The gener ic space for the CIN connects entities with entities and states with states. According to the logic proper to the network, the events that occur within each source domain have causes that follow from the rules that govern the behavior of entities that populate the domain. Stubbornness in the human domain reflects personal idiosyncrasies and may be abetted by exter nal circumstances that render the current situation unsatisfactory. According to conventional wisdom, people are stubborn either because they were born that way or because they are unhappy with the way things are and will not take any action (other than being stubbor n) until things change. Not-starting in the domain of automobile mechanics is caused by electromechanical conditions that are insufficient to initiate or produce sustained combustion. The car will not start because there is something wrong with the engine. It is important to note that, although the gener ic space may have a structure that is strongly image-schematic, generic spaces are often r ich with detail. Generic spaces 42. Note that to ascr ibe a state associated with a living entity to a nonliving entity is not the same thing as to endow the latter with life. The statement “The car won’t start— I think it died” does not entail a belief in animistic vehicles, but only cor relates a particular state associated with living beings (being dead, or being no-longer-alive) with the mechanical state of the car (never-to-start-again).

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aspe c t s of cog n i t ive st ruc ture

Generic space • mapping between entities and entities, states and states

Non-human domain • Non-human entities and events related to them

Human domain • Human entities and events related to them

Anthropomorphic domain • Non-human entities endowed with human characteristics

figure 2.6

CIN for anthropomorphic blend

are not necessar ily primitive or schematic — they only define the basic topography common to all of the spaces in the blend. Tovey activates the mental space of anthropomorphism early in his essay when he writes, “The Pastoral Symphony has the enor mous strength of some one who knows how to relax.”43 Within the blend that results from cor relating the human and musical domains, musical events become actors endowed with their own characteristics and capable of their own acts of volition. Thus the transition that follows the first subject of the opening movement of the symphony “leads in three indolent strides to a second subject which slowly stretches itself out over tonic and dominant as a sort of three-part round.”44 Tovey develops an anthropomor phic perspective on nature more gradually, bringing it to fruition only in his account of the end of the slow movement. “Suddenly for a moment all is silent; we have no ears even for the untir ing brook, and through the silence comes the voice of the nightingale, the quaint rhythmic pipe of the quail, and the syllabic yet impersonal signal of the cuckoo.”45 Here elements of nature (brooks and birds) become actors, each endowed with individual character istics and capable of individual acts of volition. In both cases, the cor relation of human and non-human domains gives rise to imaginative conceptual blends: symphonies that know how to relax, musical passages that str ide, brooks that do not tire, and cuckoos capable of impersonal signals. 43. Tovey, Essays in Musical Analysis, 1: 46. 44. Tovey, Essays in Musical Analysis, 1: 47. 45. Tovey, Essays in Musical Analysis, 1: 52.

c ro s s - doma i n map p i ng

Generic space • anthropomorphic space: non-human entities with human characteristics

Anthropmorphized music • musical entities and events with human characteristics

Anthropomorphized nature • entities and events from nature with human characteristics

Tovey’s interpretive blend • storms with the voices of timpani and double basses; storm climax/trombones; rainbow/oboes

figure 2.7

CIN for Tovey’s analysis of the Beethoven Pastoral Symphony

Construing both music and nature in anthropomorphic ter ms makes it possible for Tovey to connect the two in a further blend, shown in figure 2.7. The gener ic space for this network is the blended space of figure 2.6. One of the input spaces is that of anthropomorphized nature, which includes natural agents who act within and respond to their native environment (“nature”). The other input space is that of anthropomorphized music, which includes musical agents who act within and respond to their native environment (“music”). In the blend, aspects of the input spaces are combined to create unique entities and relations. Here the murmur of a brook becomes an articulate melody for clar inets and bassoons; here Beethoven’s music can be conceived as natural without having been reduced to nature. The three operations that produce emergent structure in the blended space — composition, completion, and elaboration — are all evident in Tovey’s account of the end of the fourth movement: “The stor m moves in grand steps to its climax. This is marked by the entry of the trombones. . . . Then the stor m dies away, until with the last distant mutter ings of the thunder the oboes give a long slow fragment of bright sustained melody on the dominant of F. This has been aptly compared with a rainbow.”46 Composition unites the lives and interests of natural agents and musical agents. In the final twenty measures of the fourth movement, the thunder mutters with the voices of the timpani and double basses, who also prepare the tonality of the closing fifth movement precipitated by the retreat of the stor m. 46. Tovey, Essays in Musical Analysis, 1: 55.

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aspe c t s of cog n i t ive st ruc ture Completion supplies additional structure. Beethoven’s terse title for the fourth movement is “Gewitter, Sturm” (“Thunderstorm, Tempest”), which says nothing of the after math of a stor m. Nonetheless, we know that rainbows often follow stor ms, and so the “bright sustained melody” of the oboes can summon the image of a rainbow, a completion suggested but not necessitated by the input spaces.47 Elaboration develops the blend by pursuing its logic. The stor m, as a magnificent entity, moves with grand steps. The climax of its ter ror and wrath (enacted through musical agents) is marked by the entry of new musical agents (the trombones). As these passions abate, musical agents g radually disappear (a change only implicit in Tovey’s prose) until only a bare few remain. Perhaps most str iking about this elaboration is that a single natural agent (the stor m) appears to be brought fully to life only through a multiplicity of musical agents. Such a genesis, while inexplicable in the natural domain, is fully consonant with the idiosyncrasies of the musical domain. There, individual musical entities (such as movements or entire symphonies) are often understood to emerge from the actions of the subentities (such as themes or tonal areas) that they compr ise. Tovey thus mobilizes a number of mental spaces to provide an account of Beethoven’s symphony. The most active spaces are those that contr ibute to a blend of anthropomorphized natural and musical elements. This blend gives Tovey a way to descr ibe music that seems naturalized but does not reduce to a simple cor relation of natural and musical sounds. Less active, but still important, are spaces involved in blends fundamental to this pr imary network. These include spaces built up from the domain of human entities and events, along with the domains of nature and music. Tovey’s descr iption makes only spar ing use of these subsidiar y blends, since they cannot provide the naturalized account of music that is the goal of his essay. Far in the background is the gener ic space common to anthropomorphic blends, which defines the core cross-space mapping and logic that underlie the entire network.

Summary Conceptual blending is a dynamic process of meaning construction that involves small, interconnected conceptual packets called mental spaces, which temporar ily recruit structure from conceptual domains in response to local conditions. When blending occurs, a portion of the structure from two cor related input spaces is projected into a third, blended space. As part of this process, the operations of composition, completion, and elaboration produce structure within the blend that is not found within either of the input spaces. This structure only becomes possible through the concepts and relations produced by conceptual blending. The str ucture common to the mental spaces within a conceptual integ ration network is reflected in the gener ic space. This space defines the core cross-space mapping and is organized according to a basic logic that remains consistent throughout the network. Generic spaces are not necessar ily pr imitive or image47. This suggestion is also followed by the animators of Walt Disney’s Fantasia, who not only supply a rainbow to accompany this moment in Beethoven’s symphony but integrate it within the multileveled, quasi-mythical story they set to the music.

c ro s s - doma i n map p i ng schematic — they only define the basic topography common to all of the spaces in the blend. In a basic blend, four spaces will be active (although not necessar ily to the same degree): the gener ic space, the input spaces, and the blend. It often will be the case, however, that additional spaces will be activated, to a greater or lesser extent, as the construction of meaning proceeds. In certain passages within Tovey’s account of Beethoven’s Sixth Symphony, as many as six spaces may be active. In addition to the blend, these include mental spaces built up from the domains of music and nature, from the domains of anthropomor phized music and nature, and from the gener ic domain of anthropomorphism. This multiplicity of spaces explains the complexity of Tovey’s account, as well as its inter pretive richness. It also serves to explain the seeming contradiction entailed by Tovey’s desire to deny the programmatic aspect of Beethoven’s symphony while responding to the powerful impressions to which it gives rise. More generally, evidence from conceptual blending lends credence to the idea that music is an independent conceptual domain. As I have shown in my analyses of text painting and program music, musical concepts combine with concepts from other domains to create blended concepts that suggest str iking possibilities for the imagination. More to the point, musical syntax (from the perspective developed in chapter 1) can be seen contr ibuting to the blended concepts associated with Wert’s text painting and Beethoven’s program music. In the for mer,Wert’s deployment of musical mater ials sets the stage for an enactment — both by the voices of the singers and by our imaginations — of the sort of death with which Guar ini’s poem is concerned. As but one example from the latter, Beethoven’s conclusion of the fourth movement and preparation for the fifth (the distant mutter ings of the timpani notwithstanding) provide a moment of contrast and articulation that clearly supports our imagining one process ending (the stor m) and another beg inning (the shepherd’s song of joyful thanksgiving). And musical spaces can infor m our understanding of gener ic spaces: to hear Wert’s musical climax is to get new insight into climax as a general phenomenon, be that climax sexual, cerebral, or even visual; to hear Beethoven’s transition is to get a glimpse of how natural events like stor ms can be thought of not simply as personages but also as processes. Each of these aspects of conceptualizing music will be taken up in more detail in chapter 6, within the context of the analysis of the nineteenth-century Lied. There it will be possible to see, to a greater extent, how processes of cross-domain mapping and conceptual blending construct and contr ibute to our understanding of both music and the world as a whole.

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chapter three

Q conceptual models and theories

s part of her efforts to understand the everyday knowledge with which people make sense of music, the music theor ist Jeanne Bamberger has often asked young children to develop ways to represent familiar melodies or simple rhythmic patter ns. One way Bamberger does this is to have a child ar range a specially constructed set of bells, called Montessor i bells, so that he or she can play a given tune. Bamberger then asks the child to invent instructions so someone else could play the tune on the bells as they’ve been ar ranged. For those who have even a passing acquaintance with music, an encounter with Montessor i bells can be a truly disor ienting exper ience. Developed as part of the mater ials for the Montessor i curriculum, the bells are designed to encourage children’s exploration of sound and music.With this in mind, they are carefully constructed to be identical in appearance: the lowest-sounding bell looks just like the highest-sounding one, as do all those in between. Only by striking each bell with a small mallet can the different pitches of the various bells be discovered. Each bell is attached to a wooden stem mounted on a wooden base so that the bells are physically independent of one another. There is, in consequence, no set ar rangement of the bells, just as there are no visual cues as to their pitch: how the bells might be arranged, whether in casual play or in the perfor mance of some tune, has to be determined by each person who uses them. As a further challenge (or an additional resource), a complete set of Montessor i bells contains duplicates: there are eight bells with white bases, which make up a diatonic scale from C4 to C5, and thirteen bells with brown bases, which make up a chromatic scale from C4 to CS5. Thus for each white-based bell there is one brown-based bell with a matching pitch — but again, just which bells match must be discovered by the user. In the course of her research, Bamberger discovered that children use one of two general strategies when building a tune with the bells. Children following the first strategy ar range the bells in the order in which the pitches occur in the tune. To build the first phrase of “Happy Birthday,” for instance, the bells might be placed one after another to create a bell-path of the sort shown in figure 3.1, with the arrow indicating the order in which the bells are set down. (Note that two G-bells are used, one for each time the pitch G occurs anew in the tune. That is, a separate

A

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conc e p tual mode l s and th e ori e s

G

A

G

C

B

figure 3.1 Bell-path no. 1 for the first phrase of “Happy Birthday” (open bases, white bells; solid bases, brown bells; arrows show direction of play)

bell is not provided to accommodate repeated notes in immediate succession. In this illustration, the second G-bell is taken from the set of brown-based bells.) Playing this much of the tune is a relatively simple matter of retracing the building process and str iking each bell in tur n (with the first bell getting two hits). The spatial arrangement of the bells, then, is in direct cor respondence with the succession of pitches in the first phrase of the tune. Children following the second strategy start by putting the bells in order, typically from low to high. Once this is done, they figure out the sequence in which to strike the bells in order to play the tune. Figure 3.2 illustrates the results of this strategy for the first phrase of “Happy Birthday.” The bells are arranged from low to high (left to r ight); numbers indicate the order in which the bells should be struck, and arrows indicate the direction of motion. (Note that only one G-bell is required by this strategy; however, the path through the bells is considerably more complex.) As figure 3.2 shows, the placement of the bells no longer cor responds to the succession of pitches that make up the tune. The second strategy does not rely on a spatial analogue for the succession of pitches in the tune, as does the first. Compensation for this loss in immediacy is provided by a gain in flexibility: to play a different tune, the child needs simply to discover what new succession of hits will produce the cor rect results — the bells themselves do not need to be reordered. Bamberger calls the representation produced by the first sort of strategy “figural” and that produced by the second “formal.”1 Figural representations highlight the unique “figures” (or groupings of musical mater ials) that make the tune what it is. 1. Jeanne Bamberger, The Mind behind the Musical Ear: How Children Develop Musical Intelligence (Cambridge, Mass.: Harvard University Press, 1991), 24– 26; idem, “Cognitive Issues in the Development of Musically Gifted Children,” in Conceptions of Giftedness, ed. Robert J. Sternberg and Janet E. Davidson (Cambr idge: Cambridge University Press, 1986), 398– 99. In personal cor respondence (20 May 2000), Bamberger notes that for mal strategies, as far as she has seen them among both children and adults, only occur with people who have had some training in music or who play an instrument. Bamberger also observes that “representation” (the ter m I favor here) tends to imply more fully worked-out cognitive processes than a ter m like “description.” Although I respect this distinction (especially where it applies to the activities of young children who may not really be concer ned with “representing” anything), I shall retain “representation” in my discussion, but with the understanding that it applies to a quite general set of cognitive structures. Representation, defined thus, embraces imageschematic constructs, perceptual symbols, concepts, and actions — whatever is necessar y to make realworld phenomena available (to re-present them) to the higher-level cognitive processes associated with theories. For further discussion of this approach to representation, see Mark Turner, “Design for a Theory of Meaning,” in The Nature and Ontogenesis of Meaning, ed.Willis F. Overton and David S. Palermo (Hillsdale, N.J.: Erlbaum Associates, 1994), 91– 108; and Antonio R. Damasio, The Feeling of What Happens: Body and Emotion in the Making of Consciousness (New York: Harcourt Brace, 1999), 320.

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aspe c t s of cog n i t ive st ruc ture

G 1 3 figure 3.2

A 2

B 5

C 4

Bell-path no. 2 for the first phrase of “Happy Birthday”

Formal representations, in contrast, tend to obscure the unique character istics of the tune but situate musical elements within a more general context applicable to any number of tunes. Bamberger’s research suggests that figural representations are among the earliest for med by children. Formal representations develop somewhat later as the child’s sense of how to organize and represent mater ials matures. Bamberger’s primary interest in the distinction between figural and for mal representations was with the developmental changes that led to the transfor mation of the one into the other. Nonetheless, the contrast between these two strategies also points to different ways to construe relationships among musical concepts. That is, figural strategies offer one way to character ize these relationships, and for mal strategies another. Perhaps more important, both remain options even after the passing of childhood, as is shown by the transfor mational networks employed by David Lewin in his analyses of late-nineteenth- and early-twentieth-century music.While Lewin’s networks certainly have their abstract side — they owe much to theor ies of mapping that are employed in for mal algebra — they also offer a way to represent unique relationships among musical events: they are figural as well as for mal.2 These different ways to think about the essential relationships that obtain within what is putatively the same sonic domain (here, the first phrase of “Happy Birthday”) demonstrate the role of two basic cognitive structures— conceptual models and theories — in our understanding of music. Conceptual models, which are the more basic structures, are made up of relatively limited cor relations of concepts and are specific to a given domain. (We caught glimpses of such models in the discussion of categorization in chapter 1 and saw the role they played in cross-domain mapping in chapter 2.) Theories, in contrast, are extended structures that coordinate a number of conceptual models to provide a more comprehensive account of the world.3 Figural 2. See David Lewin, Generalized Musical Intervals and Transformations (New Haven, Conn.:Yale University Press, 1987); and idem, Musical Form and Transformation: Four Analytic Essays (New Haven, Conn.: Yale University Press, 1993). Lewin makes explicit reference to Bamberger’s work in his analysis of Karlheinz Stockhausen’s Klavierstück III; see Lewin, Musical Form and Transformation, 45– 47. I should note that Bamberger’s work is by no means limited to early childhood development, and that she, too, takes the position that figural and for mal strategies are not restricted to developmental stages in childhood. For instance, in dialogues built into The Mind behind the Musical Ear, she attributes figural strateg ies to one college-age interlocutor and for mal strategies to another. 3. As is evident from this initial character ization, “theory,” as I define it, embraces cognitive structures far more modest than those with which moder n scientific theor y is occupied. The connection between such cognitive structures and scientific theory is explored in greater detail in the next section.

conc e p tual mode l s and th e ori e s strategies, on the one hand, rely on one set of conceptual models and lead to one theory of musical organization. Formal strategies, on the other hand, rely on another set of conceptual models and lead to a somewhat different theory of musical organization. Both conceptual models and theor ies are central to our understanding of the world as a whole; however, both often remain implicit. It is only when they are teased out in the course of work such as Bamberger’s, or as the result of deliberate reflection on our thought processes, that either conceptual models or theor ies come to the fore. In this chapter, I explore the structure and function of conceptual models and theor ies and show the part they play in both infor mal and for mal accounts of musical organization. In the first section I examine the role conceptual models and theor ies play in the musical representations of one of Bamberger’s subjects, an eight-year-old boy named Jeff. Jeff ’s encounters with music engage him in a struggle to come to ter ms with basic musical concepts, and they reveal music theory— that is, a theor y specific to music— in the making. In the second section, I show how the cognitive structures demonstrated by Jeff ’s nascent theor ies of music connect with similar structures proposed by researchers in a wide variety of fields, from artificial intelligence and cognitive science to anthropology and ethnomusicology. This will serve to generalize the construal of conceptual models and theor ies beyond Jeff ’s specific situation and lay out some of their additional properties. In the third section, I turn to two of the more influential theor ies of music within the last three centur ies of the Western tradition: the music theory of Jean-Philippe Rameau and that of Heinrich Schenker. My objective is to show how they employ the same basic cognitive structures that can be seen in children’s figural and for mal strategies for tune building.

developing a theory of musical organization Learning to Play “Twinkle” on the Bells Jeanne Bamberger worked with Jeff for about six months in the Children’s Learning Lab at MIT, starting in the fall of 1975.4 She set him the task of building the tune “Hot Cross Buns,” first with the sonic resources provided by a simple computer program and later with the Montessor i bells. After Jeff achieved some facility with these tasks, Bamberger had Jeff concentrate on the tune “Twinkle, Twinkle, Little Star,” using only the Montessor i bells. In consequence, at the point we take up Jeff ’s story he has already lear ned some things about tunes and the properties of the bells, although “Twinkle,” with its comparatively more complex structure, presents new challenges. In what follows, the focus is on the first phrase of “Twinkle” (“Twinkle, twinkle, little star, / How I wonder what you are”; the musical notation is given in ex. 3.1) and on two of the bell-paths Jeff constructed in order to play it.

4. “Jeff ” is a pseudonym adopted by Bamberger to preserve the boy’s anonymity. An extensive account of Bamberger’s work with Jeff is given in chaps. 6– 12 of The Mind behind the Musical Ear.

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aspe c t s of cog n i t ive st ruc ture example 3.1

The first phrase of “Twinkle, Twinkle, Little Star”

Twin kle, twin kle,

lit

tle

star,

How

I

won der

what you are.

In preparation for Jeff ’s work with “Twinkle,” Bamberger had selected eleven bells from the complete Montessor i set and put them out on a table.5 Included were all of the white-based bells (providing a complete C major scale) and three brownbased bells: the C-, E-, and G-bells. Once Jeff had familiar ized himself with the bells, Bamberger proposed that he tr y building “Twinkle.” After beginning with the C-bell, Jeff searched among the available bells until he found one that matched the next pitch of the tune. He placed this bell next to the C-bell, and then played both to re-create the beginning of the tune (that is, the pitches that fit the words “Twinkle, twinkle”). To find the bell for “little,” he once again searched among the available bells, and when he found the r ight one he placed it next in line. He again played what he had assembled of the tune (“Twinkle, twinkle, little”) before returning to the remaining bells to find the one cor responding to the next pitch of the melody.6 Jeff ’s preference was to use the white-based bells first. He turned to the brownbased bells only when there was no white-based bell left that would provide the pitch for which he was looking; this first happens with the recurrence of the note G on the word “star.” As a way of giving a visual representation of the division between the two subphrases (or “figures”) of “Twinkle,” Jeff left a space between the first four bells and the second four bells (marking the first four bells as one group and the second four bells as another). This produced the ar rangement shown in figure 3.3. The result is a figural representation of the tune, with each successive bell cor responding to a successive pitch of “Twinkle.” Performing the tune is simply a matter of beginning at one end of the bell-path and proceeding to the other (but with some bells getting two hits, and others only one). After Jeff had completed his bell-path, Bamberger asked him to come up with instructions so someone else could play “Twinkle” on the bells as he had set them out. Jeff ’s initial solution was quite straightforward: he simply drew eight short vertical lines, with each line cor responding to a bell. The cor responding notation looked something like this: 兩

兩

兩

兩

兩

兩

兩

兩

His intent was that the player should start at the beginning and play straight ahead to the end (mimicking, incidentally, his process of setting up the bell-path), some-

5. Bamberger’s account of Jeff ’s first work with “Twinkle” can be found in The Mind behind the Musical Ear, 183– 92. 6. The strategy of playing through as much of the tune as he had built before searching for the next pitch is one Jeff used throughout the tune-building exercises I discuss here.

conc e p tual mode l s and th e ori e s

C figure 3.3

G

A

G

F

E

D

C

Jeff ’s initial bell-path for the first phrase of “Twinkle, Twinkle”

thing made manifest when, at Bamberger’s prompting, he put in numbers to show the sequence of actions: 兩 1

兩 2

兩 3

兩 4

兩 5

兩 6

兩 7

兩 8

With a bit of additional prompting, Jeff concluded his notation by adding another set of numbers to show how many times each bell was to be struck: 2 兩 1

2 兩 2

2 兩 3

1 兩 4

2 兩 5

2 兩 6

2 兩 7

1 兩 8

With this, Jeff ’s first session with “Twinkle” was complete: he had constructed a bell-path with which he could play the first phrase of the tune, and he had come up with a notation that would allow another child to do the same (once the meaning of the numbers and lines had been explained).7

Conceptual Models and Theor ies in Jeff ’s First Version of “Twinkle” Jeff ’s actions, as he constructs a bell-path for “Twinkle” and then invents a notation for both the path and the actions to be perfor med on it, are based on a number of suppositions: • The pitch-events of the tune are embodied by the bells that reproduce them.8 In this way, each pitch-event (which is invisible and ephemeral) is given visible manifestation by a bell. • Each of the pitch-events of the tune is unique. It follows that there will be a different bell for each pitch-event; Jeff does not, at this point, recognize the pitch equivalence of the two G-bells or of the two C-bells. • The succession of temporal events that make up the tune can be represented through the spatial disposition of the bells. Since this succession is 7. It is worth noting that Jeff ’s notation is tied to his bell-path: were the additional space between the fourth and fifth bells eliminated, his notation would almost assuredly lead to a distortion of the temporal spacing of the pitches of “Twinkle.” 8. By “pitch-event” I mean a pitched sound framed relative to some temporal context (so that it is an “event”). As will be seen, because building the tune involves ar ranging the bells in space, the temporal aspect of pitch-events is almost always conflated with spatial location.

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aspe c t s of cog n i t ive st ruc ture conceived of as linear, the bell-path is likewise linear; similarly, the pause between the two subphrases is represented by a greater amount of space between the fourth and fifth bells. • Playing the tune is a matter of performing actions along a path specially constructed for this tune. These actions are unidirectional — the player starts at one end of the bell-path and proceeds straight through to the other — and mimic the process of building the path. Playing the tune constitutes one large, continuous motion, articulated by the smaller motions of striking each individual bell. These suppositions, the relationships between them, and the way they help guide Jeff ’s actions as he sets up his bell-path can be character ized in ter ms of four sor ts of cognitive constructs: concepts, conceptual models, conceptual domains, and theories. Concepts. Musical concepts, as noted in chapter 1, have the following attr ibutes: they are a product of processes of categorization, they are part of the means through which we guide present and future action, and they are not necessar ily linguistic. The concepts basic to Jeff ’s perspective include (but are not limited to) those associated with pitched sounds, with the individual Montessor i bells, with the pitch-events that make up the first phrase of “Twinkle,” and with the notion of performing the tune (as distinct from, say, listening to the tune). Conceptual models. Conceptual models consist of concepts in specified relationships. Three conceptual models play a prominent role in Jeff ’s figural strategy. The first model cor relates pitch-events and objects. Accordingly, the constituent pitch-events of “Twinkle” are construed as objects that endure even after the acoustic signal has faded away. This perspective is reinforced by the physical and visual evidence provided by the bells. In turn, each bell can stand for a pitch-event, even when it has not been struck.9 The second model translates temporal relationships into spatial relationships. Events separated by equal amounts of time are inter preted as objects separated by equal amounts of space; events separated by unequal amounts of time are inter preted as objects separated by unequal amounts of space. This model infor ms Jeff ’s arrangement of the bells on the table, so that there is a greater space between the two bells that mark the end and the beginning of the two consecutive subphrases (the fourth and fifth bells) than between the bells within each subphrase. The third model links physi-

9. While I believe that the conceptual models I descr ibe here accurately reflect the cognitive structures that guide Jeff ’s actions, they should be generalized only with great caution. Bamberger notes that some children believe that a bell will sound differently if it is moved to another place. Indeed, there is good evidence that Jeff is more concer ned with spatial location than with pitch. For discussion of a particularly revealing moment in his development, see Bamberger, The Mind behind the Musical Ear, 204 – 09. To simplify matters I shall continue to focus on pitch-events (since these ultimately infor m the “meaning” given to any particular location along the bell-path or action-path), with the understanding that the full descr iption of an “event” requires specification of both its temporal and spatial coordinates.

conc e p tual mode l s and th e ori e s cal actions with a sequence of sounds. As a result, “Twinkle” acquires a corporeal dimension to go with its acoustic dimension. Each action produces another of the pitch-events of “Twinkle,” and, just as the pitches of “Twinkle” form a coherent whole, so does the sequence of physical actions.10 Conceptual domains. Each of these conceptual models sets up a conceptual domain. The first model sets up a domain of sound-objects, populated by physical embodiments of ephemeral sonic events. The second model sets up the domain of pitch-space, quite apparent in the ar rangement of bells on the table. As Jeff has constructed it, pitch-space consists of temporal and structural relationships between sound-objects. The third model sets up a domain associated with a practiced sequence of actions, what Bamberger calls a “felt path.”11 It should be noted that these conceptual domains are not completely exclusive of one another: in general, conceptual domains will overlap to the extent that the conceptual models on which they are based share concepts and relationships. Theories. Theories coordinate a number of conceptual models in order to guide inference and reason. In this case, the three conceptual models described above are coordinated by a theory— Jeff ’s theory— of “Twinkle.” According to this theory, a representation of the tune can be constructed by arranging a ser ies of unique sound-producing objects in space in order of their appearance in the tune, producing a unidirectional path that, if traversed with the appropriate actions, will yield a sounding version of the tune. Jeff ’s notation for “Twinkle” is a symbolic manifestation of this theory: each sound-producing object is represented by a separate line.12 The uniqueness of these objects is indicated by the ser ies of numbers that is placed beneath these lines; the actions that will yield the tune are indicated by the numbers that are placed above. There will be more to say about each of these constructs, but first let us see how Jeff ’s theory of “Twinkle” changes as Bamberger alters one aspect of the task of constructing a representation of the tune.

Jeff ’s Second Version of “Twinkle” Jeff continued to work with “Twinkle” for a number of weeks and became quite adept at building the tune according to his first theory. One day, as an outgrowth of a pitch-matching task that she had asked Jeff to do, Bamberger changed the set of 10. In some cases, these physical actions are constitutive of the tune in a way that the ar rangement of the bells is not. For instance, the bell-path gives no clues as to how many times each bell should be hit, which, of course, is an integral part of the action-path. 11. Bamberger, The Mind behind the Musical Ear, 213. 12. My use of “symbol” with respect to Jeff ’s notation is not very heavily freighted — the symbols are at best ad hoc, and under different circumstances Jeff might use quite different symbols to accomplish the same notational goals. However, I do want to say that Jeff ’s notation cor relates with his concepts — that is, the marks he puts down stand as symbols for some of the concepts in ter ms of which he understands “Twinkle.”

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C figure 3.4

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Jeff ’s modified bell-path for the first phrase of “Twinkle, Twinkle”

bells Jeff had to work with by removing the brown-based bells.13 This left Jeff with only one bell for each pitch-type. Jeff built the tune as usual until he came to the place where, in accordance with the strategy based on his first theory, he would find and position the brown-based G-bell. When he could not find the bell, he stopped his work and said, “I need another bell.” Bamberger did not press Jeff further at this point, but a few days later she returned to the task. This time, Jeff decided to look for the needed bell among those he had already arranged in the bell-path. After first trying the C-bell, he moved to the G-bell (second in the bell-path) and discovered that it provided the pitch he was looking for. Jeff eventually was able to build up the entire tune using only the white-based bells, creating the bell-path and action-path shown in figure 3.4.While this ar rangement of the bells is more parsimonious — only six bells are needed instead of eight — the action-path through the bells is more complex, requiring both switchbacks and leaps over intervening bells. As a result, the bell-path and action-path are no longer in simple cor respondence with one another. As before, Bamberger asked Jeff to come up with a notation that would enable someone else to play “Twinkle” on the bells as he had ar ranged them. This time, however, the complexities of the action-path required to play the tune on the new arrangement of bells posed some challenges, and it was only after a number of attempts that Jeff was able to develop the notation shown in figure 3.5. The notation shows two important innovations. First, by means of arrows, Jeff is able to show just how one negotiates the switchbacks and leaps necessary to play “Twinkle.” Second, the numbers now refer to only one thing: the number of hits each bell gets. The ser ial notation Jeff used for his first version of “Twinkle” has been abandoned, since there is no longer a one-to-one mapping of bells to pitches.

Conceptual Models and Theor ies in Jeff ’s Second Version of “Twinkle” While some of the suppositions behind Jeff ’s construction and notation of the second version of “Twinkle” are the same as those for his first version, some are different. Unchanged are the notions that the pitch-events of the tune can be embod-

13. Bamberger did this in part to see if she could move Jeff from a figural representation of the tune toward a for mal representation. For a fuller account of this aspect of Bamberger’s work with Jeff, see The Mind behind the Musical Ear, chap. 10.

conc e p tual mode l s and th e ori e s

figure 3.5 Twinkle”

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Jeff ’s notation for his modified bell-path for the first phrase of “Twinkle,

ied by the bells that reproduce them and that playing the tune is a matter of performing actions along a path in a specially constructed pitch-space. Changed are Jeff ’s ideas about pitches and about the relationship between temporal events and spatial disposition. In a conceptual shift that ultimately had profound implications for Jeff ’s understanding of musical organization (as Bamberger’s further work with Jeff showed), he now recognizes that pitch-events are not entirely unique: some pitches will be repeated over the course of a tune. A given bell can thus serve as a sound-source for more than one pitch-event. This realization has the consequence of loosening the relationship between when pitches happen in the tune and how representatives of these pitches can be disposed in space. As a result, playing “Twinkle” is no longer a matter of following a unidirectional path through pitch-space. Even though time might still be conceived of as moving unifor mly in one direction, the motions needed to play “Twinkle” are no longer unidirectional and ser ial: the player moves forward and backward, sometimes str iking the bells ser ially, sometimes leaping over one or more bells to find the next pitch of the tune. The conceptual shift associated with Jeff ’s changed ideas about pitches, pitchspace, and temporal order is an example of what Douglas Hofstadter calls conceptual slippage. As Hofstadter defines it, conceptual slippage is the context-induced dislodging of one concept by a closely related one, within the mental representation of some situation.14 Here, the context is provided by Bamberger’s removal of the brown-based bells from those Jeff had to work with in constructing “Twinkle.” What has slipped is Jeff ’s concept of a pitch-event — specifically, how pitch-events are unique. Jeff still clearly realizes that the G that comes after the first C of “Twinkle” is different from the G that comes after the first A— after all, they occur at different points in the tune. He now knows, however, that both can be played on the same bell. This in tur n means that the temporal uniqueness of pitch-events will not necessar ily translate into spatial uniqueness: the two distinctly different Gs of the tune can be found in the same place on the bell-path. Jeff ’s concept of pitch-event as a specific pitch in “Twinkle” has been dislodged by a concept of pitch-event as a general type of sonic event that is manifested at a particular point in the temporal progress of “Twinkle.” Because all of the conceptual models through which Jeff structures his under14. Douglas R. Hofstadter and the Fluid Analogies Research Group, Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought (New York: Basic Books, 1995), 198. The idea of conceptual slippage has proven quite important in Hofstadter’s work in that it introduced a level of flexibility and fluidity into the computer programs his group developed, features that were absent from earlier artificial intelligence programs.

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aspe c t s of cog n i t ive st ruc ture standing of “Twinkle” incorporate the concept of pitch, the slippage of this concept cascades through the system. The cor relation between sounds and objects provided by the first conceptual model is now looser than before, and the domain of soundobjects it sets up is populated with gener ic, rather than specific, entities. In consequence, the functional distinction Jeff made between brown-based bells and whitebased bells (preferring to work with the latter first) is no longer necessar y— now there are only bells. The second model, which maps temporal relationships onto spatial relationships, is more profoundly affected. While temporal and spatial events are still connected ( Jeff ’s bell-path still has a beg inning and an end), the independence of temporal succession and the spatial ar rangement of sound-sources is far more evident. Reflecting this, the domain of pitch-space has been reshaped: once pitches are conceived as gener ic entities, they start to have more to do with each other than they do with the specific sounds that make up “Twinkle.” These alterations in the notion of spatial disposition then influence the third conceptual model. While the physical actions that produce “Twinkle” can still be seen as a coherent whole, it is a whole made of a larger number of disparate parts (including switchbacks and leaps). This creates a physical manifestation of the growing separation of the tune from the medium through which it sounds: one can now get lost along the action-path in a way that would have been unlikely with the first bellpath Jeff constructed. As a result of these changes, Jeff ’s theory of “Twinkle” is changed as well. According to this modified theor y, “Twinkle” can be built using various gener ic sound-producing objects in space in the approximate order of their occur rence in the tune. A relatively complex action-path is then imposed on this ar rangement, which, if properly executed, will yield a sounding version of the tune. Again, Jeff ’s notation for “Twinkle” is a symbolic manifestation of this theory: there are no longer unique entities that cor respond to each of the constituent pitches of the tune, and perfor ming the tune involves a ser ies of complex actions. In ter ms of the two basic strategies Bamberger observed, Jeff has begun to move from a figural representation to a for mal one.

The Function and Structure of Theories At this point, it will be useful to pause and consider five features of theories revealed by Jeff ’s two approaches to constructing “Twinkle” on the bells. First, theories serve as a guide for actions, both mental and physical. Each of Jeff ’s theories of “Twinkle” allows him to create an ar rangement of the bells that will enable him to play the tune. Using these theor ies, Jeff would be able to find a way to arrange similar objects — glasses filled with varying amounts of water, marimba bars, pots and pans — so that he could play “Twinkle” on them. Should something change in one of these ar rangements (for instance, if one of the bells was covertly switched for a bell with a different pitch), Jeff would most likely be able to find the problem and suggest ways of remedying it. In order to avoid confusion later, I want to broaden the character ization of this feature and say that theor ies serve as a guide to understanding and reasoning. Although this seems a bit g rand when applied to Jeff ’s situation — after all, Jeff is someone who is much more predisposed to action

conc e p tual mode l s and th e ori e s than to talking about action — it makes clear that the actions with which I am concerned are not of an automatic or unconscious sort but are a manifestation of either implicit or explicit patter ns of reasoning. Second, theories provide answers to conceptual puzzles.When Jeff, using his first theory of “Twinkle,” could not find a brown-based bell to complete the tune, his theory told him that he could not continue building the tune, and he stopped. Of course, this is not a very satisfying answer to the puzzle, not the least because it points to the inadequacy of the theor y as a guide for further actions. Jeff ’s second theory of “Twinkle,” in which the concept of a pitch-event has slipped toward a more gener ic perspective, is able to provide a solution by reinterpreting the function of one of the bells already in the bell-path, thereby permitting him to continue building the tune. Third, theories simplify reality. Jeff does not attempt to make the proportional spacing of the bells replicate the temporal intervals between the pitch-events of the tune — it is enough that there is a somewhat larger space between the bells that end the first subphrase and those that begin the second. Jeff ’s notation (and, presumably, his theory) also do not specify the tempo at which “Twinkle” should be played, how hard the bells should be struck, whether the player should be seated or standing, and so on. Fourth, theories are relatively extended cognitive structures. As analyzed here, both of Jeff ’s theories involve at least three conceptual models, which descr ibe relationships among a number of concepts and which set up conceptual domains. Each conceptual model can operate independently of the others: construing pitches as objects does not necessar ily require arranging the objects in any particular way, nor does it necessar ily involve physical actions perfor med on these objects (to which mental rehearsal by musicians bears testament); temporal successions (particularly those that do not involve music) can be represented spatially without involving pitch-objects, and so on. Theories, however, coordinate such models into systems for inference. The systematic quality of theories (in the sense that they involve coordinated — and thus inter related — conceptual models) is evident in the way the slippage of Jeff ’s concept of pitch-event cascades through his theory of “Twinkle”: it affects each of the conceptual models involved. Fifth, theories are dynamic.When Jeff ’s concept of pitch-event changes, his theory of “Twinkle” changes as well. Theories thus respond to changes in circumstances and (as Bamberger’s further work with Jeff shows quite clearly) can g row even more extensive as they are developed to deal with a broader range of circumstances. Although Jeff ’s efforts to construct and notate bell-paths for playing “Twinkle” give a glimpse into how we structure our understanding of music, the view is limited by the specificity of his situation, which is that of a young boy struggling with basic musical concepts. In order to know what it means to have a theory, and to connect Jeff ’s functional and implicit theor ies with the abstract and explicit theories of writers like Rameau and Schenker, we need to consider in greater depth the nature and function of the cognitive structures — conceptual models and theor ies — basic to our understanding of the world as a whole.

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conceptual models and theories As chapter 1 demonstrated, the last quarter of the twentieth century bore witness to a great deal of research on categor ization — research that fundamentally changed our understanding of the process of categor ization and its role in human cognition. And as shown by chapter 2, at about the same time, work in metaphor theory and cross-domain mapping blossomed, resulting in similar changes to our understanding of the role played by mapping structure from one domain onto another. It does not appear, however, that we will come to regard this time as one in which work on conceptual models and theor ies came to fruition. While much interesting work has been done — work to which I shall refer in the following — it has not converged on broad agreement as to what counts as a conceptual model (or even what such structures should be called), nor has it produced any unified view of what constitutes a theory. Two factors have contr ibuted to this situation. First, the functions we call “the mind” and the organ we call “the brain” are both stagger ingly complex — indeed, Gerald Edelman has called the brain the most complicated mater ial object in the known universe.15 Further, mind and brain are not coextensive in any simple way: mind functions extend at the least to the central nervous system, and much of what the brain does is not directly involved with what we conventionally accept as mind functions.16 Mind and brain thus admit of any number of structural descr iptions, and in consequence there is great diversity in how wr iters have character ized constructs like conceptual models and theor ies. The second factor, which is related to the first, is that researchers have tended to focus either on conceptual-model-like structures or on theor y-like structures, but rarely on both. The advantage of this strategy is that it limits the amount of cognitive structure that has to be explained. The disadvantage is that it makes it difficult to explain how relatively low-level structures like conceptual models coordinate with relatively high-level structures like theor ies. In what follows, I give an account of cognitive structure that begins with concepts and extends through theor ies. In line with my analysis of the cognitive structure behind Jeff ’s strategies for building “Twinkle,” I distinguish among concepts, conceptual models, conceptual domains, and theor ies. I should make clear that I assume humans rarely, if ever, make explicit reference to structures of this sort in the process of reasoning about a g iven situation. Instead, as is evident from Jeff ’s responses to the challenges presented by building tunes with the Montessor i bells, we most typically are completely unaware of things like concepts and conceptual models, no matter how evident they are in our patter ns of reasoning. Concepts, conceptual models, conceptual domains, and theor ies are, by and large, implicit cognitive structures: they can be teased out through exper iment or analysis, but they need 15. Gerald M. Edelman, Bright Air, Brilliant Fire: On the Matter of Mind (New York: Basic Books, 1992), 17. 16. Things get even more complicated when emotions and feelings are factored into our account of cognition, for there is strong evidence that these are both “of the body” and “of the mind.” Antonio Damasio has offered compelling arguments on this point; see in particular Damasio, Descartes’ Error: Emotion, Reason, and the Human Brain (New York: Avon, 1994); and idem, The Feeling of What Happens.

conc e p tual mode l s and th e ori e s not be explicit to be useful to us in reasoning about the world. I also do not want to suggest that these constructs have unitary representations, either cognitively or physiologically. Indeed, recent work indicates that the lines between entities such as concepts, models, domains, and theor ies are more often blurry than clear and that there are no simple neurobiological explanations for any of them. My distinctions are thus pragmatic ones, intended to reflect the different sorts of cognitive work done at different levels of structural complexity and the compass of the conceptual structures that result. In the first subsection that follows, my focus is on conceptual models and their relationships to concepts and conceptual domains. In the second subsection, I turn to theor ies and explore what recent research in anthropology and developmental psychology can tell us about what it means to have a theory.

Conceptual Models

basic features of conceptual models

As I define it here, a conceptual model consists of concepts in specified relationships. To get a better idea what this means, let us return to one of the models used by Jeff in his initial attempts to construct a bell-path for “Twinkle,” the model that translates temporal events into spatial events. The concepts required for the model are event and object. Both of these are very broad Type 1 categor ies: the typical event is something that happens in time; the typical object is something that persists over time. And, as always with this sort of category, there are boundary cases that challenge what is typical: a rainbow is in some respects an event (since it happens only as a result of certain atmospher ic conditions), but, in other respects, an object (since it persists — if briefly — over time). In the model, events and objects are related to one another by a cross-domain mapping between pragmatic construals of time and space, which interprets durations (that is, the amount of time between events) as spatial dispositions (that is, the amount of distance between objects).17 Large units of time are represented by distantly spaced points, small units of time are represented by closely spaced points, and equivalent temporal units get equivalent spacing. This way of interpreting time can be seen in the distr ibution of marks for minutes on the face of an analog clock: marks for five-minute intervals are relatively far apart, marks for one-minute intervals are relatively close together, and equivalent units get equivalent spacing.18 Conceptual models are drawn from two sources. The first, and perhaps most important, is culture, especially as it is represented by the people around us.We learn conceptual models by observing and imitating the actions of others and by abstracting models from the lessons we are taught. Conceptual models are thus part of the shared body of knowledge that constitutes culture. As Naomi Quinn and Dorothy

17. Modern physics, of course, does not retain the clear separation between the categor ies time and space that is necessary for this mapping. 18. The spatial representation of temporal units on the face of an analog clock reflects in part the mechanism that moves the hands at a steady rate across the clock face. Compare this to the face of a sundial, on which the marks for equal units of time are not spaced equally.

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aspe c t s of cog n i t ive st ruc ture Holland put it, culture is “not a people’s customs and artifacts and oral traditions, but what they must know in order to act as they do, make the things they make, and interpret their exper ience in the distinctive way they do.”19 Conceptual models may also be created through cross-domain mapping. The propositions and structure of a model framed relative to one domain are applied to another domain; if the process is successful (if it allows us to structure effectively our knowledge of some aspect of the target domain), a new conceptual model is bor n. Models, once lear ned or created, are stored in memory and called up to organize our understanding of a given set of circumstances. Each of the models Jeff used in his theory of “Twinkle” was lear ned or developed before he attempted to build the tune (even if, as in the case of the model that cor relates pitch-events with objects, it was lear ned only when he worked with “Hot Cross Buns”) and was recalled from memory when needed for the new task. Although there has been wide interest in constructs like conceptual models, there has been an almost equally wide variety of construals of mental models of this sort.20 There is general agreement on two basic features, however. First, conceptual models are of relatively restricted extent — that is, they structure a quite limited portion of our knowledge of the world. Second, conceptual models are abstractions from exper ience — they do not replicate the outside world in all its detail but model

19. Naomi Quinn and Dorothy Holland, “Culture and Cognition,” in Cultural Models in Language and Thought, ed. Dorothy Holland and Naomi Quinn, Cambridge Readings in the Literature of Music (Cambridge: Cambridge University Press, 1987), 4. 20. Analogues for conceptual models, and the relevant literature, include the following. mental models: Philip Nicholas Johnson-Laird, Mental Models: Towards a Cognitive Science of Language, Inference, and Consciousness (Cambridge, Mass.: Harvard University Press, 1983); Lawrence W. Barsalou, Cognitive Psychology: An Overview for Cognitive Scientists (Hillsdale, N.J.: Erlbaum Associates, 1992); Dedre Gentner and Albert L. Stevens, eds., Mental Models (Hillsdale, N.J.: Erlbaum Associates, 1983); Jane Oakhill and Alan Garnham, eds., Mental Models in Cognitive Science: Essays in Honour of Phil Johnson-Laird (East Sussex: Psychology Press, 1996). idealized cognitive models: George Lakoff, Women, Fire, and Dangerous Things: What Categories Reveal about the Mind (Chicago: University of Chicago Press, 1987); Robert N. McCauley, “The Role of Theories in a Theory of Concepts,” in Concepts and Conceptual Development: Ecological and Intellectual Factors in Categorization, ed. Ulric Neisser (Cambr idge: Cambridge University Press, 1987), 288– 309. cultural models: Quinn and Holland, “Culture and Cognition”; Roy G. D’Andrade and Claudia Strauss, eds., Human Motives and Cultural Models, Publications of the Society for Psychological Anthropology (Cambr idge: Cambridge University Press, 1992); Roy G. D’Andrade, The Development of Cognitive Anthropology (Cambridge: Cambridge University Press, 1995); Bradd Shore, Culture in Mind: Cognition, Culture, and the Problem of Meaning (New York: Oxford University Press, 1996). cognitive domains: Ronald W. Langacker, Theoretical Prerequisites and Descriptive Application, vols. 1 and 2 of Foundations of Cognitive Grammar (Stanford, Calif.: Stanford University Press, 1987, 1992). frames: Marvin Minsky,“A Framework for Representing Knowledge,” in The Psychology of Computer Vision, ed. Patrick Henry Winston (New York: McGraw-Hill, 1975), 211– 77; idem, The Society of Mind (New York: Simon and Schuster, 1985); Douglas B. Lenat and R.V. Guha, Building Large Knowledge-Based Systems: Representation and Inference in the Cyc Project (Reading, Mass.: Addison Wesley, 1989); knowledge structures: Robert P. Abelson and John B. Black, “Introduction,” in Knowledge Structures, ed. James A. Galambos, Robert P. Abelson, and John B. Black (Hillsdale, N.J.: Erlbaum Associates, 1986). Needless to say, these constructs are by no means equivalent to each other. However, all involve the basic features I outline for conceptual models.

conc e p tual mode l s and th e ori e s aspects of it as a guide to understanding. Modifying a distinction drawn by Clifford Geertz, these are models for understanding a particular set of circumstances rather than models of the circumstances themselves.21 Conceptual models are thus a very basic and yet abstract construal of how the world is organized — they are examples of how concepts first become useful through being related to other concepts.22 Because we cannot think without thinking in terms of relationships of concepts, conceptual models are part of the warp and woof of our knowledge of the world: they represent the way the world is. However, this is not to say that conceptual models reflect, in a simple way, an objective and unchanging reality, even if they are crucial to the way we construct our reality. In earlier work, I proposed, following George Lakoff, that models of the sort I am concer ned with here were idealized.23 Idealization is a way to account for instances when there is a poor fit between a conceptual model and actual circumstances. For example, the conceptual model that sets up the notion of a soundobject runs into something of an obstacle when it comes to the human voice, since it is difficult to find the physical object that cor relates with vocal sound. Most of the time this difficulty is ignored: confronted with the sounds of the human voice, we continue to think in ter ms of sound-objects. A conceptual model concer ned with sound-objects could thus be regarded as an ideal to which actual circumstances may or may not confor m. I now think it better to regard idealization as belonging to a later stage in conceptualization. As they typically function, conceptual models are immediate and transparent: they represent our working notion of reality. Accounting for why a conceptual model does not fit a given situation belongs to a less immediate level of cognitive structure occupied with reasoning and causal explanation. This is the level of the theory. One job of theories, then, is to explain discrepancies between circumstances and conceptual models, even if this explanation is little more than the recognition that the model works in most, but not all, cases. The distinction reflected in this perspective is one I shall maintain throughout the following: conceptual models are immediate and not consciously evaluative; theories are always evaluative— they provide an inter pretation of circumstances and possible courses of action based on this inter pretation. Conceptual models are a response to, not a simple reflection of , the outside world. They deal with only a small portion of that world and represent its structure 21. Geertz draws his distinction between models without reference to cognitive processing, focusing only (but quite importantly) on how models are used. A “model for” is used to guide physical relationships; a “model of ” is a symbolic representation of a particular situation. See Clifford Geertz, “Religion as a Cultural System,” in Anthropological Approaches to the Study of Religion, ed. Michael Banton (New York: Frederick A. Praeger, 1966), 7– 8.While I assume that conceptual models have a symbolic representation, I do not assume these symbols are necessar ily available for conscious manipulation (that is, they may be what Lawrence Barsalou calls “perceptual symbols,” which were mentioned above in chap. 2). 22. In function and structure, conceptual models bear a resemblance to the very simple, imageschematic stor ies descr ibed by Mark Turner in The Literary Mind (New York: Oxford University Press, 1996), chaps. 2 and 3. Such stor ies may involve little more than a record of the action of throwing a ball but nonetheless are essential to our understanding of the world. 23. Lawrence Zbikowski, “Large-Scale Rhythm and Systems of Grouping” (Ph.D. diss.,Yale University, 1991), chap. 4.

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aspe c t s of cog n i t ive st ruc ture in ways that have more to do with cognitive efficiency than with accuracy. Nonetheless, changes in the structure of the outside world will at times require changes to a conceptual model. As we saw in the preceding discussion, the absence of the brown-based bells caused Jeff ’s concept of a pitch-event to slip, resulting in changes to the conceptual models basic to his theor y of “Twinkle.” On a more local level, biological processes will have a similar, if more incremental, effect on the structure of our conceptual models. For instance, every time we remember something, we strengthen some synaptic connections and weaken others,“re-wiring” our brain on a micro-level and subtly transfor ming the memor y we would seek to recall. Such changes will have an influence, slight but cumulative, on our conceptual models. Conceptual models are thus dynamic at both the global and the local level, although, because of their immediacy, this fluidity is rarely evident.

representing conceptual models

My thinking about conceptual models has been shaped in important ways by research in artificial intelligence from the 1970s and 1980s — in particular, the work of Marvin Minsky and of Roger Schank and Robert Abelson24 — and I find it useful to character ize conceptual models in ter ms of simple propositions linked together to create a very basic system of inference. I thus represented the conceptual models in chapter 1 as a collection of interlinked nodes and shall use similar representations in chapters 4 and 5. I should note, however, that I propose these models, and this way of representing them, much in the spir it of that early work in artificial intelligence: as a place to start a descr iption of the processes basic to reason and inference. The models are generalized, and they are presented in a way that connects with a wide body of research. But they are not meant to represent a true, or even empirically verified, picture of what humans have in their heads when they reason about various situations. This is not to say that there is no empir ical evidence for conceptual models, only that my purpose in this book is to show how conceptual models are used rather than to make an argument for exactly what they compr ise or how they are structured. As I discuss in the concluding chapter, I believe much work has to be done before a detailed picture of the structure and function of conceptual models can be developed.

conceptual models and conceptual domains

In the conceptual model for sound-objects, the concept of a sound is linked with the concept of an object through a process of cross-domain mapping. Elements from the invisible and ephemeral domain of sound are cor related with those from the visible and enduring domain of objects, and structure is mapped between the domains, giving rise to sound-objects. The domains involved in this mapping — the domain of sound and the domain of objects — are broad and relatively gener ic. In compar ison, the domain of sound-objects is rather more specific. I shall call the more specific domains set up by conceptual models conceptual domains. The specificity of conceptual domains is manifested in two ways. First, because

24. Minsky, The Society of Mind; Roger C. Schank and Robert P. Abelson, Scripts, Plans, Goals and Understanding: An Inquiry into Human Knowledge Structures (Hillsdale, N.J.: Erlbaum Associates, 1977).

conc e p tual mode l s and th e ori e s some of the relationships proper to a conceptual domain may not obtain in the more gener ic domain (or domains) from which it descends, the scope of the conceptual domain is more limited: for example, not everything that can be said of sound-objects can be said either of sounds or of objects. Second, conceptual domains are typically associated with specific phenomena or exper iences. The conceptual domain of sound-objects set up by Jeff ’s model pertains to his exper ience with the Montessor i bells and with the task of building a bell-path for “Twinkle.” This particular domain is instantiated by the various bells used to construct the bell-path for “Twinkle,” but it can be expanded to include things whose relationship to sounds or objects is more abstract, such as marks on a page or physical places on a musical instrument. I regard conceptual domains as distinct from mental spaces; again, this is a departure from my earlier work. As descr ibed in chapter 2, mental spaces are complex and transitory sites for meaning construction and for reasoning. Furnishing a mental space requires drawing on a number of coordinated conceptual domains. One way to achieve this coordination is through the recursive application of conceptual models. Through recursion, the structur ing principles that give rise to a conceptual model are subsequently applied to the elements of a conceptual domain or iginally created by the same, or another, conceptual model. For example, consider applying a conceptual model for anthropomor phism to the conceptual model for soundobjects. (Anthropomor phism, it will be recalled from the discussion of anthropomorphic blends in the second part of chapter 2, maps the properties of living beings onto objects.) This application maps the properties of living beings onto soundobjects, yielding a mental space populated with animistic pitches. Admittedly, such a space is fairly fantastic — even those with a steadfast belief in the viability of an organicist inter pretation of pitch structure usually rely on conceptual blends rather than on the rather cur ious idea of animistic pitches — but not entirely dissimilar from mental spaces populated by pitches that obey the laws of classical physics.25 Another way to achieve the coordination of conceptual domains is by linking conceptual models into a system for reasoning about the world — that is, by creating a theory.

Theories When I outlined the structure and function of theories in the preceding discussion, I did so with reference to an eight-year-old boy’s attempts to ar range some rather unusual bells so as to play the first phrase — and only the first phrase — of “Twinkle, Twinkle, Little Star.” But is this really a theory in the way Darwin’s theor y of natural selection is a theory, or in the way Einstein’s special theory of relativity is a theory? Scientific theor ies, viewed from a broad perspective, have the features of theories 25. Organicist construals of pitch relationships are discussed in chap. 7. Early in his career, JeanPhilippe Rameau construed pitch relations in ter ms of Newtonian physics; for a discussion, see Thomas Christensen, Rameau and Musical Thought in the Enlightenment, Cambridge Studies in Music Theory and Analysis, 4 (Cambr idge: Cambridge University Press, 1993), 7– 11.

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aspe c t s of cog n i t ive st ruc ture I outlined above. They serve as a guide for understanding and reasoning, and they provide answers to conceptual puzzles. Thus Darwin’s theory sought to explain (among other things) why finches on various islands of the Galápagos g roup had different-shaped beaks and why similar variations could be observed in other species.26 Scientific theor ies also simplify reality. For instance, Darwin’s theory did not take into account the effect of inheritance on variation: if natural selection were the only process affecting variation, variation should become less with each successive generation until it finally disappears altogether. However, because there is a recombination of parental traits in offspr ing, each successive generation has new variations. Finally, scientific theor ies are extended cognitive structures that are subject to change: Darwinian evolutionary theory was eventually refined to take into account the effect of inheritance, as well as natural selection, on the evolution of species. Despite these similar ities, there are nonetheless significant differences between scientific theor ies and theor ies of the sort that Jeff used in his encounters with “Twinkle.” Jeff ’s theories are of quite limited extent, pertaining only to the way bells or similar objects might be ar ranged to play a particular song, and they have the limited function of guiding his actions within this specific context. Scientific theories, by contrast, attempt to account for as broad a range of phenomena as possible, and they offer predictions that can be proved true or false by any of a number of researchers working independently. These features have contr ibuted to the success of scientific theor ies as a type, a success demonstrated by the incredible explosion of knowledge in the hard sciences over the past two centur ies. It is no wonder that explorations of the structure and function of scientific theor ies generated an extensive literature in the twentieth centur y and that scientific theor ies have become a standard to which all other theor ies are compared. The distance, then, between Jeff ’s theories and scientific theor ies is considerable, enough so that using “theory” for the for mer might seem ill advised. Nonetheless, work by anthropologists and others over the past thirty years has provided evidence that scientific theor ies are but one sort of general theory and that the process of theorizing is both various and omnipresent. More recently, research by developmental psychologists has shown that even very young children make use of theory-like structures to guide their actions. These two lines of research, which I review briefly in the following paragraphs, do not diminish the distance between Jeff ’s theories and those of modern science, but they do suggest that these two types of theory represent points along a continuum rather than discrete entities.

cultural theorie s

The notion of a cultural theor y (as distinct from a scientific theory) came to prominence in the 1960s and reflected a growing aware26. One can see the puzzle that challenged Darwin emerging in his earliest wr itings. After noting, in The Voyage of the Beagle (first published in 1839, three years after the Beagle returned home), the gradation in the sizes of the finches’s beaks, Darwin makes this prescient comment: “Seeing this gradation and diversity of structure in one small, intimately related group of birds, one might really fancy that from an or iginal paucity of birds in this archipelago, one species had been taken and modified for different ends.” Charles Darwin, The Voyage of the Beagle, with an introduction by Leonard Engel (Garden City, N.Y: Doubleday, 1962), 381 (chap. 17).

conc e p tual mode l s and th e ori e s ness among anthropologists that Wester n models for representing knowledge, including those of anthropology, were not always adequate or appropriate for nonWestern cultures. Here are three examples of the kind of knowledge that caused anthropologists and those working in related fields to rethink what was meant by a theory. 1. Research by Brent Berlin and his associates on ethnobotanical classification (mentioned in chapter 1 in connection with the way processes of categor ization were reconceptualized dur ing the 1970s) demonstrated that the taxonomic systems of indigenous cultures could be every bit as complex as those of Wester n biologists. Berlin’s further work has shown that ethnobotanical classification reflects, in great part, the order that is inherent in nature and that it also achieves a measure of comprehensiveness by classifying unknown species through making reference to known species.27 2. For more than a thousand years, long-distance noninstrumental navigation has been practiced in Polynesia and Micronesia. Experienced navigators routinely sail their outr igger canoes up to one hundred fifty miles between islands in an area where less than 0.2 percent of the surface is land. Edwin Hutchins — perhaps uniquely qualified as someone with expertise in navigation, ethnography, and artificial intelligence — has shown that this method of navigation is based on a computational system distinct from (yet comparable to) that of Western navigation.28 3. The cure for snakebite among the Rama Indians of Nicaragua is a complicated affair involving ritual, diet, beliefs in the super natural, and herbal medicines especially prepared by snakebite doctors. For instance, after someone has been bitten, the victim must make sure the snake is killed; if the snake is not killed, the Rama believe the person cannot be cured. While under cure, the patient is placed on a special diet, with foods prepared in a special way; the Rama believe that this is necessar y to avoid endanger ing the lives of other members of his or her household. Although it is difficult to sort out just which aspects of the snakebite cure have medical efficacy and which do not, the cure appears to be reasonably effective, saving the patient over three-fourths of the time.29 One way to account for the stability and efficacy of the knowledge represented by each of these sets of cultural practices is to construe it as organized by a theory (a theory of botanical classification, or navigation, or snakebite cure). In that this knowledge is specific to a particular culture or ethnographic context, anthropolo-

27. Brent Berlin, Ethnobiological Classification: Principles of Categorization of Plants and Animals in Traditional Societies (Princeton, N.J.: Princeton University Press, 1992); idem, “How a Folkbotanical System Can Be Both Natural and Comprehensive: One Maya Indian’s View of the Plant World,” in Folkbiology, ed. Douglas L. Medin and Scott Atran (Cambr idge, Mass.: MIT Press, 1999), 71– 89. 28. Edwin Hutchins, Cognition in the Wild (Cambridge, Mass.: MIT Press, 1995), 65– 93. 29. Franklin O. Loveland, “Snakebite Cure among the Rama Indians of Nicaragua,” in Medical Anthropology, ed. Francis X. Grollig and Harold B. Haley (The Hague: Mouton, 1976), 97.

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aspe c t s of cog n i t ive st ruc ture gists have designated the cor responding theor ies cultural theor ies, folk theor ies, or ethnotheor ies.30 One thing that distinguishes cultural theor ies from scientific theor ies is that scientific theor ies have an explicit tradition of verification: it has to be possible to replicate exper imental results that support the theor y, or the theor y is cast into question.While cultural theor ies clearly have efficacy — the classification of a wealth of plant life, navigation between distant islands, and cure from snakebite all actually occur — they are not subjected to the open and constant scrutiny that marks the modern scientific method. Cultural theor ies, in contrast to scientific theor ies, organize a relatively stable body of knowledge that changes only gradually — and most often imperceptibly.31 Cultural theor ies, as a further manifestation of cultural knowledge, thus both reflect and constitute culture. As I construe them, cultural theor ies need not be explicit; indeed, theories are often manifested as patter ns of behavior rather than as explicit statements descr ibing how a specific situation should be understood or what actions are appropriate for a given set of circumstances.32 This is particularly important for music, for theories of music may be both implicit and nonverbal.33 A glimpse of an implicit and at least partially nonverbal theor y of music was provided by Steven Feld’s research on the Kaluli of Papua New Guinea, which was touched on in chapter 2. Feld showed that Kaluli ter minology centers around waterfall imager y, which yields a number of highly distinctive ways to descr ibe the contour of musical descents. By contrast, there is only a single ter m in Kaluli to descr ibe musical ascents.34 This does not mean that the Kaluli conception of musical ascent is undifferentiated — were an

30. Of course, “ethnotheor y,” as a sort of Third World shadow of “theory,” is not a very comfortable concept: “theory” always remains the pr ivileged ter m. For discussion of the related topic of the relationship between ethnopsychology and psychology, see Cather ine Lutz, “Ethnopsychology Compared to What? Explaining Behavior and Consciousness among the Ifaluk,” in Person, Self, and Experience: Exploring Pacific Ethnopsychologies, ed. Geoffrey M.White and John Kirkpatr ick (Berkeley: University of California Press, 1985), 35– 79. For an illuminating discussion that also bears on this matter, framed with respect to folk models (which have the function I here ascr ibe to theor ies), see Ladislav Holy and Milan Stuchlik, “The Structure of Folk Models,” in The Structure of Folk Models, ed. Ladislav Holy and Milan Stuchlik (London: Academic Press, 1981), 1– 34. 31. Although histor ical evidence suggests that changes in the theor ies (and the cor responding conceptual models) that are constitutive of culture have often been so gradual as to escape notice, the incursion of Wester n commercial and technological culture into traditional societies dur ing the past two decades has accelerated the rate of change markedly — all of the researchers I cite note the effect of this incursion into the cultural practices they study. Further discussion of this point, framed relative to musical practice, is taken up in chap. 5. 32. My construal of cultural theor ies as at least potentially implicit differs from that of Roy D’Andrade, who has proposed that cultural theor ies are always explicit. See D’Andrade, The Development of Cognitive Anthropology, 172– 73. 33. My thinking here follows that of John Blacking, who proposed that implicit theor y embraces both verbal and non-verbal discourse about music. See Blacking, “Music, Culture, and Exper ience,” in Music, Culture, and Experience: Selected Papers of John Blacking, ed. Reginald Byron, with a foreword by Bruno Nettl (Chicago: University of Chicago Press, 1995), 228 – 31. 34. Steven Feld, “Flow Like a Waterfall: The Metaphors of Kaluli Musical Theory,” Yearbook for Traditional Music 13 (1981): 31– 32.

conc e p tual mode l s and th e ori e s ascending melody played improperly, they would be quick to call attention to the mistake— but that, within the broader cultural context relative to which musical concepts are framed, ascents are not pr ivileged and thus require only the barest of descriptive terms.35 In sum, cultural theor ies have the same general features that Jeff ’s theories and scientific theor ies have. They serve as a guide to reasoning and inference, provide answers to conceptual puzzles, and simplify reality. They are extended cognitive structures, and they are subject to change. But cultural theor ies suggest two extensions to the conception of theory that I have outlined thus far. First, theories should be seen as manifestations of cultural knowledge. Jeff ’s theor ies must thus be understood as developed within the context of a larger set of cultural practices, and so should those of modern science. Second, theories can be implicit and to some extent nonverbal.Without a doubt, explicit theor ies are immeasurably important to the advancement of knowledge, for their precepts are available for public debate, discussion, and modification. Even so, implicit theor ies make up a great part of our cultural and pr ivate knowledge, knowledge that becomes visible only when these theories are subjected to challenge or analysis.

theory in very young children

The fact that theor ies are everywhere— in science, in culture, and in our personal construals of the world — suggests that they are basic to human understanding. This perspective has received support from recent research by Alison Gopnik and Andrew Meltzoff, who have shown that children use patter ns of reasoning quite similar to those of scientists to organize their understanding of the world. Focusing on exper imental evidence gathered from studies with nine- and eighteen-month-old children, Gopnik and Meltzoff have demonstrated that children’s understanding of the world replicates the structure and function of scientific theor ies.36 For instance, six-month-old infants do not appear to realize that spatial contact is required to move an object: they assume that if the object moved shortly after they perfor med some action (like kicking their legs), it was this action that caused the object to move. At around eight to ten months, however, infants begin to develop a theor y of action on objects — that is, they appreciate that their actions can affect objects only if they are spatially in contact with those objects. As they grow older, children come to realize that this theory does not work in all circumstances: if an object is out of reach and she is given a toy rake, the one-year-old will use the rake to make contact with the object 35. For other work on implicit theor ies of music, see Simha Arom, African Polyphony and Polyrhythm: Musical Structure and Methodology, trans. Martin Thom, Barbara Tuckett, and Raymond Bond (Cambridge: Cambridge University Press, 1991), 139 – 40; idem, “New Perspectives for the Descr iption of Orally Transmitted Music,” World of Music 23 (1981): 43; James R. Cowdery, The Melodic Tradition of Ireland (Kent, Oh.: Kent State University Press, 1990); and Ruth M. Stone, Let the Inside Be Sweet: The Interpretation of Music Event among the Kpelle of Liberia (Bloomington: Indiana University Press, 1982). 36. Alison Gopnik and Andrew N. Meltzoff, Words, Thoughts, and Theories (Cambridge, Mass.: MIT Press, 1997). Those who have worked with infants and young children will appreciate the cleverness with which the exper iments which produced this data were designed and the r igor with which they were carried out. For a report intended for a more general audience, see Alison Gopnik, Andrew N. Meltzoff, and Patricia K. Kuhl, The Scientist in the Crib: Minds, Brains, and How Children Learn (New York: William Morrow, 1999).

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aspe c t s of cog n i t ive st ruc ture (where the six-month-old might simply wave the rake at random), although this contact alone will not make the object come any closer. By eighteen months of age, children refine the theory of action on objects further still, and, now realizing that just touching the object is not enough, an eighteen-month-old will adjust the rake so that it captures the object cor rectly.37 According to Gopnik and Meltzoff ’s view, infants and young children develop their knowledge much as scientists do. They start with an initial theor y for a particular set of circumstances (the relationship between actions and objects). They conduct a variety of exper iments (reaching out to g rab objects, observing how objects move as a result of their actions). Then they refine and adapt the theor y on the basis of the exper imental results (when touching the object alone does not produce the desired results, for example, infants and young children will modify the theory to acknowledge that spatial contact must be of a specific sort). Indeed, Gopnik and Meltzoff go even further to argue that it is not so much that there is a scientist in the child as it is that there is a child in the scientist: the cognitive role of theories in earliest childhood is the same as the cognitive role of theories at maturity. The strong claim that Gopnik and Meltzoff make in Words, Thoughts, and Theories — that theory (scientific or developmental) is a means of finding truth and that theorizing is an evolutionary adaptation conducive to the survival of the species — gives occasion for pause, if only because each theor y frames “truth” a bit differently.38 Nonetheless, the weaker version of the claim — that the theor ies of children resemble those of scientists — is somewhat more promising. Thomas Kuhn, as part of the central conceptual frame for his essay on thought exper iments, noted that both children and scientists sometimes hold paradoxical views of phenomena and that both lear n when these paradoxes are made evident.39 According to Kuhn’s argument, thought exper iments — which introduce no new evidence and would thus seem to offer no opportunity for lear ning — are one way of making paradoxical views of phenomena evident and thus advancing scientific knowledge. Although only implicit in his discussion, Kuhn appears to consider the thought processes of children to be analogous to those of scientists inasmuch as both exper ience the same sort of “nonempir ical” learning. While we have much to lear n about the cognitive structures that guide the behavior of very young children — it is hardly a pun to say that developmental psychology is still in its infancy — evidence has begun to accumulate in support of the 37. Gopnik and Meltzoff, Words, Thoughts, and Theories, chap. 5. 38. Paul L. Harris offers a somewhat different argument against what Gopnik and Meltzoff call the “theory theory” (that is, the theory that children have theor ies of the world), based on two points: first, that the theor ies of children and lay adults do not count as true theor ies; second, that the pursuit of truth is not what guides the scientist’s day-to-day activities. As is evident from the preceding, I differ from Harris on the first point; however I am in broad agreement with his second point. See Harris, “Thinking by Children and Scientists: False Analogies and Neglected Similar ities,” in Mapping the Mind: Domain Specificity in Cognition and Culture, ed. Lawrence A. Hirschfield and Susan A. Gelman (Cambr idge: Cambridge University Press, 1994), 294 – 315. 39. Thomas S. Kuhn, “A Function for Thought Exper iments,” in The Essential Tension: Selected Studies in Scientific Tradition and Change (Chicago: University of Chicago Press, 1977), 242 – 46.

conc e p tual mode l s and th e ori e s notion that theor ies are a basic structure of human understanding.40 Whether the theories of children are of exactly the same sort as those of modern science remains to be seen; however, it does seem that these two sorts of theories have a similar structure and that they are responses to the same impulse to understand the world.

cognitive theorie s and music theorie s

Based on his work building “Twinkle” with the Montessor i bells, I do not think that there is a strong case to be made for character izing Jeff as a scientist. Jeff is not really involved in a wide-ranging search for knowledge, aided by a protocol of experiment and analysis. Jeff is instead doing his best to meet a fairly specific and, for him, relatively challenging task. He is similar to a scientist, however, in that theory is an important cognitive tool, serving to guide his actions and make the elusive world of sound a bit more comprehensible. On the basis of evidence from anthropology and developmental psychology, Jeff is not alone in using theory in this way, for theor ies are part of the very fabric of human thought. Given this context, the fact that Jeff should have a theory of music, primitive as it may be, is not sur prising. Indeed, we should only be sur prised if we could find no evidence for the sort of cognitive theor ies I have described. Even so, if the distance between Jeff ’s theor ies and those of modern science is considerable, the same can be said of the distance between his theories and those of music theory as a discipline. In the next section, I shrink this distance just a bit by showing how the same cognitive structure evident in Jeff ’s theories can be seen in the mature work of two authors who made music theory their life’s work: Jean-Philippe Rameau and Heinr ich Schenker.

conceptual models, theories, and music theory During the eighteenth century, Jean-Philippe Rameau (1683 – 1764) was widely recognized as the foremost opera composer in France. Rameau had intellectual aspirations, as well as musical ones, however, and these he first brought to fruition in his Traité d’harmonie of 1722. The Traité offered two ideas that changed thinking about musical organization throughout Europe. First, it suggested that the r ich but complex lexicon of chordal sonor ities used in early-eighteenth-centur y music could be simplified and rationalized by granting certain ar rangements of notes pr iority (the theory of chord inversion). Second, it proposed that musical organization was governed by privileged relationships between specific har monic entities (the theory of harmonic progression). In part because of the novelty of these ideas, in part because of Rameau’s famously treacherous prose, these theor ies were subject to a variety of reinterpretations and misunderstandings by those who adopted them, and Rameau himself continued to revise and refine his theor ies through no fewer 40. For further work on the role of theories in reasoning by children, see Frank C. Keil, Concepts, Kinds, and Cognitive Development (Cambridge, Mass.: MIT Press, 1989); and Frank C. Keil, Daniel T. Levin, Bethany A. Richman, and Grant Gutheil, “Mechanism and Explanation in the Development of Biological Thought: The Case of Disease,” in Folkbiology, ed. Douglas L. Medin and Scott Atran (Cambridge, Mass.: MIT Press, 1999), 285 – 319.

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aspe c t s of cog n i t ive st ruc ture than five additional treatises and a host of other wr itings until almost the last years of his life.41 Heinrich Schenker (1867 – 1935) was an Austrian pianist, critic, and music theorist who supported himself primarily through giving pr ivate lessons. Schenker’s writings include the jour nal-like ser ies Tonwille and Meisterwerk, analyses of Beethoven’s piano sonatas and Ninth Symphony, and three main treatises: Harmonielehre (1906), Kontrapunkt (1910 – 1922), and Der freie Satz (1935). Through these publications, Schenker developed two ideas that had a profound influence on AngloAmerican music theor y during the latter half of the twentieth centur y. First, he maintained that highly complex musical compositions were the result of elaborations of more basic and abstract structures. Second (and related), he held that musical works consisted of a number of hierarchical levels, proceeding from the most basic and abstract to the most complex and concrete, and that each successive level involved a further elaboration of a preceding level.42 The theor ies of music developed by Rameau and Schenker are complex, highly formalized systems for descr ibing and analyzing music. In what follows, I consider each from the perspective on theor ies developed in this chapter, using short musical analyses by Rameau and Schenker to provide glimpses into their respective theories. This will allow me to show some of the cognitive substructure of their theories, and it will also reveal some important features of extended theor ies of music.

Rameau on a Recitative by Lully As do most of the music treatises of the early eighteenth centur y, Rameau’s contain few if any analyses of actual works of music. An exception is found in his Nouveau système of 1726, where he provides an analysis of an entire recitative from JeanBaptiste Lully’s opera Armide of 1686, written on a libretto by Philippe Quinault.43 An excer pt from the analysis is given in example 3.2. The top two staves are as they would have appeared in Lully’s score: a vocal line with text, below which is the basse example 3.2 Rameau’s analysis (1726) of mm. 18– 22 of Armide’s recitative from act 2, scene 5 of Lully’s Armide 18

A che vons . . . je fré mis!

ven geons nous

9

7

7

7

7

7

je sou

pi

re!

Basse continue

7 Basse fondamentale

41. For a more complete and more elegant account of Rameau’s music theor y, see Christensen, Rameau and Musical Thought in the Enlightenment. 42. The notion of hierarchy employed by Schenker is somewhat complex and is discussed further in chap. 7. 43. Jean-Philippe Rameau, Nouveau système de musique théorique et pratique (Paris: Ballard, 1726), 80 – 90.

conc e p tual mode l s and th e ori e s continue part, with Arabic-numeral figures to indicate how the har monization should be completed. Added beneath these is a staff for Rameau’s basse fondamentale, which encapsulated his analysis of Lully’s music. Rameau’s basse fondamentale had its or igins in the precept that each chord had one fundamental sound (in moder n ter ms, its root), from which the remaining notes were derived. In his analyses and descr iptions of various successions of chords, Rameau would notate each of these fundamental notes on an additional staff, thus giving an account of what he considered to be the basis of any given harmony. The basse fondamentale was more than just a record of chord roots, however: it also allowed Rameau to g ive an account of musical syntax. The way Rameau accomplished this is more than a little complicated, but the essential points are as follows.44 To explain why chord Y followed chord X rather than chord Z, Rameau exploited the notion of cadence prevalent in eighteenth-centur y music theory: chord Y followed chord X because the two were part of a nor mative cadence for mula. As part of this for mula, chord X would invariably be a major chord to which was added a minor seventh (in moder n ter minology, a dominant-seventh chord). Rameau came to regard the dissonance introduced by this seventh as the mechanism that led to cadence: the dissonant notes str ike together, and the collision leads to the appearance of the chord that completes the cadence — what Rameau called the tonique. The chord that preceded the tonique, with its fundamental bass a fifth above that of the tonique, was called the dominante-tonique.45 Of course, music of even the simplest sort involves more than tonic chords preceded by their dominants, but the basic patter n gave Rameau a place to begin his explanation of musical syntax. This he did by using the basse fondamentale to show the cadential relationships he took to be the motive force in music, even if this meant that the note indicated in the basse fondamentale could be related through only the most circuitous means to the chord that actually appeared in the music.46 Returning to the passage from Lully’s recitative, there are two places where the note of the basse fondamentale is different from that of the basse continue. In m. 19, Rameau indicates that the fundamental of the chord B-D-G is G, an inter pretation wholly in keeping with moder n thought about chordal inversion. In m. 20, however, Rameau takes E as the fundamental of the C-E-G chord and implies that a D should be added to the chord; thus the 7 above the E of the basse fondamentale. This inter pretation reflects his belief that the chord with A as its fundamental should be preceded by its dominante-tonique, which has E as its fundamental and which should be accompanied by the dissonant seventh; thus the E and D of m. 20. As an additional complication, Rameau added the figure 9 to the basse continue part of the version of Lully’s score that appeared in the Nouveau système. In this way he was able to accept Lully’s bass-note C and accommodate his own added D by 44. My discussion draws on that of Christensen in Rameau and Musical Thought in the Enlightenment, 106– 23. 45. As mentioned in n. 25, Rameau employs a cross-domain mapping between the physical and musical domains to character ize musical progression. Consequent to this mapping, individual pitches are construed as physical objects that obey the laws of Newtonian physics. 46. For more on the function of the basse fondamentale as an extra-musical commentary on music, see Allan Keiler, “Music as Metalanguage: Rameau’s Fundamental Bass,” in Music Theory: Special Topics, ed. Richmond Browne (New York: Academic Press, 1981), 83– 100.

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aspe c t s of cog n i t ive st ruc ture suggesting that the latter should appear as a dissonant ninth above the bass. The fact that the E of the basse fondamentale appears above the C of the basse continue is not a problem for Rameau, since the C is explained by his notion of supposition—it functions as an or namental note below the true bass note E.47 From the perspective of modern music theory, Rameau’s inter pretation of m. 20 is viewed as completely wrongheaded, whereas his inter pretation of m. 19 is viewed as essentially r ight. It is important to note, however, that both interpretations follow from Rameau’s theory of musical organization and its account of musical syntax. Rameau’s treatment of Lully’s recitative in the Nouveau système was not to be his last. In 1753, Jean-Jacques Rousseau offered a competing analysis of Lully’s recitative, taking Rameau’s discussion as a point of departure.48 Rousseau’s intent was to show that French musicians — even the most celebrated — had no idea of how to set text (in contrast to Italian musicians who, in Rousseau’s view, did). Singling out the passage cited in example 3.2, Rousseau wr ites Certainly here is the most violent moment in the whole scene. It is here that the greatest struggle is taking place in Armide’s heart. Who would believe that the Musician has left all this ag itation in the same key, without the slightest intellectual transition, without the slightest har monic distinction, in a manner so insipid, with a melody so little distinguished and so inconceivably clumsy, that instead of the last verse spoken by the Poet, Achevons; je frémis. Vengeons-nous; je soupire [End it; I tremble. Avenge myself; I sigh] the Musician says precisely this: Achevons, achevons. Vengeons-nous, vengeons-nous. [End it; end it. Avenge myself; avenge myself.]49

Rameau responded to Rousseau’s polemic with the 1754 Observations sur notre instinct pour la musique, et sur son principe, which set out to prove two points: that harmony is the most important aspect of music (prior to both the melody or the text that is sung) and that French music excels in the way it uses har mony. The idea that har mony was the most important aspect of music was not new for Rameau, for he had argued the point in his 1722 Traité. In the Observations, however, the argument takes a slightly different for m, based on the premise that our understanding of music begins at an instinctual level that reflects a natural pr inciple. This pr inciple exists, Rameau argues, in the har mony that results from the reso47. For further discussion, see Chr istensen, Rameau and Musical Thought in the Enlightenment, 120 – 29; and E. Cynthia Verba, “The Development of Rameau’s Thoughts on Modulation and Chromatics,” Journal of the American Musicological Society 26 (1973): 69– 91. 48. Jean-Jacques Rousseau, “Letter on French Music,” in Essay on the Origin of Languages and Writings Related to Music, trans. and ed. John T. Scott, Collected Writings of Rousseau, 7 (Hanover, N.H.: University Press of New England, 1998), 168– 73. 49. Rousseau, “Letter on French Music,” 171– 72. At this “most violent moment,” the princess and sorceress, Armide, is about to take her revenge on the hero Renaud, who, enchanted, sleeps before her. However, confusion freezes Armide’s vengeful hand as love casts a spell more powerful than that which grips the sleeping hero. At the point singled out by Rousseau, Armide swings back and forth between a steely deter mination to kill her foe and a desire to melt into his ar ms.

conc e p tual mode l s and th e ori e s nance of every vibrating system, or corps sonore, including musical instruments and the human voice.50 The essential elements of this har mony— the principle it reveals — are the intervals of the octave, twelfth, double octave, and seventeenth, or, in a more compact representation, root, third, and fifth. According to Rameau, these intervals are generated not only above the root (as overtones) but below the root as well.51 These “undertones” gave Rameau a way to explain the or igins of the minor mode. In the Observations, he also used the intervals below the root to explain the affectual qualities of the subdominant in contrast with those of the dominant. The dominant is a product of the overtones; in consequence, it arouses feelings of vigor and joy. The subdominant — literally, the “underdominant”— is a product of the undertones; thus, it gives rise to feelings of weakness, gentleness, tenderness, and sadness.52 Having established this perspective on har mony and har monic function, Rameau argued that Quinault’s text was served perfectly by Lully’s music, most particularly so in the case of the passage quoted in example 3.2. Rameau’s argument, illustrated by the example given in example 3.3, runs as follows: shortly before this point, the music has been in E minor. With the D dominante-tonique of m. 18 (which sets the ang ry, ascending “Achevons”), the music establishes G major (Ton de Sol in ex. 3.3). At “je frémis,” this G is converted into the dominante-tonique of C. This represents a move to the subdominant of G (Ton d’Ut), which is accompanied by a melodic descent. With “vengeons-nous,” the dominante-tonique of D is introduced. This represents a move to the dominant of G (Ton de Re), which is accompanied by a melodic ascent. Finally, with “je soupire,” D is converted into the dominante-tonique of G. Although this signals a return to G (Ton de Sol), it is also a move to the subdominant of the immediately preceding key of D, and it is accompanied by a final melodic descent. According to Rameau, Lully relies on our example 3.3 Rameau’s analysis (1754) of mm. 18– 22 of Armide’s recitative from act 2, scene 5 of Lully’s Armide [18]

[22]

A che vons . . . je fré mis!

7

6

5

ven geons nous . . . je sou

7

pi

re!

7

Basse continue Ton de Sol

Ton d’Ut Ton de Re

Ton de Sol

50. Jean-Philippe Rameau, Observations sur notre instinct pour la musique, et sur son principe (Paris: Prault fils, 1754; facs. ed., Monuments of Music and Music Literature in Facsimile. Second Ser ies, Music Literature, 54 [New York: Broude Brothers, 1967]), 2. 51. The claim is first made in Rameau’s Génération harmonique ou traité de musique théorique et pratique (Paris: Prault fils, 1737; facs. ed. Monuments of Music and Music Literature in Facsimile. Second Ser ies, Music Literature, 6 [New York: Broude Brothers, 1966]), 4– 5. 52. Rameau, Observations, xii–xiii.

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aspe c t s of cog n i t ive st ruc ture instinctual responses to these oscillations between the dominant and the subdominant to summon Armide’s swings between revenge and love: each move toward the dominant arouses in us feelings appropriate to her revenge; each move toward the subdominant arouses feelings appropriate to the dissolution of her resolve. Rameau’s analysis of this passage serves as the capstone to his argument in the Observations: the excellence of French music, the appreciation of which had eluded Rousseau, is embodied in the way it exploits our instinct for music in the service of musical expression. Rameau’s revised analysis necessitated some important changes in his basse fondamentale for this passage. In the Observations, he reads the second half of each of mm. 18– 21 as including a dissonant seventh (which is in inversion in m. 19), reflecting the dominante-tonique chords that establish the keys of G, C, D, and finally G. Perhaps more important, the chord in the first half of m. 20 no longer serves as the dominante-tonique of the chord in the second half of the measure, for this would undercut Rameau’s assertion that C major is in effect at the beginning of the measure: the note in the basse fondamentale is now C instead of E, and there is no 7 above it. As Rameau’s theory changed, so did his analysis. Rameau’s intent with this analysis, as with the theor y of music on which it is based, is to explicate the pr inciples of musical organization and musical syntax. He does this by focusing on har monies and har monic relationships, reading out the larger implications of the basse continue — that is, not only the notes that will complete the musical texture but also the musical sense made by the bass line itself — and making them explicit through the basse fondamentale. The project is a large and complex one, and Rameau’s analysis of Lully’s recitative lets us glimpse only a portion of all that he would try to say about musical organization. Nonetheless, this vignette is enough to show how Rameau’s music theor y is a theor y in the more general sense developed in this chapter, for all of the five features of theories are clearly in evidence:

theorie s guide unde r standing and reasoning

Rameau’s theory gives an account of harmonic progression — that is, it provides an explanation of why one chord follows another. Given a bit of context connected with a particular chord, we could make a reasoned judgment about what the following chord would most likely be. Through the notion of chordal inversion, his theory also explains relationships between chords that compr ise the same pitch classes. In the analysis shown in example 3.3, the har mony in the first half of m. 19 is “the same” as that in m. 22, even though their bass notes are different. Finally, by locating the origin of music in the naturally occur ring corps sonore, Rameau’s theory offers a way to account for the emotions music evokes in humans. One set of emotions (broadly, the happy ones) is associated with notes generated above the cor ps sonore; another set (the sad ones) is associated with notes generated below the cor ps sonore.

theories provide answers to conceptual puzzles One of the profound puzzles that Rameau sought to solve in the Observations is why music moves us. This he did by proposing that the cor ps sonore was not simply an acoustic phenomenon but a natural one, too: we are moved by music in confor mance with

conc e p tual mode l s and th e ori e s natural laws. A more parochial puzzle concer ns successions of bass notes that do not confor m to his notions of harmonic progression (such as the C3 to A3 in m. 20 of ex. 3.2, from Rameau’s first analysis in the Nouveau système). Rameau suggests that the given bass note has, essentially, an or namental function and the real bass note (indicated in the basse fondamentale) is the one that confor ms to the proper progression of harmonies. Of course, the “puzzle” here could be seen as simply a manifestation of the limitations of Rameau’s theory— it is one that disappears when the theory changes, as it has by the time of the Observations. Nonetheless, the issue raised by this puzzle/non-puzzle points up something important about theor ies and conceptual puzzles: theories, through the way they descr ibe situations, tend to create puzzles, for which the theor y then offers solutions. When the theor y changes, these puzzles often disappear, to be replaced by new puzzles specific to the new theory.53

theories simplify reality

As a composer of many successful operas, Rameau knew well that music consisted of more than just successions of dominant and tonic chords. Focusing on this succession to the exclusion of others, however, allowed Rameau to give an explanation of why one har mony followed another, and thus to give an explanation of harmonic progression. And Rameau’s account of the way humans respond to music greatly simplifies the emotional response to music, reducing it to an essential binar ism at a variance with the range of emotion evoked by effective musical works.

theories involve a number of conceptual models

Rameau’s complete theor y coordinates a large number of conceptual models, ranging from models for pitch-events and intervallic relationships to models for or nament and expressivity. Three models stand out in both of his analyses of Lully’s recitative: the conceptual model associated with the cor ps sonore, which uses basic acoustic properties to explain relationships among musical events; the conceptual model for musical mechanics, which maps Newtonian physics onto musical events to explain musical syntax; and the conceptual model for chordal inversion, which descr ibes relationships between the notes that make up a har mony in terms of a set of dependencies created by chord generation. Although the notion of the cor ps sonore was ultimately absorbed into general thinking about the acoustic or igins of music, the latter two models had a profound effect on the music theory of succeeding generations: the success of Rameau’s theory was such that later theor ists either incor porated these models into their own theor ies or found substitutes for them in alternative conceptions of chordal progression and inversion.

theories are dynamic

As is evident from the two analyses of Lully’s recitative, Rameau’s theor y of music changes over time: in the 1726 version, the 53. This situation is somewhat more common in the humanistic disciplines than in the hard sciences. In the latter, the puzzles are typically independent of humans — they obtain whether humans are observing the phenomena or not — whereas in the for mer the puzzles (and the disciplines, for that matter) would not exist without humans.

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aspe c t s of cog n i t ive st ruc ture chord at the beginning of m. 20 acts as a dominante-tonique for the chord that follows; in the 1754 version (expanded to account for the drama evoked by the passage), the same chord represents a temporar y, but affectually important, harmonic goal. It should be said that when Rameau changed his theor ies, it was not always for the better: even though these changes allowed him to account for a wider range of phenomena, they often introduced complications that made his theor y more unwieldy. Although Rameau’s is a complex and highly elaborate theory, embedded in history and pertaining to a relatively limited musical repertoire, it nonetheless shares significant features with the cognitive theor ies that are the basic tools of human understanding. To fully comprehend Rameau’s theor y requires our reclaiming its historical context and br inging our own conceptual models into cor respondence with those on which his theor y is based. Certain models, such as that for chordal inversion, pose few problems. Others, such as the conceptual model for supposition, have little in common with our own models and require much greater effort to understand. Nonetheless, the distance between his way of understanding and ours, or between either of these and Jeff ’s, is only a matter of the concepts and conceptual models employed. The basic cognitive structures that make this understanding possible are the same.

Schenker on a Waltz by Schubert Although Heinr ich Schenker adopted some of Rameau’s theoretical precepts, his attitude toward them changed over the course of his wr itings.54 In his Harmonielehre of 1906, Schenker speaks approvingly of Rameau’s work, but after World War I, Schenker became highly cr itical of all things French, Rameau included. His late essay “Rameau or Beethoven?” is a sustained diatr ibe in which he portrays Rameau as at best ignorant, at worst a malevolent force who contr ibuted to the downfall of music.55 Rameau was not the only theor ist Schenker cr iticized, however. Even before the war, Schenker had become convinced that Ger man music was being pulled into mediocr ity and that music theor ists had aided and abetted the process.56 A central and explicit goal of Schenker’s writings on music was to retard or ar rest this process by showing the basis for the super iority of a select repertoire of music associated with the her itage of German-speaking countr ies. Schenker believed that only when the work of composers from Johann Sebastian Bach to Johannes Brahms was once again fully appreciated could humanity be saved from its own excesses.

54. For a fuller account of how Schenker’s attitude toward Rameau changed over the course of his writings, see Harald Krebs, “Schenker’s Changing View of Rameau: A Compar ison of Remarks in Harmony, Counterpoint, and ‘Rameau or Beethoven?,’ ” Theoria 3 (1989): 59– 72. 55. Heinrich Schenker,“Rameau or Beethoven? Creeping Paralysis or Spir itual Potency in Music?,” in The Masterwork in Music: A Yearbook, trans. Ian Bent, ed.William Drabkin, Cambridge Studies in Music Theory and Analysis 5 (Cambr idge: Cambridge University Press, 1994– 97), 3: 1– 9. 56. Heinrich Schenker, Counterpoint: Book I: Cantus Firmus and Two-Voice Counterpoint, ed. John Rothgeb, trans. John Rothgeb and Jürgen Thym, New Musical Theor ies and Fantasies, 2 (New York: Schirmer Books, 1987), xxvii–xxx.

conc e p tual mode l s and th e ori e s Basic to Schenker’s music theory were two ideas: first, that the forces that shape music are independent of humans; second, that these forces deter mine fundamental aspects of musical syntax.57 These forces are made manifest in what Schenker called the Naturklang, or chord of nature, consisting of the overtones generated from a single fundamental, with priority granted to those closest to the fundamental.58 Couching his argument in strongly organicist ter ms, Schenker proposed that these overtones were first witness to the desire of the tone to propagate itself .59 This desire also gave rise to various Ursätze, or fundamental structures, each of which began with either the third, fifth, or octave of the fundamental. As shown in example 3.4, an Ursatz consists of a simple two-part counter point. The notes with upward stems make up the Urlinie (or fundamental line), which descends stepwise from the Kopfton (or head note — here, the third of the fundamental).60 Below this, in one-to-one counter point, is the Brechung (or arpeggiation); in example 3.4, this consists of an alter nation between the fundamental and fifth of the Naturklang. The Ursatz represents an idealized succession of musical mater ials, all of which are in clearly specified relationships with each other. It thus provides an account — abstract, minimal, but nonetheless complete — of musical syntax: that is, how musical materials are organized to produce the elements of musical discourse. As Schenker would have it, the skilled composer, in intuitive response to the powerful urges of the Naturklang, elaborates an Ursatz further and further until, finally, a complete work is bor n. The possible elaborations of Ursätze are manifold example 3.4

A Schenkerian Ursatz beginning on the third of the fundamental

I

V

I

57. These two aspects of Schenker’s music theory are discussed in a bit more depth in chap. 7. 58. Although there are obvious affinities between Rameau’s cor ps sonore and Schenker’s Naturklang, the latter is more complex in both the overtones proper to the system and their application to musical structure. In general, the idea that there was an acoustical basis to musical organization was a commonplace of nineteenth-century musical thought, and there is little evidence that Schenker’s thinking on this matter was directly linked to that of Rameau. 59. “It is self-evident that the urge to produce unending generations of overtones belongs to every tone in equal measure. One might also compare this urge to that of animals, for it appears in fact to be in no way infer ior to the procreative urge of a living being.” [“Es ist selbstverständlich, daß den Trieb, Generationen von Obertönen ins Unendliche zu zeugen, jeder Ton in gleichem Maße besitzt. Man darf, wenn man will, auch diesen Trieb einem animalischen vergleichen, denn er scheint in der Tat dem Fortpflanzungstr ieb eines Lebewesens durchaus nicht nachzustehen.”] Heinr ich Schenker, Harmonielehre, Neue musikalische Theor ien und Phantasien, 1 (Stuttgart: J. G. Cotta’sche, 1906), §13, p. 42. 60. Translating Schenker’s terminology is a notor iously fraught issue. For a discussion, see Robert Snarrenberg, “Competing Myths: The American Abandonment of Schenker’s Organicism,” in Theory, Analysis and Meaning in Music, ed. Anthony Pople (Cambr idge: Cambridge University Press, 1994), 29– 56. In the following, I shall rely on Schenker’s original ter ms (followed, at their introduction, by common translations) as presented in Schenker, Der freie Satz, Neue musikalische Theor ien und Phantasien, 3 (Vienna: Universal-Edition, 1935).

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aspe c t s of cog n i t ive st ruc ture and, for all intents and pur poses, are coextensive with the repertoire Schenker sought to explain. Within these possibilities, two main types of elaboration can be distinguished. The first is a manifestation of the desire of individual components of the Ursatz to assert control over longer spans of music. This occurs through the process of Verwandlung (transfor mation or prolongation), realized through a variety of compositional stratagems.61 The second type of elaboration replicates whole sections of the Ursatz on subsidiar y levels of musical structure, thus presenting the Ursatz in a sort of structural diminution. In both cases, the Ursatz is a first level of musical syntax, whose elements are subsequently transfor med or reiterated to create more extensive musical utterances. This notion of syntax is different from Rameau’s in two important respects. First, rather than descr ibing local, event-toevent relationships, Schenker’s theory attempts to account for relationships over the course of an entire work. Second, where harmony was the starting point for Rameau, for Schenker, musical syntax starts with the contrapuntal voice-leading of the Ursatz. Of course, composers rarely if ever committed the successive elaborations of the Ursatz to paper. According to Schenker, creating a musical composition that both confor med to and properly expanded on an Ursatz was the work of genius. The best a nongenius could do was to come to an appreciation of the finished work by retracing the successive elaborations of the Ursatz through a ser ies of hierarchical levels, which proceed from the backg round (the most minimal elaboration of the Ursatz) to the foreground (which often resembles a simplified version of the finished work).62 The result is a str iking image of musical structure that shows musical syntax operating on a number of levels and within a number of different time frames within each composition. To represent the elaborations of an Ursatz and the hierarchical levels that resulted, Schenker developed a unique set of graphical symbols that he used in his analyses. These allowed him to show relationships among structural elements and also made manifest the replication of elements across the various levels of an elaborative hierarchy. As an example, let us tur n to Schenker’s analysis of the first of Franz Schubert’s Valses nobles, Op. 77. The score for the work is given in example 3.5; Schenker’s graphic analysis appears in example 3.6 (the Ursatz for the analysis is the same as that g iven in ex. 3.4). Although not all of the features of Schenker’s graphic notation need concer n us here, a few will be useful for or ienting ourselves and for understanding his analysis. Open note heads in the graph (with the exception of the F5 neighbor note after the double bars) represent components of the Ursatz; generally speaking, slurs and beams mark off larger syntactic units. The graph omits the rhythmic figuration, filled-out chords, and much of the registral detail of Schubert’s waltz, as well as various subsidiar y passing and neighbor notes

61. The transfor mation (or prolongation) of elements of the Ursatz is more than a little complicated, and Schenker used a number of terms in order to capture the variety of ways it is accomplished. See Schenker, Der freie Satz, §45, p. 49. 62. Actual musical analysis most often proceeds in the reverse direction, going from completed musical work, to foreground, to background.

conc e p tual mode l s and th e ori e s example 3.5

Franz Schubert, Valse noble, Op. 77 No. 1, D. 969

6

8va

11

example 3.6

Schenker’s analysis of Schubert’s Op. 77 No. 1

and br ief arpeggiations. Nonetheless, it does not take too much imagination to see (and hear) the outlines of the opening of the waltz in the first portion of Schenker’s graph. After the double bars, the connection between Schubert’s music and Schenker’s graph is somewhat less immediate, and the graph becomes somewhat more complicated. Schenker’s basic argument, however, is clear: mm. 9– 11 serve as contrasting mater ial that prolongs the Kopfton, and after m. 12, the music returns to a modified version of the opening mater ial that culminates in the completion of the Ursatz. The completion of the Ursatz is accomplished in spite of two complications. First, scale degree 2 is not actually present in the music — Schenker shows this by placing the 2 of the Ursatz in parentheses. Second, the Ursatz is brought to com-

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aspe c t s of cog n i t ive st ruc ture pletion in a higher octave than that established by the Kopfton in m. 8, which runs counter to Schenker’s principle of obligate Lage (obligatory register).63 Schenker’s theory, then, offers a view of Schubert’s waltz as a sort of abstract discourse structure. The first eight measures (the a1 section) serve as introduction, providing an Anstieg (initial ascent) from C5 through D5 to the Kopfton E5. The next four measures (the b section) offer a contrast, prolonging the Kopfton through a neighbor-note figure (indicated with “Nbn” in ex. 3.6). The final four measures (the a2 section) return to the opening mater ial, modified in order to complete the Urlinie and br ing about the conclusion of the piece. According to Schenker, to the extent that we understand this discourse structure, we understand how the Ursatz is elaborated to create this unique composition. The force of this understanding is such that we “supply” the D6 of the Ursatz at the conclusion of the waltz, even though it is not literally present in the music. In the hundreds of analyses that accompanied the exposition of his theor y, Schenker showed evidence of similar discourse structures in the works of all of the principal composers from Germany and Austria dur ing the eighteenth and nineteenth centur ies, and a few others besides. The theory of music that emerges, not unlike the works whose structure it seeks to explicate, is fascinating in its extent and complexity. Nonetheless, it is a theory with all of the features of a cognitive theory outlined in this chapter.

theorie s guide unde r standing and reasoning

Schenker’s theory provides a broad account of musical syntax by explaining how musical materials relate to one another in confor mance with the rules of counter point and harmonic progression. His intent is to descr ibe the entirety of musical works. Given this objective, and the organicist imperative relative to which the theory is framed, Schenkerian analysis provides an explanation for the function and meaning of even the smallest part of a musical composition: one can proceed, in an orderly fashion, from the graph of example 3.6 back to the music of example 3.5. From a larger perspective, Schenker’s theory gives an account of form, understood as the various roles that different sections of music play within an overall discourse structure. The indication of a return to the opening mater ial of Schubert’s waltz in m. 12 (indicated by Schenker’s a2 below the staff ) marks not only a reprise of the opening figure but also a return to the syntactic process initiated by the opening of the waltz. Finally, Schenker also offers an aesthetic theory: he believed that the works most worthy of his theoretical accounts were also the most valuable aesthetically.

theories provide answers to conceptual puzzles One of the modest puzzles presented by Schubert’s waltz concer ns the attention we should pay to it. It is one of dozens if not hundreds of waltzes Schubert tossed off to gen63. The principle of obligate Lage is a reflection of the urge of the notes of the Ursatz to return to their source, which in all cases should involve a descent from the Kopfton to the octave above the fundamental (as in ex. 3.4). However, Schenker himself did not seem to regard obligate Lage as obligatory in all cases — he notes the Schubert waltz discussed here as an instance in which the pr inciple is violated. See Schenker, Der freie Satz, §268, p. 175.

conc e p tual mode l s and th e ori e s erate income. Does it bear the mark of his compositional genius, or is it simply another bit of doggerel chur ned out to fit the needs of the moment? Schenker’s analysis decidedly affir ms the for mer: whether it was wr itten in a few minutes or over the course of several days, the waltz confor ms to and properly expands on one of the Ursätze basic to music. As with Rameau’s account of Lully’s recitative, we also see the theory providing answers to puzzles specific to the theory. In the analysis of the Schubert waltz, these are the complications presented by the apparent departures from the Urlinie in the concluding measures.

theories simplify reality

One of the superficial cr iticisms made of Schenker’s theory is that his graphic analyses leave out all of the surface detail that makes a musical work distinctive and rewarding, and that register, dynamics, and rhythmic figuration are often obscured or ignored. Indeed, the graph given in example 3.6 bears this out. This is not a deficiency, however, but simply something that marks Schenker’s theory as a theor y: one that simplifies reality as do all theories.64 The process of theorizing, then, is one of selecting data from a given situation and using them to build a more comprehensive understanding of that situation.

theories involve a number of conceptual models

Schenker’s propensity for neologisms, his attempts to vivify the realm of tones through comparisons to human and animal domains, and his adaptations of the theoretical work of earlier theor ists give rise to an astounding number of conceptual models. Two in particular give his analysis of the Schubert waltz a distinctive flavor: the conceptual model associated with the Naturklang, which supplies the organicist basis for his account of musical syntax; and a conceptual model of hierarchy (also organicist, and discussed in further detail in chap. 7) that cor relates numerous layers of musical syntax as a way of explaining how basic syntactic structures account for the syntax of an entire work.

theories are dynamic In as br ief a summary as this, it is not possible to show in any compelling way the dynamic aspect of Schenker’s theory over time. Indeed, about the best that can be done is to note Schenker’s flexibility with regard to obligate Lage, which suggests that his approach to musical structure is not as r igid as he would sometimes have us believe. Nonetheless, there is a wealth of research that shows that Schenker’s theory was a dynamic one, changing in response to both the repertoire and problems he engaged. Many claims have been made for Schenker’s theory of music, a theory that, in its ambition and extent, has few competitors in the Western tradition. No one to my knowledge, however, has claimed that it is cut from the same cloth as the music theory of Rameau or that of an eight-year-old boy from the Boston area. Indeed, I would not want to make such a claim, or at least not without considerable qualifi-

64. Ronald Langacker makes a similar point about the analyses produced by theor ies of language, noting that “there is certainly some truth in the view that analysis and descr iption inevitably distort subject matter since they cannot be their subject matter.” Langacker, Foundations of Cognitive Grammar, 1: 14.

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aspe c t s of cog n i t ive st ruc ture cation. In the things that matter most to music theor ists, Schenker’s theory is simply of another order. Nonetheless, in its general features — in the cognitive work that it does, and in the way that it does it — it shares much not only with Rameau’s theory of music and with Jeff ’s theor ies of “Twinkle” but also with cognitive theor ies as a whole.

Features of Extended Theor ies The theor ies of Rameau and Schenker, unlike those of Jeff, are sophisticated intellectual constructs that can account for a wide range of complex musical phenomena. Such theor ies, which I shall call extended theories (in order to differentiate them from more ad hoc theor ies like Jeff ’s), have three prominent features. First, extended theories usually engage a problem or problems of long standing, like those of musical expression or musical coherence. Ancillary to this, extended theor ies often reveal — or create — problems through the constructs they apply to music. Second, extended theor ies, as the product of traditions of discourse that often stretch across generations, are utterly embedded in culture. This was quite apparent in the nationalism that infor med — indeed, fueled — both Rameau’s and Schenker’s work. Although it might be easy to dismiss such cultural trappings as extraneous to the business of music theory, judging from the wr itings of Rameau and Schenker, it is hardly so: they see music as thoroughly implicated in the business of history and nation. Third, theories like those of Rameau and Schenker are invested in developing systematic accounts of musical organization. This systematic quality can take the form of developing an exhaustive account of musical structure. In some measure, this is what Schenker aspired to, as did Allen Forte in his efforts to provide a theory of pitch organization for atonal music.65 The systematic aspect of a theory, however, may be somewhat more circumscr ibed, especially when its focus is musical syntax. Here the goal is not so much to explain everything about musical organization but, rather, what is s in musical organization. This is closer to the goals of Rameau’s theory, and it tempered both the repertoire Schenker chose to deal with and the problems he engaged. The topic of musical syntax, especially as a manifestation of the systematic quality of extended theor ies, brings us back to the paradox that theor ies simultaneously treat and create problems. The very notion of musical syntax — the idea that musical discourse is in some way organized — is in part a creation of theories that seek to explain musical organization. Depending on the models music theory brings to bear on the problem, musical syntax can be seen to be quite different things: a matter of how one har mony leads to another; an account of how basic contrapuntal and harmonic frameworks are elaborated into full-fledged musical works; or a different explanation altogether. As shall be seen in the next chapter, my own approach to musical syntax is different yet, involved as it is with the way musical mater ials are arranged to take advantage of and to exploit our ability to categor ize musical events. 65. Allen Forte, The Structure of Atonal Music (New Haven, Conn.:Yale University Press, 1973).

conc e p tual mode l s and th e ori e s

conclusions Theories, as general cognitive constructs manifested in a wide range of human activity, accomplish their work by correlating a number of conceptual models, each of which sets up a conceptual domain. In some cases, these conceptual domains will be quite similar to one another, but in others, the domains may have very little in common. This means that the topography of any theory, reckoned in ter ms of the conceptual domains it compr ises, will not necessar ily be unifor m. A theor y may thus appear to make contradictor y claims when in fact it has simply shifted focus from one conceptual domain to a second, and incommensurate, conceptual domain. Thinking about a theory in terms of its constituent conceptual models can thus be a tool for coming to understand it better, especially where these models are novel or lead the theory in surprising directions. Theories are also part of culture. The culture specific to music theory, it must be admitted, is a quite rarefied one. Nonetheless, the broader influence of culture can be seen here, too, as was demonstrated by the nationalistic claims made by both Rameau and Schenker. These claims are not extraneous to Rameau’s and Schenker’s theories but are in fact integral to them — manifestations of the broader culture of which these theor ies are a part and relative to which they are framed. This is not to deny the uneasiness we may feel when reading the str ident claims of the music theory of another era but only to say that they are not so very different from the notions about pitch relationships and chordal inversion common within the same cultural milieu. Finally, theories of music can tell us something about cognitive structure as a whole. Because the focal domain for music theory is a nonlinguistic one, theories of music demonstrate how we have and cor relate nonlinguistic concepts. The abstraction of Rameau’s and Schenker’s theories notwithstanding, theories of music are often action or iented. These actions can be of a quite visible kind, as demonstrated by Jeff ’s attempts to set up different bell-paths for “Twinkle,” but they can also involve actions less apparent to the eye: theories often suggest ways to attend to or respond to music. Given their involvement with nonlinguistic entities and their concer n with action, theories of music can be seen to be deeply involved with embodied understanding in ways that few other highly developed cognitive theories are. While the preceding chapters have sketched how work in cognitive science can be applied to problems of musical understanding — or, put another way, how our accounts of musical understanding can be brought into line with what is cur rently known about the mind and brain — much work remains to be done to fill out this picture. The chapters that follow make a start by showing how the framework developed thus far can be used to give accounts of musical syntax, cultural knowledge, musical ontology, text-music relations, and the structure of theories. As I noted in the introduction to this volume, I regard every analysis as based on some theory or collection of theories. The theor ies I highlight in part II, however, are theories about how basic cognitive processes are manifested in and exploited by musical understanding. In consequence, the analyses that follow are of a somewhat different character than “musical analysis” as it is usually practiced, for my intent is

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aspe c t s of cog n i t ive st ruc ture not only to shed light on specific issues of concer n to music scholars but also to refine a theor y of music cognition. The examples around which I build my argument are not simply case studies, but are also tools that will help us probe further into the issues discussed thus far.66 As should be clear, the view of cognitive structure, theory, and analysis that I have presented thus far is of necessity preliminary, and it deals with only a small part of the potential issues raised even when the domain of inquiry is restricted to the conceptual level of cognition. Nonetheless, as the following chapters will make clear, even this partial view offers str iking new perspectives on musical understanding and on what it means to theor ize about music.

66. This approach to the role examples play in explorations of the structure of thought is similar to that noted by Mark Turner in his discussion of cognition and rhetor ic. See in particular Turner,“Figure,” in Figurative Language and Thought, ed. Albert N. Katz, Cristina Cacciar i, Raymond W. Gibbs, Jr., and Mark Turner (New York: Oxford University Press, 1998), 80.

part ii

Q

analysis and theory

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chapter four

Q categorization, compositional strategy, and musical syntax

arly in his Theory of Semiotics, Umberto Eco surveyed the communicative processes and cultural systems that might be included in the field of semiotics, moving through a list worthy of Jorge Luis Borges: zoosemiotics, olfactory signs, tactile communication, codes of taste, paralinguistics, medical semiotics, kinesics and proxemics, formalized languages, written languages, unknown alphabets, secret codes, natural languages, visual communication, systems of objects, plot structure, text theory, cultural codes, aesthetic texts, mass communication, and rhetor ic. Midway through this list he considered what he called “musical codes.” He began by proposing that the whole of musical science since the Pythagoreans has been an effort to descr ibe musical communication as a r igorously structured system.1 However, Eco also observed that, in spite of this tradition of structuralism from which musical semiotics can draw, music poses ser ious difficulties for semiotic theor y: “Music presents, on the one hand, the problem of a semiotic system without a semantic level (or a content plane): on the other hand, however, there are musical ‘signs’ (or syntagms) with an explicit denotative value (trumpet signals in the ar my) and there are syntagms or entire ‘texts’ possessing pre-culturalized connotative value (‘pastoral’ or ‘thr illing’ music, etc.).”2 Eco developed a somewhat fuller account of what he meant when he characterized music as a semiotic system without a semantic level a bit further on, just prior to setting out the combinator ial rules for semiotic codes. The problem was not that musical syntax cannot be inter preted — indeed, Eco argued that any syntactic system can be inter preted on some level— but that the inter pretation of music is resolutely indeter minate. There is thus no depth to the semantic levels produced by musical syntax.3

E

1. Umberto Eco, A Theory of Semiotics, Advances in Semiotics (Bloomington: Indiana University Press, 1976), 10. The idea that musical communication is a r igorously structured system is, of course, another way to theor ize about music. Interest in such an approach has waxed and waned along with musicians’ interest in numerology, mathematics, and science as possible models for musical organization. 2. Eco, A Theory of Semiotics, 11. 3. Eco, A Theory of Semiotics, 88– 90. In advancing this point, Eco engages in a dialogue with Louis Hjelmslev’s distinction between semiotic and non-semiotic systems; see Louis Hjelmslev, Prolegomena to

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analysis and theory I find Eco’s comments interesting, not for the view of musical semiotics they provide (since the passages to which I have referred are pretty much all he has to say about music in A Theory of Semiotics), but for their clear focus on the importance of musical syntax for musical understanding. Musical syntax is where any semiotics of music must begin. In what follows, I build on this idea, using the perspective on musical syntax introduced in chapter 1. There, I proposed thinking of syntax as a connected or orderly system. In the case of music, organized sequences of musical events properly recognized as syntactic are typically created through a set of musical practices shared among a number of musicians. Within most traditions of music making, however, there is also some latitude in how musical mater ials can be arranged, and the syntax specific to a particular musical work may emerge only over time. This was the case with the Leidensmotiv from Wagner’s Tristan und Isolde, for the importance of three successive statements of the motive was something that became evident only once we were well into the opera. In situations such as this, certain aspects of the systematic quality associated with musical syntax are determined by the expressive goals of the individual ultimately responsible for ar ranging the musical mater ials. My term for the way such expressive goals are realized is “compositional strategy.”4 Compositional strategy, conceived in these ter ms, assumes an alliance between syntax and processes of meaning construction: composers arrange musical mater ials with relatively specific expressive or communicative goals in mind. This approach takes inspiration from recent work in cognitive linguistics, which does away with a hard-and-fast distinction between syntax and semantics and instead construes language as made up of symbolic structures that consist of form-meaning pairs.5 A similar perspective can be seen in Mark Turner’s work on the iconicity of rhetor ical figures. Turner argues that, in some cases, the for m of a rhetor ical figure is matched to the meaning the speaker wishes to convey, connecting the imageschematic structure of the for m with the image-schematic structure of the meaning. Thus a rhetor ical figure based on repetition, such as anaphora (which involves the repetition of the same word or group of words at the beginning of successive clauses, sentences, or lines), can be used to summon the image of repeated blows, as in an example attr ibuted to Longinus: “By his manner, his looks, his voice, when

a Theory of Language, rev. ed., trans. Francis J.Whitfield (Madison: University of Wisconsin Press, 1963), 111– 13. Hjelmslev, for his part, leaves open the question of whether music is a semiotic system in the strict sense he develops. 4. It should be clear from the general way I have formulated the notion of “compositional strategy” that these strateg ies are not the exclusive property of those traditionally recognized as “composers.” In certain situations, performers and even listeners may use such strategies to organize musical mater ials. Throughout this chapter, I shall simplify things by assuming that composers are the architects of compositional strategies, with the understanding that (mutatis mutandis) these strategies can also be implemented by those not conventionally recognized as “composers.” 5. Ronald W. Langacker, “Conceptualization, Symbolization, and Grammar,” in The New Psychology of Language: Cognitive and Functional Approaches to Language Structure, ed. Michael Tomasello (Mahwah, N.J.: Erlbaum Associates, 1998), 2. Langacker’s notion of a symbol is spelled out in g reater detail in his Theoretical Prerequisites (vol. 1 of Foundations of Cognitive Grammar)(Stanford, Calif.: Stanford University Press, 1987), 11– 12, 56– 58.

cate g ori zat i on, st rate g y, and sy ntax he strikes you with insult, when he str ikes you like an enemy, when he str ikes you with his knuckles, when he str ikes you like a slave.” The efficacy of such a connection is straightforward enough — as Turner notes, “Involving members of the audience in the image schema of the iconic for m automatically involves them in the basic structure of the meaning, thus moving them part way toward accepting the whole.”6 In what follows, I show how compositional strateg ies in music make use of similar connections between expressive goals and the for ms expressions take. Music being music, the meaning that is conveyed is not as direct as that which concerned Longinus, nor as quotidian as that which concer ns cognitive linguists. Nonetheless, I argue for a direct connection between compositional strategy and musical syntax: the organization of musical elements into systematic structures is part and parcel of meaning construction in music.7 The particular focus of what follows is on the part processes of categorization play in compositional strateg ies. As discussed in chapter 1, categor ies of musical events have immediate salience for listeners and are thus important guides to any understanding of how musical mater ials are organized. Building on the perspective developed in chapter 3, we can say that they are basic to any theory of music. Inasmuch as composers try to shape their music to confor m to the capacities of listeners (trying, in Schoenberg’s ter ms, to create musical coherence so that the work can be comprehensible), processes of categorization will also play an important part in compositional strategies. Musical categor ies are thus a place where the concer ns of listeners and the concer ns of composers meet. In the first section of this chapter, I explore the role categor ies of musical events play in the compositional strategies basic to a musical game attr ibuted to Wolfgang Amadeus Mozart. The game in question is one of a genre, which seems to represent the very antithesis of compositional strategy, since such games produce finished — or nearly finished — musical works simply through tosses of the dice. Embedded within their structure, however, is a set of rather traditional strategies for wr iting two-part

6. Mark Turner, “Figure,” in Figurative Language and Thought, ed. Albert N. Katz, Cristina Cacciar i, Raymond W. Gibbs, Jr., and Mark Turner (New York: Oxford University Press, 1998), 50 – 51. Turner’s discussion of the iconicity of rhetor ical for m appears on pp. 49– 51. The quotation attr ibuted to Longinus is from Aristotle, On the Sublime, trans. W. Hamilton Fyfe, Loeb Classical Library, 199 (Cambr idge, Mass.: Harvard University Press, 1995), §20, p. 190. Both a poetic and musical use of anaphora can be found in Bob Dylan’s “Knockin’ on Heaven’s Door,” which first appeared in his 1973 album Pat Garrett and Billy the Kid. The chorus of the song — consisting of reiterations of the line “Knock, knock, knockin’ on heaven’s door”— makes use of a repeated note in the melody, as well as a repeated word. Both repetitions cor relate with the meaning of the text. Note as well that the meaning is at least potentially figurative, rather than literal, since nowhere in the song is it assumed that heaven actually has a physical door on which one can knock. 7. As I have character ized it here, compositional strategy bears a strong resemblance to the tactical logistics of rhetoric, and it might thus be seen as another instance of the use of ideas drawn from rhetor ic to conceptualize musical design (something discussed in greater detail in the first part of chap. 7). As will become apparent, I construe the idea of compositional strategy as rather more general than its rhetor ical counter part, and more involved with issues of immediate importance to musical expression (such as how the temporal succession of musical mater ials should be ar ranged). This construal of compositional strategy seems largely consonant with the approach Edward Cone took in his article “On Der ivation: Syntax and Rhetor ic,” Music Analysis 6 (1987): 237 – 55, which was discussed in chap. 1.

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analysis and theory musical for ms, realized through the manipulation of categor ies of musical events. During the eighteenth century, these same strategies were applied, on a much larger scale, to sonata for m, guiding the way harmonic and thematic mater ials were laid out. They could also be applied to melodic mater ial alone, however. In the second section of this chapter, I show how this was accomplished through an analysis of the syntax of the principal motive from the first movement of Mozart’s “Dissonance” Quartet (K. 465). Taking the different versions of the motive as members of a Type 1 category, the patter n of typicality descr ibed by these members as they appear over the course of the movement shows strong similar ities to the basic strategies for sonata for m. The syntax for these motive forms nonetheless occupies a different layer than the syntax that guides the for mal organization of the movement as a whole. As with the grouping of statements of Wagner’s Leidensmotiv, the syntax of the principal motive from the first movement of the “Dissonance” Quartet emerges over the course of the movement. Both the emergence of musical syntax and the independence of syntactic levels is further demonstrated by the first movement of Ludwig van Beethoven’s String Quartet, Op. 18 No. 6, which is taken up in the third section of the chapter. Although there is little variation of the principal motivic mater ial for the movement, Beethoven is nonetheless able to imbue two versions of the motive with distinctly different syntactic functions. The categor ies of motive forms that compr ise these versions then become elements at a higher level of syntax. The nesting of syntactic functions can also be seen, in a slightly more complicated way, in the first movement of Beethoven’s String Quartet, Op. 18 No. 1, which is discussed in the fourth section of the chapter. There, different versions of the main motive are distinguished by melodic structure and by compositional strategy, and the categor ies for each become syntactic elements within the movement as a whole. In a concluding section I review the perspective on musical syntax developed over the course of the chapter and g ive a bit further consideration to how syntax contr ibutes to the construction of meaning in music.

musical games and compositional strategy A Musical Game Attributed to Mozart Europe in the latter half of the eighteenth centur y saw the blossoming of a number of musical games that allowed any person, “without the least knowledge of Musick,” to compose minuets, marches, waltzes, and contredanses simply by tossing dice or spinning a top.8 As if by magic, a ser ies of throws or spins produced a workable piece of music that was different every time the game was played. The game descr ibed here— the Musikalisches Würfelspiel — allowed its players to 8. One example is Pier re Hoegi’s A Tabular System Whereby the Art of Composing Minuets Is Made So Easy That Any Person, without the Least Knowledge of Musick, May Compose Ten Thousand, All Different, and in the Most Pleasing and Correct Manner (London: Welcker, 1770). For further infor mation about such games and comprehensive lists of them, see Leonard G. Ratner, “Ars combinatoria: Chance and Choice in Eighteenth-Century Music,” in Studies in Eighteenth-Century Music: A Tribute to Karl Geringer on His Seventieth Birthday, ed. H. C. Robbins Landon (New York: Da Capo Press, 1979), 343 – 63; Stephen A. Hedges, “Dice Music in the Eighteenth Century,” Music and Letters 59 (1978): 180 – 87; and Sebastian Klotz,

cate g ori zat i on, st rate g y, and sy ntax

figure 4.1

Number table for mm. 1– 8 of the Musikalisches Würfelspiel

write a sixteen-measure waltz. It is one of several such games attr ibuted to Mozart and is catalogued as K. Anh. C 30.01, but the ascr iption is hardly secure.9 Mozart’s authorship, in any event, is not my central concer n. Instead, I want to focus on the compositional strategies that can be teased out of this particular game. The game requires the use of a set of dice, and of two tables — a number table (the one used for the first eight-measure per iod of the waltz is shown in fig. 4.1) “Ars combinatoria oder ‘Musik ohne Kopfzerbrechen’: Kalküle des Musikalischen von Kircher bis Kir nberger,” Musiktheorie 14 (1999): 231– 45. 9. See Wolfgang Amadeus Mozart, Musikalisches Würfelspiel: Eine Anleitung “Walzer oder Schleifer mit zwei Würfeln zu componieren ohne Musikalisch zu seyn, noch von der Composition etwas zu verstehen,” ed. Karl Heinz Taubert (Mainz: B. Schott’s Söhne, 1956). On the matter of the authenticity of the attr ibution of this particular game to Mozart, see Paul Löwenstein, “Mozart-Kuriosa,” Zeitschrift für Musikwissenschaft 12 (1930): 342– 46; Otto Er ich Deutsch, “Mit Würfeln komponieren,” Zeitschrift für Musikwissenschaft 12 (1930): 595; Herbert Gerigk, “Würfelmusik,” Zeitschrift für Musikwissenschaft 16 (1934): 359 – 63; Ludwig Ritter von Köchel, Chronologisch-thematisches Verzeichnis sämtlicher Tonwerke Wolfgang Amadé Mozarts, 8th ed., ed. Franz Giegling, Alexander Weinmann, and Gerd Sievers (Wiesbaden: Breitkopf and Härtel, 1983), 581, 910; and Hedges, “Dice Music in the Eighteenth Century,” 183. It is known from sketch studies (unrelated to the particular game under consideration) that Mozart had an interest in musical diversions of this sort; see Köchel, Chronologisch-Thematisches Verzeichnis, 581. And a musical dice game survives that is perhaps more reliably attributed to Mozart; it appears, in his hand, on the verso of a manuscr ipt that contains a fragment — also in Mozart’s hand — of the G minor Str ing Quintet K. 516. See Hideo Noguchi, “Mozart— Musical Game in C Major, K.516f,” Mitteilungen der Internationalen Stiftung Mozarteum 38 (1990): 89– 101. K. 516f is significantly different from the game to be discussed below, however, and the dispar ities that distinguish the two could be seen as arguing against the authenticity of the latter one. The game from K. Anh C 30.01 that produces the waltz, and that I will consider, was published under Mozart’s name soon after the composer’s death by Johann Julius Hummel (Amsterdam and Berlin, 1793). This is hardly a guarantee of Mozart’s authorship, since his name could readily have been used simply to boost the sales of a work by another (and unknown) author.

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analysis and theory

figure 4.2

Portion of the notation table for the Musikalisches Würfelspiel

and a notation table (a portion of which is shown in fig. 4.2). For the first measure of music, the player throws the dice and uses the result to find a number in the first column of the table. Thus, the throw 11 gives the result 3 in the first column. The player then tur ns to the notation table, finds the music designated with a 3 there, and uses it for the first measure of the waltz. For the second measure of music, the player throws the dice again and uses the result to find a number in the second column of the number table. The throw 10 gives the result 142 in the second column; the music that cor responds to 142 on the notation table is then used for the second measure of the waltz. A complete waltz produced by the game is shown in example 4.1. Although the dance is hardly distinctive, it is nonetheless completely serviceable, equal to if not exceeding the quality of the Tafelmusik produced by knowledgeable amateurs of the period. Of course, the point of such games was not the production of works of music, but diversion. There were a number of ways the game could be played: a group of players might sit in a circle and take turns throwing the dice, so that each successive measure was deter mined by a different player; players might each create their own waltzes, which could then be compared with one another; the entire piece might be wr itten down and then perfor med; or players might take turns perfor ming the piece as it progressed. In any event, the game offered an amusing and pleasant way to spend a portion of an evening, with the added benefit that music produced by what appeared to be total chance was orderly and coherent, no matter what the skill of the player. In truth, chance played little part in the success of the music produced by such games. Instead, what was required of the compilers of games such as this one were

cate g ori zat i on, st rate g y, and sy ntax example 4.1 Dice throw Result in notation table

7

11

3 134

7 150

Waltz produced by the Musikalisches Würfelspiel

11

10

9

5

8

5

3

142

114

85

99

2

7 91 1

6 125

3 117

5 176

2

9 51

8 168

8 89

5 170

a little knowledge about how to put the game together and an understanding of the formal design of waltzes, contredanses, and the like. One first needs to construct a number table.10 A table for a sixteen-measure waltz using two dice, for instance, starts with an 11 by 16 grid (for the eleven possible throws of the dice and sixteen measures of the piece; the table shown in fig. 4.1 provides only one-half of this grid). The numbers 1 through 176 are then randomly distr ibuted on the 176 squares of the grid to complete the table. To construct a notation table, it is necessar y to write eleven variations on a sixteen-measure waltz, preferably arranging these on a single sheet with the first variation at the top and the eleventh at the bottom. The various numbers of the number table are then mapped onto the individual measures of the eleven variations. For instance, the number table used in our Musikalisches Würfelspiel would map the number 96 (found at the intersection of the first row and first column) onto the first measure of the first variation, the number 22 onto the second measure of the first variation, and so on for all 176 measures of the eleven variations. An example of how this might look, derived by working backward from the number and notation tables, can be seen in example 4.2.11 Once each measure 10. Another approach would be for a number table to be adopted from a previous publication. In fact, the number table for our waltz game is exactly the same as that for the the one published in the Weimar Journal des Luxus und der Moden of February 1787. See Karl Heinz Taubert (ed.) Das Menuett: Musikalisches Wurfelspiel, Paris 1786 (Zurich: Musikhaus Pan, 1988). 11. There is no way to know whether the eleven variations shown in ex. 4.2 are actually the source variations for the game attr ibuted to Mozart: the number found in the first square of the number table

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analysis and theory example 4.2 Eleven variations with numbers derived from the number table for the Musikalisches Würfelspiel m. 96

1

2 22

3 141

4 41

5 25

6 122

7 14

1.

8 30

**2.

*1.

32

6

128

63

146

46

34

2.

31

**2.

*1.

69

95

158

13

153

55

110

3.

24

**2.

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40

17

43

85

161

2

159

4.

100

**2.

*1.

48

4

163

45

5.

80

97

36

107

**2.

*1. * The notes with stems down are used for the first ending. ** The notes with stems up are used for the second ending.

could, in theory, be mapped onto any of the variants of m. 1, and the game would still function properly. However, my focus in the following is not on establishing the or iginal for m of each of the eleven variations but on the way the mater ial of each measure is varied. The principal function of ex. 4.2, which puts each measure into its proper column, is to aid discussion of this aspect of the musical game. Readers who would like to try their luck at composing a piece with the Musikalisches Würfelspiel can use ex. 4.2 (supplying their own dice). The number cor responding to each variation can be read as the result of the throw of the dice; the columns denote the measures of the dance, as in the or iginal number table. Of course, playing the game with the number table and the notation table collapsed together (as in ex. 4.2) takes most of the mystery and pretty much all of the fun out of the game.What remains is the somewhat thin pleasure of finding out what combinations of measures chance will dictate.

cate g ori zat i on, st rate g y, and sy ntax (continued)

example 4.2 9

10

11

12

13

14

15

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70

21

26

9

112

44

109

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117

39

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56

174

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66

139

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58

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79

90

176

7

34

67

160

52

170

25

143

64

125

76

136

1

93

(continued)

has been assigned a number, all of the measures are rewritten, in ascending numerical order, to create the notation table. The permutational combination required by the game — each of the variants of m. 1 had to make sense with each of the variants of m. 2; each of the variants of m. 2 had to make sense with each of the variants of m. 3; and so on — placed significant constraints on what could be varied and what sort of music was produced by the game. In general, all of the variants of a given measure had to have the same har-

145

example 4.2 m. 104

(continued)

1

2 157

3 27

4 167

5 154

6 68

7 118

6.

8 91

**2.

*1.

152

60

171

53

99

133

21

7.

127

**2.

*1.

119

84

114

50

140

86

169

8.

94

**2.

*1.

98

142

43

156

75

29

62

9.

123

**2.

*1.

3

87

165

61

135

47

147

10.

13

**2.

*1.

54

130

10

103

28

11.

37

106

5

**2.

*1. * The notes with stems down are used for the first ending. ** The notes with stems up are used for the second ending.

146

(continued)

example 4.2 9

10

11

12

13

14

15

16

138

71

150

29

101

162

23

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65

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8

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4

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35

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analysis and theory mony, and they typically had the same bass note. The melody for each measure was restricted to gener ic figures — arpeggios, an occasional scalar run, or sometimes a single note — that could easily be concatenated with other such figures. In truth, the compiler of the game wrote not so much variations on a waltz as variations on the harmonic plan for a waltz, using melodic fragments that served the minimal contrapuntal plan of the whole.12 Rhythmic figuration offered the chief means of deriving the variants of a given measure, although changes to the beg inning melodic note, overall melodic contour, or number of nonhar monic tones were also used to render each variant unique. The result of a game constructed according to this plan was a set of variations that was, for all practical pur poses, inexhaustible: there are theoretically 11¹⁶— that is, 45,949,729,863,572,161— different waltzes that could be wr itten from the mater ials provided in example 4.2. The waltzes would not be great music, but their for mulaic melodies and predictable har monic plan were perfectly in keeping with dance for ms of the late eighteenth century. The success of the compositions produced by such games is often attr ibuted to the rationalization of musical mater ials effected dur ing the eighteenth centur y, which allowed specific compositional functions to be attr ibuted to musical materials.13 Although such rationalization is quite evident in the work of music theor ists like Joseph Riepel and Heinr ich Chr istoph Koch,14 and while it is supported by the interchangeability of the components of example 4.2, it is not the only thing that makes the waltz of example 4.1 believable as music.What is also at work is a compositional strategy that shapes the whole of the waltz. The strategy is evident in the overall har monic plan for the dance, an outline of which is given in figure 4.3. The waltz is divided into four-measure sections; the first section (mm. 1– 4) establishes the tonic, the second (mm. 5– 8) modulates to the dominant, and then the two sections repeat. The third section (mm. 9– 12) remains in the dominant, the fourth section (mm. 13– 16) returns to the tonic, and these, too, are repeated. Every one of the waltzes generated by the game will have this basic har monic syntax. However, a succession of harmonies alone does not create convincing music — Rameau’s harmonic theor y notwithstanding, every succession of dominant to tonic does not make for a cadence. What is crucially important for the compositional strategy embodied by the Musikalisches Würfelspiel is the way the mater ial for each measure is varied. For instance, note that only one version of m. 8 appears in example 4.2 12. Mostly, the counter point above the bass is relatively free (within the str ictures of style). In a few cases, however— mm. 9– 10, for example, where the dominant in ⁴₂ position leads to a tonic ⁶₃, and at the cadences that conclude each per iod — the melodic possibilities are constrained by the overall counterpoint in the outer voices. 13. Ratner, “Ars combinatoria,” 344– 45. 14. See Joseph Riepel’s Anfangsgründe zur musicalischen Setzkunst (1752 – 68), included in his Sämtliche Schriften zur Musiktheorie,Wiener musikwissenschaftliche Beiträge (Vienna: Böhlau, 1996); and Heinr ich Christoph Koch, Versuch einer Anleitung zur Composition (Leipzig: Adam Fr iedrich Böhme; Rudolstadt: gedruckt mit Schr iften der Löwischen Erben, und Schirach, 1782 [vol. 1]; Leipzig: Adam Fr iedrich Böhme, 1787 – 93 [vols. 2– 3]; repr. Hildesheim: Georg Olms, 1969), esp. vol. 2. For a translation of portions of the latter, see Heinr ich Chr istoph Koch, Introductory Essay on Composition: The Mechanical Rules of Melody, Sections 3 and 4, trans. Nancy Kovaleff Baker, Music Theory Translation Ser ies (New Haven, Conn.:Yale University Press, 1983). The work of both Riepel and Koch is discussed more extensively in the first half of chap. 7 in this volume.

cate g ori zat i on, st rate g y, and sy ntax Section 1

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and, save for the ending of the tenth variation, only one version of m. 16.15 By contrast, none of the versions of m. 1 are identical. Shaping each of the trillions of waltzes that might be generated by the game is a template that regulates the degree and kind of variation that can occur within the sixteen-measure framework of the dance.

A Template for Compositional Strategy We can discover the plan of the template if we approach each column of measures in example 4.2 as a Type 1 category of the sort discussed in chapter 1. Each measurecategory can be defined in ter ms of attributes (such as har mony, rhythmic figuration, beginning melodic note, and so on), to which each of the members of the category (that is, the different variants included in the category) supplies values. Each measure-category also has a distinctive profile of typicality, determined by the range of values its members assign to the various attr ibutes and the weight given any particular set of values. For example, the members of measure-category 16 assign two different values for the attr ibute rhythmic figure, but assign one of these ten out of eleven times (as shown in fig. 4.4). With respect to the attr ibute rhythmic figure, we can say that the profile of typicality for measure-category 16 is clearly defined. By comparison, the members of measure-category 15 assign seven different values for the attr ibute rhythmic figure; one value is assigned five times, the other six are assigned once each. The profile of typicality for rhythmic figuration is thus somewhat less clearly defined for measure-category 15. Two patterns can be glimpsed from figure 4.4. The first concerns which attributevalues change from measure-category to measure-category and which stay the same — for instance, there is no rhythmic figure in common between measurecategor ies 15 and 16. The second patter n concer ns changes in the profile of typi15. The lack of variation in mm. 8 and 16 means that only (1114) ⫻ 2— merely 759,499,667,166,482 — different waltzes can be wr itten using this particular game.

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analysis and theory measurecategory 16

measurecategory 15 rhythmic figure

figure 4.4

number of times used

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cality between measure-categor ies— as can be seen, there is a relatively sharp contrast between the profiles of measure-categor ies 15 and 16. These patter ns, taken together, create the template that shapes each of the waltzes generated by the game. A somewhat more complete perspective is provided by looking at the values assigned to just two attr ibutes —harmony and rhythmic figure — in the first section of the waltz, as illustrated by figure 4.5. As can be seen, there is little change in the values that members of measure-category 1 and measure-category 2 assign to these attributes: one new rhythmic figure is introduced and one is dropped, but otherwise the categor ies are (at least with respect to these two attr ibutes) identical. While measure-category 3 retains most of the rhythmic figures of measure-category 2, the values assigned the har mony are completely different and markedly more various. Finally, measure-categor y 4 has significant changes in the values assigned both attributes: two new rhythmic figures come to prominence, and the attr ibute-values for har mony change once more.

cate g ori zat i on, st rate g y, and sy ntax q q q Q ä

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figure 4.5 Attribute-values for harmony and rhythmic figure in measure-categor ies 1 through 4 (left side: the values assigned to the attr ibute harmony by the members of measure-categor ies 1 through 4 and the number of members within each measurecategory that assign that value; right side: the values assigned to the attr ibute rhythmic figure and the number of members within each measure-category that assign that value)

There are also changes to the profile of typicality for the measure-categor ies in this section. While the profile for measure-categor ies 1 and 2 is identical — a typical variant will have a root-position tonic har mony and use either the first or second rhythmic figure— it is less clearly defined for measure-categor y 3. Although the number and range of rhythmic figures do not change dramatically, there are now four possible values for the attr ibute har mony, and only a bit of additional weight is put on one of these attr ibute-values (the root-position dominant is assigned by five of the eleven members of the category). Things come back into focus with measure-category 4 — the most typical variant is a first-inversion harmony using either of the last two rhythmic figures — but the profile of typicality is still not quite as clearly defined as it was in the first two measure-categor ies. The syntax of this section (reckoned in ter ms of harmony and rhythmic figure) is one in which new mater ials are gradually introduced and displace previous material. At the same time, measure-categor ies with a fairly clear profile of typicality give way to ones that have a less clearly defined profile (a trend reversed somewhat by measure-category 4). Similar syntactic patter ns structure the remaining three sections of the waltz. The most important features of the syntactic template for the waltzes produced by the game, taken as a whole, are as follows:16 New attr ibute-values — especially for rhythmic figure— are introduced throughout the first three sections. At the beginning of section 4, this process is temporar ily halted and, coincident with the return C major in m. 13, rhythmic figures are for the first time brought back. Cadences (such as those that occur in measure-categor ies 7 – 8 and 15 – 16) are marked by a distinctive treatment of attribute-values: values that occur in

16. In developing this character ization of the changes in attr ibute-values and typicality that can be found in the measure-categor ies collected in ex. 4.2, I considered the attr ibutes of contour, number of non-chord tones, bass motion, and starting pitch of the melody, as well as har mony and rhythmic figure. I found, however, that focusing on the latter two attr ibutes provides the clearest picture of typicality within — and across — the measure-categor ies. In consequence, my account of the syntactic template tends to emphasize these attr ibutes.

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analysis and theory no other measure-category occur here, and the number of different attr ibutevalues within each measure-categor y is shar ply attenuated. In particular, the measure-categor ies that cor respond with har monic ar rivals (that is, 8 and 16) have the most clearly defined profile of typicality of any of the sixteen. The syntax of sections 1 and 2 involves complementary processes: section 1 begins with measure-categor ies that have clearly defined profiles of typicality; the profiles of the measure-categor ies at the end of the section are less clearly defined. Section 2 begins with measure-categor ies that have less clearly defined profiles of typicality; at the end of this section, the profiles of the measure-categor ies are clearly defined. The syntax of sections 3 and 4 involves contrasting processes: section 3 has the broadest range of attribute-values of any of the sections (there are, for instance, over two times as many different rhythmic figures in section 3 as there are in section 1) and the most poorly defined profiles of typicality. By compar ison, the range of attribute-values is much more limited in section 4, and the clar ity of typicality is perhaps second only to section 1. The compositional strategy embodied in this syntactic template is one that would be familiar to aspir ing composers of the eighteenth century, for it is in complete accord with the compositional strateg ies for sixteen-measure dance for ms proposed in treatises of the per iod. Theorists like Riepel and Koch taught that the tonic should be plainly stated in the first section (the measure-categor ies with tonic harmony in this section have the most clearly defined profile of typicality); there should be clear cadences at the end of the second and fourth sections (in the musical game, this is accomplished by the distinctive treatment accorded the end of sections 2 and 4); and the third section should be planned so that it does not become independent from the whole — in Koch’s words, “it must be for med so that it loses its completeness and is bound more closely with the following fourth melodic section”17— something achieved in the template by the large amount of variation among the members of measure-categor ies 9 through 12. At a more abstract level, the compositional strategy incor porated in the template is, of course, similar to late-eighteenth-century conceptions of what is now conventionally called sonata for m.18 These conceptions divided sonata for m into two main 17. Koch, Introductory Essay on Composition, 100. Koch’s discussion of sixteen-measure dance for ms is on pp. 78– 117. 18. The classic study of eighteenth-century conceptions of sonata for m is Leonard Ratner’s “Harmonic Aspects of Classic Form,” Journal of the American Musicological Society 2 (1949): 159 – 68. The viability of eighteenth-century conceptions of sonata for m, and their relevance for recent literature on the topic of form, have been given a thorough discussion recently in Mark Evan Bonds, Wordless Rhetoric: Musical Form and the Metaphor of Oration, Studies in the History of Music, 4 (Cambridge, Mass.: Harvard University Press, 1991). A thoughtful cr itique of Bonds’s work can be found in Peter Hoyt, “Review of Mark Evan Bonds, Wordless Rhetoric,” Journal of Music Theory 38 (1994): 123 – 43. It should be noted that recent scholarship has argued for a substantially more complicated view of sonata for m than that presented by either Ratner or Bonds. For an insightful discussion, see Scott Bur nham, “The Second Nature of Sonata Form,” in Music Theory and Natural Order from the Renaissance to the Early Twentieth Century, ed. Suzannah Clark and Alexander Rehding (Cambr idge: Cambridge University Press, 2001), 111– 41.

cate g ori zat i on, st rate g y, and sy ntax parts, whose functions were determined by harmonic syntax: the Exposition (which set out the tonic and, in major keys, closed on the dominant); and the Development and Recapitulation (which closed on the tonic).19 The Exposition presented the pr incipal mater ials of the movement, much as sections 1 and 2 of the musical game present tonic and dominant; the Development departed from these mater ials, as does section 3 of the game; and the Recapitulation returned to the mater ial of the Exposition, just as there is a reprise of previously used mater ial in section 4 of the game. Given these similar ities, we can see that the conception of compositional strategy behind the template provides a link between modest sixteen-measure dance forms and sonata for m: both rely on the same syntax for organizing musical materials.20 This points out something rather important about the teaching of composition in the eighteenth centur y: the highly detailed accounts of dance for ms by Koch and others did indeed set out the means by which modest utilitar ian works could be generated, but they also schooled students in compositional strategies that could be applied to larger works. These larger works, then, were not simply generated by repeated applications of the compositional techniques descr ibed for minuets and the like, but by the reinterpretation of these techniques as strateg ies for composition that could be applied to categor ies of musical events. When these categories were realized over longer spans of time, extended works (such as those by Mozart and Beethoven discussed in the following sections) were born.

Typicality Effects and Musical Syntax What emerges from this analysis of the Musikalisches Würfelspiel is the significance of typicality effects for compositional strategy. Important structural points in the syntactic template — the establishment of tonic in the opening measures, the cadence on the dominant at the end of the second section, and the cadence on the tonic at the end of the fourth section — were all marked by measure-categor ies with clearly defined profiles of typicality. Indeed, a functional distinction between tonic and dominant can be made simply on the basis of the amount of variation present among the members of the measure-categor ies associated with each. Taking the template as a whole, there is less variation in (and thus a clearer profile of typicality for) measure-categor ies associated with the tonic (that is, measure-categor ies 1– 2, 4, 13– 14, and 16); there is comparatively more variation in (and consequently a less clear profile of typicality for) measure-categor ies associated with the dominant (that is, measure categor ies 3, 6, 8, 10, 12, and 15).21 19. In the following, I capitalize “Exposition,” “Development,” and “Recapitulation” when they refer to components of sonata for m, reserving the uncapitalized versions of the ter ms for the compositional techniques through which musical mater ials are laid out, developed, and reprised. There is, of course, a certain measure of anachronism in applying these ter ms to eighteenth-century works, especially when sonata for m is conceived as a two-part structure; nonetheless, the ter ms do single out compositional strategies recognized, if not so named, by eighteenth-century theorists. 20. The absence of an explicit link between the discussion of the appropriate compositional strategy for dance for ms and that for sonata for m has been noted by Bonds; see Wordless Rhetoric, 26– 27. 21. I interpret the C major har mony of measure-category 11 as the subdominant of G major; note the FS3 in the bass of the sixth variation.

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analysis and theory What also emerged was the possibility of describing the syntactic structure for a two-part form purely in ter ms of a general set of compositional strategies realized through the manipulation of categories of musical events. There is no doubt that, in the case of the waltz created by the game, harmonic syntax is of central importance; nor is there any doubt that those who have descr ibed for m with an emphasis on harmonic syntax do it with the assumption that this syntax also embodies compositional strategies applied to other aspects of music. Nonetheless, the account I have provided shows how certain compositional strategies — viewed as a generalized set of processes on musical mater ials — operate independently of the strategies associated with har monic syntax. With these thoughts in mind, let us tur n to some actual musical compositions — as opposed to recreational games — that make use of some of the compositional strategies seen in the Musikalisches Würfelspiel, as well as more novel strategies that are appropriate for extended and adventuresome instrumental works.

mozart, string quartet in c major (k. 465), first movement. alleg ro The Allegro of Mozart’s String Quartet in C major (K. 465) was one of Arnold Schoenberg’s favorites for illustrating motivic development of the sort discussed in chapter 1 of this volume. He found the work appropriate for these pur poses in part because of the prominence of the motive among the various musical mater ials and in part because it is easy to find traces of the motive even after it has left the scene (thus supporting the organic conception of musical composition of which Schoenberg was so fond).22 Because my concer n here is not with developing an account of the way a musical whole is der ived from a single theme, but with the motive as an element in an unfolding musical discourse, my account approaches the syntax of the principal melodic motive as independent from syntactic levels occupied with harmony and stylistic for mulae, and independent from musical signs or syntagms of the sort noted by Eco. I shall, however, consider how these are cor related with the syntax of the principal motive toward the end of my analysis. Mozart completed the quartet in C major dur ing January of 1785, and in September of that year it was published by Artaria in Vienna as one of a set of six quartets dedicated to Joseph Haydn.23 The first movement of K. 465 begins with an Adagio (mm. 1– 22) remarkable for its har monic peregrinations and rather odd pitch juxtapositions, which together ear ned the work its nickname as the “Dissonance” Quartet. The ensuing Allegro, by contrast, has hardly anything dissonant 22. For a discussion of Schoenberg’s analyses of this movement, see the Commentar y by Patricia Carpenter and Severine Neff in their translation of Schoenberg’s The Musical Idea and the Logic, Technique, and Art of Its Presentation (New York: Columbia University Press, 1995), 53. Schoenberg first developed his idea of “developing variation”— which he later, and famously, applied to the music of Brahms — in an analysis of this movement made in 1917; see Arnold Schoenberg, Coherence, Counterpoint, Instrumentation, Instruction in Form, ed. Severine Neff, trans. Severine Neff and Charlotte M. Cross (Lincoln: University of Nebraska Press, 1994), 41. 23. For a fuller account of the quartet and its companions, see John Irving, Mozart: The “Haydn” Quartets, Cambridge Music Handbooks (Cambr idge: Cambridge University Press, 1998).

cate g ori zat i on, st rate g y, and sy ntax about it. The Allegro is cast in sonata for m, and the pr incipal melodic motive appears prominently in five places: the opening and end of the Exposition (mm. 23– 51 and 91– 106, respectively); the Development section (mm. 107– 54); and the opening and end of the Recapitulation, extending into the Coda (mm. 155– 70 and 211 – 46). My discussion concentrates on the first three of these, with br iefer comments on the beginning of the Recapitulation and the Coda.

Measures 23 – 51 of the Allegro Example 4.3 g ives the first twenty-nine measures of the Allegro. The principal motive of the movement is presented in the first violin in mm. 23– 24, and then again in mm. 25– 26 (symbolized with ␣ in ex. 4.3). Using an analytical perspective that will infor m each of the remaining analyses, I shall approach the various for ms of this motive as a cognitive category, structured around a conceptual model. I shall leave open the question of the status of these conceptual models — that is, whether they are empir ically verifiable constructs or simply convenient analytical tools — and proceed on the general understanding developed in chapter 1 and br iefly reviewed at the beginning of this chapter: categor ies are basic structures in ter ms of which we understand the world, they are organized around conceptual models, and they represent a common g round where the concer ns of listeners and composers meet. The model for the categor y consists of three cor related conceptual elements, character ized as the things necessary for a melodic fragment to count as an instance of the motive: • a rhythmic patter n that spans two measures of common time: ch,Ω≈≈ç « h qŒ • a rather specific diatonic contour, consisting of four elements (each is shown in ex. 4.4); in order of succession, they are (i) a sustained first note (ii) an ascending stepwise motion through a third (iii) an upward skip of a third (iv) a downward step • an implied har monic change from the first to the second measure of the motive The contour of the motive gives rise to two distinctive intervals: the fifth spanned by ii and iii; and the fourth between i and the last note of iv. Although the implied change in har mony is masked in mm. 23– 24 (owing to the viola’s pedal point), in most other cases it is quite apparent. After mm. 23– 26, there are three further instances of the motive that cor respond to this model: two in mm. 31– 34 (with the motive accompanied by the second violin), and one in the cello in mm. 44– 45 (with the cello’s concluding half note taking the place of the quarter-note and quarter-rest of the original). Somewhat lesstypical for ms appear in the first violin in mm. 27– 28 and in the ascending cascade of mm. 45– 48 (␤ in ex. 4.3). In each case, the very end of the motive has been

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W. A. Mozart, String Quartet K. 465, first movement, mm. 23– 51

Allegro

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analysis and theory example 4.4 Schoenberg’s analysis of the main motive from W. A. Mozart, String Quartet K. 465, first movement i

iii

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modified: in mm. 45– 48, the most significant change is to the end of the rhythmic figure; in mm. 27– 28, both the end of the rhythmic figure and contour patter n have been changed. One additional version of the motive, heard in the first violin in mm. 35– 36 (␥ in ex. 4.3), is still less typical, retaining most of the rhythmic patter n of the original, but only element ii of the contour. One other bit of musical mater ial (shown with ␦ in ex. 4.3) seems to demand affiliation with the motivic category. As but a subcomponent of the motive— the ascending gesture that ends on a strong beat — it is hardly typical of the category. Indeed, hearing the fragment as a member of the category requires that it appear in close proximity to more typical members of the categor y.When a similar gesture occurs in mm. 62– 63 and 64 – 65 in the midst of the first subsidiar y theme (as shown in ex. 4.5), it is decidedly subservient to the alter nation of ascending and example 4.5

W. A. Mozart, String Quartet K. 465, first movement, mm. 61– 66 δ?

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cate g ori zat i on, st rate g y, and sy ntax descending skips that dominates the musical scene, having lost its connection to the principal motive. The change in the way we hear this fragment — in mm. 48– 51, as belong ing to the categor y that includes the pr incipal motive; in mm. 62– 65, as a rather gener ic bit of filler — is an example of the phenomenon of conceptual slippage noted in chapter 3, but one applicable to purely musical concepts. The context that induces this slippage is the absence of the principal motive and the presence of new mater ial associated with the first subsidiary theme. The melodic syntax for these opening measures, then, involves setting out the most typical members of the category first— indeed, these provide the basis for the conceptual model for the categor y.24 Less typical members of the categor y follow (in mm. 27– 28 and 35 – 36), and, in mm. 37– 43, the motive temporar ily disappears altogether (save for the ␦ fragments). It then reappears in its most typical for m in m. 44, immediately followed by three slightly less typical versions. After this, there are further ␦ fragments that lead to the gener ic cadential mater ial that prepares for the entrance of the first subsidiary theme in m. 56. Taken as a whole, the motive forms presented in mm. 23– 51 are a relatively normative Type 1 category.What is str iking, however, is the dynamic shape of the category as it is presented over the course of time. Although typical members dominate the musical texture in the first half of the section, they momentar ily disappear from the texture in the second half , to be brought back at an important moment preceding the transition to the first subsidiary theme. The importance of the principal motive for the melodic syntax of mm. 23– 51, then, is less a function of its constant presence and more a function of its memorability and cognitive utility. These make possible a musical syntax of both exposition and development: exposition as the motive is first established in its most typical for m; and development as lesstypical variants are then introduced.

Measures 90 – 106 of the Allegro After its gradual departure in mm. 44– 51, the motive disappears completely for forty measures, during which time two subsidiary themes are presented in the dominant. When the motive does return, it is at a moment of opportunity, following a final emphatic cadence of the sort that usually signals the conclusion of a section or that prepares the way for additional thematic mater ial. By bringing back the main motive at this point, Mozart ties together the beginning and end of the Exposition. The bonds are relatively loose ones, however, for it is a variant of the main motive rather than the or iginal that is introduced, and the compositional strategy applied to the statements that follow is closer to development than it is to exposition. As shown in example 4.6, the motive enters in the second violin in m. 91, just as the first violin achieves its cadential G5.25 The first violin responds by taking up 24. As noted in chap. 1, it is also possible for the conceptual model for a category of motive forms to emerge over time, although the longer the process is delayed, the more the conceptual model comes into conflict with the global model for a musical theme. 25. The sustained note at the beginning of the motive allows Mozart to introduce it under the cover of cadence, something he exploits at various developmental moments throughout the movement.

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W. A. Mozart, String Quartet K. 465, first movement, mm. 90 – 106 β

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cate g ori zat i on, st rate g y, and sy ntax the motive as well, beginning a short game of motivic tag in which some for m of the motive enters in each of the succeeding measures. Here, the initial motive forms are of the ␤ variety, highly similar to the or iginal for m but with a slightly modified ending. Although har monic change is still evident, the constant overlap of motives limits the har monic possibilities to the tonic and dominant of G major. The sense of harmonic progress that accompanied the or iginal statement of the motive is markedly attenuated: contr ibuting factors are the constant alter nation between tonic and dominant, the cello’s pedal point in mm. 91– 95, and the halving of harmonic rhythm that follows in m. 96. This reprise of the motive bears witness to new, and somewhat more extensively varied, members of the motivic category. In mm. 93– 94 and 94 – 95, the second and first violins present embellished versions of the motive forms they have just stated (indicated with a ␥ in ex. 4.6); were it not for the temporal proximity of these to the preceding motive forms, it might be difficult to make a case for their der ivation from the or iginal. More obvious is the inverted for m of the motive that appears in the first violin in mm. 96– 99, and which is then used in the simultaneous presentation of motive forms in all four instr uments in mm. 103 – 104. Finally, the ␦ fragment that provided a measure of unity at the opening of the exposition reappears in mm. 100 – 103 to serve as a link between the motive forms that precede and follow it. Given the absence of the or iginal for m of the motive in these measures, a case could be made for modifying the conceptual model for the category so that variants of the sort shown with a ␤ in example 4.6 would be regarded as typical (indeed, such a move would be the first step along a slippery slope of motivic development of the sort that Wagner leads us down with his transfor mations of the Leidensmotiv). Nonetheless, retaining the sense that we have moved away from what is typical of the category is important for what happens next. If the repeat sign of m. 106 is observed and the Exposition reprised, the typicality of the original version of the motive will be reaffirmed: we will have moved from the edges of the category (as represented by mm. 91– 106) back to the center. If we instead proceed from m. 106 into the Development, we will move yet farther toward the fr inges of the category.

Measures 107 – 35 of the Allegro As shown in example 4.7, Mozart begins the Development with a slightly modified version of the or iginal motive, but with changes now made to the middle of the motive rather than to the end: he starts the ascending-third figure a step higher than the sustained note, instead of repeating the sustained note at the beg inning of the figure. As a result, the motive, as a whole, now spans a fifth and implies no change of harmony. The chromatic alteration in the first violin at m. 111 moves the motive a bit further away from its typical for m, but it is the version in the viola at mm. 112– 13 that accelerates the process of transfor mation. In this version (indicated with a ␥ in ex. 4.7), the ascending-third figure is replaced with an ar peggio, which becomes a feature of the following motive forms. At m. 117, the arpeggio figure takes over, and the subsequent dissolution of the motive leads to a momentar y cadence on the dominant of A minor in m. 121.

161

example 4.7 107

W. A. Mozart, String Quartet K. 465, first movement, mm. 107 – 35 β

β

β

β

β

γ

β

112

cresc.

cresc. γ

γ

cresc.

cresc.

116

γ

162

example 4.7

(continued)

120

β

β

δ

124

γ

δ

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128

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132

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164

analysis and theory At m. 121, the cello returns to the for m of the motive used at the beginning of the Development (but now within the context of A minor). After two statements, the rising arpeggio figure once again replaces the ascending third within the motive, after which point it displaces the main motive or its variants altogether (as indicated by the preponderance of ␦ symbols after m. 125 in ex. 4.7). In m. 147 (which is not g iven in ex. 4.7), the for m of the motive used at mm. 107 and 121 makes a final appearance (beg inning with the cello’s G2, but pointing toward C minor). Given the events that followed the previous two appearances of this form of the motive, this third appearance seems to suggest yet another episode of development. Nonetheless, in m. 151, the motive yields to an ascending cascade of arpeggio-figures (all outlining a G dominant-seventh), which br ings the Development to a close. As was the case in the Exposition, in the Development more typical for ms of the motive are followed by less typical for ms.What is distinctive is the repetition of this pattern in close order (which occurs three times within the forty-odd measures of the Development), and the emergence of the ascending ␦ figure as the means for Mozart to advance his musical argument. While the slightly varied for m of the motive that marks the beginning of each patter n has prominence as a point of reference for this musical argument (and thus represents what is “typical” of thematic mater ial), it lacks the sense of balanced har monic progression summoned by the original for m of the motive. Given the variation of the motive that takes place over the course of mm. 107 – 35, however, just what is typical of the or iginal motive is something of an open question by the time we arrive at the dominant-seventh of mm. 151– 55.

Measures 155 – 60 and 211 – 46 of the Allegro The question of motivic identity posed by the Development is answered by the understated but nonetheless confident return of the original motive in mm. 155– 58, shown in example 4.8. Although the accompaniment is somewhat different than that used in mm. 23– 26, the motive itself is unchanged from its or iginal for m: this is the motive at its most typical. Mozart is not content to leave it at that, however. The accompaniment for the second statement of the paired motives, in mm. 163– 66, is not only fuller, but it br ings back the overlapped motive forms used at the end of the Exposition and at the beg inning of the Development. These slightly varied forms of the original (indicated with ␤ in ex. 4.8) recall the developmental cast of the earlier passages, as do the ascending ␦ figures in the cello. Mozart nonetheless quickly tur ns away from any further dissolution of the main motive and instead moves with dispatch toward the first subsidiary theme, which commences at m. 176. The end of the Recapitulation restates the end of the Exposition almost exactly: mm. 91– 106 are transposed into C major for mm. 211– 26. From this point, the music proceeds either back to the beg inning of the Development (if the repeat is taken) or forward to the Coda (which occupies mm. 227 – 46). As shown in example 4.9a, the latter grows out of the opening of the Development but uses yet another modification of the original motive. This version owes much to that used in mm. 211– 13 (the transposed quotation of mm. 91– 93), but applies a chromatic

example 4.8

W. A. Mozart, String Quartet K. 465, first movement, mm. 155 – 70 α

155

α

β

159

163

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α

β

β

δ

δ

δ

δ

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γ

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167

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analysis and theory inflection to the note at the beginning of the ascending-third figure. A further variant then concludes the movement, which is shown in example 4.9b: the end of the motive, shortened from the or iginal half-note–quarter-note figure to the successive quarters of mm. 227 – 29, is shortened yet again to two successive eighth-notes. Although a similar figure occurs in mm. 229– 30, that variant refers back to mm. 27– 28, for the successive eighths lead immediately to additional mater ial (in the case of mm. 229 – 30, a repetition of the ascending-third figure). In mm. 242 – 45, the eighths simply represent a compression of the original motive, and it is with this abbreviated for m of the motive that the movement ends. Although the concluding section recalls the opening of the Development, Mozart allows the prospect of further divergence from the main motive to linger for only a moment before banishing it with a vigorous and tr iumphant cadence in C major in mm. 234 – 35. Nonetheless, it cannot be said that the movement ends with an unequivocally typical for m of the motive: if the or iginal for m of the

example 4.9 W. A. Mozart, String Quartet K. 465, first movement: (a) mm. 227 – 30; (b) mm. 242 – 46 a 227

β

β

cresc.

cresc. β

β

cresc.

cresc. b 242

β

β

cate g ori zat i on, st rate g y, and sy ntax motive represents the stable center of the cognitive categor y of motive forms, the conclusion does not return us to that center. Two factors infor m the ending; both are related to global models, which provide a context for the conceptual model that defines what is typical of this motivic categor y. First, the ending is har monically quite stable: the final version of the motive introduced in mm. 242 – 45 reinforces this stability by outlining scale deg rees 5 and 1 and by placing the ar rival on 1 as close as practicable to the fir st beat of the metr ic cycle while retaining the appogiatura figure character istic of the motive. Second, the most typical version of the motive, in accordance with the global model for music themes relative to which it is framed, represents musical mater ial to be acted upon — it is a theme in the sense of a topic for discourse. At this point in the movement, however, discourse must be concluded: what is required is not a highly typical version of the main motive but a reminiscence of the motive suited to the pur poses of ending.

Compositional Strategy, Categor ization, and the Allegro Although I chose not to emphasize it in the preceding discussion, the overall compositional strategy that shapes the Allegro (as opposed to its pr incipal motive alone) has, not sur prisingly, a high deg ree of conformance both with models for sonata form proposed by music theor ists dur ing the late eighteenth century and with the syntactic template for the musical game discussed above. The first main section of the work (mm. 23– 106, which I have called the Exposition) moves from tonic to dominant, with themes or thematic groups for each key area. The second main section (mm. 107 – 204) begins by moving through a number of different key areas (the Development) and then tur ns to music that emphatically confir ms the tonic (the Recapitulation). The syntax of this for m is articulated by important cadential arrivals (such as the ar rival on the tonic in m. 44 or the ar rival on the dominant in m. 91), and although melodic themes are important for projecting a key and rendering a particular key area distinctive, they are not the dr iving force behind this portion of the musical discourse. Running parallel to this for mal syntax, but independent from it, are the compositional strateg ies that shape the categor y compr ising the various versions of the principal melodic motive of the Allegro. While the most typical members of this category are associated with tonic (and, in their typicality, serve to emphasize the importance of tonic within the for mal syntax), members with a high degree of conformance to the conceptual model for the category are also used to initiate presentations of the motive at points not associated with the tonic (such as the end of the Exposition or beg inning of the Development). Each of these presentations of the motive (whether on or off the tonic) leads to an increasing number of less typical members of the category, a process that ends either with the introduction of a more typical for m (as in m. 44 or m. 155), or with a move toward new thematic mater ial (as happens following m. 49). Through the accumulating evidence of these processes we come to understand the motive as a basis for Mozart’s musical discourse —

167

168

analysis and theory something to be introduced, varied, and ultimately reprised. A similar understanding does not develop in connection with the subsidiary themes first introduced in the dominant dur ing the Exposition; instead, these are melodic mater ials with the highly localized syntactic function typically attr ibuted to such themes by eighteenthcentury theor ists. Understanding the pr incipal motive as the basis for Mozart’s musical discourse, however, is not the same thing as regarding it as the generator of discourse throughout the movement. As I pointed out in connection with example 4.5, snippets of material reminiscent of some other aspect of the motive can be found elsewhere in the movement.26 Nonetheless, without the context provided by more typical members of the motivic category, we tend not to hear such fragments as related to the principal motive and thus do not hear them contr ibuting to the discourse of which the motive is a part. It is important to emphasize that the syntax associated with the pr incipal motive of the Allegro is not entirely unique to this movement. As Robert Gjerdingen has shown, composers of the late eighteenth century relied on a variety of stylistic formulae for both the substance and shape of their melodic and har monic mater ial, and these for mulae infor m the compositional strateg ies applied to the motive.27 However, the way this particular motivic category unfolds — how many typical members of the category are presented before variation ensues, the relative typicality of subsequent members, and the amount of time before more typical members return— is something specific to the Allegro. The principal motive of the Allegro should also be understood as an instance of the sort of musical topics to which eighteenth-centur y composers regularly made recourse (and to which Eco referred in his acknowledgement of musical “signs”). Mozart’s motive is a good example of the “singing style” as character ized by Leonard Ratner, and the lyr ical presuppositions of this topic do much to shape just what components of the motive are called on for the pur poses of variation.28 Nonetheless, I think Mozart’s motive is also more than simply a musical topic, for in its status as a remarkable musical categor y— remarkable in the variety of members the category compr ises, and remarkable in the way the manipulation of these members contributes to Mozart’s overall musical argument — it transcends topicality to become an essential element within the musical discourse peculiar to the Allegro of the C major quartet.

26. A thorough analysis that makes an argument for the omnipresence of the principal motive can be found in Bonds, Wordless Rhetoric, 102– 10. 27. See in particular Robert O. Gjerdingen, A Classic Turn of Phrase: Music and the Psychology of Convention, Studies in the Cr iticism and Theor y of Music (Philadelphia: University of Pennsylvania Press, 1988); idem, “Revisiting Meyer’s ‘Grammatical Simplicity and Relational Richness,’ ” in Cognitive Bases of Musical Communication, ed. Mari Riess Jones and Susan Holleran (Washington, D.C.: American Psychological Association, 1992), 225 – 43; and idem, “Courtly Behaviors,” Music Perception 13 (1996): 365– 82. 28. For examples and discussion of musical topics, see Leonard G. Ratner, Classic Music: Expression, Form, and Style (New York: Schirmer Books, 1980), 9– 29. For a discussion of musical topics of this sort within the specific context of musical semiotics, see Victor Kofi Agawu, Playing with Signs: A Semiotic Interpretation of Classical Music (Princeton, N.J.: Princeton University Press, 1991), 17– 34.

cate g ori zat i on, st rate g y, and sy ntax

beethoven, string quartet in bb major, op. 18 no. 6. first movement Joseph Kerman devoted the first quarter of his classic study of the Beethoven str ing quartets to the Op. 18 set (which date from 1798 to 1800), rightly believing that these early works held important keys to understanding how Beethoven transformed what had been a relatively modest genre into the ne plus ultra of chamber music.29 But Kerman had little patience with the first movement of the sixth quartet, for he found scant evidence of the sort of motivic development that would become the hallmark of Beethoven’s mature style.30 In truth, the opening motive of the work undergoes hardly any transfor mation over the course of the movement: its syntax is not easily explained in ter ms of relative degrees of typicality among category members. What is involved instead is a categor y that includes two distinctly different for ms of the motive, forms distinguished not only by the mater ials from which they are fashioned but also by the way they are used. The different uses of these two forms suggests a higher level of syntax that includes both, and this in tur n gives a glimpse into the process by means of which musical topics, of the sort discussed by Ratner and alluded to by Eco, are formed. Ratner, for his part, character ized this movement as “pure buffa, a dancing cartoon.”31 As can be seen in example 4.10, the two forms of the principal motive contribute much to the effect, providing a musical Tweedledum and Tweedledee to the listener’s Alice.32 The first of these (␣ in ex. 4.10) sketches a rapid ascent through a broken ar peggio on the tonic and, aided in the first case by a slightly overemphatic fortepiano, sets out the first beats of mm. 3 and 5 as points of arrival. The second for m of the motive (␤ in ex. 4.10), suave and somewhat understated, introduces the dominant and is metr ically more open. In mm. 7 and 9, it ends on the second main beat of the measure; in its third appearance, it ends on the first beat of the measure, but only after its ending is extended by mm. 12– 13. The overall har monic contour of the ␤ form is also relatively flat: in mm. 5– 7, for instance, it begins and ends on Bb2, while m. 6 is preoccupied with a simple alter nation of the fifth and root of the dominant chord. 29. With this character ization I mean to take nothing away from the accomplishments in this genre by Haydn or Mozart, but only to suggest that it is with Beethoven that the quartet eventually becomes a site for the active contestation of musical values and that this represents a new possibility for chamber music. See, for instance, Daniel K. L. Chua, The “Galitzin” Quartets of Beethoven: Opp. 127, 132, 130 (Princeton, N.J.: Princeton University Press, 1995). The issue for musicologists, then, is the extent to which the early quartets prepare the way for this transfor mation of the genre. 30. Joseph Kerman, The Beethoven Quartets (New York:W.W. Norton, 1966), 71– 74. 31. Leonard G. Ratner, The Beethoven String Quartets: Compositional Strategies and Rhetoric (Stanford, Calif.: Stanford Bookstore, 1995), 89. 32. In Through the Looking Glass, Alice quotes a nursery rhyme about Tweedledum and Tweedledee, and, after hear ing this, the two brothers reply: “I know what you’re thinking about,” said Tweedledum; “but it isn’t so, nohow.” “Contrar iwise,” continued Tweedledee, “if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.” Lewis Carroll, The Annotated Alice: Alice’s Adventures in Wonderland and Through the Looking Glass, introduction and notes by Martin Gardner, illustrated by John Tenniel (New York:W.W. Norton, 2000), 181. In a note to this passage, Gardner observes that the nursery rhyme may descend from a bit of doggerel by John Byrom (an eighteenth-century hymn writer and teacher of shorthand), which recounted the rivalry between George Fr ideric Handel and Giovanni Battista Bononcini.

169

example 4.10 mm. 1– 30

Ludwig van Beethoven, String Quartet, Op. 18 No. 6, first movement,

Allegro con brio

α α

Violino I

Violino II

Viola β Violoncello β 6

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11

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cate g ori zat i on, st rate g y, and sy ntax example 4.10 21

(continued) β

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Commenting on the deliberate and somewhat stagy entrances of ␣ and ␤ is a fragmentar y form of the motive (␥ in ex. 4.10). This consists of only a tur n and a leap (first ascending, then descending); its entrances reverse the expansion of the distance between strong metr ic accents occasioned by the extension of mm. 12– 13, shrinking it first to one-measure and then (in mm. 17– 18) half-measure intervals. This process of acceleration culminates in an ar rival on the dominant in m. 18, embellished with a run in the cello that returns the music to the tonic and to the ␣ form of the motive. To better understand the distinctive features of and relationships between these three forms of the motive, as well as their progress through the movement, let us consider conceptual models for each; diagrams for the models are given in figure 4.6. The conceptual model for the categor y of ␣ forms consists of five cor related conceptual elements, character ized as the things necessar y for a melodic fragment to count as an instance of this version of the motive: • the rhythmic patter n C√∫∫µ «qqqq «hd • the motive begins with a tur n figure (here, around 5) • the continuation of the motive involves a broken ar peggio with ascending contour (here beginning on 3 and ascending through a sixth to 1)

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analysis and theory b.

a.

C qqqq

q

C q q q q q q q q h.

C qqqq q q q q h q

rhythmic pattern

begins with turn figure

begins with turn figure

begins with turn figure

rhythmic pattern

rhythmic pattern

a

c.

broken arpeggio with ascending contour

b

overall contour flat, with internal skip of a fifth

g

ends with ascending or descending skip

no change of harmony

harmony alternates I-V-I

no change of harmony

melody with accompaniment

stated in dialogue

stated in dialogue

figure 4.6 Conceptual models for the three forms of the principal motive from Beethoven, String Quartet, Op. 18 No. 6, first movement, mm. 1– 30: (a) the ␣ form; (b) the ␤ form; (c) the ␥ form

• there is no change of harmony implied by the motive • the motive is presented as a melody supported by accompaniment in the remaining str ings33 Each of these elements could, of course, be broken down into smaller parts. This is particularly true of the rhythmic patter n, which is extended by the ␤ form of the motive and truncated by the ␥ form. As indicated by figure 4.6b, the conceptual model for the ␤ form retains most of the first two components but alters the last three. The ␥ form continues this process, retaining only the tur n figure that is the motive’s most character istic feature. Slightly varied restatements of the ␣ and ␤ forms of the motive in mm. 19– 29— the texture thickened somewhat, and with the two violins taking part in the dialogue proper to the ␤ form of the motive— lead to a long pedal on the dominant of F major preparatory to the statement of the second theme, which commences in m. 45.What is remarkable, from the perspective on musical syntax I have developed thus far, is the nearly complete lack of typicality effects among these mater ials.While it would be quite possible to include them all in a single category for the motive, framed relative to a conceptual model that combines the essential elements of those included in figure 4.6, there does not seem to be a compelling argument for regarding either the ␣ and ␤ form as more typical of the category. A better case could be made for conceiving of the ␥ form as a less typical member of the category (if only on account of its fragmentar y nature), but it is a bit hard to say just 33. There are, of course, other ways the motive could be character ized. For instance, the rhythmic figure I identify does not include the very first note of the piece. My chief reason for seizing upon this figure is for compar ison with other for ms of the motive. Should one wish to include the first note, the remaining for ms of the motive would represent even more radical departures from the standard established by the ␣ form.

cate g ori zat i on, st rate g y, and sy ntax what it is less typical of . It could be der ived from either the ␣ or the ␤ form, and without further variants it remains somewhat difficult to settle the question. Subsequent to a cadence on F major in m. 80 that wraps up the exposition of the second theme, the ␤ form of the motive reappears, as shown in example 4.11. Although it has been transposed to F, and its third statement in the cello is accompanied by parallel tenths in the viola and by a reprise of the passagework from the bridge in the first violin, it is otherwise exactly the same as when it appeared in the context of the first theme g roup. This restatement has two consequences. First, it confir ms the character of the ␤ form of the motive that was established in the opening measures — that is, it reinforces the conceptual model outlined in figure 4.6b. Second, it draws out a function of ␤ implicit in the initial exposition of motive forms, which was to close off musical discourse.Where the ␣ form of the motive sets out the conditions for musical discourse — establishing a two-measure hypermeter and opening the melodic range to cover more than two octaves— the ␤ motive, with its pedestr ian alter nation of tonic-dominant-tonic and restricted range, provided closure. Following m. 80, the motive has a similar function, but now it serves to close off the discourse of the entire Exposition. The syntactic functions of the ␣ and ␤ forms of the motive are due in part to example 4.11 mm. 79– 87

Ludwig van Beethoven, String Quartet, Op. 18 No. 6, first movement, β

79

β

84

cresc.

cresc.

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174

analysis and theory their resemblance to similar figures in other compositions: ␣ has all the features of a prototypical opening gesture within eighteenth-century style, and ␤ has much in common with prototypical closing gestures. It should be emphasized, however, that how such motives are used is also important. As Janet Levy has pointed out, Joseph Haydn, at least on occasion, used closing gestures as his opening mater ial.34 The use of a closing gesture in this way is in part comic — it creates a piece that seems to end before it has begun — but it also makes possible some marvelously ambiguous seams: one is not sure whether a particular passage is a beginning or an ending. The possibility of this ambiguity testifies to the importance of the way musical mater ials are used within a particular composition, as distinct from how similar mater ials are used in other compositions. For a gesture to signify “opening,” it has to be used in openings; for a gesture to signify “closing,” it has to be used for closings. The ␣ form of the motive’s function as an opening gesture is confir med when it initiates the Development, which begins with a tutti statement of the motive, immediately echoed by a solo statement in the first violin (as shown in ex. 4.12). These slightly less than typical versions of the motive (which has heretofore always appeared as melody with accompaniment) are followed immediately by the ␥ form, which tosses a repetition of the head of the ␣ form just heard back and forth between the upper str ings. In mm. 103– 110, two further variants of the ␣ form appear, which extend the motive both metr ically (to four measures) and intervallically (to a compass of an eleventh, and then a twelfth). These expansions lead to G minor, which initiates a rapid cycle of keys explored through the medium of the thematic mater ial that first served as a br idge between Bb and F back in mm. 33– 43. In m. 139, there is a weak cadence on F, followed immediately by a reappearance of the ␤ form of the motive (shown in ex. 4.13). Stated, as it is, in F major, it recalls the end of the Exposition; however, this particular version does not confor m completely to the conceptual model diag rammed in figure 4.6b. The rhythmic profile has been changed and is now the same as that of the ␣ form; the dialogue presentation typical of ␤ forms is absent, replaced here by one unaccompanied and one accompanied statement. Nonetheless, although close to thirty measures of the Development remain, this entry of the ␤ form of the motive signals the end of the harmonic exploration initiated by the variant ␣ forms in mm. 103 – 10: F major having been regained, the remainder of the Development simply serves to postpone the inevitable return to the opening mater ial. Just as it has each time before, the ␤ form of the motive confir ms a closing of harmonic structure. With the return to Bb in m. 175, there is an exact reprise of the first eighteen measures of the movement, after which the ␥ form of the motive is presented in a series of close-order repetitions that initiate the br idge to the second theme. At the conclusion of the movement, the ␤ form returns once more, as it did in mm. 80 – 86, only this time confir ming a final close on Bb.

34. Janet Levy, “Gesture, Form, and Syntax in Haydn’s Music,” in Haydn Studies: Proceedings of the International Haydn Conference, Washington, D.C., 1975, ed. Jens Peter Larsen, Howard Serwer, and James Webster (New York:W.W. Norton, 1981), 355– 62.

example 4.12 mm. 91– 110 91

Ludwig van Beethoven, String Quartet, Op. 18 No. 6, first movement,

2

α

α

γ

γ

γ

96

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cresc.

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cresc.

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101

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106

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analysis and theory example 4.13 mm. 138– 43 138

Ludwig van Beethoven, String Quartet, Op. 18 No. 6, first movement,

β

β

As Kerman noted, there is little development of the principal motive in the first movement of Beethoven’s Quartet, Op. 18 No. 6. This is not to say that the motive is uninvolved in the syntax of the movement, however, only that the musical discourse is not, in any significant way, about this motive. Thus the ␣ form of the motive signals an opening for musical discourse, but it is not discourse about ␣. Even when the ␣ form makes an attempt to grab center stage at the beginning of the Development, the effort ends up being little more than comedic bluster: knowing only how to begin, it cannot quite figure out how to continue, and after two attempts (in mm. 102 – 10), it gives up. Similarly, the ␤ form of the motive closes off discourse, but it is not always a discourse in which ␤ has been involved (as in its appearances at the end of the Exposition and Recapitulation, and in the Development). Thus the two motive forms, by virtue of the way they are used, contr ibute to a larger syntax concerned not with them but with the progress of the movement as a whole. Despite their similar ities, I believe these two motive forms are distinct enough in their features to be regarded as separate, though related, categories (something illustrated by the conceptual models of fig. 4.6). The syntactic function that accrues to each over the course of the movement — with the ␣ form used only for openings, and the ␤ form used only for closings — gives further support to this distinction. Nonetheless, I regard distinguishing the motive forms on the basis of syntactic function to belong to a later and more theoretical stage of understanding. Accordingly, categor izing the motives is relatively immediate, while understanding the way they function within the work emerges only over time. As I have noted, these two forms of the motive bear resemblance to stylized musical gestures that signal openings and closings. However, I would argue that, at least on the abstract level concer ning processes that pertain to musical categor ies, their function within the movement does not der ive from these gestures. To be blunt, I do not believe knowledge of such stylized figures is necessary to understand Beethoven’s musical argument. That it would enr ich this understanding I have no doubt, but this is not the same as asserting such knowledge as a precondition for making sense of the discourse of the movement. Instead, the function of the ␣ and

cate g ori zat i on, st rate g y, and sy ntax ␤ forms of the motive is an emergent property consequent to the way they are constituted (as contrasting yet similar motivic structures) and the way they are used within this movement. The notion that Beethoven’s use of these motives bestows particular functions on them further suggests how musical topics come to signify the things they do. Granted, the musical mater ial for any topic needs to meet certain prerequisites of harmony and counter point and confor m to general expectations about affect. But beyond this, one must acknowledge the significance of the way composers have used particular musical gestures— that is, their prevalence within a certain histor ical and cultural milieu — in establishing the things these gestures come to signify. Put another way, signification is not an inherent property of musical mater ials but derives from how they are deployed in particular works of music — that is, from the syntactic function with which they are invested.

beethoven, string quartet in f major, op. 18 no. 1, first movement Where the discourse of the first movement of Beethoven’s Bb major quartet tends not to be about its opening motive, the discourse of the first movement of the F major quartet has difficulty being about anything else: as A. B. Marx famously observed, the opening motive occurs no fewer than 131 times within the 427 measures of the movement.35 Within this multiplicity, two categor ies of motive forms can be distinguished, differentiated both by their constituent features and by the compositional strategy that is applied to them. The distinction between these two categories becomes especially plain in the Development, when a new and highly dynamic variant of the motive appears that combines features of both. The importance of this variant for developing Beethoven’s musical argument is affir med in the Coda, which revisits all three forms of the motive. The compositional strategy associated with these various motive forms is relatively complicated, and it was not completely successful in Beethoven’s first attempt at the movement, a version descr ibed in great detail in a thorough study by Janet Levy.36 In what follows, I discuss how this strategy is manifested in the Exposition, Development, and Coda of the second (and final) version of the F major quartet, and then turn to Beethoven’s first version to explore how it was brought to its final for m.

The Exposition In a manner similar to the first movement of the Bb major quartet, the F major quartet opens with a pr incipal motive that takes two distinctly different for ms. The first (␣ in ex. 4.14) is assertive, direct, and ends on the first beat of the measure. The second (␤ in ex. 4.14) is voiced in a lighter manner, is har monically fluid, and ends 35. Adolph Ber nhard Marx, Ludwig van Beethoven: Leben und Schaffen, 6th ed., ed. Gustav Behncke (Berlin: Otto Janke, 1908), 203. 36. Janet M. Levy, Beethoven’s Compositional Choices: The Two Versions of Opus 18, no. 1, First Movement, Studies in the Cr iticism and Theory of Music (Philadelphia: University of Pennsylvania Press, 1982).

177

Ludwig van Beethoven, String Quartet, Op. 18 No. 1, first movement,

example 4.14 mm. 1–29

Allegro con brio α

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Violoncello 8

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cate g ori zat i on, st rate g y, and sy ntax on the third beat of the measure. Joining these is a fragmentary form (␥ in ex. 4.14) whose character is less distinctive, and which plays a much more subsidiary role in the Exposition. This fragment consists of little more than the stylized tur n figure common to all for ms of the motive (and which was almost certainly the basis for Marx’s impressive tally). It is this feature of commonality that, as Ratner has noted, allows the motive to fit seamlessly into a variety of different contexts.37 As with the preceding analyses, we can character ize the distinctive features of and relationships between various motive forms by consider ing conceptual models for each; diagrams for the models are given in figure 4.7. The conceptual model for the category of ␣ forms consists of five cor related conceptual elements, characterized as the things necessar y for a melodic fragment to count as an instance of this version of the motive: • • • • •

the rhythmic patter n T qd√µ Ωç «q �� the first part of the motive outlines a stylized tur n figure the motive ends with a small downward skip the motive is stated tutti the motive has a relatively static har monic context

Save for the change in dynamics from the first to the second pair of statements — piano replaced by forte — all four of the statements of this for m of the motive in the opening measures confor m to this model. Put another way, the members of the category presented in mm. 1– 4 and 9 – 12 assign a relatively restricted range of values to the attr ibutes picked out by the conceptual model. Where the members of the ␣ motivic category are all quite similar to one another, the members of the ␤ category are rather more diverse. In mm. 13– 18, the b.

a. 3 4 q. q q q q

3 4 q. q q q q

q Î Î

rhythmic pattern

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first part of motive outlines stylized turn figure

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figure 4.7 Conceptual models for the three forms of the principal motive from Beethoven, String Quartet, Op. 18 No. 1, first movement, mm. 1– 29: (a) the ␣ form; (b) the ␤ form; (c) the ␥ form 37. Ratner, The Beethoven String Quartets, 12– 13.

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analysis and theory first measure of each statement of the motive is unaccompanied, an appogiatura over a fully-diminished seventh chord is introduced (in mm. 14 and 16), and the end of the last statement (in mm. 17– 18) has a slightly modified rhythmic profile.38 Versions of the motive that appear in mm. 21– 26 are similar to those of mm. 13– 18, but include echoes provided by the ␥ fragment as part of their accompaniment. The category of ␤ motives is, as a consequence, much more diverse: category members represent a relatively wide range of attribute-values. In the remainder of the Exposition, not only are these two categor ies of motives maintained but also Beethoven continues to treat them as he did in laying out the first key area. The ␣ motives (for the most part) continue to stay close to the conceptual model around which their motivic category is structured, and the ␤ motives (for the most part) continue to diverge in various ways from the conceptual model around which their motivic category is structured. The Exposition thus reinforces both the structure of the two categor ies and the compositional strateg ies through which they were first presented. After the opening thematic group, the ␣ form of the motive is prominent in four places, putting in appearances twice in the transition to C major: once in the middle of the second thematic group, and preparatory to the cadences that conclude the exposition. In each case, one of two relatively minor variants is used. The first variant, which initiates the transition that begins in m. 30 (as shown in ex. 4.15a), differs from the model in that it is stated solo against accompaniment and in alter nation with a competing figure in the first violin and then concludes with a skip down an octave. From a har monic perspective, this variant is more static than the or iginal ␣ form in that it prolongs but a single pitch-class (here, C) through the combination of the tur n figure and an octave skip; Ratner has noted that, in this for m, the motive evokes the sound of a musette.39 The second variant of the ␣ form of the motive, introduced by the viola in mm. 41– 42, is similar to the first, but it concludes with a repeated note instead of an octave skip (as shown in ex. 4.15b): rather than a single pitchclass, now only a single pitch (Eb3) is prolonged. Appearing against the ␣ form is a ␤ form (in the first violin), whose features are discussed below. This same variant of ␣ is used by the cello in mm. 72– 77 in the midst of the second theme group (see ex. 4.15c).40 An interesting complication here is that the figure with which this appearance of the variant competes (stated in the first violin) can easily be heard as a further variant of the ␣ form of the motive: admittedly, only the rhythmic profile and the beg inning of the tur n figure are retained (and, unlike other ␣ variants, this one is sequenced upward), but placed against the second ␣ variant the similar ities are striking. 38. In the first version of the quartet, the initial statement of the ␤ form of the motive (in mm. 5– 6) was also unaccompanied. The difference in texture, however, is less str iking than the clar ification of harmonic context provided by the accompaniment Beethoven added, which helped emphasize the contrast between the ␣ and ␤ forms. 39. Ratner, The Beethoven String Quartets, 14. 40. Note that the cello appears here an octave lower than in most published scores. This reading of the passage reflects that of the new Beethoven Werke.

example 4.15 Ludwig van Beethoven, String Quartet, Op. 18 No. 1, first movement, variants of the principal motive: (a) mm. 30 – 35; (b) mm. 41– 48; (c) mm. 72– 77; (d) mm. 101– 8 a 30

α

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(continued)

182

analysis and theory example 4.15

(continued)

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Heard as a variant of the ␣ form of the motive, it offers the first real challenge to the standard of typicality for the motivic category. The first variant of ␣ returns in the cello in mm. 101– 104 (shown in ex. 4.15d) against a figure in the first violin that can be related to the ␤ form of the motive; this passage is discussed in a bit more detail below.

cate g ori zat i on, st rate g y, and sy ntax In contrast to the ubiquity of the ␣ form of the motive, the ␤ form makes only two appearances after m. 30. The first, already mentioned above, is in m. 42 (see ex. 4.15b). Here the motive appears with an altered rhythmic profile (lacking its first note and using the variant ending first introduced in m. 18), and, in its role as counterstatement to the modified ␣ form in the viola, with less independence than before. The third entrance of the variant (in m. 46) departs further still, with its ending a durational augmentation of that used in the preceding measures. A similar augmentation of the tail of the ␤ form is heard in mm. 89– 91 (as shown in ex. 4.16) after a general pause that inter rupts the mater ial from the second thematic g roup. Save for this augmentation, this variant of the ␤ form of the motive is quite close to the very first version of ␤, heard in mm. 5– 6. The variant heard in mm. 89– 91 is the last explicit reference to the ␤ form of the motive before the conclusion of the Exposition. Nonetheless, the appogiatura figure that came to be a feature of ␤ beginning in m. 14 figures quite prominently in the counterstatement to the final appearance of the ␣ form in mm. 101– 104 (shown in ex. 4.15d). When this counterstatement is embellished with a repeated turn figure in m. 106 (answering the embellishment of the ␣ variant in m. 105), the connection becomes somewhat more plausible: the counterstatement could be heard as a further variant of the ␤ form of the motive. This inter pretation is supported by two things: first, there is the close relationship between the ␣ and ␤ forms of the motive throughout the Exposition (exemplified by their juxtaposition in mm. 41– 48). Second, the tur n figure typical of all for ms of the motive is replicated, in compressed for m, by the combination of the trill and ter mination on the third beat of m. 102 and the appogiatura of m. 103 (and further varied in mm. 104– 105). The possibility of extending the category of ␤ motives to include the counterstatement of mm. 102 – 105, together with the connection between the category of ␣ motives and various counterstatements (in mm. 41– 48, 72– 77, and 101 – 108), suggests a way our concept of the ␤ form of the motive might slip further still. If we return to the transition that begins in m. 30 (ex. 4.15a), we note a similar ity between

Ludwig van Beethoven, String Quartet, Op. 18 No. 1, first movement,

example 4.16 mm. 88– 91

β

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184

analysis and theory the accompanimental figure in the first violin and the ␤ variant from mm. 17– 18: the rhythmic patter n and contour of mm. 31, 33, and 35 is the same as that of m. 18. Our return to these measures becomes literal rather than imaginary if the Exposition is repeated: hearing mm. 30 – 35 after the several pair ings of the ␣ form of the motive with counterstatements and the extensions of the ␤ form that occur during the first pass through the Exposition could provide enough pressure to cause significant slippage within our concept of the ␤ form. This, in turn, might lead us to embrace the accompanimental figure of mm. 30 – 35 within that for m when we encounter it for the second time. Perhaps more remarkable than the conceptual fluidity of the ␤ form of the motive is the resistance of the ␣ motive to change: despite numerous juxtapositions with rival mater ials, it remains constant. Indeed, these two categor ies of motive forms can be further distinguished by the compositional strategies associated with each. Over the course of the Exposition, ␣ forms are subjected to relatively little variation, and most members of the category are close to the conceptual model outlined in figure 4.7a. In contrast, ␤ forms are varied almost from the outset. While the conceptual model for the category of ␤ forms still makes sense — it captures the salient features of members of the category as presented in the opening measures and serves to distinguish them from members of the category of ␣ motives— the range of values that members assign to the attr ibutes picked out by the conceptual model is much broader, and a given variant is rarely repeated. The difference between the compositional strategies applied to each category of motive forms lends a distinctive character to them: ␣ as stable in the face of various challenges; ␤ as an agent of change and transition. Although qualities such as these are part of the elemental materials of sonata for m, as they are manifested in the first movement of the F major quartet they also pose a kind of problem. The sort of fluidity with which the ␤ form of the motive is associated operates pr incipally in contrast to the stability of the ␣ form. By itself, it is not quite sufficient to create the dynamic energy — the sparks of real transfor mation — that the Development section will require. For this sort of drama, a new form of the motive is required, but one that draws on the musical materials and syntax developed over the course of the Exposition.

The Development After a br ief A major flour ish, the Development revisits ␣ and ␤, recalling the opening of the Exposition (as shown in ex. 4.17; the example does not include the A major flourish).While each motive departs slightly from its respective conceptual model — the ␣ motive includes light accompaniment in the upper str ings, and the ␤ motive acquires an echo — for the most part the conceptual model for each category is reaffirmed. Beethoven then introduces a new form of the motive that reconfigures the properties of ␣ and ␤ and transfor ms the possibilities for musical discourse. The new motive form (shown with a ␦ in ex. 4.17) is launched in m. 129 through a ser ies of imitative entrances. Although motive forms have appeared at one-measure intervals before, here they differ only in the octave in which they are stated. This manner of presentation makes reference to a topic to which Beethoven often made recourse in the Development sections of his instrumental works: the

example 4.17 mm. 119– 46

Ludwig van Beethoven, String Quartet, Op. 18 No. 1, first movement,

119

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186

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example 4.17 δ 137

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learned style that includes fugue and canon.41 This new motive form resembles a member of the category of ␣ motives. It is new in its isolation, harmonic stasis, and clear assertion of the downbeat of each measure as a point of initiation (rather than a point of articulation within a larger gesture, as it is in the second measure of a typical member of the ␤ category of motives). However, the dissonant interval for med by the downward leap consequent to the tur n figure (a diminished seventh— Bb3 to CS3 in mm. 129– 30) demands continuation beyond the downbeat, a fluidity reminiscent of the ␤ form of the motive.42 This amalgam of features and the way they dominate the measures that follow suggest that ␦ constitutes a new category of 41. For a discussion of the learned style, see Ratner, Classic Music, 23– 24. 42. Given both the emphasis of the large downward leap and the fact that the leap is dissonant, the ␦ form of the motive is more ambiguous at the hypermetric level than either the ␣ or ␤ forms: where the previous for ms of the motive can be heard in ter ms of pairs of strong and weak measures, such a grouping in the case of the ␦ motive is much more arbitrary. This is not to say that deter mining which measure of the ␣ and ␤ forms of the motive is strong or weak at any given point is a simple matter, however. Janet Levy and Roger Sessions, for instance, give interpretations of the accentuation of mm. 1– 2 that are the exact opposite of one another. See Levy, Beethoven’s Compositional Choices, p. 10, n. 28; and Roger Sessions, The Musical Experience of Composer, Performer, Listener (Princeton, N.J.: Princeton University Press, 1950), 13– 14.

cate g ori zat i on, st rate g y, and sy ntax

figure 4.8 Conceptual model for the ␦ form of the principal motive from Beethoven, String Quartet, Op. 18 No. 1, first movement, mm. 129 – 44

motive forms. The conceptual model for this categor y (diagrammed in fig. 4.8) consists of five cor related conceptual elements, character ized as the things necessary for a melodic fragment to count as an instance of this version of the motive.While this model has much in common with those diag rammed in figure 4.7, it also demonstrates enough differences to warrant its being used to distinguish the ␦ form from any of the other for ms of the motive important in the movement. Beethoven follows mm. 129 – 34 with two similar sections, the first beginning in m. 135, the second in m. 141. Each section begins with a slightly different patter n of entrances among the instruments, and each section prolongs a single fully diminished seventh chord: CS⁷ (mm. 129 – 34), FS⁷ (mm. 135 – 40), and B⁷ (mm. 141– 46).43 Each section also includes a variant of the ␥ fragment, based on the tur n common to all for ms of the motive but with a sforzando on the second beat: it first appears in the second violin in mm. 133 – 34, and subsequently in the viola and cello (mm. 139– 40) and first violin (mm. 145– 46). In truth, the variant of ␥ is difficult to hear, for within these imitative sections it must compete with the Ωçµqd figure that comes to dominate the first half of each measure in which the fragment appears. Nonetheless, as can be seen in example 4.18, the fragment is gradually transfor med, 43. This is in fact the same sequence of fully diminished seventh chords initiated in mm. 14– 16; however, that sequence led not to a B⁷ chord but to a Bb pedal preparatory to the first full cadence on F in mm. 19– 20. In his analysis of mm. 129ff., Ratner inter prets each fully diminished seventh chord as a leading-tone harmony with a nor mal resolution; see Ratner, The Beethoven String Quartets, 15. Indeed, on the very last eighth-note of mm. 128 and 129 there is a D minor chord, as there is a G minor chord in mm. 139 and 140, a C minor chord in mm. 145 and 146, and F and Bb minor chords in mm. 147 – 50. However, I hear these har monies as simply embellishing the fully diminished seventh chords that dominate these measures. This hear ing is not without its theoretical problems — it suggests the kind of dissonant prolongation that has vexed a number of music theor ists over the past two decades — but it has the advantage of capturing the intensity and uncompromising nature of this passage.

187

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analysis and theory example 4.18 mm. 145– 54 145

Ludwig van Beethoven, String Quartet, Op. 18 No. 1, first movement,

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over the course of mm. 147– 51, into the ␥ fragment as it or iginally appeared. So transfor med, it leads in a cascading sequence to the ar rival on the dominant of F major in m. 167. In one sense, however, this is not the ␥ fragment as it was first heard in mm. 22– 27, for that fragment was one-half of a two-measure motive. By contrast, the fragment of m. 151 and following is heard as the extension, in one voice, of the imitative entrances initiated in m. 129. With its abrupt introduction of the lear ned style, combination of features from both the ␣ and ␤ forms of the motive, and prolongation of dissonant har monies, the ␦ form of the principal motive provides elements of contrast and continuity with the preceding music. And compared with the various changes visited upon ␣ and ␤ in the course of the Exposition, the repetitions of mm. 129 – 46— both on the level of the individual motives that make up the imitative passages and on the level of the separate sections that prolong three different fully diminished seventh chords— make for an island of stability within the changing fortunes of the principal motive. Nonetheless, this moment of stability provides its own disruptions, and not only because it is based around a sequence of fully diminished seventh chords. The balance that had existed between the ␣ and ␤ forms of the motive— one associated

cate g ori zat i on, st rate g y, and sy ntax with a syntax of stability, the other with a syntax of fluidity, and each necessary for the other — has now disappeared: what is left after ␦ has done its work is only the chatter ing of the ␥ form of the motive. This, and passagework scales over a dominant pedal, is all that remains until the ␣ form of the motive reasserts itself at the beginning of the Recapitulation.

Recapitulation and Coda The appearance of motive forms in the Recapitulation, which begins with a literal return to the opening of the movement in m. 179, follows the same general outline as that of the Exposition. Missing, however, are almost all of the members of the ␤ category of motives. After the initial response to the ␣ motives (mm. 183 – 86, an exact repetition of mm. 5– 8), ␤ disappears, along with other vestiges of the opening twenty-odd measures, including the sequence of fully diminished seventh chords from mm. 14– 16 that had their extension in mm. 129 – 46. Beethoven replaces mm. 9– 29 with a br ief episode that veers off toward Gb major, which in its latter half makes reference to the transition that began in m. 30, and which also absorbs the function of the statement and counterstatement of motive forms in mm. 41– 48.44 The consequence of these changes is that the ␣ form of the motive goes virtually unchallenged in the Recapitulation, for both the ␤ form and the syntax of fluidity with which it was associated are absent. What we are left with is a clear impression of the stability — even obstinateness — of the ␣ form of the principal motive.45 Beethoven does offer a final challenge to this stability in the Coda, which begins in m. 274. After a pair of short ascending passages in staccato quarter notes (mm. 274 – 81) that recall the quarter notes that followed ␦ in the Development and a brief descending figure built from the paired sixteenth-note portion of the stylized tur n figure (mm. 282– 83), the main motive reenters in the first violin in m. 284 (see ex. 4.19). With the viola’s entrance at the octave below in m. 285, and continuation with the same sort of staccato quarter-notes that began the Coda, the reference is clear: Beethoven means to summon the ␦ form of the motive, although without its fortissimo entrances or dissonant har monies. On the one hand, the subsequent entr ies (beginning in m. 288) hint at the possibility of further development as the motive is tossed back and forth between different voices; on the other hand, they all serve to prolong the dominant. The possibility of development becomes a bit more real with the move to the submediant, in m. 294, and the reprise of a variant of the ␤ form of the motive.While the rhythmic figure is different from a typical member of the ␤ category, the syntactic references are clear: the motive is sequenced upward (as it was in mm. 13– 18, 21– 26, and 123 – 27), and its har monic

44. Levy notes that these changes tend to draw together various features of the original transition; see Levy, Beethoven’s Compositional Choices, 79– 83. 45. The impression of the solidity of the ␣ form of the motive is given further support by Beethoven’s decision to eliminate the repeat of the second section of the movement (that is, the Development and Recapitulation), one of the significant changes he made between the first and second versions of the quartet.

189

example 4.19 mm. 284 – 302

Ludwig van Beethoven, String Quartet, Op. 18 No. 1, first movement,

δ 284

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cate g ori zat i on, st rate g y, and sy ntax context is thoroughly fluid, including four fully diminished seventh chords (in mm. 295, 296, 298, and 299) and a cadential dominant (in mm. 300 – 301). Against the resolution of the ∞ over this dominant, the ␣ form of the motive finally enters (in the first violin in m. 301), and for the first and only time in the movement, its concluding downward leap outlines a falling 5-1, signaling an end to the peregrinations suggested in the preceding measures. After this closing gesture, there is one more bit of dialogue between ␣ and ␤ (not shown in ex. 4.19). The cello, beginning and ending on F2, repeats the variant of ␣ that ends with a repeated note (in mm. 302– 303 and 304 – 305, a variant first heard in mm. 41– 42). It is answered by a variant of ␤ reminiscent of that just heard in mm. 294 – 299 (played in thirds in the first and second violins in mm. 306 – 307 and 308 – 309). True to for m, these ␤ variants pull away from F major by introducing its b6 (Db), but they are answered by a cadential gesture that returns the movement, for once and for all, to F major. With regard to the pr incipal motive of Beethoven’s F major quartet, the Coda has a summational function that is twofold. First, the Coda revisits each of the three categories of motive forms that appeared over the course of the movement, doing so in reverse order of their initial appearance. Second, the Coda revisits the syntax with which each of these categor ies was associated. The Coda begins (much as did that of the first movement of Mozart’s “Dissonance” Quartet) with a reference to the Development; the subsequent allusions to ␦ suggest a challenge to the integrity of the principal motive (through fragmentation) but also take place within a context of overall stability (with the bulk of the entrances linked to the dominant of F). The ␤ motives that follow these ␦ forms exemplify the syntax with which ␤ is most often associated: although the broad range of features exhibited by members of the category of ␤ motives is not in evidence, the har monic fluidity typical of the category is well represented by the fully diminished seventh chords prominent in the passage. And the final ␣ motive, with its summoning of cadence, is the very embodiment of general, processive stability, yielded by the compositional strateg ies most often used for the category of which it is a member.

Changes between the First and Second Versions of the F Major Quartet Janet Levy observed that one of the principal differences between the first and second versions of the F major quartet is the greater concision of the second version.46 Beethoven accomplished this in a number of ways, which together resulted in the elimination of a significant number of statements of the ␣ form of the principal motive. Basic elements of the plan Beethoven followed in his revisions are evident in the changes made to the episode involving the ␣ motive initiated in the midst of the second key area. The passage as or iginally wr itten is given in example 4.20. In the fourteen measures spanned by the episode, there are seven clear statements of the ␣ motive. In the second version of the movement, this episode was cut back to

46. See Levy, Beethoven’s Compositional Choices, 2–4.

191

example 4.20 Ludwig van Beethoven, String Quartet, Op. 18 No. 1 (first version), first movement, mm. 72– 85 72

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cate g ori zat i on, st rate g y, and sy ntax six measures (which are given in ex. 4.15c), with only three statements of the ␣ form of the motive. But perhaps more important than simply reducing the appearances of the ␣ motive, Beethoven appears to have rethought how it fits into the overall musical fabric, as a closer inspection of his first attempt at this episode reveals. The or iginal version of the passage divides into two parts, the first in C minor (mm. 72– 79), the second in C major (mm. 80 – 86). In both parts, there are three main statements of the ␣ motive: in the C minor section these are in the second violin, and each ends with a large ascending leap; in the C major section the statements are given in the cello and end with a repeated note. (The latter for m of the ␣ motive is heard in a pr ior episode, given in ex. 4.15b, which is substantially the same in both versions of the movement.) Each of the second violin’s statements is answered by a counterstatement in the first violin. The counterstatements in mm. 73 and 75 beg in with a tur n figure and share their rhythmic profile with the ␣ form of the motive. On the other hand, the counterstatement of m. 77 answers with the same variant of the ␣ motive that will be heard momentar ily in the cello. The cello’s three statements of this ␣ variant are not given similar counterstatements but are answered instead by passagework in the first violin, which ultimately leads out of the episode. When revising this passage, Beethoven cut the C minor section, salvaging the first violin’s counterstatements of mm. 73 and 75. These he placed an octave lower, but still in the first violin (see ex. 4.15c). He omitted the counterstatement of m. 77, changing the first violin’s music so that it starts with what appears to be another counterstatement, but which then dissolves into passagework that leads out of the episode. The effect of these alterations is not just concision but a view of the ␣ motive that is changed in three ways. First, by dropping the three statements of the motive made by the second violin in the C minor section, Beethoven eliminated a further variant — namely, one that ends with a large leap — from the category of ␣ forms. Second, the counterstatements made by the first violin, now closer in register to the cello’s statements of the motive, make a direct if limited challenge to the structure of the ␣ motivic category. Third, changing the last counterstatement so that it leads out of the episode (rather than echoing the cello’s third statement of the ␣ motive, as the or iginal version of m. 77 would) lets the challenge stand, albeit only for a moment or two. Thus, in the revised version of the passage Beethoven has not only achieved great concision, but he has also accomplished two strategic goals: he has tightened the boundar ies of the ␣ motivic category, and he has intimated how these boundar ies might be challenged. A similar elimination of outright statements of the ␣ motive and modification of the structure of motivic categor ies occurs with the final statement of the motive at the end of the Exposition. In the first version of the passage, shown in example 4.21, the “musette” variant of the ␣ motive (in mm. 109 and 111) is answered by a counterstatement with a tr ill and appogiatura (in mm. 110 and 112). When the phrase is repeated (in mm. 113 – 16), the counterstatement is embellished by repeated tur n figures, but the ␣ motive is not. In Beethoven’s revisions, both the counterstatement and the “musette” variant are embellished when the phrase is repeated (mm. 105 – 108 of ex. 4.15d). Although this removes two explicit state-

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analysis and theory example 4.21 Ludwig van Beethoven, String Quartet, Op. 18 No. 1 (first version), first movement, mm. 109 – 16 109

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ments of the ␣ motive (and, consequently, could be seen to weaken the structure of that category), the change makes it possible to hear the first violin’s counterstatements as further variants of the ␤ motivic categor y (a possibility raised in the earlier discussion of ex. 4.15d). A further result of Beethoven’s decision to reduce the number of appearances of ␣ in the revised version of the movement was a clearer distinction and more even balance between the ␣ and ␤ forms of the motive. In the Development of the first version of the movement, for instance, the two forms of the principal motive blend into one another. As shown in example 4.22, the entrances of the ␣ form subsequent to the A major flour ish that opens the Development are first answered by an ␣ form of the motive and then by a variant of ␤ (mm. 127 – 32). Appearing above the extended tail of this answering ␤ is another ␤ (a quite typical member of the categor y), which leads, after a pause, to yet one more entrance of ␤ (itself answered by a ␥ fragment, as it was in m. 21 and following). Thus an episode beginning with the ␣ form of the motive ends with the ␤ form of the motive, blurring the distinction between the two. In Beethoven’s revised version (ex. 4.17),

example 4.22 Ludwig van Beethoven, String Quartet, Op. 18 No. 1 (first version), first movement, mm. 127 – 43 127

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analysis and theory the two for ms are successive but do not overlap: ␣ and ␤ stand out more clearly as separate entities. Beethoven’s revisions to the Development also resulted in a shar per distinction between the ␦ form of the motive and the ␣ and ␤ forms, especially where the syntax of the motivic categor ies is concer ned. In the or iginal version, the answering statements by the second violin (first ␣ in m. 128 of ex. 4.22, then ␤ in m. 130) both enter at the octave above the viola. They thus anticipate the imitative entrances of ␦ in mm. 137 and following.When these answers are removed in the second version (cf. ex. 4.17, m. 119 and following), the entrances of ␦ seem fresher — the introduction of the lear ned style seems more of an innovation. The entr y of ␦ in the first version of the movement, moreover, leads to a consonant har mony (the dominant of G minor), and the downward leap at this point is a minor sixth (ex. 4.22, mm. 137 – 38). In the revised version, ␦ leads to a dissonant har mony (ex. 4.17, mm. 129 – 30), and the downward leap is a diminished seventh. In sum, in the or iginal version of the Development ␦ seems to grow out of a generalized idea of the principal motive (␣ and ␤ blurring together); after Beethoven’s revisions, the introduction of ␦ is more striking, and it contrasts shar ply with the statements of ␣ and ␤ that precede it. Revisions to the Coda offer a final bit of evidence that the changes Beethoven made were with the intent of more clearly differentiating between different versions of his principal motive. The original version of the Coda, starting at the point that references to the pr incipal motive become explicit, is given in example 4.23. In the first half of this excer pt, Beethoven relies heavily on the ␣ form of the motive, providing statements of it that beg in variously on G and C in the first violin, and Bb and A in the second violin. Because the latter have an ascending skip after the tur n figure, they could also be heard as a variant of the ␤ form of the motive, but the quality of the ␣ form of the motive still pervades. In m. 312, with the shift away from the dominant to the submediant, the ␤ form of the motive enters in ear nest, with a clear reference to the successive entr ies between ␤ and ␥ over the fully diminished seventh chords found in the Exposition. This ser ies of ␤ motives leads ultimately to a conventional, if deliberately under played, cadence. In the second version of the Coda (ex. 4.19), the ␣ motive is withheld, and the first references are to the ␦ form. As noted in the discussion of example 4.19, the syntax of the passage owes much to the fluidity associated with the process of developing musical mater ials and extends to the ␤ motive that enters in m. 294. When the ␣ form of the motive finally returns in m. 301, it is coincident with a perfect authentic cadence and signals a definitive end to the possibility of further development raised by the entrances of the ␦ motive. The changes Beethoven made to the first movement of the F major quartet, then, had two important results. First, they created a more balanced relationship between the ␣ and ␤ forms of the motive in the Exposition. Second, the distinctions between the three main categor ies of motive forms are more sharply drawn. These changes make the syntax associated with each categor y somewhat more apparent— that is, we can more easily hear the role of each motive form in the discourse of the movement as a whole.

example 4.23 Ludwig van Beethoven, String Quartet, Op. 18 No. 1 (first version), first movement, mm. 302– 19 α

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analysis and theory Compositional Strategy and Multiple Levels of Musical Syntax As A. B. Marx noted, the principal motive of the first movement of Beethoven’s F major str ing quartet is a nearly constant presence, never far from the listener’s ear. The function of this dense network of motives, however, is not so much to lend the movement coherence — after all, Beethoven actually reduced the number of times the ␣ form of the motive appeared when he revised the movement — but to set up a musical discourse separate from but coordinated with the har monic and thematic syntax of sonata for m. This discourse involves not simply a syntax specific to the principal for m of the motive (as in the case of the first movement of the “Dissonance” Quartet), but higher levels of syntax of the sort seen in the sixth quartet from the Op. 18 set. Beethoven’s compositional strategy depends on clear distinctions between different for ms of the motive. These distinctions are made not only on the basis of audible features of the motive (of the sort captured in the conceptual models of fig. 4.7) but also on the compositional strategies that lend a distinctive character to each category of motive forms: ␣ as stable in the face of various challenges and ␤ as an agent of change and transition. By the end of the Exposition, a delicate balance has been established between the two, a balance not in evidence in the first version of the quartet, where the category of ␣ motive-forms dominated. This balance is maintained through the first part of the Development, but it is disrupted by the introduction of the ␦ form of the motive and the topic of the learned style (ex. 4.17, m. 129). It is only with the Recapitulation that the focus comes back to the ␣ form of the motive, where it stays (with little or no competition from ␤) until the Coda. The disruption created by ␦ and the recuperation facilitated by ␣ suggest a function for the topic of the lear ned style within Beethoven’s compositional practice: the fugato on the ␦ form of the motive creates the impression of “development” by temporar ily suspending the nor mative syntax for the projection of tonal areas associated with ␣ and ␤, a syntax restored only with the reprise of ␣ at the beginning of the Recapitulation. This function of ␣ is in evidence again at the end of the movement when, after hints at further development and har monic fluidity in the Coda, ␣ returns as the melodic voice of the final cadence in F major. The distinctions among these three forms of the principal motive— distinctions that make possible a musical discourse that is focused on the changing fortunes of the motive over the course of the movement, and that were made more apparent in Beethoven’s revisions to the movement — suggest that motivic analysis could be refined by attending to how motives are used, rather than to how successfully they can be traced back to some Ur-type. Such a refinement makes possible an appreciation of multiple levels of syntax — levels that interact with the overall har monic and thematic syntax of the musical work, and which collectively engage more and less immediate levels of cognitive processing. Ultimately, an appreciation of this refinement leads to a better understanding of how compositional strateg ies shape our conceptions of musical organization.

cate g ori zat i on, st rate g y, and sy ntax

conclusions For Umberto Eco, one of the mysteries of semiotics was that music could have a fairly well developed syntax and yet no apparent semantic depth. Music meant something, but outside of conventionalized signs like those associated with military or pastoral music, it was quite difficult to say what this was. In this chapter, I have not tr ied to address this problem head on; indeed, describing the or igins and scope of musical meaning is an endeavor far more ambitious than what I undertake here. I have, however, tried to argue that musical syntax and semantics are better viewed as points along a continuum than as discrete domains. More directly, composers (as well as others who br ing music to life) make use of strategies that disrupt and redefine musical syntax as part of a process of meaning construction. My path into these compositional strategies has been through categor ization, on the assumption that categor ies of musical events represent a common ground where the concer ns of composers and listeners meet. The viability of this assumption was demonstrated by the structure of the waltzes produced by the musical dice game. Where formal structure needed to be clearly defined (for instance, at the end of each half of the waltz), the range of category members within each measurecategory was quite nar row, and what was typical of the relevant measure-category was quite apparent.Where formal structure could be more open (for example, at the beginning of the second half of the waltz), the range of category members was quite wide and typicality harder to deter mine. Typicality could thus be used to define formal syntax, a syntax that not incidentally coordinated with — and thus confir med— harmonic syntax. A somewhat different example of a compositional strategy organized around typicality was seen in the category for the pr incipal motive of the first movement of Mozart’s “Dissonance” Quartet. At important moments in the movement — at the beginning and close of the Exposition and Recapitulation, and in the Coda — either thoroughly or highly typical for ms of the motive made their appearance. These were followed by less typical members of the motivic categor y, leading either to a reprise of a typical for m or to new musical mater ial. This basic process — a syntax of typicality yielding to atypicality — was repeated three times in the course of the Development, ending only with the appearance of a thoroughly typical for m that signaled the start of the Recapitulation. While the compositional strateg ies that shaped the different versions of the principal motive ran parallel to the for mal syntax of the movement, they were nonetheless independent. The motive thus emerged as a topic for musical discourse, whose progress could be followed along with the other strands of musical discourse compr ised by the movement. By contrast, the principal motive of the first movement of the Bb major quartet from Beethoven’s Op. 18 never functioned as a topic for musical discourse. Although the motive forms fell into two distinct categor ies, individual members never strayed far from their respective conceptual models. In consequence, the immediate level of syntax for the categor ies of motive forms was not particularly interesting, since members were almost always quite typical of their categor y. However, over the course of the Exposition each category acquired distinct functions: one (␣)

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analysis and theory signaled the opening of musical discourse; the other (␤) signaled the close of discourse. This emergent syntax was then exploited in the Development and more generally served to show how musical topics of the sort descr ibed by Ratner could come into being. It was in Beethoven’s F major quartet from Op. 18 that we saw both of these levels of syntax come together. As with the Bb major quartet, Beethoven introduced two categor ies of motive forms (␣ and ␤) in the Exposition, with a third (␥) playing a decidedly subsidiary role. A compositional strategy focused on typicality was applied to both categor ies, but where the range of variation for ␣ was relatively narrow, for ␤ it was quite wide. Contextual pressures on ␤ even suggested that the concept of what counted as a member of the category could slip to include a number of rather remote variants, a kind of slippage that never seemed to threaten ␣. By the end of the Exposition, and even into the beg inning of the Development, ␣ and ␤ appeared to maintain a delicate balance, the for mer stable in the face of various challenges, the latter an agent of change and transition. Beethoven then introduced a new form of the motive (␦) to disrupt this balance, creating a species of development of high drama: ␣ and ␤ were swept from the stage, vanquished by a volatile combination of properties drawn from each. Balance within the movement as a whole (but not between ␣ and ␤) was restored with the return of ␣ at the start of the Recapitulation. Even the developmental urges of the Coda could not threaten this equilibr ium. The compositional strategies applied to the pr incipal motive, then, operate on both a local level (within a g iven category) and global level (among groups of categor ies). Again, these syntactic levels are independent of but coordinated with those for the overall har monic and thematic structure of the movement — the syntactic strands associated with the pr incipal motive are multiple, but they do not exhaust the syntax of the whole. In sum, these analyses suggest that the construction of meaning in music can be achieved through the way composers choose to deploy the elements of musical syntax. Of course, compositional strategy is not the only source of meaning construction in music— I have also pointed out the contr ibutions of musical topics and cross-domain mapping to musical semantics — but it is one to which our knowledge of categorization can be profitably applied. As the meeting place for the concerns of composers and listeners, categor ies of musical events are important to both compositional strategy and musical syntax, for they represent a means through which uniquely musical meaning can be created.

chapter five

Q cultural knowledge and musical ontology

s part of a search for an inter pretive theory of culture and consequent to a cr itique of early work in cognitive anthropology, Clifford Geertz momentar ily and somewhat famously tur ned his thoughts to music as an example of culture. Taking a Beethoven str ing quartet as his case in point, he suggested that no one would identify the quartet with its score, with the skills and knowledge needed to play it, with the understanding of it possessed by its perfor mers or audience, with a particular perfor mance of it, or with some mysterious entity transcending mater ial existence. There was one perspective, however, that Geertz thought would meet with general agreement: “That a Beethoven quartet is a temporally developed tonal structure, a coherent sequence of modeled sound — in a word, music — and not anybody’s knowledge of or belief about anything, including how to play it, is a proposition to which most people are, upon reflection, likely to assent.”1 By this example, Geertz intended to put to rest, for once and for all, the notion that culture exists as some sort of program inside people’s heads. Nonetheless, if music is not knowledge or belief, then what is it? Geertz’s definition of music as “a coherent sequence of modeled sound” is simply too broad, for it would have to include str ings of Morse code, speech in an unknown tongue, and the cr ies of various animals. Indeed, from the perspective of this definition, there is, in principle, nothing to distinguish music from noise or noise from music.2 “Music” is a category constructed by humans, not a substance or set of relations floating free in the world.

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1. Clifford Geertz, “Thick Descr iption: Toward an Inter pretive Theory of Culture,” in The Interpretation of Cultures: Selected Essays (New York: Basic Books, 1973), 11– 12. 2. Much can and has been said regarding the relationship between music and noise. Three sources from the last ninety years represent the range of issues engaged by the topic: Luigi Russolo, The Art of Noises (1916), trans. Barclay Brown (New York: Pendragon Press, 1986); Jacques Attali, Noise: The Political Economy of Music, trans. Brian Massumi, with a foreword by Fredric Jameson and an afterword by Susan McClar y, Theory and Histor y of Literature, 16 (Minneapolis: University of Minnesota Press, 1985); and the improvised performances by Derek Bailey, Pat Metheny, Gregg Bendian, and Paul Wertico on The Sign of 4 (Knitting Factory Works, [CD] KFW 197, 1997). I indicate the media of the recordings I cite with the following abbreviations: CD = compact disk; LP = 33 RPM record; 78 = 78 RPM record.

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analysis and theory As such, the notion of music is dependent upon and constrained by human knowledge, which presumably resides with individual humans. Having said this, it must also be said that the continued existence of a Beethoven str ing quartet does not depend on the personal knowledge of any one individual. Music is indeed a cultural fact, and culture is largely public and inter personal. Cultural knowledge, as represented by Geertz’s example, is thus a bit of a paradox. On the one hand, it is not something that is deter mined by any one individual: culture is, as Geertz maintained, public. On the other hand, individuals need such knowledge if they are going to participate in culture, and it is through the participation of individual humans that culture— and cultural knowledge — is maintained. The problem, as framed by Geertz’s example of a Beethoven quartet, is more specifically one of musical ontology— that is, the ontological status of a work of music. In the West, it is common to regard pieces of music as having an objective status, speaking of a “work of music” as one might of a painting or sculpture. This habit of thought persists in spite of the transience of musical phenomena: unlike a painting or sculpture, a “musical work” has no endur ing mater ial existence. The enigma of “works” that are of profound cultural importance and yet are totally ephemeral has led to a number of attempts by philosophers and others to account for the objective status of the work of music and, by extension, music itself; thus the problem of musical ontology.3 A contrasting perspective has developed among ethnomusicologists who, working chiefly with non-Western music, have noted the fluidity of musical practice and a concomitant absence of any ascription of permanence to the products of musical activity. These observations render doubtful any universal solution to the problem of the ontology of the musical work, or even “music,” since many cultures do not show linguistic or practical evidence of equivalent concepts.4 And yet, musical practice within these cultures, while fluid, is certainly not 3. Thoughtful discussions of the problem of musical ontology can be found in Lydia Goehr, The Imaginary Museum of Musical Works: An Essay in the Philosophy of Music (Oxford: Clarendon Press, 1992); Philip V. Bohlman, “Ontologies of Music,” in Rethinking Music, ed. Nicholas Cook and Mark Everist (Oxford: Oxford University Press, 1999), 17– 34; and Nicholas Cook, “At the Borders of Musical Identity: Schenker, Corelli and the Graces,” Music Analysis 18 (1999): 179 – 233. See also the essays collected in Michael Talbot, ed., The Musical Work: Reality or Invention? (Liverpool: University of Liverpool, 2000). 4. Examples of cultures the languages of which lack a word equivalent to “music” or concepts equivalent to that of a “musical work” include the Hausa of Nigeria, the Macuma Shuar of Ecuador, and the Mapuche of Argentina; Charles Keil reports such a lack in over twenty languages of the African continent and gives detailed discussion of the methodological problems involved in studying such cultures. See David W. Ames and Anthony V. King, Glossary of Hausa Music and Its Social Contexts (Evanston, Ill.: Northwestern University Press, 1971), ix;William Belzner, “Music, Modernization, and Wester nization among the Macuma Shuar,” in Cultural Transformations and Ethnicity in Modern Ecuador, ed. Norman E. Whitten, Jr. (Urbana: University of Illinois Press, 1981), 735 – 36; Carol E. Robertson-DeCarbo, “Tayil as Category and Communication among the Argentine Mapuche: A Methodological Suggestion,” Yearbook of the International Folk Music Council 8 (1976): 39; and Charles Keil, Tiv Song (Chicago: University of Chicago Press, 1979), 27– 52. I should make clear that what I find dubious is a universal solution to the problem of the ontology of a musical work. I do not think it is impossible, however, to speak about “music” in the case of a culture that does not show linguistic or practical evidence of such a concept, as long as one does not attempt to colonize that culture by insisting that its members, when they try to make sense of their own experiences and cultural practices, make use of the term.

cultural knowle dge and musical ontology unregulated. In general, the habit of objectifying aspects of musical practice is omnipresent; in consequence, the problem of musical ontology, while most properly one that ar ises only among those who believe in an objective status for the work of music, also has applications to situations where no such object is posited. In this chapter, I propose that solutions to the problems of cultural knowledge in general, and of musical ontology in particular, can be found in what we now know about processes of categorization. In brief, knowing that Beethoven’s quartet is music — or that anything else is music, for that matter — means knowing how to categorize sequences of sound-events in accordance with conceptual models shared with other members of a culture. More specifically, each “work of music”— or whatever other unit of cultural cur rency we choose to focus on — constitutes a Type 1 category of the sort discussed in chapter 2.5 On the one hand, the transparency and immediacy of the conceptual models that guide the process of categorization explain why we describe works of music in the same language we use for objects: we speak of “the Beethoven quartet” just as we speak of “the red cup,” even though the for mer (as sounding music) is a phenomenon completely unlike the latter.6 On the other hand, because membership in Type 1 categor ies is by degree, a certain amount of fluidity is possible, varying in degree with the cultural context relative to which the conceptual model for the categor y is framed. We might include a wide variety of performances in the categor y for the Beethoven quartet — some more, some less competent, even some in an ar rangement for four-hand piano — but we could well draw the line at a version for pitched percussion and automobile hor ns. In what follows, I explore the idea that musical works can be thought of as Type 1 categor ies and that such categor ies are a manifestation of cultural knowledge. I approach this issue by taking a close look at two popular songs from the early twentieth century: “I Got Rhythm” and “Bye Bye Blackbird.” Songs like this challenge our ideas about what constitutes a “work of music”: while they are almost always associated with a score (as is a Beethoven quartet), they are also part of a performance tradition that involves some level of improvisation (introducing the fluidity typical of many non-Western perfor mance traditions). “I Got Rhythm” provides a good example of this situation, for there were multiple competing versions of the song almost from the moment it appeared on Broadway late in 1930. In the first section below, I consider a number of recordings 5. Of course, a work of music could be regarded as a Type 2 category were necessary and sufficient conditions for categor y membership specified. This is how I would inter pret Nelson Goodman’s proposal that the score is the absolute deter minant of musical identity. Goodman wr ites, “If we allow the least deviation [from the score], all assurance of work-preservation and score-preservation is lost; for by a ser ies of one-note er rors of omission, addition, and modification, we can go all the way from Beethoven’s Fifth Symphony to Three Blind Mice. Thus while a score may leave unspecified many features of a performance, and allow for considerable variation in others within prescr ibed limits, full compliance with the specifications g iven is categor ically required.” Nelson Goodman, Languages of Art: An Approach to a Theory of Symbols, 2nd ed. (Indianapolis: Hackett Publishing, 1976), 186– 87. 6. There are, of course, aesthetic perspectives that support this habit (such as that associated with the “work-concept,” as descr ibed by Lydia Goehr in The Imaginary Museum of Musical Works, 89– 119) and technological innovations that give it credence (like music notation and sound recording), but these are not preconditions for the notion of a musical object.

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analysis and theory of the song made dur ing the 1930s and 1940s, explore how the model for the song changed and how it stayed the same, and show that both the fluidity and the stability of this model are straightforward consequences of our use of categor ization to organize our understanding of music. “Bye Bye Blackbird” presents a somewhat different problem, which takes us deeper into the relationship between categor ization and cultural knowledge.Written as a popular song dur ing the 1920s and quite successful when it first appeared, it never really entered the standard repertoire until a recording by Miles Davis in 1956 transfor med the song into a jazz tune.7 Because there was no tradition of gradual change, it was possible for radically different models for the song to coexist and come into conflict. In the second section below, I consider this sort of conflict in light of what Mikhail Bakhtin called double-voiced discourse and what Henr y Louis Gates Jr. calls Signifyin(g). I attempt to show that a fuller account of how we categorize musical works requires that we go outside of the relatively parochial concerns of musical perfor mance and consider the context in which musical performance takes place. In the third section, I offer some concluding thoughts on cultural knowledge, musical ontology, and the cognitive processes through which we structure our understanding of the world. I end the chapter with some reflections about how the perspective on musical ontology I offer here can change the way we view music theory.

categorization, musical ontology, and cultural knowledge A Multiplicity of “Rhythm”s, 1930 – 1946 “I Got Rhythm” was wr itten by George and Ira Gershwin for their musical Girl Crazy, which opened on Broadway on 14 October 1930. The song, intended to be a show stopper, appeared near the end of the first act, and its refrain was repeated a number of times: to accompany a tap dance chorus after the final vocal refrain; as an encore for Ethel Mer man, whose success with the song became legendar y; as part of the mostly instrumental entr’acte before the second act; and, sung by the whole company, as the show’s concluding number. The song itself, the score for which is given in example 5.1, comprises an introduction, verse, and refrain. The melody of the verse begins with an eight-measure phrase in G minor (featur ing a prominent b5 at its midpoint), which is given a var-

7. I borrow the distinction between a song and a tune from Richard Crawford, who wr ites, “in the jazz tradition, we usually speak of tunes, not songs. A jazz tune is defined first and foremost by its structure: by the patter n of repetition and contrast in its melodic phrases and the har monic framework underlying them. Second, it is defined by its ethos: by the mood it projects and the tempo at which it is played. Only third does its melody come into play, for in the jazz tradition the melody is often little more than an entrée into the perfor mance; after being heard, it is usually discarded for free melodic invention by the performers.” Richard Crawford, “George Gershwin’s ‘I Got Rhythm’ (1930),” in The American Musical Landscape (Berkeley: University of Califor nia Press, 1993), 221, 225.

cultural knowle dge and musical ontology example 5.1 Version of George and Ira Gershwin’s “I Got Rhythm” used in act 1 of Girl Crazy. “I Got Rhythm,” words and music by George Gershwin and Ira Gershwin, © 1930 WB Music Cor p. (Renewed). All rights reserved. Used by permission. Warner Bros. Publications U.S. Inc., Miami, FL 33014.

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ied repetition. This is followed by a four-measure phrase, which is also repeated (again, with variations), after which a two-measure transition leads to the refrain. The refrain is in the AABA form typical of popular songs of this period, but it includes an ascent to F5 near the end of the last A section. This climactic r ise requires a two-measure tag to br ing the melody back to Bb4 and yields a 34measure AABA' form. “I Got Rhythm” was only rarely recorded as it appeared in the or iginal show. Although it contr ibuted significantly to her professional career, Ethel Mer man did not record it until 1947. Many amateurs and semi-professional musicians must have performed the song from the sheet music, which did reproduce the music as it

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appeared in Girl Crazy. This was not the case, however, with professional musicians. Even in the earliest recordings (made within a few weeks of the show’s opening), the verse loses its introductory (and nar rative) function and is used instead as an interlude between repetitions of the refrain. For example, the recording made on 23 October 1930 by Red Nichols and His Five Pennies (a group drawn from the pit orchestra for Girl Crazy) begins with an instrumental version of the or iginal refrain,

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analysis and theory example 5.1

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followed by the refrain with vocal.8 Only after this does the music for the verse enter, but without vocals. The recording concludes with two more statements of the refrain, also without vocals. A very similar ar rangement was used by Fred Rich and a studio band in their recording of 29 October 1930. The overall for m of their rendition consists of three refrains (the second with vocal), followed by an instrumental verse, followed by one complete and one partial statement of the refrain (the latter using only the B and A' sections to conclude the perfor mance).9 In the two years following the opening of the show, almost all of the recordings that appeared made use of vocals, although none of which I am aware used the words for the verse.10 With the instrumental version recorded by Don Redman and 8. Red Nichols and His Five Pennies, “I Got Rhythm,” in Rarest Brunswick Masters, 1926 –1931: Red Nichols and His Five Pennies (MCA Records, [LP] MCA 1518, 1982). 9. Fred Rich and His Orchestra, “I Got Rhythm,” in 1930 —You’re Driving Me Crazy: Portrait of a Year in Music (Phontastic, [CD] PHONT CD 7618, 1992). 10. A fairly comprehensive list of recordings of “I Got Rhythm” from 1930 to 1942, based on Br ian Rust’s The American Dance Band Discography 1917–1942 (New Rochelle, N.Y.: Arlington House, 1975), is included in Crawford’s “George Gershwin’s ‘I Got Rhythm,’ ” 222– 25.

cultural knowle dge and musical ontology His Orchestra on 30 June 1932, however, we encounter a new approach to the song.11 In this ar rangement, the verse was eliminated completely, as was the role of the vocalist. The result is something very much like the version of “I Got Rhythm” that can be found in jazz fake books, such as shown in example 5.2.12 After 1932, the number of recordings that include vocals drops off precipitously, and “I Got Rhythm” became a tune used by dance bands for instrumental improvisation — a jazz “standard”— as may be observed in recordings by Red Norvo and His Swing Sextette in 1936 or Chick Webb and His Little Chicks in 1937.13 Seen from the perspective of these recordings, George Gershwin’s own perfor mance of “I Got Rhythm” as a set of variations for piano and orchestra is somewhat anomalous, for there is little if any sense of improvisation, nor is this music intended for dancing.14 From 1932 to 1942, recorded perfor mances are remarkably consistent in their approach to “I Got Rhythm”: all use the same thirty-four-measure form, all make example 5.2 Jazz fake book version of George and Ira Gershwin’s “I Got Rhythm.” “I Got Rhythm,” words and music by George Gershwin and Ira Gershwin, © 1930 WB Music Cor p. (Renewed). All rights reserved. Used by permission. Warner Bros. Publications U.S. Inc., Miami, FL 33014.

11. Don Redman and His Orchestra, “I Got Rhythm,” in Don Redman and His Orchestra, 1931–1933 (Classics, [CD] 543, 1990). 12. Jazz “fake books” typically contain hundreds of songs. Generally, as is true of the piece in ex. 5.2, each is given as a melody, along with chord symbols that outline a basic har monization and some minimal instructions for perfor mance; the words for the songs may or may not be included. These mater ials allow players familiar with jazz perfor mance practice to give an acceptable rendering of a song even if they have never played it before— that is, they can “fake” their way through a perfor mance. 13. Red Norvo and His Swing Sextette, “I Got Rhythm,” in Red Norvo (Time-Life Records, [LP] STL-J14, 1980), originally recorded 16 March 1936; Chick Webb and His Little Chicks, “I Got Rhythm,” in Spinnin’ the Webb: Chick Webb and His Orchestra (GRP Records, [CD] 513678L, 1994), originally recorded 21 September 1937. 14. George Gershwin, “I Got Rhythm,” in Gershwin Performs Gershwin: Rare Recordings 1931–1935 (Musical Her itage Society, [CD] 512923A, 1991), originally recorded 19 February 1934.

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analysis and theory some reference to the or iginal melody, and all preserve the affect and tempo of the original. However, an ar rangement recorded by the Jimmy Dorsey Orchestra on 28 November 1942 signaled yet another approach to “I Got Rhythm,” for after employing the customar y thirty-four-measure format for the head, the band switched to a thirty-two-measure format for the solos.15 In truth, this was not the first time the musical mater ials of “I Got Rhythm” had been associated with a thirty-two-measure form. Early on, the song had been used as the basis for a number of other compositions.16 These der ived tunes typically retain the har monic framework, overall for m, and affect of the or iginal song but substitute a new melody and g ive the whole a new title. In the case of “I Got Rhythm,” derived tunes allowed jazz players to keep what was useful from the song — its fast tempo, lively affect, and straightforward harmonic structure— yet escape the limitations of its simple, predominantly pentatonic melody. The earliest recorded tune der ived from “I Got Rhythm,” Sidney Bechet and the New Orleans Feetwarmers’“Shag” (recorded 15 September 1932), did retain the thirty-four-measure form of “I Got Rhythm,” with its two-measure tag at the end of the final A section.17 However, Fletcher Henderson’s “Yeah Man,” which appeared the following year, did away with the two-measure tag, yielding a thirty-two-measure form in which all of the A sections were of equal length.18 There were two advantages to this change. First, the excision of the two-measure tag made the connection between “Yeah Man” and “I Got Rhythm” more obscure: “Yeah Man” could sound a bit more like a brand new tune. Second, jazz practice of this per iod was beginning to embrace longer solos. The 34-measure for m of “I Got Rhythm,” it will be recalled, ends with a two-measure tag added to its final A section. A musician who wanted to take two “choruses” in succession would consequently find the regular flow of eight-measure phrases in the backg round har monic structure inter rupted in midstream with the appearance of the ten-measure A' section. When a musician took two “choruses” on the 32-measure form, however, the succession of eight-measure phrases was constant: the improvisation could stretch seamlessly across the two refrains, allowing the player to build longer melodic lines and to shape the dynamic structure of the solo over larger spans of music. Although after “Yeah Man” the tunes der ived from “I Got Rhythm” were invariably based on the thir ty-two15. Jimmy Dorsey and His Orchestra, “I Got Rhythm,” in Jimmy Dorsey and His Orchestra,Vol. 2: 1942–44 (Hindsight Records, [LP] HSR-153, 1980). For perfor mances with an emphasis on improvisation that are guided only by a relatively informal ar rangement, the practice among jazz perfor mers is to state the tune at the beg inning and end of the perfor mance. In these cases, the tune functions as the “head.” The head is typically followed by solos over the har monic framework of the tune, which are, in turn, followed by a concluding statement of the tune. 16. Richard Crawford calls such der ived tunes “contrafacts,” borrowing the ter m from one of several medieval practices to which it is linked. The specific practice invoked is one in which new texts are grafted on to preexistent music, which was itself freely adapted. See Crawford, “George Gershwin’s ‘I Got Rhythm,’ ” 225, 228– 29. 17. Sidney Bechet and the New Orleans Feetwarmers,“Shag,” in Sidney Bechet (Time-Life Records, [LP] STL-J09, 1980). 18. Fletcher Henderson and His Orchestra, “Yeah Man,” in Fletcher Henderson, Developing an American Orchestra, 1923–1937 (Smithsonian Collection, [LP] R 006, 1977), originally recorded 18 August 1933.

cultural knowle dge and musical ontology measure form, it was only around 1942 that this form was brought to “I Got Rhythm” itself. At first, the thirty-two-measure form was used only for solos — the head retained its thirty-four-measure form, complete with the two-measure tag (as in the Jimmy Dorsey arrangement). By the mid-1940s, however, even the tag for the head had fallen away.When Charlie Parker recorded “I Got Rhythm” with a group of all-star perfor mers on 22 April 1946, the thirty-two-measure form was used for the head, as well as for the twenty-three choruses that followed.19 The transfor mation of “I Got Rhythm” into a platfor m for improvisation is even more evident in a recording made two years earlier by Lester Young and the Kansas City Six. In this performance, not only is the thirty-two-measure harmonic patter n used throughout, but also the melody of the song is never stated.20 In this for m— that is, as a thirty-two-measure, AABA harmonic structure—“I Got Rhythm” came to be one of the basic elements of the jazz player’s musical vocabulary: the “Rhythm changes” shown in example 5.3.21 example 5.3 Scheme for “Rhythm changes” (based on the har monic structure of the thirty-two-measure for m of “I Got Rhythm”). “I Got Rhythm,” words and music by George Gershwin and Ira Gershwin, © 1930 WB Music Cor p. (Renewed). All rights reserved. Used by permission. Warner Bros. Publications U.S. Inc., Miami, FL 33014. 1

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19. Charlie Parker and others, “I Got Rhythm,” in Bird: The Complete Charlie Parker on Verve (Verve/Polygram Classics, [CD] 837 142 – 2, 1988). 20. Lester Young with the Kansas City Six, “I Got Rhythm,” in The Tenor Sax: Lester Young, Chu Berry and Ben Webster: The Commodore Years (Atlantic, [LP] SD 2-307, 1973), originally recorded 28 March 1944. That the perfor mance by Young’s group resulted from an ar rangement employed for successive performances rather than happenstance is suggested by an alter nate take of the same tune recorded the same day (included on this album), which uses precisely the same ar rangement. 21. The ter m “changes” refers to a conceptual structure that consists of a succession of harmonies correlated with a metr ic and hypermetric framework. Knowing this structure— knowing where and when the har monies change — is essential for creating convincing improvisations. On the importance of “Rhythm changes” as a basic har monic prototype, see Paul F. Berliner, Thinking in Jazz: The Infinite Art of Improvisation, Chicago Studies in Ethnomusicology (Chicago: University of Chicago Press, 1994), 76– 78.

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analysis and theory From the evidence provided by recordings, then, what counted as “I Got Rhythm” changed from 1930 to 1946 as the song was transfor med from a Broadway or popular song, to a jazz standard, to a platfor m for improvisation. This précis is not quite accurate, however, for even as new conceptions of the song emerged, older ones remained in circulation. Benny Goodman, for instance, continued to use the thirtyfour-measure form of the refrain even after others had adopted the thirty-twomeasure form;22 productions of the musical (including the 1943 movie Girl Crazy, starring Mickey Rooney and Judy Garland) continued to use the entire song after most other perfor mances had omitted the verse.23 From almost the moment of its introduction, there were multiple “Rhythm”s in circulation, and what belonged under the rubric “I Got Rhythm” depended on where you stood in the stream of American popular culture.

Categorizing “I Got Rhythm” Collected in table 5.1 are all of the versions of “I Got Rhythm” discussed thus far. How might someone go about categorizing these various versions were they encountered in the course of daily life rather than as a pre-selected list? That is, assuming one were not so fortunate as to have each perfor mance identified as “a perfor mance [or recording, or rendering] of ‘I Got Rhythm,’ ” what would be the basis for including any or all of these in the category performances of “I Got Rhythm”? As shown in chapter 1, categories like this are organized around a conceptual model that sets up an idealized representation of what counts as a typical member of the category.24 As a place to begin, let us consider a conceptual model focused on the attr ibutes of the song as it first appeared in Girl Crazy (leaving aside the variants created as the song was reprised over the course of the musical). The model (which I shall call the “pop-music” model, for reasons that will become clear below) is diagrammed in figure 5.1 and consists of five cor related conceptual elements, character ized as the things necessar y for an adequate perfor mance of the song. Two aspects of this model should be clar ified. First, although the verses of popular songs were often omitted in perfor mance, I take the fact that composers still bothered to wr ite verses and that the verse was included, in some for m or another, in early recordings as evidence of its importance to the identity of the song. Second, my distinction between variation and improvisation is based on the extent rather than the presence of musical mater ials not specified by the score: if these mater ials are relatively limited, I would tend to regard them as a product of variation; if they are extensive, I would tend to regard them as a product of improvisation. Where to draw the line involves another set of conceptual models for perfor mance practice; nonetheless, the distinction is relatively clear in early recordings.

22. Benny Goodman Sextet, “I Got Rhythm,” in Benny Goodman (CBS Records, [LP] P5 15536 CP, 1981), originally recorded 18 September 1945. 23. Although the plot line for the movie is completely different from that of the musical, the musical numbers are the same. 24. By “categor ies like this” I mean not categor ies involving musical works specifically, but the categories we use in daily life generally.

cultural knowle dge and musical ontology table 5.1. Select Performances of “I Got Rhythm” Performers

Date of Recording

Red Nichols and His Five Pennies Fred Rich and His Orchestra Don Redman and His Orchestra George Gershwin Red Norvo and His Swing Sextette Chick Webb and His Little Chicks Jimmy Dorsey and His Orchestra Lester Young with the Kansas City Six The Benny Goodman Sextet Charlie Parker and others

23 October 1930 29 October 1930 30 June 1932 19 February 1934 16 March 1936 21 September 1937 28 November 1942 28 March 1944 8 September 1945 22 April 1946

Applying this model to the perfor mances listed in table 5.1 yields the typicality effects character istic of Type 1 categor ies. Most typical would be the perfor mances by Red Nichols’s and Fred Rich’s groups; performances from the or iginal production of the musical (which are not included in the list of recordings) would of course also be reckoned as highly typical.25 By contrast, the perfor mance led by Gershwin, which drops the verse and lyr ics, would not confor m as well with the model. Even less typical would be the perfor mances led by Redman, Norvo,Webb, and Goodman, for all these add a substantial emphasis on improvisation. Finally, on the fr inges of the category would be the perfor mances led by Dorsey, Young, and Parker, for these not only omit the verse and lyr ics but also use a thirty-twomeasure form of the refrain as a platfor m for extended improvisations. As we see in this example, conceiving of various renditions of a song as a Type 1 category organized around a conceptual model offers a way to explain the peculiar ontological status of musical works. Our sense that there is only one thing that should be called “I Got Rhythm” is supported by the idealization basic to the model and to the model’s role as the conceptual anchor for the categor y. At the same time, our ability to accept as members of the category things that do not fully correspond to this model shows how the model functions as a guide to understanding the structure of the category as a whole. Although Charlie Parker’s “I Got Rhythm” is not like Ethel Mer man’s “I Got Rhythm,” it shares enough attr ibutes with the latter that we will not want to exclude it from the category outr ight. Further, the model can provide a basis for descr ibing why we would grant Parker’s performance a liminal rather than a central status within the category— we might say something along the lines of “He uses too much of that crazy improvisation, so he really isn’t playing ‘I Got Rhythm.’ ” 25. There was no recording of the original production of Girl Crazy. However, there was a painstaking recreation of the 1930 production undertaken by Elektra Nonesuch in 1990, and Lorna Luft’s performance there (in the part of Kate Fothergill or iginated by Merman) agrees in most respects with the version of “I Got Rhythm” recorded by Merman in 1947. See George Gershwin and Ira Gershwin, Girl Crazy (Elektra Nonesuch, [CD] 79250-2, 1990), recorded 26 – 28 February 1990.

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figure 5.1

Pop-music model for the category performances of “I Got Rhythm”

Useful as this approach to musical ontology is, it demands at least a bit of further elaboration: we need to find a way to descr ibe how the conceptual model for a musical work changes over time. After all, while Parker’s 1946 perfor mance might have been regarded as unusual by some, it is clear from the musical practice of his contemporar ies that it was far from exceptional. Here Richard Crawford’s account of three different approaches taken to “I Got Rhythm” during the years 1930 – 1942 provides a helpful guide.26 The first approach, in which “I Got Rhythm” was treated as a popular song, is similar to that assumed by the pop-music model diagrammed in figure 5.1. The second approach descr ibed by Crawford is one in which “I Got Rhythm” is treated as a jazz standard. A conceptual model that fits this approach is diagrammed in figure 5.2 and consists of five things necessary for an adequate perfor mance.27 Adopting this model would, of course, change what counted as a typical version of the tune. Now the perfor mances led by Redman, Norvo, Webb, and Goodman would be central to the categor y, and the performances led by Dorsey, Young, and Parker only a bit less typical. Far more atypical would be the perfor mance led by Gershwin, with its relative lack of emphasis on improvisation, and the perfor mances by Red Nichols’s and Fred Rich’s groups, with their inclusion of the verse. The third approach to “I Got Rhythm” noted by Crawford was as a musical structure that served as the basis for various der ived tunes. I would like to generalize this somewhat to accommodate the slightly expanded time frame represented by the recordings collected in table 5.1. After 1942, “I Got Rhythm” served not only as the basis for der ived tunes but also as a framework for improvised perfor mance —

26. Crawford, “George Gershwin’s ‘I Got Rhythm,’ ” 218. 27. Explicit mention of the melody in this conceptual model is intended as a hedge against confusing “I Got Rhythm” with any of the tunes der ived from it.

cultural knowle dge and musical ontology

figure 5.2

Jazz-standard model for the category performances of “I Got Rhythm”

a framework embodied in the “Rhythm changes” of example 5.3. This leads us to a third model for “I Got Rhythm,” which is diagrammed in figure 5.3. This “improv” model, conceived as a skeletal vehicle for improvisation and composition, consists of four things necessary for an adequate perfor mance. Once again, what would count as a typical version of the tune changes. From the perspective provided by the improv model, the perfor mances led by Young and Parker would be most typical, with that led by Dorsey following close behind. The perfor mances led by Redman, Norvo,Webb, and Goodman, with their allegiance to the or iginal for m and melody of Gershwin’s song, would now be regarded as less typical, and the perfor mances led by Gershwin, Nichols, and Rich would have to be considered as thoroughly atypical. Let us now return to the matter of how the conceptual model for a musical work changes over time. If we take these three models as an histor ical sequence — the pop-music model followed by the jazz-standard model, which is followed by the improv model — we can see that each successive conceptual structure retains some of the elements of the previous structure and either modifies or drops others. • The jazz-standard model retains from the pop-music model the elements concer ning affect and the mater ials of the refrain. It changes those relating to function and lyr ics, and it adds an element specifying the presence of the melody. (The latter is implicit in the “materials of the refrain” inherited from the pop-music model, but it is made explicit here). • The improv model retains from its jazz-standard counter part the element concer ning affect. It changes the components of the model associated with the refrain, melody, and function, and it drops any requirement for the lyr ics. As is evident from table 5.1, these are not the only models possible, nor should my descriptions of the model be taken as comprehensive or final. One could easily

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figure 5.3

Improv model for the category performances of “I Got Rhythm”

imagine idiosyncratic or transitional models that blend features of those outlined here. Thus a model based on the perfor mance led by George Gershwin, for instance, would bor row some features from the pop-music model and some from the jazz-standard model; a model based on the ar rangement played by the Jimmy Dorsey band would incor porate some aspects from the jazz-standard model and some from the improv model. And were such models taken as the basis for our determinations as to what belonged in the category performances of “I Got Rhythm,” there would of course be changes in what counted as a typical or atypical member of the category. When people share the conceptual model for a song (realizing that all such sharing is approximate), they will tend to make similar judgments about what counts as a typical or an atypical rendering of the song (or whether a succession of sounds should even be counted as an instance of the song). As I proposed in chapter 3, sharing knowledge in this way is one of the bases of culture. This becomes especially clear when we consider other roles played by the model for a musical work: as a set of cognitive resources for perfor mance, as a basis for negotiations on how musical practice should proceed, and as a focus for how musical practice can be regulated.

Conceptual Models and Performance Up to this point, we have considered music that is part of a tradition of performance at least partially regulated by the score. But what of performance traditions in which scores play no part— that is, music that is part of an aural tradition? Where scores (or similar artifacts) are absent, performers must rely on a store of knowledge about music and music making, knowledge often gathered through a long and painstaking process that starts in earliest childhood and continues for many years. Constantin Brailoiu was perhaps the first to suggest that musical perfor mance within aural traditions relies on stored cognitive constructs. As a way of explaining the source of the divergent perfor mances folk musicians gave of the “same” song, Brailoiu proposed that such perfor mances were ephemeral incar nations of an ideal

cultural knowle dge and musical ontology archetype stored in the mind of the musician.28 In his work on African music, Simha Arom adopted Brailoiu’s idea, but he called the archetype a “model.”29 James Cowdery, whose research has focused on Ir ish music, proposed a similar cognitive basis for perfor mance practice, but one der ived from the tradition of inquiry centered on the tune family.30 Cowdery called the construct a “tune model” and conceived of it as a generating patter n in the mind of the perfor mer or musical community.31 Finally, James Porter has developed detailed descr iptions of a succession of conceptual perfor mance models for the chang ing versions of the song “My Son David” sung by the Scottish singer Jeannie Robertson between 1953 and 1960.32 For Porter, the conceptual perfor mance model represented a holistic, self-contained concept of a particular song in the mind of the singer.33 This model enabled the singer to g ive successive but nonidentical perfor mances of the “same” song on a number of occasions, but the model was nonetheless subject to change over time — that is, the “same” song gradually became a different song as the conceptual performance model changed. The idea behind all of these approaches is that perfor mers who work within aural traditions base their perfor mance of a given tune on a cognitive construct that is stored in memory and that represents essential features of that tune. In their basic features, such constructs are essentially the same as the conceptual models I described in chapter 3. I have used these same models in this chapter to explain how individuals deter mine whether a particular perfor mance is of a specific tune and how typical that perfor mance is. The difference that distinguishes my models from those of Brailoiu, Arom, Cowdery, and Porter is that the sort of constructs they pro-

28. The relevant texts in translation and the or iginal are as follows: “Lacking an unchallengeable [musical] text, we must admit that we never collect more than variants and that latent in the singers’ minds lives an ideal archetype of which they offer us ephemeral incar nations.” [“A défaut de tout texte irrécusable, force nous est d’admettre que nous ne recueillons jamais que des variantes et que, dans l’esprit des chanteurs, vit, d’une vie latente, un archétype idéal, dont ils nous offrent des incar nations éphémères.”] Constantin Brailoiu, “Le Folklore musicale,” in Musica aeterna: La Vie et la production musicales de tous les temps et de tous les peuples, en tenant compte particulièrement de la Suisse, de la Belgique, de la France et de la musique de nos jours, ed. Gottfr ied Schmid (Zur ich: M. S. Metz, 1949), 2: 319. 29. Simha Arom, African Polyphony and Polyrhythm: Musical Structure and Methodology, trans. Martin Thom, Barbara Tuckett, and Raymond Bond (Cambr idge: Cambridge University Press, 1991), 148. 30. The idea of a tune family was first proposed by Samuel P. Bayard in his classic essay “Prolegomena to a Study of the Pr incipal Melodic Families of British-Amer ican Folk Song,” Journal of American Folklore 63 (1950): 1– 44. 31. James R. Cowdery, The Melodic Tradition of Ireland (Kent, Oh.: Kent State University Press, 1990), 33. 32. James Porter, “Jeannie Robertson’s My Son David: A Conceptual Performance Model,” Journal of American Folklore 89 (1976): 7– 26; and idem, “Context, Epistemics, and Value: A Conceptual Performance Model Reconsidered,” in Selected Reports in Ethnomusicology: Issues in the Conceptualization of Music, 7, ed. James Porter and Ali Jihad Racy (Los Angeles: University of California, Department of Ethnomusicology, 1988), 69– 97. Porter’s thoughtful appraisal of what might be involved in a conceptual performance model goes well beyond the pr imitive models I sketch here and should be taken into account in any further application of theories of categor ization to ethnographic research. It should be noted that while Arom, Cowdery, and Porter all use the ter m “model” for their hypothetical cognitive constructs, they do so without reference to any of the cognitive science research on models or related constructs. 33. Porter, “Context, Epistemics, and Value,” 71.

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analysis and theory pose are used not for categor izing musical perfor mances, as I attempt to do, but for producing them. In truth, we have already seen conceptual models used in this way, for Jeff ’s conceptual models for “Twinkle” not only helped him organize the Montessor i bells in particular patter ns but also guided his actions when he performed the song. In the present context, however, the network of knowledge with which we are concer ned is far more extensive than that with which Jeff was engaged. The skills required for an adequate perfor mance of a tune like “I Got Rhythm” (relative to the perfor mance tradition descr ibed above) are extensive: a trumpet player, for instance, must know where to find the notes for the tune on her instrument, how to produce these notes in the r ight order, how to shape this production to create a convincing version of the tune, how to coordinate her playing with that of other members of an ensemble, and so on.34 For perfor mers, then, there will be a number of conceptual models related to the various challenges of creating musical sound, as well as the conceptual model for a particular piece. The complexity of this network of knowledge emphasizes once again the importance of the global models relative to which local models are framed. With regard to the conceptual model for a musical work, the global model speeds the process of learning the conceptual model for a new tune and also provides a framework for discourse among musicians. For instance, among perfor mers the jazzstandard model for “I Got Rhythm” (which was diagrammed in fig. 5.2) is framed relative to a global model for jazz practice, which includes the five elements diagrammed in figure 5.4. A comparison of figure 5.4 with figure 5.2 shows that each generic element in the for mer has its more specific cor respondent in the latter. Confronted for the first time with a tune like “I Got Rhythm,” a musician who has internalized the global model will already have a start on assembling a local conceptual model to use as a guide in perfor ming the tune. The global model also serves as a frame for discourse (both verbal and musical) about local models. That is, approaching “I Got Rhythm” as a song that belongs to the perfor mance practice of jazz means that features such as its har monic structure, melody, and character are what are relevant, rather than whether there is a definitive score on which to base performance. Conceptual models, then, are used not only to structure our understanding of 34. Of necessity, this network of knowledge will include embodied knowledge: what it feels like to make musical sounds and to coordinate this activity with other physical activities. Richard Powers touches on the importance of such knowledge in his novel Galatea 2.2, which centers on a hypothetical exper iment to replicate aspects of human intelligence on a vast and spreading neural network, implemented via parallel processing on a massive supercomputer. At one point, the implementation, named Helen, asks “How do you sing?” The narrator responds by singing a fragment of a song he lear ned as a child: “Bounce me high, bounce me low, bounce me up to Jericho.” To his amazement, the implementation not only absorbs this song but can later be heard singing it, over and over, like a child trying out her voice.Yet “sing” is not quite the r ight word, for Powers’s nar rator realizes that there is something missing: “Helen did not sing the way real little girls sang. Technically, she almost passed. Her synthesized voice skittered off speech’s earth into tentative, tonal Kitty Hawk. Her tune sounded remarkably limber, given the scope of that mechanical tour de force. But she did not sing for the r ight reasons. Little girls sang to keep time for kickball or jump ropes. . . . Helen didn’t have a clue what keeping time meant, never having twirled a jump rope, let alone seen one.” Richard Powers, Galatea 2.2 (New York: Farrar Straus Giroux, 1995), 205.

cultural knowle dge and musical ontology tunes have a basic harmonic pattern and a clearly articulated form

tunes have melodies which function as the head of the tune

“the jazz tune”

tunes often have words, but these are not essential for the identity of a tune

tunes have various functions, chief among which is to serve as a vehicle for improvisation

tunes have an identifiable character

figure 5.4

Partial representation of the global model of jazz practice

what we hear but also to create the things we hear. In both cases, the model is part of a network of knowledge that, through being shared by the members of a musical community and realized in sound, constitutes musical culture.

Negotiating Conceptual Models Musical practice is not a steady state, as may be seen in the different versions of “I Got Rhythm” collected in table 5.1. Over time, conceptual models will be modified in response to changes in cultural pr iorities. Rarely are such modifications the result of creative fiat by one individual (although one such case is discussed below, in connection with “Bye Bye Blackbird”). More commonly, they are the product of a gradual ser ies of negotiations within a musical community. The basic outlines of the process of negotiating the structure of conceptual models can be illustrated by consider ing two highly simplified situations. Each involves a musician who initiates the process of negotiation by suggesting changes to the constituent elements of a given conceptual model. In the first case, the negotiations occur within a g roup of musicians occupied with perfor ming the same work; in the second case, the negotiations occur between the musician and an audience of non-perfor mers. The first situation can be conceived of as taking place in a rehearsal or a performance of the version of “I Got Rhythm” associated with the jazz-standard model. Instead of playing the usual har monic progression for the refrain, the pianist, without comment, introduces a completely new ser ies of harmonies for the A section and truncates the overall for m to thirty-two measures. The other musicians may accept this change (by adjusting their perfor mance to the new harmonies), reject it

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analysis and theory (by resolutely hewing to the structure of the or iginal model), or suggest further modifications (by offering their own inter pretation of the har monic progression). This process could also play out with the aid of language (the changed har monic progression could be announced in advance) or symbols (a chord chart for the changed refrain could be supplied to the other musicians), or through various combinations of musical perfor mance, language, and symbols by any or all participants. The second situation can be conceived of as taking place dur ing a perfor mance of “I Got Rhythm” by a solo pianist, playing for an audience of nonperfor mers. Again, instead of the usual har monic progression for the refrain, the pianist introduces a new ser ies of harmonies and truncates the overall for m to thirty-two measures. The audience may respond by accepting the change (through applause or a similar activity), rejecting it (by shouting catcalls or throwing bottles), or suggesting further modifications (by shouting “More!” or “Too much!”). (Of course, it is quite probable that an audience would not even notice changes of this sort, but for the sake of the argument, I shall assume that it did.) In each of these imaginary situations, some elements of the conceptual model for the tune are changed and some are retained. The conceptual models thus for m a framework for negotiation — that is, negotiation is conducted in ter ms of the conceptual model for the tune. Series of such negotiations then lead to the more substantive changes in conceptual models of the sort suggested by my account of how such models might be linked in a histor ical succession. Of course, the imaginary situations I have described are highly simplified: as the works of Ruth Finnegan, Paul Berliner, and Ingrid Monson have demonstrated, actual negotiations among musicians are much more complex than those outlined here.35 Musical discourse is r ich and creative, and it includes comedy and irony, as well as meaningful exchanges about the business at hand. Nonetheless, what makes this communication possible is the knowledge shared among musicians, knowledge that is organized by conceptual models.

Limits on Negotiation The mutability of conceptual models under the social and cultural pressures of negotiation has the potential to destabilize cultural knowledge by transfor ming it until it becomes alien and unfamiliar. Under certain circumstances, the interconnectedness and dispersion character istic of cultural knowledge can counteract destabilization, a process noted by Mantle Hood.36 Under other circumstances, however, the challenge to stability may be significant. In the case of musical practice, such challenges might come from a number of sources: from the innovations of influen-

35. Ruth Finnegan, “The Relation between Composition and Performance: Three Alternative Modes,” in The Oral and the Literate in Music, ed.Yoshihiko Tokumaru and Osamu Yamaguti (Tokyo: Academia Music, 1986), 73– 87; Berliner, Thinking in Jazz; Ingrid Monson, Saying Something: Jazz Improvisation and Interaction, Chicago Studies in Ethnomusicology (Chicago: University of Chicago Press, 1996). 36. Mantle Hood, “The Reliability of Oral Tradition,” Journal of the American Musicological Society 12 (1959): 201– 09.

cultural knowle dge and musical ontology tial individuals, from contact with other cultures, from a sudden increase in the complexity of musical practice, or from changes in technology. Faced with this sort of challenge, a musical community may develop strategies to eliminate or control the instability of the conceptual models upon which the practice of that community is based. One common strategy is to represent key structural elements of a local conceptual model through artifacts such as scores or recordings. Although the score illustrations used for “I Got Rhythm” carry the aura of author ity, they actually follow from the conceptual models for the song: a score is an artifactual manifestation of the elements of the conceptual model deemed most relevant to the musical practice of which the model is a part, created as a means of stabilizing the model. The score for the or iginal version of “I Got Rhythm” (ex. 5.1) can thus be seen as a reflection of the conceptual model for pop songs (fig. 5.1). Such songs invariably had a verse, even if it was only rarely perfor med. Since the songs were often perfor med by musicians with only limited score-reading abilities, chord symbols (which often do not match the chords indicated by the music notation) are almost always included, and they serve to indicate the minimal mater ials necessary to accompany the voice. The jazz fake book rendering of “I Got Rhythm” (ex. 5.2) does away with the verse and any specifics about how the accompaniment is to be realized; it reflects the essential features of the jazz-standard model (fig. 5.2). And the “Rhythm changes” of example 5.3 preserve only the bare essentials, cryptic to anyone not schooled in jazz but more than enough to serve musicians as a starting point for improvisation, provided they are familiar with the concepts and relations embodied in the improv model (fig. 5.3). Thus, both in its production and inter pretation, musical notation reflects (rather than generates) the local and global conceptual models that constitute musical practice.37 The idea that musical notation could serve as a way to control (rather than simply enable) musical practice is not a new one, having been proposed by Charles Seeger over fifty years ago.38 With respect to Western practice, the limits on negotiation that follow from this reliance on musical notation operate on two levels. First, any given instance of musical notation, as an embodiment of “the work of music,” limits negotiation to those aspects of music deemed “nonessential” to the work (such as the specifics of dynamics, timbre, and tempo): these are the things left relatively ambiguous by the score.39 Second, the terms for negotiation become artifactual: any aspect of musical practice that would vie for deter mining the identity of a musical work must be such that it can be expressed artifactually. Arguments over 37. Leo Treitler has made similar points about the role of notation in medieval music. See Treitler, “Transmission and the Study of Music History,” in Report of the Twelfth Congress, Berkeley 1977, ed. Daniel Heartz and Bonnie Wade (Kassel: Bärenreiter-Verlag; Philadelphia: The American Musicological Society, 1981), 202 – 11; and idem, “History and the Ontology of the Musical Work,” Journal of Aesthetics and Art Criticism 51 (1993): 483 – 97. 38. Charles Seeger, “Oral Tradition in Music,” in Funk and Wagnalls Standard Dictionary of Folklore, Mythology, and Legend, ed. Maria Leach and Jerome Fried (New York: Funk and Wagnalls, 1950), 2: 825– 29. 39. Nelson Goodman observes that where the score attempts to capture what I have called the “nonessential” aspects of music it ceases to be, in his ter ms, notational. See Goodman, Languages of Art, 183– 86.

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analysis and theory musical identity (such as those that play out in discussions about the Urtext for a score) are arguments about the status and inter pretation of artifacts, and any competing account of musical identity must be expressed in artifactual ter ms. It bears mention that the author ity of notation is not monolithic: most musicians accept notation as something to be inter preted and consider the way it is to be used to create a musical perfor mance a matter for negotiation. And even where notation has been introduced with the explicit intent of eliminating variation within musical practice, it may be circumvented. As Ruth Davis has shown, the modified Western notation applied to Tunisian art music beginning in the 1930s for the pur pose of standardizing its melodic tradition has been tur ned into a creative tool for reinterpreting and redefining that tradition.40 Notation has thus slowed, but not eliminated, the fluidity of Tunisian musical practice.

Categorization, Musical Ontology, and Cultural Knowledge By the late 1940s, as we have seen, there were multiple versions of George and Ira Gershwin’s “I Got Rhythm” in circulation. There was the show stopper and popular tune from the Broadway musical, the “hot” jazz tune played by any number of dance bands, and the relatively abstract platfor m for improvisation used as the basis for any number of derived tunes by jazz composers and for extended improvisations by smaller ensembles. Confronted with this multiplicity of “I Got Rhythm”s, how might a listener discr iminate between them? Based on what we now know about processes of categor ization, we can say that our listener would almost certainly recognize that, while all these versions belonged in the category performances of “I Got Rhythm,” not all would represent the category equally well. Depending on the conceptual model around which the category was organized, some versions would be regarded as quite typical of the category, others as less typical, and still others in danger of being excluded from the category altogether. Following Richard Crawford’s description of three different approaches to “I Got Rhythm,” I proposed three models — the pop-music model, the jazz-standard model, and the improv model — which would yield different inter pretations of typicality when applied to a range of performances of the tune. The knowledge represented by such models, when combined with knowledge about musical technique and framed by global conceptual models applicable to an entire repertoire, can also serve as the basis for musical performance within aural traditions. Because they are retained by individual members of a musical community, who may wittingly or unwittingly change the model as they use it, conceptual models are subject to change over time. When such changes are brought to the attention of other members of the musical community, a ser ies of negotiations about what constitutes the model may ensue. At times, changes to conceptual models may be perceived as a threat to the integ rity of a musical community, and the community may then seek either to halt or to retard change by placing limits on what can be negotiated. 40. Ruth Davis, “The Effects of Notation on Performance Practice in Tunisian Art Music,” The World of Music 34 (1992): 111.

cultural knowle dge and musical ontology Given the various conceptual models we have considered and the ways these models are inter preted and cor related with other types of knowledge, it is clear that the network of knowledge within which any musical work (or similar construct) is embedded is a complex one. And yet we have thus far restricted ourselves to an almost purely musical world. Matters only stand to become more complicated when we contemplate how this world might connect with the cultural context within which musical practice is itself embedded. In the next section, we encounter some of these complications and gain a sense of the richer understanding of musical practice to which they lead, as we explore some of the different ways “Bye Bye Blackbird” was conceived during the middle of the twentieth century.

“ bye bye blackbird,” signifyin(g), and cultural knowledge On 5 June 1956, Miles Davis, John Coltrane, Red Garland, Paul Chambers, and Philly Joe Jones went into Columbia’s 30th Street Studio in New York and recorded three tunes: “Tadd’s Delight,” “Dear Old Stockholm,” and “Bye Bye Blackbird.”41 Although the recording session took place at a time when Davis was actively shaping the sound and repertoire of his quintet, the choice of “Bye Bye Blackbird” was nonetheless somewhat odd. Unlike the other two tunes, “Bye Bye Blackbird” had never been a part of the jazz repertoire, but was simply an upbeat popular song usually played as a foxtrot. Recorded by Davis as a ballad, it acquired a melancholy and an irresistible groove that were thoroughly exceptional. The choice was made odder still by the racial overtones associated with the tune. First published in 1926, “Bye Bye Blackbird” played a role in the racially charged election campaign for the mayoralty of Chicago in 1927. Big Bill Thompson, a Republican who had successfully cultivated the African American vote to become mayor of Chicago in 1915, returned in 1927 to challenge Democratic mayor William E. Dever. As part of their strategy to fight off this challenge, the Democrats appealed to racial prejudice, voiced specifically through “Bye Bye Blackbird.” The ploy ultimately backfired, for it galvanized African American support for Thompson: When some of the Dever supporters sent calliopes through the streets piping the strains of “Bye Bye Blackbird,” and spreading a circular which displayed a trainload of Negroes headed from Georgia with Thompson as pilot of the train, and the caption: “This train will start for Chicago, April 6, if Thompson is elected,” the obvious answer of the colored leaders was: “Elect Big Bill or it’s going to be bye-bye blackbirds in Chicago.”42 41. These three tunes, together with “’Round Midnight,” “Ah-leu-cha,” and “All of You,” were released on Miles Davis, ‘Round about Midnight (Columbia, [CD] CK 40610, 1987), originally recorded 27 October 1955 and 5 June and 10 October 1956. There are extensive transcr iptions and a discussion of this recording of “Bye Bye Blackbird” in Berliner, Thinking in Jazz; see esp. pp. 678– 88. 42. Harold F. Gosnell, Negro Politicians: The Rise of Negro Politics in Chicago, with an introduction by James Q.Wilson (Chicago: University of Chicago Press, 1966; originally publ. in 1935, with an introduction by Robert Park, Social Science Studies, 35), 54– 55. There is a discussion of a similar cartoon from around the same time that invokes the phrase “Bye Bye Blackbird” in Lloyd Wendt and Her man Kogan, Big Bill of Chicago (Indianapolis: Bobbs-Mer rill, 1953), 256.

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analysis and theory In a similar vein, Jack Chambers reports that dur ing the 1930s, the few African Americans who participated in activities dominated by whites, like the semiprofessional National Football League, had the song sung to them by the all-white spectators.43 What seems to be reflected in Davis’s adoption of the tune is the sort of doublevoiced discourse first descr ibed by Mikhail Bakhtin: on one level of discourse, Davis’s “Bye Bye Blackbird” is an aging pop song, with racial overtones that tur n against its perfor mers; on another level, it is a deeply felt rewriting —“felt” both in terms of melancholy and groove— that makes a mockery of the simplistic messages of the song, not least by rising above them. This process of repetition (in the sense of returning to an earlier “text”) and revision is associated with a kind of intertextuality Henr y Louis Gates Jr. called “Signifyin(g),” which he argued is fundamental and specific to African American rhetor ical practice.44 While Gates’s primary focus was on literature, he extended his argument to other domains, music among them, and his arguments have proved compelling to musicologists. Adopting one of Gates’s examples, Ingrid Monson was able to show in some detail how John Coltrane’s 1960 recording of Richard Rodgers and Oscar Hammerstein’s “My Favorite Things” (written in 1959) accomplishes this sort of Signifyin(g). Coltrane’s interpretation completely revises the song: the focus is changed from the verse to the interludes, Rodgers and Hammerstein’s waltz is transfor med into a polyrhythmic extravaganza, and what was an upbeat tune becomes a brooding one.45 There is, however, a problem with claiming, in any simple way, that Davis is Signifyin(g) on “Bye Bye Blackbird,” and that problem is profiled vividly by a recording of the tune in 1955 by Peggy Lee. In her perfor mance, Lee adopts an exceptionally slow tempo — slower than Davis’s— and completely vanquishes the upbeat sentiments of the or iginal song.46 Lee, too, seems to have engaged in double-voiced discourse, but would we want to say that she is Signifyin(g)? Indeed, this sort of performance practice is so common in jazz — within and without the African American community — that Signifyin(g), present everywhere, would seem to signify nothing.47 Two sets of issues, then, are raised by Davis’s recording of “Bye Bye Blackbird.” First, what is the nature of the double-voiced discourse of Signifyin(g)? Is it in any way distinct from double-voiced discourse as a whole? Second, what part does the reinterpretation of musical works — or, from the perspective developed in the pre-

43. Jack Chambers, Milestones I: The Music and Times of Miles Davis to 1960 (Toronto: University of Toronto Press, 1983), 237. 44. Henry Louis Gates, Jr., The Signifying Monkey: A Theory of African-American Literary Criticism (New York: Oxford University Press, 1988), chap. 2. The parenthetical g in “Signifyin(g)” is meant to signal African American pronunciation, as well as to distinguish it from the more general process of “signification”; for discussion, see The Signifying Monkey, 46. 45. Monson, Saying Something, 106– 21. 46. Peggy Lee, “Bye Bye Blackbird,” in Songs from Pete Kelly’s Blues (Decca, [LP] DL 8166, 1955), recorded 6 May 1955. 47. The practice of revisiting the work of other composers and musicians was also common in the music of the previous century: we thus have Beethoven Signifyin(g) on Diabelli in his Op. 120 variations and Brahms Signifyin(g) on Paganini in his Op. 35 variations.

cultural knowle dge and musical ontology ceding section, revisions to the conceptual model for a musical work — play in Signifyin(g)? In what follows, I begin by developing an approach to double-voiced discourse in ter ms of a cultural theory of information exchange proposed by the linguist Eve Sweetser. I proceed then to explore some of the conceptual models for “Bye Bye Blackbird” in circulation dur ing the per iod 1926 – 1955, and, finally, I return to Davis’s inter pretation of the tune.

Double-Voiced Discourse and a Cultural Theory of Information Exchange Mikhail Bakhtin developed his notion of double-voiced discourse with reference to the novels of Dostoevsky, going so far as to claim that this rhetor ical mode was essential to Dostoevsky’s style.48 Double-voiced discourse is actually the third of three types of discourse distinguished by Bakhtin. The first type is “direct discourse,” which is essentially the unmediated disquisition of the author. The second type Bakhtin called “objectified” or “represented discourse”; its most common for m is the direct speech of characters. In “double-voiced discourse” (the third type), the author takes the direct discourse of someone else and infuses it with the author’s own intentions and consciousness while still retaining the or iginal speaker’s intentions. Thus two discourses and two consciousnesses are present at the same moment.49 With this taxonomy in place, Bakhtin further distinguished three types of double-voiced discourse. In the first, the discourse of the author and that of the other person essentially cooperate — the author inflects, but does not substantially change, the discourse of the other person. The second type of double-voiced discourse is associated with parody and irony (this is essentially the sort of discourse Monson deals with in her analysis of Coltrane’s “My Favorite Things”). Here the discourse of the author is opposed to that of the other person; as Bakhtin puts it, “the second [that is, authorial] voice, once having made its home in the other’s discourse, clashes hostilely with its pr imordial host and forces him to serve directly opposing aims. Discourse becomes an arena of battle between the two voices.”50 In the third type of double-voiced discourse, the other person’s discourse remains outside the purview of the author’s, which nonetheless becomes influenced by that of the other person. The result is often a hidden polemic: the author’s discourse represents a reaction to the discourse of the other person, but the latter can be heard only by implication — it is never directly represented. Each of these three types of discourse— and, most important, the three types of double-voiced discourse — can be analyzed with reference to a cultural theor y of 48. Mikhail Mikhailovich Bakhtin, Problems of Dostoevsky’s Poetics, ed. and trans. Caryl Emerson, with an introduction by Wayne C. Booth, Theory and History of Literature, 8 (Minneapolis: University of Minnesota Press, 1984), chap. 5. 49. The premise of double-voiced discourse is that the two domains of discourse remain separate and identifiable; it is thus different from the process of conceptual blending discussed previously in chap. 2 (in that blending is concer ned with how elements from two distinct domains come together in a third domain), but it may be seen as a related phenomenon. 50. Bakhtin, Problems of Dostoevsky’s Poetics, 193. I shall follow Bakhtin’s practice and speak of the first voice in double-voiced discourse as that of the “other” and the second voice as that of the author.

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analysis and theory information exchange developed by Eve Sweetser. Sweetser used the theor y to explain the results of an exper iment by Linda Coleman and Paul Kay that was designed to show that the English word “lie” (in the sense of “to prevaricate”) functioned like a Type 1 categor y. That is, rather than following a clear-cut definition, some statements were regarded as typical lies, others as atypical. Coleman and Kay hypothesized that a statement is judged to be a more-or-less good example of a lie on the basis of three conditions. First, the actual statement must be false (a condition that is commonly taken as necessar y and sufficient when “lie” is construed as a Type 2 category). Second, the speaker must believe the statement to be false. Third, in utter ing the statement, the speaker must intend to deceive the listener.51 To test this hypothesis, Coleman and Kay constructed eight stor ies that satisfied all, only some, or none of these conditions. They then asked sixty-seven subjects to determine whether, in the case of each story, a lie had been told. In support of their hypothesis, the results indicated that “lie” functioned as a Type 1 categor y: judgments of what constitutes a “lie” were not made comprehensively, but, rather, could be made by degree. Although they were able to prove their hypothesis, Coleman and Kay were not able to explain satisfactor ily what it was about the word “lie,” or about the conditions sur rounding its proper use, that made it function as a Type 1, rather than as a Type 2, category. Sweetser, for her part, proposed that judgments about lies were made relative to a cultural theor y of information exchange.52 The theory, as formulated by Sweetser, consists of three relatively straightforward propositions, which can be stated as rules: 1. Try to help (do not harm). This rule is combined with the belief that knowledge is helpful and that misinfor mation is har mful (which leads to the next rule). 2. Give knowledge (do not misinform). Sweetser argues that what counts as knowledge, in everyday terms, is what we believe. All things being equal, we assume that what we believe matches some state of affairs or possible state of affairs: we take what we believe to be true, to count as knowledge. Using this understanding of knowledge together with (1) and (2), we arrive at the final rule. 3. Say what you believe (do not say what you do not believe). If what we believe counts as knowledge, and if we wish to be helpful, we must give knowledge. This chain of entailments represents a cultural theory of information exchange that allows us to reach the somewhat sur prising conclusion that if a speaker (S) utters a

51. Linda Coleman and Paul Kay,“Prototype Semantics: The English Word Lie,” Language 57 (1981): 26– 27. 52. Eve E. Sweetser, “The Definition of Lie: An Examination of the Folk Models Underlying a Semantic Prototype,” in Cultural Models in Language and Thought, ed. Dorothy Holland and Naomi Quinn (Cambr idge: Cambridge University Press, 1987), 43– 66. Sweetser’s “models” have the same function as the theor ies descr ibed in chap. 3; I have simplified some aspects of her account in the interests of concision.

cultural knowle dge and musical ontology proposition (P), then that proposition is true. The causal chain can be represented schematically: a. S said P. [as part of an infor mation exchange; from rules (1) and (2)] b. S believes P. [(a) combined with rule (3)] c. Therefore, P is true. [(b) combined with the understanding that we believe what is true and do not believe what is false] This is, without a doubt, a greatly simplified perspective.What is important is that the model of information exchange set out by the theory works quite a bit of the time, and when it does not work, the theory provides a way to inter pret where things went wrong. To illustrate, let us consider two situations. In the first, I claim that I saw a fr iend of mine walking down the street. On closer inspection, it turns out to be someone who just looked like my friend. According to the simplest definition, my claim is a lie — a statement that is not true. However, since my behavior as a whole fits with the cultural theor y of information exchange (my intent was to provide helpful information), my claim will most likely not be judged a lie. In the second situation, I see someone walking down the street whom I mistake for my friend. Remembering that I owe my friend money and being a cheap sort, I claim that the person I see is not my friend. According to the simplest definition, this is not a lie, since my claim is true: the person walking down the street is not, in fact, my friend. Nonetheless, since I deliberately said what I thought to be misinfor mation, I have violated the theory of information exchange and my claim might well be judged a lie. Of course, this straightforward theory of information exchange does not operate in isolation but is inter preted through other cultural theor ies to explain types of discourse that seem to contravene the theory. Jokes, tall tales, and fiction all may have limited truth-value, but their “lies” are permitted as part of a cultural theor y that interprets certain types of exceptional behavior as entertainment. Social lies are based on the recognition that not all for ms of knowledge are helpful: rarely when someone remarks “How are you?” do they really want to know how we are. The cultural theory of information exchange is thus filtered through a theory that says maintaining social order through polite behavior is more important than saying what you believe to be true.53 Applying Sweetser’s example of a cultural theor y of information exchange to Bakhtin’s first two types of discourse is relatively straightforward. All things being equal, we assume that direct discourse — the voice of the author — involves the truth; we similarly give the benefit of the doubt to the objectified discourse of the author’s characters.54 With double-voiced discourse, however, the application of the 53. For a related view of how information exchanges contr ibute to and constitute social order, see Michael B. Bakan’s account of how various Balinese musicians reported the results of a gamelan competition in Music of Death and New Creation: Experiences in the World of Balinese Gamelan Beleganjur, Chicago Studies in Ethnomusicology (Chicago: University of Chicago Press, 1999), chap. 5. 54. The genre of fiction, which is the focus of Bakhtin’s analysis, requires an intr iguing nesting of theories about infor mation exchange. On the level of everyday life, fiction is generally recognized as nonfactual (except by the delusional).Within a given work of fiction, however, we usually apply the theory of information exchange outlined by Sweetser: we assume that characters say what is true in the con-

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analysis and theory theory is a bit more complicated. With the first type of double-voiced discourse— where the discourse of the author and the other person essentially cooperate — the idea that both voices speak the truth is easily accommodated. What results is a sort of heterophony of discourse: two voices saying the same thing in different ways. With the second and third types — parody and hidden polemic — the contradictions and tensions between the two voices suggest that one of the voices must be violating the pr inciples of the cultural theor y of information exchange. The traditional resolution of the problem, implicit in Bakhtin’s analysis of discourse as a whole, is that in double-voiced discourse, the voice of the author is to be pr ivileged: it is the voice of author ity.55 This resolution requires modification of Sweetser’s cultural theory of information exchange by the addition of one further proposition: 4. The voice of authority is always helpful. On the one hand, it is difficult to ascr ibe this inter pretation to Bakhtin without a crushing sense of irony, given his personal history. But on the other hand, it is certainly the case that, in his analyses of double-voiced discourse, the “first” (nonauthor ial) voice is the one he most often distrusts. Given this analysis, equating Gates’s notion of Signifyin(g) with Bakhtin’s double-voiced discourse brings us to two conclusions. First, the voices of black rhetor ic become voices of authority: they are the helpful voices that speak the truth. Second, Signifyin(g) is by no means unique to the African American community — indeed, Dostoevsky and countless other “authors” are also Signifyin(g). But these conclusions are hardly satisfying, for they trivialize the points Gates wishes to make about African American literature and culture and miss the ways language can be used against oppressors. The solution to these problems lies in two important adjustments to the cultural model of information exchange adumbrated here. First, a distinction must be made between “author” and “author ity.” For the African American community, the first voice in double-voiced discourse was almost always the voice of “author ity.” Since experience had shown that the voice of authority was almost always unhelpful, it was a voice to be distrusted. Rather than trusting one of the voices of a doublevoiced discourse, it was important actively to distrust one of those voices; by default, the nonauthor itative voice of the author was to be regarded as the helpful one. Second, it did not particularly matter if the statements of the author were true or not. Indeed, as Gates points out, one of the common African American ter ms for Signifyin(g) is “lies.”56 What mattered more was whether the author, in some way, adhered to the first principle of information exchange: to be helpful. And it is clear that, to an oppressed people, speech that co-opts, mocks, or indirectly challenges the voice of authority, whether the statements made in the course of that speech are

text of the story.When a character says something that is not true within the context of the story (even though it may be true in the everyday world), we then have to fall back on this theory or its elaborations to make sense of the utterance. 55. The pun is not sur prising, since “authority” and “author” share the same Latin root (auctor). 56. Gates, The Signifying Monkey, 56, 71.

cultural knowle dge and musical ontology true or not, is singularly helpful.With these adjustments, distinctions between doublevoiced speech and Signifyin(g) become clear: Signifyin(g) relies on a modified theory of information exchange that assumes that the first voice in double-voiced discourse is the voice of an extracultural author ity and that this author ity is not to be believed. Under these circumstances, double-voiced discourse is, as Bakhtin characterized it, “an arena of battle between the two voices.” However, it is an arena in which the author is at a distinct disadvantage and must rely on whatever combination of truths, half-truths, and lies is necessary to win the day. My intent with this analysis is to show how Bakhtin’s notion of double-voiced discourse functions relative to a highly simplified, yet quite serviceable, rendering of a cultural theory of information exchange and how the double-voiced discourse of Signifyin(g) relies on a modified version of this theory. In applying this perspective on discourse to music, I restrict my discussion to the level of the conceptual model for a work. Musical discourse, understood in this way, is thus concer ned with the realization and projection of the conceptual model for a work. In ter ms of the cultural theor y of information exchange (extended to music), our assumption is that the perfor mer intends to project this model and that it is valid for the piece. My decision to impose this restriction is based on practical reasons. It will keep discussion focused on the main topics of this chapter, it will greatly simplify the analyses, and it requires no strong analogy between linguistic and musical discourse. There is, however, no reason that, mutatis mutandis, this treatment could not be extended to more finely grained levels of musical discourse.

Conceptualizing “Bye Bye Blackbird,” 1926 – 1955 “Bye Bye Blackbird” was wr itten in 1926 by the song-wr iting team of Mort Dixon and Ray Henderson. The score, given in example 5.4, reveals a song typical of the thousands wr itten dur ing the days of Tin Pan Alley. It consists of an eight-measure introduction (taken from the concluding phrase of the refrain); a two-measure vamp to allow the vocalist to get ready; a thirty-two-measure verse in AABA' form; and a thirty-two-measure refrain in AA'BA" form (where A' presents the mater ial of the A section a diatonic step higher, and A" changes the or iginal A section at midphrase so that it ends on the tonic).57 The general topic of the song centers around a nar rator in alien or unhappy surroundings, symbolized in the first verse by the trope of winter, the blackbird’s doleful pronouncements, and the use of minor mode. The nar rator rejects these conditions and looks to where “there’s sunshine galore,” a promise held out by the refrain: a waiting loved one, a familiar bed, and a light burning in the window, all intro-

57. At least two other scores for “Bye Bye Blackbird” have been in circulation. Both of these are in F major, and both shorten the verse to a sixteen-measure form by omitting the inter nal AB sections. One score, with the copyright renewed and assigned to the Remick Music Cor poration, has a short, fourmeasure introduction; the sixteen-measure verse; and the refrain. The other, copyrighted in 1948 by the Remick Music Cor poration, was printed by Francis, Day and Hunter, London. It gives the refrain first, followed by the introduction and verse. I have found no recordings of performances based on either of these scores.

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analysis and theory example 5.4 Music Group

Ray Henderson and Mort Dixon’s “Bye Bye Blackbird,” © Fred Ahlert

duced against the backdrop of a spr ightly G major. The second verse (which replaces the blackbird with a bluebird) reflects the hope offered by the refrain, conditioned nonetheless by the return to minor mode and references to longing, fading like a flower, and hours that are like “one long tear.” Recordings of the period indicate typical treatments of the song. In their version of 22 April 1926, for example, Bennie Krueger’s Orchestra begins with a short introduction (which bears no resemblance to the published one) and proceeds to an

cultural knowle dge and musical ontology example 5.4

(continued)

(continued)

instrumental version of the refrain, verse, and refrain.58 (As with the early recordings of “I Got Rhythm,” the Krueger ar rangement uses the verse as an interlude between the refrains.) This is followed by a sung refrain and one final instrumental refrain. The tempo of the recording (h = 116 – 120) is a bit faster than the “Moderato” indicated by the score, but it is perfectly suitable for a foxtrot.59 Gene Austin’s 58. Bennie Krueger’s Orchestra, “Bye Bye Blackbird” (Brunswick, [78] no. 3186, 1926). 59. The song is in fact identified as a foxtrot on the label of the record, which also includes the rubric “for dancing.”

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analysis and theory example 5.4

(continued)

recording, made a week later, follows the score rather more closely.60 Although he adds his own introduction and piano accompaniment and varies the melody in the third phrase of the verse, his perfor mance otherwise confor ms to the score given in example 5.4, even adher ing to a somewhat slower tempo than did Krueger’s group (h = 96 – 100). By most standards, “Bye Bye Blackbird” was a hit: it was recorded at least fourteen times between March and June of 1926, and Austin’s recording was no. 1 on the Billboard charts of 4 September of that year.

60. Gene Austin, “Bye Bye Blackbird” (Victor, [78] no. 20044-B, 1926), originally recorded 29 April.

cultural knowle dge and musical ontology example 5.4

(continued)

The various perfor mances of “Bye Bye Blackbird” recorded in 1926 could be collected into a category organized around a conceptual model quite similar to that used for early versions of “I Got Rhythm.” The model, which is diag rammed in figure 5.5, consists of five cor related conceptual elements, character ized as the things necessary for an adequate perfor mance of the song. However, where the popmusic model for “I Got Rhythm” continued to have some cur rency in the years just after the first appearance of the song (in part because of its association with the musical), the model for “Bye Bye Blackbird” appears to have gone dor mant for a

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figure 5.5

Model for the category performances of “Bye Bye Blackbird”

time: there are few signs of the song having been recorded after 1926 and throughout the 1930s.61 New recordings of “Bye Bye Blackbird” did begin to appear in the 1940s. There are a number of indications, however, that by then the conceptual model for the song had changed. The “novelty” recording by Freddie “Schnickelfritz” Fisher and His Orchestra (made on 22 February 1941), with its rapid succession of unlikely instruments (including solo whistling and bar itone saxophone) and its “shave-anda-haircut” ending, is just short of an all-out joke.62 In a 1941 Ger man propaganda recording by Charlie and His Orchestra, the words of the song are altered to celebrate early Axis victor ies in the Second World War and to taunt the Br itish (“Bye Bye Blackbird” becomes “Bye Bye Empire”).63 And in a tr ibute to the songs of 1926 recorded on 27 May 1942 by the piano duo of Marlene Fingerle and Arthur Schutt, “Bye Bye Blackbird” is the final song in a medley that includes “I Know That You Know” and “Baby Face.”64 In each of these recordings, only the refrain of the song is used, and the tempo varies from the moderate swing of Charlie and His Orchestra (h = 84) to the Fisher Orchestra’s foxtrot (h = 120 – 126).While there are some signs the song has entered the repertoire of “standards”— its verse has

61. Recording, of course, is not the only measure of popular interest in a song: sales of records, piano rolls, and sheet music; programming of the song in live performances; and the playing of recordings on radio broadcasts and in juke boxes would also provide an indication of continued interest in the song. Unfortunately, no infor mation on these indicators is presently available for “Bye Bye Blackbird.” 62. Freddie “Schnickelfritz” Fisher and His Orchestra, “Bye Bye Blackbird” (Decca, [78] no. 25357/3788, 1941). 63. Charlie and His Orchestra, “Bye Bye Blackbird,” in Charlie & His Orchestra: German Propaganda Swing 1941–1942 (Harlequin, [CD] HQ CD 03, 1990). 64. Marlene Fingerle and Arthur Schutt, “Medley:‘I Know That You Know,’‘Baby Face,’‘Bye Bye Blackbird,’ ” in Song Hits of 1926, Songs of Our Times (Decca, [LP] DL 5170, 1950).

cultural knowle dge and musical ontology the musical materials for the refrain

the lyrics for the refrain

“Bye Bye Blackbird” (pop song, ca. 1941)

intended for entertainment or dancing; performers use variation but little improvisation

performed with a lively affect

acknowledgment (explicit or implicit) that the song was written for a previous generation

figure 5.6

Model for the category performances of “Bye Bye Blackbird,” ca. 1941

fallen away, and it is readily available for parody— it is also clearly marked as an “old” song. The conceptual model for the categor y performances of “Bye Bye Blackbird,” ca. 1941, then, would consist of five cor related conceptual elements (which are diagrammed in fig. 5.6).65 As a consequence of a growing interest in the 1920s as an era, this model was, if anything, reinforced dur ing the post–World War II per iod. Following the phenomenal success of The Jolson Story in the fall of 1946,Warner Brothers films contracted in 1947 for the filming of a similar story with (and about) Eddie Cantor. Although Warner Brothers ultimately dropped the project, Cantor and Sidney Skolsky (producer of The Jolson Story) eventually filmed The Eddie Cantor Story independently, and it was released in 1953.66 As part of the soundtrack for the movie, Cantor recorded “Bye Bye Blackbird” in something approximating the style of the 1920s, although using only the refrain of the song.67 A similar approach can be heard in 65. I do not mean to suggest, with the idea that “Bye Bye Blackbird” was “written for a previous generation,” that the fifteen years between 1926 and 1941 actually fill the span of a human generation. However, I do think this per iod is long enough to mark a significant change in popular tastes, which is what this portion of the conceptual model aims to capture. 66. Herbert G. Goldman, Banjo Eyes: Eddie Cantor and the Birth of Modern Stardom (New York: Oxford University Press, 1997), 283 – 84. 67. Eddie Cantor, “Bye Bye Blackbird,” in Songs by Eddie Cantor from The Eddie Cantor Stor y (Capitol, [LP] L-46, 1954). There is no evidence that Cantor recorded “Bye Bye Blackbird” during the 1920s or 1930s, although he might well have performed it in live shows; in fact, Goldman character izes it as one of the standards of Cantor’s repertory from the 1920s. By most accounts, The Eddie Cantor Story was a flop; its failure is generally attr ibuted to the inadequacies of Keefe Brasselle (who played the role of Cantor) and to a scr ipt that was little more than a remake of The Jolson Story. Of the soundtrack, however, Goldman wr ites: “The musical ar rangements were first rate, and the vocals better than might be

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analysis and theory Johnny Maddox’s recording of the song on piano (accompanied by a rhythm section), released in 1955, which inter prets it in a quasi-ragtime style as part of a collection of 1920s songs intended to accompany tap dancing.68 During this same per iod the general fascination with the character and music of the 1920s was given a specific focus when there was a resurgence of interest in early jazz, variously called “New Orleans” or “Dixieland” jazz.69 Partly, this came about because of a str ike by musicians against the recording industry from 1942 to 1944, which led record companies to reissue older recordings. Around the same time, there emerged an audience who felt the swing era had passed but who were not attracted to be-bop, the new jazz style that emerged dur ing the Second World War. In 1950, the actor Jack Webb (now chiefly remembered for his role as Sergeant Fr iday on the Dragnet radio and television ser ies) developed a radio ser ies around a jazz musician in 1920s Kansas City, reflecting contemporary interest in the “roaring 20s” and Webb’s own enthusiasm for early jazz.70 The radio ser ies was eventually developed into the movie Pete Kelly’s Blues, which Webb directed and in which he also starred. In the movie, Pete Kelly is a bandleader threatened by a gangster who is attempting to extract protection money from musicians. Kelly initially tr ies to resist but eventually capitulates. As part of his agreement with the gangster, Kelly’s band has to take on the gangster’s girlfriend, Rose Hopkins (played by Peggy Lee), as a singer. Rose is an alcoholic but can still render a moving ballad. A tragic character, Rose is eventually reduced to the mentality of a five-year-old by alcoholism and by a beating from the gangster. As part of the promotion of Pete Kelly’s Blues as a “jazz” movie, Lee, together with Ella Fitzgerald (who played a blues singer working in a roadhouse), recorded an album of songs associated with the movie on 10 May 1955. Although “Bye Bye Blackbird” appears in the movie, neither Lee nor Fitzgerald sings it. Instead, it is rendered by a drunken chorus of band members returning from a late-night party. On the album, Lee retains Rose’s persona from the movie and sings the song (consisting only of the refrain) as a slow ballad (q = 72 – 76), with slight allusions to Billie Holiday’s distinctive style of inflection.71 The arrangement makes use of complicated har monies typical of the treatment of ballads in 1940s and 1950s jazz and

expected, considering that Cantor had suffered a major heart attack less than three months earlier and that his voice had lost its for mer brilliance after World War II.” Goldman, Banjo Eyes, 284. 68. Johnny Maddox, “Bye Bye Blackbird,” in Tap Dance Rhythms (Dot, [LP] DLP 3008, 1955). 69. Chip Deffaa, Traditionalists and Revivalists in Jazz, Studies in Jazz, 16 (Metuchen: Scarecrow Press; Institute of Jazz Studies, Rutgers, The State University of New Jersey, 1993), 132. In the following I refer to this style of jazz as “traditional” jazz, retaining the quotation marks to highlight the function of the term as a rubric rather than a judgment about the place of this music within any histor ical account of jazz styles. See also Ber nard Gendron, “ ‘Moldy Figs’ and Moder nists: Jazz at War (1942 – 1946),” in Jazz among the Discourses, ed. Krin Gabbard (Durham, N.C.: Duke University Press, 1995), 31– 56. 70. Charles Emge, “Meet ‘Jazzman’ Jack Webb: Swing Era Helped Make Him Music-Conscious,” Downbeat 22 (10 August 1955): 8. 71. The character of Rose seems to have had a profound personal effect on Lee. In her autobiography, she speaks of Rose in the third person, speculates on whether a visit from James Dean was intended for her or for Rose, and wr ites of “moving out of Rose’s trailer [on the set]” once the film was completed. See Peggy Lee, Miss Peggy Lee: An Autobiography (New York: Donald I. Fine, 1989), 165– 67.

cultural knowle dge and musical ontology adds words for the second pass through the refrain that signal a new perspective on the song: A while ago when I was young, I heard a song and heard it sung [male chorus sings as distant echo] Bye bye blackbird I don’t know why it makes me sad, a happy song should make me glad [male chorus] Bye bye blackbird

Singing in her persona as a dissolute, tragic chanteuse, Lee evokes a melancholy that, up to this point, had not been associated with “Bye Bye Blackbird.” Pete Kelly’s Blues was, at best, a mixed success cr itically, and Lee’s treatment of “Bye Bye Blackbird” might well have been forgotten (especially since she did not sing the song in the movie). Fate, however, intervened: the singer and pianist Bobby Short heard and liked Lee’s recording and decided to approach “Bye Bye Blackbird” in a similar fashion, finding reflective sadness in the refrain rather than joyful anticipation.72 In his recording of 15 September 1955, Short also adopts a slow ballad tempo (q = 84) and fashions his accompaniment out of rich, progressive harmonies. To provide an introduction, he starts with the B section of the refrain, the one section that retains the sense of alienation generated by the or iginal verse: “No one here can love and understand me . . .” The effect is to cast a shadow over the remaining lyr ics of the refrain, emphasizing what is negative in them — the nar rator’s care and woe, distant loved one, and need to travel late into the night — rather than the pleasant things that wait at home. Short also adds his own lyrics for the second pass through the refrain (with words adapted from the song “I’m a Little Blackbird Looking for a Bluebird”):73 I’ve been all over the east and the west, in search of clover to feather my nest, Bye bye blackbird I have a daydream the same as you do, why would a daydream have to be hoo-doo? Bye bye blackbird No one here can love and understand me, Oh, what hard luck stor ies they all hand me. (etc.)74

With these two recordings by Lee and Short, “Bye Bye Blackbird” was transformed from an upbeat popular song in a fast tempo, designed for dancing — a “hop” tune, as Short has called it75 — into a melancholy jazz ballad in a slow tempo, designed for listening. The motivation for this change was not, strictly speaking, musical, for most of the music in Pete Kelly’s Blues kept to a “traditional” or Dixieland style.76 Instead, the change was initially motivated (that is, in Peggy Lee’s

72. Personal communication from Bobby Short, 8 March 2000. 73. “I’m a Little Blackbird Looking for a Bluebird” was wr itten by Clarke Grant, Arthur Johnston, George W. Meyer, and Roy Turk. It was recorded by both Louis Armstrong and Sydney Bechet in the mid-1920s. 74. Bobby Short, “Bye Bye Blackbird,” in Bobby Short (Atlantic, [LP] 1230, 1956), recorded 15 September 1955. As will be noted, Short’s revised lyr ics return to Dixon’s or iginal refrain at midpoint (with, “No one here can love and understand me”). 75. Personal communication from Bobby Short, 8 March 2000. 76. The soundtrack for the movie (with pr iceless nar rations by Jack Webb) consisted exclusively of

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figure 5.7

Jazz ballad model for the category performances of “Bye Bye Blackbird”

recording) by a romanticized notion of the female jazz singer, itself derived from any number of nineteenth-century fantasies about perfor mers.77 The new conceptual model for “Bye Bye Blackbird” suggested by Lee’s and Short’s recordings, and diagrammed in figure 5.7, consists of four elements necessary for an adequate perfor mance. Gone is the sense of history that had freighted approaches to the song since the early 1940s; it is replaced by a sense of immediacy generated by the necessar ily reflective nature of the perfor mances. It may be useful at this point to consider differences in the way conceptions of “I Got Rhythm” and “Bye Bye Blackbird” changed over roughly the same per iod in time. Because “I Got Rhythm” was an endur ing part of the popular music and jazz repertoire, its conceptual model changed only g radually, through a process of slow but relatively constant negotiation. In contrast, no such process is in evidence for “Bye Bye Blackbird.” After its first blossoming, the tune, and its conceptual model, faded from popular consciousness. When it was recalled dur ing the early 1940s, it was as part of a larger process of revisiting, through music, an earlier era: “Bye Bye Blackbird” was simply emblematic of “a popular tune from the 1920s.” When Peggy Lee introduced her version, the change to the conceptual model was sudden and dramatic, by fiat of her character in the movie. “traditional” arrangements. See “Pete Kelly and His Big Seven” (Matty Matlock and others), Pete Kelly’s Blues (BMG Special Products, [CD] DRC12081, 1998), originally recorded 7, 9, 11 June 1955. 77. For a recent, and stimulating, discussion of some of these fantasies, see Susan Ber nstein, Virtuosity of the Nineteenth Century: Performing Music and Language in Heine, Liszt, and Baudelaire (Stanford, Calif.: Stanford University Press, 1998), chap. 3. My character ization of the persona developed by Lee in connection with Pete Kelly’s Blues should not obscure the powerful presence of African American women who sang the blues and jazz, or the very real tr ials to which these women were subjected. (For a discussion of the role of these women in shaping the blues in particular, see Susan McClary, Conventional Wisdom: The Content of Musical Form [Berkeley: University of California Press, 2000], 42– 49.) I do believe, however, that Lee, as a white entertainer in the United States of the 1950s, was able to choose this persona (much as she chose to emulate Billie Holiday’s voice in the course of her performance of “Bye Bye Blackbird”) and that part of the framework for this choice was a romanticized notion of the suffer ing perfor mer.

cultural knowle dge and musical ontology Thus by the end of 1955 there were two conceptual models for “Bye Bye Blackbird” in circulation. The first conceptualized the tune as a somewhat dated but nonetheless upbeat pop song; the second conceptualized the tune as a slow, melancholy ballad. There may have also been still circulating a third, and more sinister model, derived from the first, that inter preted the song in racial ter ms— a signal for African Americans to be on guard, that they were not wanted here. It was into the context provided by these models that Miles Davis introduced his version of “Bye Bye Blackbird.”

Davis’s “Bye Bye Blackbird,” Double-Voiced Discourse in Music, and Signifyin(g) The recording that Davis made with Garland, Chambers, Jones, and Coltrane was strictly instrumental, at a tempo slower than the “hop” version of the tune (q = 120), but notably faster than the tempos adopted by Lee and Short. After a br ief introduction by Garland, Chambers, and Jones that establishes a loose, almost loping, groove, Davis enters playing the refrain. From his first notes, Davis announces the song as a jazz ballad, using a languid approach to the melody and muted trumpet to create an understated, slightly distant reflection on the song. After the head, Davis takes two choruses, followed by two choruses from Coltrane that occasionally hint at a double-time feel. Garland takes a chorus and a half , and, at the br idge of Garland’s second chorus, Davis reenters with the melody and guides the performance to a conclusion. Davis’s principal contr ibutions are to infuse “Bye Bye Blackbird” with an ir resistible groove and to establish it as a venue for instrumental commentar y and expansion. Although these contr ibutions are by no means insignificant — Davis’s recording virtually established “Bye Bye Blackbird” as a jazz standard, something it had never been before— one can also hear the influence of Lee’s and Short’s recordings in his version. There is, obviously, the slower tempo and hint of melancholy adopted from the jazz-ballad model (although the g roove Davis sets up tends to move the tune back toward the pop-music model). There is also, however, the same sense of immediacy that marked Lee’s and Short’s perfor mances: “Bye Bye Blackbird” is not, in Davis’s hands, about nostalgia.78 Davis has modified the conceptual model for the tune used by Lee and Short, but he has also retained enough of it that we can still recognize its main elements. The immediate relationship between the jazz-ballad model for “Bye Bye Blackbird” and the model Davis set out in his recording suggests that double-voiced discourse can be accomplished in music when one conceptual model for a musical work is understood to make reference to another conceptual model for the same 78. The element of nostalgia has continued to cling to “Bye Bye Blackbird” as a popular tune (as distinct from a jazz standard) and has been exploited in a number of films. In Jonathan Demme’s Melvin and Howard (1980), “Bye Bye Blackbird” is the one song Howard Hughes is able to recall when Melvin Dummar presses him — on pain of being thrown out of Dummar’s truck — to sing something, and it becomes a deeply felt recollection of Hughes’s childhood. In Nora Ephron’s Sleepless in Seattle (1993), “Bye Bye Blackbird” is cast as the song the boy’s deceased mother used to sing to him when he couldn’t sleep.

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analysis and theory work. If we know Peggy Lee’s recording of “Bye Bye Blackbird,” hear Miles Davis’s, and understand the latter as making reference to the for mer, musical doublediscourse takes place.79 Musical double-discourse thus requires, minimally, a listener who knows at least two conceptual models for a given work. Connections between the models may be drawn out by the perfor mer, but they may be more oblique and constructed mostly by the listener. Each of the three types of double-voiced discourse descr ibed by Bakhtin can be created: an inflection of the first conceptual model by the second (which is what Davis does); a parody of the first conceptual model by the second (which is what Monson descr ibes Coltrane as doing); or tacit reference to the first model by the second (which is one way to conceive how derived tunes operate). But what of Signifyin(g)? Signifyin(g) would require that the first conceptual model be recognized as the “authoritative” one and that its author ity is not to be believed: that is, it is not a valid model for the work. Validity is then g ranted by default to the conceptual model used by the perfor mer. A consequence is that the validity of this model depends on the rejection of the model associated with authority; it is not granted independently. Under these circumstances, a case can be made that, in his recording of “My Favorite Things,” Coltrane is Signifyin(g) on Rodgers and Hammerstein’s song: the validity of the Broadway-show-tune model for this song has been rejected, and it is Coltrane’s model of the tune that is accorded validity. It is much less clear, however, whether Davis is Signifyin(g) on “Bye Bye Blackbird.” It is difficult to ascr ibe author ity of a sort that one should be skeptical of to either Lee’s or Short’s recordings, and it is unclear whether Davis was aware of, or cared about, the pop-music model for the tune (with or without its overlay of racism). This does not mean that a listener might not hear the recording by Davis as Signifyin(g) on “Bye Bye Blackbird,” only that the relationship of Davis’s rendition of the song to the concept of Signifyin(g) is much more equivocal. Under what circumstances might we hear Davis as Signifyin(g) on “Bye Bye Blackbird”? First, Davis could, in the course of a performance (recorded or otherwise), make an obvious reference to one of the earlier models for the tune, perhaps by playing a fragment of the verse or by evoking another nostalg ic tune from the 1920s. The other model for “Bye Bye Blackbird” would thus be brought to our attention (even if only as something anomalous in Davis’s performance) to be then regarded as a voice of author ity under challenge. Second, we could br ing to Davis’s performance a knowledge or awareness of one of the earlier models, hear that he reverses certain of the key elements of this model, and inter pret this as subverting authority. Third, Davis could, through either word or deed, situate himself as in dialogue with what he regarded as an author itative version of the tune. With this analysis of Davis’s recording of “Bye Bye Blackbird” I do not mean to suggest that Signifyin(g) is a rare occur rence in music, but only that it involves a complex matr ix of cultural knowledge and that the listener must understand the process of Signifyin(g) as taking place. When this matr ix of knowledge is not in place, what may be left to hear is only double-voiced discourse, or unmediated 79. Although my focus here is on recordings, the same situation would obtain were our exper ience with live, as opposed to recorded, performances.

cultural knowle dge and musical ontology authorial discourse. (Indeed, all music could be heard as involved in double-voiced discourse of a quite general kind, in that the conceptual model for each work is in dialogue with the conceptual models for other works.) Double-voiced discourse, as well as Signifyin(g), becomes interesting when tensions between the models become obvious — that is, when the tensions become as important as the models themselves.

Signifyin(g) and Cultural Knowledge Given the cognitive complexity of the process of Signifyin(g), it is well worth asking why the notion has become a trope among those who work on jazz and popular music. Three reasons come to mind. First, Signifyin(g) offers a clear alter native to the Saussurean model of meaning construction: in Signifyin(g), meaning is something that is not fixed but is created by the listener.80 Second, Signifyin(g) provides a way of interpreting the cultural practice of jazz and popular music in ter ms developed to account for the unique profile of one of its most important influences, African American culture. Third, applying Signifyin(g) to music allows music cr itics to avail themselves of the power and prestige of literary criticism. Of these three, it is perhaps only the second that has much relevance to music, as opposed to the practice of writing about music. Musical Signifyin(g) is a complex process, distinct from linguistic Signifyin(g) and thoroughly implicated in the dense matrix of cultural knowledge. To explain how it works— when it works— requires not only a theory of Signifyin(g) but also a way to account for musical ontology, an explanation of the framework for discourse provided by cultural theor ies of information exchange, and a theory of double-voiced discourse.With these in place we can start to see — and hear — how Signifyin(g) shapes musical discourse.

cultural knowledge and musical ontology Clifford Geertz was skeptical about using descr iptions of individual cognitive processes to build an account of culture, and rightly so. Cognitive structure is incredibly complex, and the relationship between individual knowledge and cultural knowledge is not a simple one. Nonetheless, one can discer n patter ns of consistency in the features selected for defining and evaluating cultural products, patterns that are indicative of cultural knowledge. The approach to cultural knowledge I have developed in this chapter is meant to capture these consistencies and to facilitate a discussion of how cultural knowledge is organized, sustained, and changed. It is not meant as a literal rendering of what someone has in mind in evaluating particular cultural products. The approach is thus an inter pretation of culture, but of a 80. This is essentially the approach taken by Robert Walser in “ ‘Out of Notes’: Signification, Interpretation, and the Problem of Miles Davis,” in Jazz among the Discourses, ed. Krin Gabbard (Durham, N.C.: Duke University Press, 1995), 165– 88.While my approach to Signifyin(g) is broadly consonant with this treatment of meaning construction, my argument is made from the perspective of research in cognitive science rather than structuralism.

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analysis and theory somewhat different sort than those called for by Geertz, for it assumes that culture is what we know, rather than the specific things we do, make, or say. As members of a culture, one of the things we know is how to categor ize sequences of sound events as “music” (or whatever other ter m is operational in our culture). Knowing that a Beethoven str ing quartet is music (to return to Geertz’s example) means that it confor ms to our conceptual model for music, no more and no less. Similarly, John Cage’s 4'33" is music if it confor ms to our conceptual model for music; if it does not, we may simply regard it as a rather strange r itual in which a group of people sit in silence for a specified per iod of time.81 The conceptual models around which we organize our categor ies of music are also the means by which we negotiate or resist cultural change, guide perfor mance, and engage in complex patter ns of musical discourse. They are, quite simply, the stuff of musical ontology. Quite obviously, what I offer here is only a beginning. In particular, the account of the conceptual models appropriate to cultural knowledge needs to be refined through further study. Coleman and Kay’s study of the meaning of “lie,” together with Sweetser’s interpretation of that study, offers an interesting example of how relevant empir ical research might be conducted. If conceptual models truly have value as a tool for descr ibing cultural knowledge, then it should be possible to develop exper imental protocols that test whether and how members of a culture use such models. What will result is not a simple picture of what someone has “in mind” when reasoning about a given situation (which is at best a dubious goal) but a better understanding of the elements of knowledge that make it possible to function as a member of a culture. Another obvious extension of the work presented in this chapter is to other repertoires, both contemporar y and histor ical. In some cases (for instance, when dealing with a remote histor ical per iod), the application may be so speculative as to be useful chiefly in providing a fresh perspective, but in others it will yield sur prising results. There are processes every bit as complex and challenging as Signifyin(g) that operate in other repertories— for instance, the intr icate patter ns of influence and innovation that abound in the music of Gustav Mahler and Arnold Schoenberg — patterns that await only our interest and efforts to discover them. Perhaps the most intr iguing consequence of the argument put forth in this chapter is that, if musical works are cognitive categor ies, and if music is a cognitive category, then music theory is about the study of categor ies or — more typically — the conceptual models around which musical categor ies are organized. Understood this way, music theory immediately escapes the g ravitational force field of “the text” that has at times kept the literary criticism of the previous generation earth-bound (even while remaining relentlessly recondite). Thus liberated, music theory’s own traditions of high abstraction and unabashed pragmatism may yet find a place in contemporary intellectual discourse. 81. Although I have not tr ied (or wanted) to develop an overarching conceptual model for music here, it is worth noting in this connection that Cage’s four-and-a-half minutes of silence has a score and has been presented in concert numerous times. If these things are important elements of someone’s conceptual model of music, they would most likely regard Cage’s piece as music.

chapter six

Q words, music, and song: the nineteenth-century lied

n 15 December 1822, the poet Wilhelm Müller noted the publication of a group of songs that took his poems as their texts. In a letter to the composer of the songs, Bernhard Klein, Müller observed, “indeed, my songs lead . . . only half a life, a paper-life, black upon white . . . until music breathes the breath of life into them, or at least, when it slumbers within, calls it out and wakens it.”1 That music could breathe life into poetr y is a sentiment also expressed in a eulogy for a composer Müller chose not to address in the foregoing letter, but whose settings have kept Müller’s poems from disappear ing into the obscure recesses of nineteenth-centur y German poetr y. Speaking of Franz Schubert’s Lieder, Josef von Spaun wrote:

O

That which moved the poet’s breast Schubert rendered true and transfigured in tone in each of his songs as none had done before him. Every one of his songs is actually a poem on the poem that he set to music — and not only for sentiment, which is doubtless at home in songs, but also for all the magic of fantasy, for its super natural char m and its noctur nal terrors, could he find the perfect moment — yes, even for the lofty seriousness of reflection he had a language.2

These two remarkably similar views of the relationship between poetr y and music are, without a doubt, as much a testament to the intellectual and artistic life 1. Quoted in Carl Koch, Bernhard Klein (1783–1832): Sein Leben und seine Werke (Leipzig: Oscar Brandstetter, 1902), 34, n. 8. The complete text runs as follows: “In der That führen meine Lieder, die zu einem declamator ischen Vortrage, wenige ausgenommen, durchaus nicht geeignet sind, nur ein halbes Leben, ein Papierleben, schwarz und weiß—(Ach, wie traur ig sieht in Letter n Schwarz auf Weiß das Lied mich an!) bis die Musik ihnen den Lebensodem einhaucht, oder ihn doch, wenn er dar in schlummert, herausruft und weckt.” 2. “Was des Dichters Brust bewegte, hat Schubert in jedem seiner Lieder treu und verklärt in Tönen wiedergegeben, wie keiner vor ihm. Jede seiner Lieder-Compositionen ist eigentlich ein Gedicht über das Gedicht, das er in Musik setzte; und nicht für Empfindung nur, die im Liede wohl daheim ist, sondern auch für jeden Zauber der Fantasie, ihren über irdischen Reitz und ihre nächtlichsten Schrecken, wußte er den eigensten Augenblick zu finden, ja selbst für den hohen Er nst des Gedankens hatte er eine Sprache.” Till Gerrit Waidelich, ed., Franz Schubert: Dokumente, 1817 –1830,Veröffentlichungen des Internationalen Franz Schubert Instituts, 10 (Tutzing, Germany: Hans Schneider, 1993), 516 – 17.

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analysis and theory and ideals of early nineteenth-century Germany and Austria as they are clear-eyed proposals for a regard of song.3 And yet they capture something important about the possibilities that ar ise when words and music come together: under certain circumstances the result is far more than simply the sum of its parts. The topic of song has fascinated wr iters on music at least for the last two centuries, and a study of the study of song could be its own book. In a 1992 essay, Kofi Agawu offered a survey of some of this work (as well as his own contr ibution to it) and identified four basic models for the analysis of song, of which three were fairly well entrenched in the literature on song.4 The first model der ives from the work of Suzanne Langer and operates on the premise that when words and music come together in song, the music wholly absorbs the words. As Langer put it, “Song is not a compromise between poetry and music, though the text taken by itself be a great poem; song is music.”5 The second model proposes that there is an ir reducible relationship between words and music; as Lawrence Kramer has put it, “A poem is never really assimilated into a composition; it is incorporated, and it retains its own life, its own body, within the body of music.”6 The third model inter prets song as a compound structure in which the words carry the primary semantic content and the music colors or enhances what the words signify. Agawu observed that this model is limited because it provides no independent account of the meaningfulness of music. In reviewing these three models, Agawu was rather too polite, resisting the temptation to note that, within the tradition of song analysis, there have been relatively few attempts to come to ter ms with how words and music combine to create the phenomena called “song.” There are thorough and painstaking analyses of song texts, with cursory mention of the music that sets the text; there are carefully crafted analyses of musical structure, supported at tur ns by isolated instances of how the words buttress or anticipate this structure; but there are few comprehensive analyses that tr y to capture how the meaning constructed by the words and the meaning constructed by the music come together to create the meaning associated with a particular song.7 As an improvement, Agawu proposed a fourth model in which song is construed as a confluence of three independent but overlapping systems: music and words and song. However, he almost immediately withheld full endorsement of this model, noting that it provided no account of a concrete iden3. Both must also be situated within the more personal agendas of their authors. Müller’s letter is part of an attempt to get the composer to set more of his poems; Spaun’s eulogy is part of an attempt to preserve what he viewed as the true legacy of his departed friend. 4. Victor Kofi Agawu, “Theory and Practice in the Analysis of the Nineteenth-Century Lied,” Music Analysis 11 (1992): 3– 36. 5. Susanne K. Langer, Feeling and Form: A Theory of Art Developed from Philosophy in a New Key (New York: Charles Scr ibner’s Sons, 1953), 152. 6. Lawrence Kramer, Music and Poetry: The Nineteenth Century and After (Berkeley: University of California Press, 1984), 127. 7. One analysis that develops a comprehensive account of a song is David Lewin’s “Auf dem Flusse: Image and Background in a Schubert Song,” in Schubert: Critical and Analytical Studies, ed.Walter Fr isch (Lincoln: University of Nebraska Press, 1986), 126 – 52. However, Lewin’s main interest in this essay is in developing an account of certain remarkable features of this particular song; his study, thus, did not set out to delineate a broad methodological approach to the analysis of song.

word s, mu s i c, and s ong tity for song but, instead, allowed song an identity only by default. This led him to muse,“Perhaps, then, what the model points to is song as process, not product.What is interesting, in other words, is not what song is, but what it becomes in its per petual str iving for a concrete mode of existence.”8 Nicholas Cook was able to steer a course between the Scylla of emphasizing the text at the expense of the music and the Charybdis of emphasizing the music at the expense of the text, as well as to give an account of a concrete identity for song, by approaching song as an instance of multimedia: words were one medium, music another.9 However, because Cook defined multimedia as the perceived interaction of different media, he tended to regard songs as successful to the extent that the syntax of their words and music remained separate — indeed, in a state of contest. The approach is effective for many songs, and the breadth offered by integrating song analysis into the analysis of multimedia as a whole makes for a very comprehensive perspective. Nonetheless, what is missing is a sense of how, despite their differences, words and music work together in song — how music can breathe the breath of life into poetry or create a poem on a poem. In this chapter, I explore further the nature of song and also the process of conceptual blending. As noted in chapter 2, conceptual blending is a pervasive and often transparent process in which elements from two cor related mental spaces combine in a third.10 And, as suggested by the examples used in chapter 2, the mental spaces basic to conceptual blends can be set up by music as well as by language. In what follows, I expand on this idea, working on the assumption that music can set up complete discourse structures, which can be cor related with the discourse structure of a text to give rise to a unique domain for the imagination. What I am concer ned with, then, are not isolated or very general cor relations between music and text but a conceptual blend produced by an entire song. In the first section that follows, I analyze two settings of Wilhelm Müller’s poem “Trockne Blumen” (Withered Flowers), taken from the cycle of poems he called Die schöne Müllerin (The Beautiful Miller Maid). The first is by the Berlin composer Bernhard Klein, whom Müller addressed in the letter quoted above; the second is by Franz Schubert. These analyses will allow me to show how different musical environments interact with the same text to produce two quite different conceptual blends, and thus two different songs. In the second section, I turn to Robert Schumann’s “Im Rhein” (In the Rhein), from his song cycle Dichterliebe (Poet’s Love). In “Im Rhein,” the music makes possible a conceptual blend whose emergent structure includes a nar rative considerably more extensive than that of the text alone. In the third section, I consider two settings of a poem by Joseph von Eichendorff, “In der Fremde” (In Foreign Lands), the first by Schumann, the second by Johannes

8. Agawu, “Theory and Practice,” 7– 8. 9. Nicholas Cook, Analysing Musical Multimedia (Oxford: Clarendon Press, 1998); see esp. pp. 98– 106 and Cook’s analysis of Robert Schumann’s “Wenn ich in deine Augen seh’ ” from Dichterliebe on pp. 136– 43. 10. A focus on the possibilities for meaning construction that ar ise in this blended space is one of the fundamental differences between the idea of conceptual blending and both Cook’s conception of multimedia and Bakhtin’s notion of double-voiced discourse.

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analysis and theory Brahms. Again, two different songs result, but, in this case, the reasons lie with the gener ic spaces that structure each conceptual blend.

“ trockne blumen ” Wilhelm Müller’s “Trockne Blumen” Müller’s Die schöne Müllerin had its genesis in the diversions of a group of young artists and intellectuals who gathered at the house of the privy councilor Fr iedrich August von Stägemann dur ing the autumn and winter of 1816– 17.11 There Müller (1794 – 1827) — together with the Stägemanns’ daughter Hedwig (1799 – 1891); the artist Wilhelm Hensel (1794 – 1861); his sister, the poetess Luise Hensel (1798 – 1876); the publisher Fr iedrich Förster (1791 – 1868); and others— put together an informal drama structured around the story of a pretty miller’s maid and her suitors. Each member of the group took a part, for which they wrote a verse scr ipt. In the enactment of the resulting Liederspiel, the participants would recite their verses, using whatever gestures or changes in vocal inflection the situation required in order to tell their part of the story. The evidence of the poems and anecdotes that survive from the Stägemann circle suggests that its Liederspiel had a thoroughly tragic ending. In what can be reconstructed of the story they developed, the miller’s daughter, named Rose (played by Hedwig von Stägemann), was courted not only by the young miller (played by Müller) but also by a country squire (played by Förster), a hunter (played by Wilhelm Hensel), and a gardener (played by Luise Hensel). The miller, after prevailing br iefly over the other suitors, falls into despair when the hunter wins the miller maid’s affections, and commits suicide. The maid, filled with remorse, then joins him in death. During the three years after the meetings of the Stägemann circle, Müller, apparently intr igued by the possibilities of the story of the miller maid and her suitors, went on to create his own version of the stor y, consisting of twenty-five poems under the title Die schöne Müllerin (Im Winter zum lesen), which was first published in 1821.12 The cycle consists of a verse prologue (in the voice of the poet), twenty11. My account of Die schöne Müllerin follows Susan Youens’s excellent work on the or igins and historical context of the cycle, which is reported in three of her publications:Youens, “Behind the Scenes: Die schöne Müllerin before Schubert,” 19th Century Music 15 (1991): 3– 22; idem, Schubert: Die schöne Müllerin, Cambridge Music Handbooks (Cambr idge: Cambridge University Press, 1992); and idem, Schubert, Müller, and Die schöne Müllerin (Cambridge: Cambridge University Press, 1997). Another important source is Graham Johnson’s copious notes for his recording of the cycle. See Johnson, “Die schöne Müllerin, The Poems and Their Backg round,” in Die schöne Müllerin, D795 (Hyperion, [CD] CDJ 33025, 1996). Although the works I discuss here, both literary and musical, use “trockne” in their titles, the proper word is “trockene,” which may be contracted to “trock’ne.” For the sake of consistency, I shall use “trockne” throughout. 12. The cycle initially appeared as part of the fancifully titled Siebenundsiebzig Gedichte aus den hinterlassen Papieren eines reisenden Waldhornisten. The edition of Die schöne Müllerin upon which I have relied and that appears below is from Wilhelm Müller, Vermischte Schriften, ed. Gustav Schwab (Leipzig: F. A. Brockhaus, 1830), 1: 1– 56.

word s, mu s i c, and s ong three poems proper to the drama, and a verse epilogue (again in the voice of the poet), together intended to take about an hour to perfor m.13 In poems 1 – 5, we are introduced to the miller, the millstream, the miller maid, her father, and the group of young workers in his charge. In poems 6 – 11, we become aware of the miller’s growing infatuation with the maiden and the depths of his unrequited love. In poems 12 – 14, the miller becomes convinced that the miller maid is, as he says in poem 12, “Mine!” Despite this belief, there is absent from the poetic nar rative any explanation for what changed his perspective from one of dreamy mooning to a self-assured sense of certain love; the poems provide no evidence that the miller maid has actually returned his love. In poems 15 – 17, the hunter suddenly enters the scene and, in the confused understanding of the miller, steals the miller maid away. Just as suddenly, the bliss of the preceding poems is replaced by anger, jealousy, and vindictiveness. In poems 18 – 21, the miller, torturing himself with visions of the hunter and miller maid in fond embrace, gradually begins to dwell more and more on death. It is in poem 21, “Trockne Blumen,” that the miller decides to commit suicide, bringing to culmination the thoughts of death and the grave that came to dominate the preceding poems. Poem 22 is a sad dialogue between the miller and the stream, and poem 23 is given to the stream alone, as it gently and eer ily caresses the drowned miller. The cycle concludes with an epilogue, which is cur iously detached from the passion of the preceding poems, and which attempts to build a bridge from Müller’s intense world of fantasy back to the world of the everyday. The basic stor y told in “Trockne Blumen,” the text and a translation of which are given here, can be seen to proceed in three stages.14 In the first three stanzas, the miller addresses a collection of withered, moribund flowers that are unaccountably wet. In the second three stanzas, he contemplates the ineffectuality of his tears (the tacit cause of the wetness of the flowers) and the insignificance of his existence in the face of love that has died. This group ends with a stanza that echoes the first stanza of the poem, both in its return to the image of the faded flowers and in the recurrence, in reverse order, of the rhyming pair “gab” and “Grab.” Together, these suggest a circular return that closes off the first six stanzas. The final stage of the story commences with the last two stanzas of the poem. These speak of a future in which the miller lies dead in his g rave, in which the miller maid recognizes the truth of his love, and in which flowers bloom once more. The poem thus involves sharp contrasts: dying flowers set against blossoming flowers, winter set against spring, and dead love set against true love. trockne blumen

withered flowers

Ihr Blümlein alle, Die sie mir gab,

All you flowers That she gave to me,

13. Müller wr ites in the prologue, “As it’s wintertime I expect you won’t regret a br ief hour here in the countryside” (as it is depicted in the cycle of poems). [“Erhoffe, weil es grad’ ist Winterzeit, / Thut euch ein Stündlein hier im Grün nicht Leid.”] Müller, Vermischte Schriften, 1: 1. 14. There are other ways to parse the poem, as we shall see later in this discussion. The analysis I offer here is simply for the pur poses of drawing out some of the aspects of the poem important for a number of its musical settings.

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analysis and theory Euch soll man legen Mit mir ins Grab.

You shall be laid With me in the grave.

Wie seht ihr alle Mich an so weh, Als ob ihr wüßtet, Wie mir gescheh’?

Why do you all Look at me so sadly, As if you knew What happened to me?

Ihr Blümlein alle, Wie welk, wie blaß? Ihr Blümlein alle, Wovon so naß?

All of you flowers, Why so faded, so pale? All of you flowers, Why are you so moist?

Ach, Tränen machen Nicht maiengrün, Machen tote Liebe Nicht wieder blühn.

Ah, tears do not make The greenness of May, They do not make dead love Bloom anew.

Und Lenz wird kommen Und Winter wird gehn, Und Blümlein werden Im Grase stehn.

And spring will come And winter will go, And flowers will Grow in the grass.

Und Blümlein liegen In meinem Grab, Die Blümlein alle, Die sie mir gab.

And flowers lie In my grave, All the flowers That she gave to me.

Und wenn sie wandelt Am Hügel vorbei, Und denkt im Herzen: »Der meint’ es treu!«

And when she walks Past the mound, And ponders in her heart: “His love was true!”

Dann Blümlein alle, Heraus, heraus! Der Mai ist kommen, Der Winter ist aus.

Then all you flowers, Come out, come out! May is here, Winter is over.

One thing immediately evident is that this poem relies, as do most, on conceptual blends.When the miller addresses the flowers, for instance, it is not as plants but as anthropomorphized beings, creatures that can not only look upon the miller but do so with pathos: “Wie seht ihr alle / Mich an so weh, / Als ob ihr wüßtet, / Wie mir gescheh’?” This, of course, is another example of the anthropomorphic blends discussed in chapter 2. Another blend is set up in the fourth stanza, where Müller combines concepts related to the seasons and to romantic love. Thus “maiengrün” becomes both a harbinger of spring and a sign of love’s first bloom.Yet a third blend crops up in the seventh and eighth stanzas, when concepts related to the seasons combine with those of life and death: the consummatory “Der Mai ist kommen / Der Winter ist aus” represents both the future tur n of seasons the miller envisions

word s, mu s i c, and s ong and his rebirth as the eter nal lover of the miller maid. The poem is thus a r ich discourse structure in its own r ight, one with intr iguing possibilities for pair ing with the discourse structures of music.

Bernhard Klein’s “Trockne Blumen” The Berlin composer Ber nhard Klein (1793 – 1832) apparently discovered Müller’s poetic cycle shortly after it was published and set “Trockne Blumen” as the last of his five Lieder und Gesänge mit Begleitung des Piano Forte. This collection was brought out by E. H. G. Christiani in 1822,15 and the inclusion of “Trockne Blumen” is all the more remarkable in that the texts for the first four songs involve rather conventional stor ies of wanderlust and relatively innocent romantic encounters. “Trockne Blumen,” as Klein clearly recognized, is a text of quite another order. Klein’s setting, the score for which is given in example 6.1, is guided by his division of the text into four strophes, each compr ising two stanzas of the poem. Although the music for each strophe is different, so much mater ial is reused that the song seems more strophic than through-composed, as the for mal outline g iven in table 6.1 indicates. The song begins with a br ief piano introduction that sets out the mater ial used to begin each of the first three strophes. This mater ial, labeled A1 in table 6.1, consists of three iterations of a motion from dominant to tonic, culminating in a passage in parallel sixths that returns to the dominant. The whole is couched in a spare twoand three-voice texture, with a repetitive melody built up from a compact succession of ascending and descending gestures that circulate around C5 and A4. Although A as tonic is scarcely in doubt, it falls short of attaining a full measure of stability, given the absence of root-position tonic tr iads in strong rhythmic positions and the emphasis on the dominant har mony at both the beginning and end of each A1 section. Sections B1 and B2 consist entirely in prolongations of the dominant, either by temporar ily transfor ming it into a leading-tone har mony (as in mm. 11– 12 and mm. 20 – 24) or through a pathos-drenched passage that introduces an unprepared VII ⁴₃# of IV that leads through IV⁶ back to VII, and then to V (as in mm. 13– 16 and mm. 25– 28). In each of the B sections, the melody struggles upward to D5 three times, only to fall back either to B4 or CS5. Of these two sections, B2 is slightly more intense. In it, a repeated Fn4 replaces the repeated E4 that signaled the opening of the B1 section, giving rise to a VII⁷ that lasts from m. 20 to m. 24. In the third strophe, Klein lightens the mood of the music by shifting to the par15. Müller is the author of all of the poems of Klein’s Lieder und Gesänge of 1822; “Trockne Blumen” is the only poem Klein selected from Die schöne Müllerin. It is unclear what motivated Klein’s choice of poet. In his letter of 15 December quoted above, Müller praised Klein’s settings and asked if he would be interested in setting more of his poetry. Given the tone of the letter, it would seem unlikely that Müller was an active participant in the selection of texts for the 1822 collection of songs. I should note, as well, that another Berlin composer, Ludwig Berger, published a setting of “Trockne Blumen” in 1818; analysis of this work, as well as the context for its publication, can by found in Lawrence Zbikowski, “The Blossoms of ‘Trockne Blumen’: Music and Text in the Early Nineteenth Centur y,” Music Analysis 18 (1999): 307 – 45.

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analysis and theory example 6.1

Bernhard Klein, “Trockne Blumen”

Andantino

A1

Voice

Ihr Blüm lein

Piano

B1

5

al

le die sie mir gab,

euch soll man le gen mit mir ins Grab.

Wie

seht

ihr

10

al

le

mich

an

so

weh

als wenn ihr wüß tet

wie mir ge

A1

15

scheh?

Ihr Blüm lein al

le wie welk, wie blaß?

Ihr Blüm lein

allel major. The repeated notes that lent an air of intensity or obsession to the dominant prolongations of the preceding B sections now reappear to keep the music from stalling on the first and second beats of each bar of section A2. Section B3 begins with another prolongation of the dominant, but instead of being transformed into a leading-tone har mony in m. 36, as it had at the analogous juncture in sections B1 and B2, it now remains a dominant, leading initially to a I⁶ in m. 38, and then to the first cadence on A thus far. With the ar rival on the I⁶ of m. 38, the melody finally reaches E5, preparatory to its ar rival on A4 in m. 40.

example 6.1

(continued) B2

19

al

le wo von so

naß?

Ach,

Trä

nen

ma

chen

nicht

23

mai

29

en

grün,

ma chen to

te

Lie

be

nicht wie der

blühn!

A2 Poco più lento

Der Lenz wird kom

men, und Win ter wird gehn

und Blüm lein

B3

32

wer den im Gra se stehn,

und

Blüm

lein

lie gen

37

in

mei

nen

C

Grab

die Blüm lein al

le

die

sie

mir

gab.

Und

wenn

sie

(continued)

example 6.1

(continued)

42

wan

delt

am

Hü

gel

vor

bei,

und

denkt im

Her

zen

A3

47

der meint’ es

treu!

dann Blüm lein al

le her aus her

men

ter

aus!

der

51

Mai

ist

kom

der Win

is

aus

55

Mai

59

ist

kom

men

der

Win

ter

ist

aus.

der

word s, mu s i c, and s ong Table 6.1.

Formal Outline of Bernard Klein’s “Trockne Blumen”

Section and Key Introduction Strophe 1

Strophe 4 Postlude

Musical Material and Melody

Measures

Stanza 1 Stanza 2 Stanza 3 Stanza 4 Stanza 5 Stanza 6 Stanza 7 Stanza 8

A1, a A1, a B1, b A1, a B2, b A1, a B3, b' C, c A2, a' A2, a' (fragment)

0–4 4–8 8–16 16–20 20 – 28 29–33 33–40 40 – 48 48–58 58– 64

A minor

Strophe 2 Strophe 3

Text Stanza

A major

The C section beg ins another prolongation of the dominant, one whose repeated notes are strongly reminiscent of sections B1 and B2. Absent, however, is the relatively active bass line that opened each of the latter sections; it is replaced here by a pedal on E3. The melody, too, has changed, now peacefully circulating around B4, with unimpeded ascents to E5. After m. 45, the intensity of the section increases with the cessation of the repeated notes and the introduction of the chromatic second alto line of mm. 46– 47. In m. 48, however, the melodic line that descends from E5 once again comes to rest on a clear dominant har mony, which leads immediately to the reprise of the A mater ial. Although section A3 opens with the same figure in parallel tenths that began the song (adjusted to fit the major mode), the figure now leads toward a dominantseventh in m. 50 and then to a relatively extensive prolongation of the tonic in mm. 51– 55. This prolongation prepares the way for the cadence of mm. 56– 58 with which the vocal part concludes. A brief piano postlude follows; it is based on the opening of the A3 section, but it includes a motion from Fn to E that recalls the minor mode of the first half of the song. Thus, Klein’s music falls into two distinct parts. The first part, through m. 28, sets out an intense and unstable A minor. Relatively lengthy and obvious prolongations of large-scale har monic dissonances (such as those associated with the dominant and leading-tone) and sudden inter ruptions mark the texture, as do persistent repeated notes. The second part, from m. 29 onward, disperses the intensity of A minor and replaces it with a goal-or iented and (for the most part) orderly A major. Here there are also prolongations of the dominant, but of a sort that seem to affir m rather than challenge the viability of tonic.What had been difficult in the first part becomes easy in the second; what had been troubled becomes calm. This music, together with Müller’s text, sets up the conceptual integration network (CIN) diagrammed in figure 6.1. Two observations should be made about the network represented by this diag ram, observations that extend to all of the CINs discussed in this chapter. First, as was the case in chapter 2, the diagram represents a kind of analytical snapshot of the elements and relations that make up the network, and that contr ibute to the emergent structure of the conceptual blend. A

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analysis and theory

Generic space • contrasting ontological states

Music space • A minor: diminishedsevenths, D5 ceiling, lack of cadence • A major: cadences, E5, F#5, limited chromaticism

Text space • present: dying flowers, tears, hopelessness • future: spring, blooming flowers, hope for the future

Blended space • obsessive, mercurial present • orderly, calm future

figure 6.1

CIN for Klein’s “Trockne Blumen”

fuller account of the way concepts combine within this network would require a series of such snapshots. Second, what I am concer ned with here is the overall discourse set up by the text and the overall discourse set up by the music. Although there are interesting details at more local levels, I am most intr igued by what conceptual blending can tell us about song and by what song can tell us about conceptual blending. Let me expand on this for just a moment before returning to Klein’s “Trockne Blumen.” The theory of conceptual blending assumes that there are structural invariances between the input spaces of a blend: these invariances, encapsulated in the elements and relations of the gener ic space, are what make conceptual blends possible. In the case of songs, the invariances are between the mental space set up by the text and the mental space set up by the music. Put another way, the fact that combinations of text and music can give rise to conceptual blends suggests that there are syntactic correspondences between linguistic and musical discourse. Although the syntax of most nineteenth-century German poetry is usually clear at or below the level of the stanza, the syntax of songs from the same milieu needs to be conceived in ter ms of the song as a whole, which was construed as a single, if often extended, musical utterance. Because of this, I find it most useful to focus on conceptual blends that encompass the entirety of a given song — that is, blends that ar ise from the overall discourse set up by the text and the overall discourse set up by the music.16 16. This perspective also leads me to regard the poem set by the composer as a text, rather than a poem. Susan Youens, for different reasons, advocates a similar approach; see Youens, Retracing a Winter’s

word s, mu s i c, and s ong What nineteenth-centur y songs can tell us about conceptual blending stems from the character istic of musical syntax I have just descr ibed. The blend set up by a song (assuming that there are structural cor relates between the mental spaces set up by the text and the music) spans at least two or three minutes, involves two different media (with two different, if related, kinds of syntax), and engages us on both emotional and intellectual levels. All these features have the potential to add immeasurably to our understanding of conceptual blending as a general cognitive process.17 With these thoughts in mind, let us return to the CIN set up by Klein’s song. The gener ic space for the CIN is structured around the notion of two linked but contrasting ontological states. Such states are often temporally indexed (as past and present or as present and future), but they can be more abstractly represented as theme and variation, or prototype and copy. The delineation of two ontological states often provides the basis for a more extensive interpretive framework. This framework then fur nishes an account of the cause for the change of state or an explanation for why one state is to be preferred over another. Contrast between the two ontological states is supported in Müller’s poem by an emphasis on the present in the first four stanzas and an emphasis on the future in the second four stanzas. There is also far less activity descr ibed in the first four stanzas than in the second four. Of course, there are exceptions to both of these generalizations. In the first half of the poem, the future is summoned at the end of the first stanza and the past is alluded to in the fourth; the gaze of the flowers and the tears of the miller suggest that the scene is not wholly devoid of activity. In the second half of the poem, the past is evoked briefly in the last two lines of the sixth stanza, the first two lines of which call up the embodiment of lifelessness. In the mental space of the music, the linked but contrasting ontological states of the gener ic space are set up by the A minor and A major music of the two halves of the song. These states are linked less by temporal index than by conceptual frame: the A minor music functions as the theme, as it were, and the A major music as the variation. Nonetheless, the A major music rewrites the character and syntax of the A minor music. It exchanges the third and sixth scale steps of minor for those of major, provides the first cadences on tonic, avoids the fully diminished seventh chords omnipresent in the first half of the song, and allows the melody to ascend to E5 and FS5. As a result, it enacts a specific shift of time frame by placing the A minor music fir mly in the past and announcing the A major music as the new present. This shift is underlined by the mir rored processes that occupy each half of the song: over the course of the first half of the song, the music becomes more intense

Journey: Schubert’s Winterreise (Ithaca, N.Y.: Cornell University Press, 1991), 307– 12. As will also become clear, I am typically concer ned with the story told by the text as a whole, a parabolic level discussed by Mark Turner in The Literary Mind (New York: Oxford University Press, 1996), esp. chap. 1. 17. Although it should be clear from the foregoing, let me emphasize that not all songs will set up conceptual blends. Among those songs that do set up blends, some blends will be more successful (that is, lead to more extended elaborations) than others. One example of the latter situation is provided by the third phrase of Brahms’s “In der Fremde”; see the discussion of the song later in this chapter.

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analysis and theory and darker; over the course of the second half, the music becomes less intense (with the exception of the poignant recollection of mm. 46– 47) and br ighter. Correlations between these idealized representations of contrasting ontological states provide an opportunity for the combination of concepts in the blended space, which draws upon elements of the input spaces to create a portrayal of the miller’s transfor mation from a tortured soul into a hopeful and ecstatic one. As was the case in chapter 2, the emergent structure of conceptual blends (including the present one) can be descr ibed in ter ms of the processes of composition, completion, and elaboration.

composition

The combining of elements from the text-space and the music-space is quite straightforward. The enervated present of the first four stanzas and the A minor music combine to create a representation of one ontological state in the blended space: a stark image of the present as dominated by obsessive thoughts, scant opportunity for rest, and a mercurial play of emotions. The active future of the second four stanzas and the A major music combine to create a representation of the second ontological state: what was shadowy has become clear; there is an orderly progress toward goals; and the sur roundings are, almost without exception, calm and soothing. The transfor mation of one state into the other occasions a strange conceptual inversion in this part of the song: the flowers that blossom after the change to A major in m. 29 seem to be the same ones that the miller predicts will lie in his grave (cf. mm. 31– 33 and mm. 34– 40), even though the latter event, according to the logic of the poem, must precede the for mer.

completion

Building on the context provided by this blend of concepts, we can imagine outward signs of the miller’s torment in the first half of the song — a sluggish, depressed body language, accompanied by sudden expressions of anguish as his agony increases — and how, in the second half of the song, these give way to gestures and behavior associated with peacefulness and happiness as the miller contemplates his future.We can also imagine that, overall, the miller grows happier and more at peace with himself as he becomes more distant from his earlier tor ment. This inference is supported in part by the music of the concluding A3 section, where the melody breaks through to the high FS5 of m. 49, a moment followed by the long prolongation of tonic in mm. 51– 55 that prepares the singer’s final cadence.

e laboration

Elaboration of the blend suggests that the miller will act in order to make the future he imagines a reality. His “Heraus, heraus!” thus calls forth not only the future’s flowers but also the future itself. Elaboration may also provide an explanation for how the state of affairs portrayed in the first half of the song is transfor med into the state of affairs portrayed in the second half . Here the music provides a useful guide, for it suggests that the present can be transfor med into the future by reinterpreting it, just as the musical mater ials from A minor were reinterpreted in A major. Thus, the dead love of the present will become the eter nal love of the future; the dying blossoms will become living ones. The strange celebration that is enacted in mm. 34– 40, as the miller contemplates the flowers that will be laid

word s, mu s i c, and s ong in his grave, then becomes more comprehensible, for in the second half of the song the withered flowers that he holds are transfor med into symbols of his eter nal love.

Franz Schubert’s “Trockne Blumen” Although the exact circumstances of Franz Schubert’s encounter with Müller’s Die schöne Müllerin are not known, it appears that Schubert came upon the poetic cycle sometime in the first part of 1823 and set twenty of the twenty-five poems dur ing the second half of the same year. The completed cycle was published the following year by the fir m of Sauer and Leidesdorf.“Trockne Blumen,” the score for which is given in example 6.2, is the eighteenth song in the cycle. Schubert’s setting divides the eight stanzas of the poem into a 3 + 3 + 2 grouping. The music in E minor for the first three stanzas is repeated for the second three, after which there is a shift to the parallel major for the final two stanzas. Schubert does not repeat any text in his setting of stanzas 1 – 6, but he does repeat the last two stanzas in the patter n 7– 8, 7– 8, 8. The song begins with the most minimal of piano introductions: two bars of a repeated E minor chord, played piano, each eighth-note chord followed by an eighth rest. This patter n continues as the voice enters with a bare melody outlining E minor. With the shift of the bass from E3 to D3 in m. 5, the E minor chord is transformed into a G chord in ∞ position. The latter leads to a cadence on G on the second beat of m. 6, coincident with the conclusion of the first stanza of text. The music of mm. 3– 6 is then repeated for the second stanza in mm. 7– 10, sustaining the spare effects created by the minimal melodic and har monic mater ials, but adding the barest hint of forward motion when the voice closes on B4 instead of on G4, as it had in m. 6. In m. 11, the music becomes more active and its har monic mater ial somewhat more variegated: the rhythmic patter n of the accompaniment is livelier; the harmonies change every beat; and the melody, as it follows these har monic changes, becomes more animated. The initial har monic strategy for the setting of the third stanza is, in compressed for m, similar to that used for the first two stanzas: E minor, now preceded by its dominant in m. 11, leads again to G in m. 12. Measure 11 is repeated in m. 13, but this time it is followed by an Italian augmented-sixth chord that leads to the dominant of E minor, while the singer reaches past E5 for the first time to grasp a high FS5. The piano then echoes this gesture, sustaining the dominant chord for a half cadence on B that lasts through m. 16. Schubert’s setting of stanzas 4 – 6 in mm. 17– 29 is virtually identical to the music he provided for the first three stanzas; the only significant change occurs in mm. 28– 29, where the E5-DS5FS5 of the melody is restated as FS5-E5-DS5. With the shift to the parallel major in m. 30, the accompaniment becomes yet more active: Schubert adds a lightly tr ipping bass melody to the animated rhythmic patter n of the right hand. In m. 31, the singer takes up the bass melody, in modified for m.With the momentar y shift toward CS minor in mm. 33– 34, however, the melody becomes streamlined once again. The CS minor chord in m. 34 yields in the following measure to another augmented-sixth chord. This leads (in m. 37) to a cadential ∞, which prepares the first cadence on E in the song. Schubert

257

example 6.2

Franz Schubert, “Trockne Blumen,” from Die schöne Müllerin, D. 795/18

Ziemlich langsam Voice

Ihr Blüm lein al

le, die sie

mir

gab,

euch

le mich an

so

weh,

als

Piano

5

soll

man le gen mit mir

ob

ihr wü ß

ins

Grab. Wie seht

ihr al

9

tet, wie mir ge

scheh? Ihr Blüm lein

al

le, wie welk, wie blaß? ihr

13

Blüm lein al

le, wo von

so naß?

Ach Trä

nen ma chen nicht

18

mai en grün, ma chen to

te Lie be nicht wie der blühn, und Lenz wird kom men, und

258

example 6.2

(continued)

22

Win ter wird gehn, und Blüm lein wer den im Gra

se stehn, und Blüm lein lie

gen in

26

mei nem Grab,

die Blüm lein

al

le, die sie

mir gab!

30

Und wenn

sie wan

delt am Hü

gel vor bei

und

33

denkt im Her zen, der meint’ es treu! dann Blüm lein al

le, her aus,

her aus,

der

37

Mai

ist kom men, der Win ter ist aus.

Und wenn

sie wan delt am

(continued)

259

example 6.2

(continued)

41

Hü

gel vor bei

und denkt

lein al

le, her aus,

im Her

zen, der meint’

es treu!

dann

44

Blüm

her aus,

der Mai

ist kom men, der

47

Win

ter ist aus,

dann Blüm

lein al

le, her

aus,

50

Mai

ist kom men, der Win

ter ist aus.

53

dim.

her aus,

der

word s, mu s i c, and s ong immediately repeats the whole of mm. 30 – 38 in mm. 39– 47 and then, without pause, repeats the last four bars, with a change of bass and a slight thickening of texture. A six-bar piano postlude, reprising the accompanimental figure of m. 30, concludes the song. In the course of the postlude, the register drops an octave, and the mode shifts to minor for the last four bars. Although this descr iption cannot do it justice, the effect of the relatively spare musical mater ials that Schubert employs in this setting is profound. A somewhat more nuanced view of the overall musical discourse can be gained through a middleground sketch of the voice-leading of mm. 1– 16 and 30 – 38, given in example 6.3. As the sketch shows, in the first portion of the song the repeated motions toward G major simply prolong E minor and the initial B4 of the Anstieg. It is only in m. 14 that the music finally begins to move, wrenched from its enervated reiteration of tonic (or the tonic-substitute mediant) by the augmented-sixth chord that leads to the dominant. The augmented-sixth chord also provides the impetus for the continuation of the Anstieg, which is temporar ily left hanging on the FS5 over the dominant. Given the long delay of the continuation of the Anstieg, almost the entirety of mm. 1– 29 remains stalled on a prolongation of tonic and B4. Only at the half cadences of mm. 15– 16 and mm. 28– 29 does the music move away from B4 and momentar ily struggle upward toward the Kopfton. With the shift to the parallel major in m. 30 the oppressive harmonic stasis of the first half of the song lifts, and the music begins to move forward, pulled along by the extended dominant preparation of mm. 33– 37. Finally, in m. 37, the voice achieves the Kopfton, but as GS5 rather than Gn5. This accomplishment is followed immediately by the descent of the fundamental line, supported by the first cadence on tonic of the entire song. Schubert’s music falls into two distinct parts in a way that parallels Klein’s setting of Müller’s poem. The first part, up to m. 29, presents a minimal, washed-out

example 6.3 Blumen”

Middleground sketch of mm. 1– 16 and 30 – 38 of Schubert’s “Trockne

3

7

11

30

35

10

10 5

6

8 6 4

7 5 3

261

262

analysis and theory

Generic space • contrasting ontological states

Music space • spare, static E minor, lurch to half cadence, arrival on F#5 • flowing, directed E major, completion of fundamental line

Text space • present: dying flowers, tears, ineffectuality, inevitability of seasons • future: Spring, blooming flowers, transcendance through death

Blended space • miller 1—numb, hopeless • miller 2—fevered, active

figure 6.2

CIN for Schubert’s “Trockne Blumen”

E minor inter rupted twice by rather overwrought cadences on the dominant. The second part, from m. 30 on, moves forward, and without so much as a backward look culminates in author itative and emphatic cadences on E major. This music, together with Müller’s text, sets up the CIN diag rammed in figure 6.2. The gener ic space, like that for Klein’s “Trockne Blumen,” is structured around the notion of two linked but contrasting ontological states. However, where in Klein’s setting the emphasis is on connections between the ontological states, in Schubert’s setting the emphasis is on their incommensurability. Klein’s approach takes the point of view of an observer: the undesirable situation represented by the first ontological state can be improved by reconstructing it in ter ms of the second. Schubert’s approach takes the point of view of a participant: recognizing that the first ontological state offers no hope, it is simply abandoned in favor of the second. The change of emphasis in the gener ic space reflects a reinterpretation of the elements of the textual space, prompted by Schubert’s division of the text into a group of six stanzas followed by a group of two stanzas (which are subsequently repeated). While the ontological states can still be character ized as present and future, the index is now emotional rather than temporal. The present is still occupied with dying flowers, thoughts of the grave, tears, and dead love, but it is also suffused with a sort of numbness, born of the miller’s inability to br ing about any change in his circumstances. He barely realizes that the tears that moisten the dying flowers are his own; he is powerless to stop them, just as he is powerless to stop the

word s, mu s i c, and s ong coming of the seasons, or of his own death. Thus the future of “Und Lenz wird kommen / Und Winter wird gehn” is contained within the present, a leaden emotional domain circumscr ibed by the echoing rhymes of the first and sixth stanzas. By contrast, the future state called forth by the last two stanzas of the poem is devoid of such dark thoughts: here the miller maid wanders past the resting place of the miller; here spring has truly arrived, and the winter of despair has been banished. Contrast between ontological states is also apparent in the musical space. Schubert’s E minor music is, for the most part, spare and static. After m. 11, it gradually pulls itself into an agitated state, lurches into a half cadence, and then returns to its barren beginning. His E major music, in contrast, exploits and adds to the quickening of pulse that precedes the half cadences of the E minor music, and it dr ives toward a consummatory cadence that effaces the equivocation and ir resolve of the first half of the song. This is music of possibility and completion, of action. Correlations between these idealized representations of contrasting ontological states provide an opportunity for the combination of concepts in the blended space, which draws on elements of the input spaces to create a portrayal of two very different personae for the miller.

composition

Composition provides the concepts basic to this portrayal. The E minor music and the first six stanzas of text combine to summon a miller who sits in numb contemplation of what seems to be a hopeless predicament.When the gravity of his situation seizes him, he stirs for a moment (responding to the augmented-sixth chords), but even the intensity of torment is denied him and he sinks back into his tor por. The E major music and the last two stanzas portray a quite different miller who, with growing confidence, reaches out toward goals — most particularly, achieving immortality through true love— beyond the grasp of the miller’s first persona.

completion

Through completion we can build on what we know about human behavior in such extreme states: we can imagine that in his first persona the miller is virtually inert until, at the moment of his anguish, he half rises, a look of panic on his face; similarly, we can imagine the expansive gestures of the miller in his second persona and perhaps also see the somewhat fevered look in his eyes as he proclaims “Der Mai ist kommen / Der Winter ist aus.”

elaboration

While the emergent structure produced by composition and completion offers a wealth of material to the imag ination, it is elaboration that offers the most str iking inter pretive possibilities. Elaboration of the blend suggests that the transition from the first persona to the second marks a decisive turn in the miller’s story.With this transition, the miller has moved beyond merely entertaining the thought of death and has now accepted the fact of it. The miller will overcome his ineffectuality, he will transfor m himself, and he will do so through suicide. Supporting this inter pretation are the almost frenetic repetitions of the second half of the song (as though the miller still needs to convince himself of the necessity of his

263

264

analysis and theory course of action) and the sad tur ning toward minor of the postlude as the enor mity of his decision begins to sink in.18

Two Settings, Two Millers These two settings of Müller’s “Trockne Blumen” give us two rather different millers.We first come upon Klein’s miller tur ning over the shards of his shattered love affair and becoming more distraught as he realizes the hopelessness of his predicament. Then there is a sudden shift, and what was dark and foreboding becomes light and promising. The miller’s burden has been lifted, for he has found a way to breathe life into dead flowers and dead love: he will welcome death rather than fear it. In contrast, Schubert’s miller has two str ikingly different personae. The first is emptied out, nearly paralyzed by despair, numbly aware of his misery and his inability to escape it. The second is effusive, expansive in welcoming a future in which the miller is no more. Schubert’s miller is, in short, psychotic: at first immobile in the face of death and then feverishly and joyously embracing it. Are both millers present in Müller’s poem? Yes and no.Yes, in that his poem can support these different inter pretations, as the CINs above have shown. And yes, in that, from the perspective of the poetic cycle as a whole, the miller is a truly complex character, a quiet psychopath destined for destruction. But no, in that it requires the agency of the music to br ing forth these specific millers. The differences between these two millers suggests that a review of the different compositional strateg ies that brought them into being is warranted so that we may better understand the role of musical syntax in breathing them to life. The similarities between these two settings of Müller’s poem are str iking: both employ a shift from minor to major mode; both avoid any definitive cadence on the tonic in the first portion of the song; and both make use of relatively delicate textures, especially in the first half of the song.19 More distinctive are Klein’s and Schubert’s respective treatments of dominant and tonic. Klein, through extended prolongations, employs the dominant as a tension-generating device, and in consequence the dominant receives more emphasis than the tonic. By contrast, Schubert is spar ing with the dominant of his home key, reserving it as a device to pull the music temporarily out of its stasis (in the first half of the song) or using it as part of a nor mative cadence (in the second half of the song). Tonic, by compar ison, is given quite a bit of emphasis, so much so that the first portion of the song becomes threatened with immobility. The conceptual blends created by Klein’s and Schubert’s songs, then, are not sim18. Further evidence for the moment of this decision is provided by the poetic cycle as a whole. In all of the poems up to “Trockne Blumen,” the miller’s presence is marked by the use of the first person. After the shift to the third person in “Trockne Blumen,” the miller never appears in the first person again. 19. In addition to the similar ities between Klein’s and Schubert’s settings of Müller’s poem, both also share features with Ludwig Berger’s 1818 setting of the poem, which was mentioned in n. 15; the common features are discussed in Zbikowski, “The Blossoms of ‘Trockne Blumen,’ ” 335. Although such similar ities are provocative, no research of which I am aware traces specific patter ns of influence between Berger, Klein, and Schubert.

word s, mu s i c, and s ong ply a matter of words and music happening at the same time (and thus being “combined” by dint of sharing the same temporal frame). For blending to take place, the mental spaces set up by the text and the music must have a shared topography, reflected in part in commonalities between the syntactic structures of the two media. This shared topography does not exhaust the resources of the input spaces. Indeed, the difference in syntax important to Nicholas Cook’s conception of multimedia (discussed at the beginning of this chapter) is no less important in conceptual blending, for it ensures that the stor ies told by both music and text are compelling in themselves. Nonetheless, common structural features (which may obtain at a different level of structure than those that lead to contest between media) are necessary for conceptual blending to take place. In the settings of “Trockne Blumen,” words and music work together to tell stories that enhance and expand on structural features inherent in the source spaces for each conceptual blend. I now tur n to a song by Robert Schumann in which the mental space set up by the music makes possible a conceptual blend whose emergent structure includes a nar rative considerably more extensive than that suggested by the text alone.

“ im rhein ” In 1840, having established himself as a composer of works for the piano, Robert Schumann tur ned his energies to song. And for midable energies they were, for by the time the year had ended, he had wr itten over 140 songs. Schumann quite obviously worked at speed: the twenty songs in the or iginal version of his Dichterliebe cycle (four were cut before its publication) were written from 24 May to 1 June. Nonetheless, among the songs wr itten that year are some of the most profound and haunting of the nineteenth century, in part because Schumann found ways to combine words and music to create fantastic worlds that extend far beyond those that can be summoned by either words or music alone.

Heine’s “Im Rhein” “Im Rhein,” the text and translation of which are given here, is the sixth of sixteen songs that make up Schumann’s Dichterliebe, first published by C. F. Peters in 1844.20 The text for all of the songs was taken from Heinr ich Heine’s Lyriches Intermezzo, a collection of sixty-five poems published in 1823. Although usually ter med a song cycle, Dichterliebe is held together not so much by common nar rative as by theme: all of the poems deal with romantic love, which is transfor med, splintered, or distorted by reminiscence or overheated emotions. im rhein

in the rhine

Im Rhein, im heiligen Strome, Da spiegelt sich in den Well’n,

In the Rhine, in the holy r iver, There, reflected in its waves,

20. The text for “Im Rhein” given here is from the song as it appears in Clara Schumann’s edition of the Lieder of Robert Schumann, but with text repetitions omitted.

265

266

analysis and theory Mit seinem großen Dome Das große, heilige Köln.

With its great cathedral, Is the great holy city, Cologne.

Im Dom, da steht ein Bildnis, Auf goldenem Leder gemalt; In meines Lebens Wildnis Hat’s freundlich hineingestrahlt.

In the cathedral there hangs a portrait Painted on gilded leather; Into my life’s wilder ness It has shone down kindly.

Es schweben Blumen und Englein Um Unsere Liebe Frau, Die Augen, die Lippen, die Wänglein, Die gleichen der Liebsten genau.

Flowers and cherubs float Around Our Dear Lady. Her eyes, her lips, her cheeks Are exactly like those of my love.

The three stanzas of “Im Rhein” can be divided into two parts. The first part, which compr ises the first stanza, summons a broad view of Cologne centered on its cathedral and reflected in the waves of the Rhein. There is a sense of vastness to the perspective (suggested by the repetitions of groß ), and of the holy (provided by the cathedral and the descr iption of Cologne as the “holy” city).21 The second part of the poem, which compr ises the second and third stanzas, moves inside the cathedral to focus on a portrait within. It is at this point that the presence of a nar rator is made explicit and the shifting perspective of the poem acquires an anchor and a rationale.We are here in this city, inside this cathedral, to view a painting of singular importance to the nar rator, for its radiance has proved a balm to the troubles of his soul. In the third stanza, the poetic lines become longer, and the nar rator takes us inside the painting itself . He begins by describing a heavenly vision of the Madonna, but as he takes us deeper into the painting, the image of the Madonna becomes ever more worldly, until it becomes apparent that the nar rator savors this image because it is the exact likeness of his beloved. The poem ends with this sudden shift from the spir itual to the car nal, and we hang in mid-air, suspended both by and within the nar rator’s vision. The elegance and power of Heine’s unsettling poem stem from two parallel processes. The first is perspectival: we start from the largest scale — the city of Cologne and its cathedral — and then nar row the scope, first to the inter ior of the cathedral, then to a painting within, and then to specific features of the face portrayed in the painting. The second process is conceptual and affectual: we begin with ideas about vastness and holiness; proceed to the active solace provided by the contemplation of a religious work of art; and then are suddenly confronted with an intense, carnal passion for a lover.

Schumann’s “Im Rhein” Schumann’s setting of the poem “Im Rhein,” the score for which is given in example 6.4, is in ABA' form. The first sixteen measures, which make up the A section, present a forceful, leaden E minor. Beginning forte, the voice (accompanied by the 21. Schumann provided additional emphasis on the holy by changing the end of Heine’s first line from “im schönen Strome” to “im heiligen Strome.”

Robert Schumann, “Im Rhein,” from Dichterliebe, Op. 48

example 6.4

Ziemlich langsam Voice

Im Rhein,

im hei

li gen Stro

me,

da

spie

gelt

Piano

6

sich

in den Well’n,

me,

das

mit

sei

li ge

Köln.

nem gros

sen

Do

12

gros

se,

hei

Im

Dom,

da

18

steht

ein Bild

mei

nes Le

niss, auf gol de nem Le der ge malt;

in

23

bens Wild

niss hat’s freund lich hin ein ge strahlt.

(continued)

example 6.4

(continued)

28

Es schwe ben Blu

men und

33

Eng

lein um un

sre

lie

be Frau;

38

die Au

gen, die Lip

ritard.

Lip

pen, die Wäng

lein,

die glei

chen der Lieb

ritard.

sten

43

48

53

ritard.

ge

nau.

pen,

die

word s, mu s i c, and s ong left hand of the piano in octaves) makes a stepwise ascent from E4 to G4 in m. 4, answered by a stepwise descent from C5 back to E4. At this point, voice and piano part ways.While the voice repeats its melodic mater ial almost exactly (save for the crucial change of the penultimate FS4 for Fn4), the piano continues the descent initiated in m. 4, sinking to the G1-G2 octave of mm. 11– 13. In the second half of m. 13, the bass echoes the voice’s descent from C to G of mm. 12– 13 but, prompted by the important Fn4 in the voice, it arrives on a G1S-G2S octave instead. This arrival coincides with the final E4 in the voice part and with the completion of the first stanza of the poem. The right hand of the piano fills out, if minimally, the bare texture created by the voice and the left hand; it does so with an accompaniment made up of cascading gestures in a halting patter n of alternating eighth- and dottedquarter-notes. The dominant ⁶₅ of mm. 15– 16, with which the A section concludes, leads to the A minor chord and piano of m. 17 that starts the B section. Here, the str iding bass of the left hand disappears, replaced by a more fluid and g ravitationally liberated adaptation of the eighth/dotted-quarter patter n of the right-hand accompaniment. In mm. 17– 21, the voice also abandons its relentless descents and floats gently between D5 and G4; both voice and piano momentar ily cadence on G major in m. 21. Although there is a br ief struggle in mm. 22– 25 as the voice counters the piano’s descending figures with an ascent from A4 to E5, once the E5 is achieved the air clears, and the equanimity of the preceding phrase is restored, an effect confir med by another cadence on G major in m. 27. There follows a br ief piano interlude that beg ins a chromatically har monized and rhythmically displaced descent through the sixth G2 -B1 (the voice-leading of which is shown in ex. 6.5). The voice joins the piano in m. 31, and the completion of the sixth-descent in m. 34 is followed by a cadence on A minor in the following measure. An A minor chord, prolonged through a chromatically inflected voice-exchange (as shown in ex. 6.5), prepares the way for the return to E minor effected by the ar rival on the B chord of mm. 42– 43. The return to E minor in m. 44 also marks a return to the mater ial of the A section, which (other than the mezzo forte dynamic) is exactly the same as in its first appearance until the left hand of the piano reaches the FS2-FS3 octave in m. 49 (as it did in m. 6 of the A section). At this point, the rhythmic displacements of mm. 27– 41 reappear, and the bass continues, now in augmentation, to the A1-A2 octave of m. 54. The A1-A2 octave then leads, through AS, to the dominant of mm. 56– 57 and the final cadence. example 6.5 27

Linear analysis of mm. 27– 42 of Schumann’s “Im Rhein” notated F

35

32

7

7

42

6 4 3

269

270

analysis and theory Schumann’s music thus enacts a threefold process. The first part of this process (in the A section of mm. 1– 16) establishes an austere, weighty E minor. It is well to note that the tonality is established with minimal reference to the sort of harmonic progressions and disjunct bass motions that are typical of tonal music of the per iod: there is no cadence on E minor in the entire section, and, moreover, the dominant of E minor is completely absent, its place taken by the leading-tone seventhchord.22 The second part of this process (in the B section of mm. 17– 43) moves completely, if only temporar ily, away from E minor. Here there are definitive cadences, but on G major and A minor. The large-scale instability of this section (a product of its avoidance of the tonal center so unequivocally established in the A section) becomes apparent only g radually. Ultimately, E minor cannot be avoided forever, and the section concludes (in mm. 42– 43) with the very first appearance of the dominant of E minor in the entire song. The third part of the process (in the A' section of mm. 44– 58), initiated by the definitive return to E minor, reprises the opening music. However, the music is now colored by rhythmic displacements that recall the latter half of the B section and that dr ive inexorably forward to a final cadence in the lowest practicable register. This music, together with Heine’s text, sets up the CIN diag rammed in figure 6.3. The gener ic space for the CIN is structured around the notion of exterior and interior domains. In the textual space, the exter ior domain is that summoned in the first stanza of the poem: the city of Cologne, with its r iver and cathedral. The interior domain is that summoned in the second two stanzas: the cathedral and the painting with which the nar rator is obsessed. In the musical space, the exter ior domain is that of E minor, with its stark octaves and str iding phrase rhythm. The interior domain is that of the contrasting (or “not-E-minor”) music of the B section, with its more flowing accompanimental patter n, softer dynamic, rhythmic displacements, and large-scale instability. Correlations between these idealized representations of exter ior and inter ior spaces provide an opportunity for the combination of concepts in the blended space, which draws on elements of the input spaces to create a r ich portrayal of the actions of the nar rator and the environment within which they take place.

composition

Composition combines the exter ior view of the river, city, and cathedral with the austere E minor music of the A section and suggests a sweeping and somewhat foreboding perspective, surveyed with a deliberative and relentless gaze. In turn, the inter ior view of the cathedral and the painting within combines with the soothing music of the B section to create a sense of refuge, a surcease from the harsh realities without.

22. It is interesting to speculate on whether Schumann himself would have differentiated between the dominant and the leading-tone chord. The distinction is of more concer n to theor ists of the period than to composers. Nonetheless, Schumann would most certainly recognize the shar per dissonance created by the leading-tone chord (with or without an added seventh), and it is worth noting that in the E minor portions of “Im Rhein” he favored these over the relative consonance of the dominant chord until m. 42.

word s, mu s i c, and s ong

Generic space • exterior and interior domains

Music space • E minor music of A section (austere, foreboding) • not-E-minor music of B section (soothing, consolatory)

Text space • exterior view of river, city, and cathedral • interior view of cathedral, painting, portrait of Madonna

Blended space • gray, cold (perhaps threatening) exterior • intimate, secure (if fragile) interior

figure 6.3

CIN for Schumann’s “Im Rhein”

completion

Completing the image, we can imagine details of each domain: an exter ior world gray and cold and in some measure threatening; an inter ior world intimate and secure, if somewhat frag ile. We can also imag ine something of the physical and emotional life of the nar rator. Outside the cathedral, he is almost certainly self-absorbed, a disheveled figure hurrying to escape the demons that tor ment him. Inside, he stands rapt, even as the tumult in his mind gradually increases to the point of becoming unbearable.

elaboration

Our elaboration of the conceptual blend produced by Schumann’s setting of Heine’s poem might well seek to develop a nar rative that could explain the forces that dr ive the nar rator into the cathedral: a personality or perspective that makes life in the outside world intolerable, or a deep obsession with the beloved that renders her both an object of worship and something to be owned and controlled. However, we could also follow the lead of Schumann’s music, which, in response to the denouement of the poem, returns to the E minor music of the opening. We are thus returned to the world outside the cathedral and there can see the nar rator, now more disturbed than ever, stagger ing under the weight of his obsession with his lover, just as the music staggers with the rhythmic displacements of mm. 49– 55. This furtherance of the nar rative by the music suggests that it is the psychic tor ment of the nar rator that is behind the sense of foreboding summoned by the exter ior domain, as well as for the ir reality of the inter ior domain. It is an oppressive torment that absorbs all, and among whose fires the nar rator

271

272

analysis and theory wanders, knowing no rest. The elaboration of the blend, then, suggests a profoundly troubled mind to whom the Rhein represents more than a mir ror for a g reat and holy place: it also offers the means to extinguish the fires that consume him.

Summary The dark twists and tur ns of love explored in Heine’s Lyriches Intermezzo are, in their way, not so very far removed from those Müller captured in his Die schöne Müllerin. However, where Müller develops the topic and its ramifications over the course of twenty-three poems, it is Heine’s gift to be able to accomplish this in the space of just one. This suggests a mastery of psychological detail — both in understanding his subjects and in what can be asked of his reader — that is altogether impressive. Equally impressive is Schumann’s ability to exploit this level of detail by combining Heine’s words with music that supports, expands on, and even offers a completion for the story told by the poem. It might be argued that Schumann’s setting str ips some of the ambiguities from Heine’s poem, ambiguities that offer even more possibilities for interpretation than those provided by the song. The point is well taken, for the conceptual blend set up by the song emphasizes certain aspects of the topography of the text space at the expense of others. And yet the gains are considerable, for the conceptual world that emerges from syntactic invariances between Heine’s text and Schumann’s music is one r ich in detail and str iking in its immediacy. The challenges and rewards of creating such worlds no doubt fueled the burst of creativity that led to Schumann’s amazing output of songs in 1840 and that produced a transfor mation in the way composers thought about how to organize their musical mater ials.

“ in der fremde ” The similar ities between Klein’s and Schubert’s settings of “Trockne Blumen” were striking in that Schubert apparently did not know Klein’s setting, and Schubert was occupied with developing a song cycle as opposed to creating a single Lied: not only are the musical details of each setting similar, but the gener ic spaces behind the conceptual blends that each song sets up are almost exactly the same. In Schumann’s and Brahms’s settings of Joseph von Eichendorff ’s “In der Fremde,” nearly the exact opposite set of conditions holds. Brahms knew and respected Schumann’s setting, but he seems to have wanted to show his fr iend and mentor what he could do with the same mater ial. The result is two songs every bit as different as those of Klein and Schubert, but whose divergences stem from the gener ic spaces that structure the blends produced by each song.

Eichendorff ’s “In der Fremde” “In der Fremde,” the text and translation of which are given here, first appeared as the text of an untitled song introduced in the course of Eichendorff ’s 1833 novella Viel Lärmen um nichts.23 The scene in the novella is a huge and gloomy hall within 23. Joseph Freiherr von Eichendorff , Viel Lärmen um nichts, ed. Gerhart Baumann and Siegfr ied Grosse, Neue Gesamtausgabe der Werke und Schr iften (Stuttgart: J. G. Cotta’sche Buchhandlung Nachf.,

word s, mu s i c, and s ong a castle; outside, a storm rages, and, tucked away in a window niche, a young woman sings to her own accompaniment on the guitar. Her song is a deeply sad one, concerned with loneliness and thoughts of a solitary death far from home. The song over, however, she springs up, full of life, to meet her beloved and his fr iends, who have chanced upon her musings. The scene within which this poem first occurs is thus one of sharp contrasts — between the cold and forbidding inter ior of the castle, which makes for scant refuge from the stor m outside, and the blushing and lively young woman who rushes to embrace her fr iends. in der fremde

in foreign lands

Aus der Heimat hinter den Blitzen rot Da kommen die Wolken her, Aber Vater und Mutter sind lange tot, Es kennt mich dort keiner mehr. Wie bald, wie bald kommt die stille Zeit, Da ruhe ich auch, und über mir Rauscht die schöne Waldeinsamkeit, Und keiner mehr kennt mich auch hier.

From home, behind the red lightning There come clouds, But Father and Mother are long dead; No one there knows me anymore. How soon, how soon will that quiet time come, When I too shall rest, and over me Shall rustle the forest’s beautiful solitude, And no one here shall know me anymore.

The poem itself offers images and impressions rather than any specific nar rative structure. Dominant are the images of nature (in the for m of the red lightning, approaching clouds, and promise of the forest’s loneliness). Of equal importance is the nar rator’s profound sense of abandonment (her father and mother are long dead, and she is unknown both in her homeland and in her final place of rest). However, there are also within the poem shar p contrasts similar to those that accompanied its introduction in the novella: the comforting images of the homeland, parents, and sylvan setting are juxtaposed with the ambiguous “here” of the poem, solitude of the forest, and oppressive anonymity of the present sur roundings. Nonetheless, connections between the stor ies told by the poem and the novella were obscured, and some of the ambiguities of the poem were muted, when it was placed by Eichendorff ’s friend Adolf Schöll in the “Totenopfer” section of an 1837 volume of Eichendorff ’s collected poetry, at which time it acquired its present title.24

Schumann’s “In der Fremde” It was in Schöll’s 1837 edition of Eichendorff ’s poetry that Schumann (or his fiancée, Clara Wieck) came upon the poem, which he began to set to music on 4 May 1840; the score is given in example 6.6.25 Although there are indications Schu1957), 478. The text provided here is the same as that in the novella; some of Schumann’s departures from Eichendorff ’s poem are discussed in the next section. 24. For a discussion of Schöll’s role as editor of Eichendorff ’s work, see Ansgar Hillach and KlausDieter Krabiel, Eichendorff-Kommentar (Munich: Winkler, 1971), 1: 47– 48. 25. For a stimulating discussion of the songs from Schumann’s Op. 39, their ordering in the cycle, and their relationship to the 1837 edition of Eichendorff ’s poetry, see Patrick McCreless, “Song Order in the Song Cycle: Schumann’s Liederkreis, Op. 39,” Music Analysis 5 (1986): 5– 40. Dates of the composition of the songs are given in Robert Schumann’s Liederbücher, which are reproduced in Viktor Er nst Wolff, Lieder Robert Schumanns in ersten und späteren Fassungen (Berlin: H. S. Hermann, 1913), 12– 19. The same

273

example 6.6

Robert Schumann, “In der Fremde,” from Liederkreis, Op. 39 No. 1 Nicht schnell

Voice

Aus der Hei

mat hin

ter den Bli

tzen rot

da

Piano

Mit Pedal 4

kom men die Wol

ken her.

A ber Va

ter und Mut

ter sind

7

lan

ge tot,

es

kennt mich dort kei

ner mehr.

Wie

10

bald,

ach wie bald

kommt die

stil

le

Zeit,

da

12

ru

he

ich

274

auch,

da

example 6.6

(continued)

14

ru

he

ich

auch

und

ü

ber mir rauscht die

17

schö

ne

schö

ne Wald

Wald

ein

sam

keit,

die

20

ein sam keit,

und

kei

23

hier,

und

kei

ner kennt mich mehr hier.

26

275

ner kennt mich mehr

276

analysis and theory mann intended “In der Fremde” to be the opening song of his Op. 39 Liederkreis, when the cycle was first published in 1842 by Tobias Haslinger, “Der frohe Wandersmann” (later published as Schumann’s Op. 77 No. 1) appeared in its stead.26 It was only with the second edition of the Eichendorff cycle, published in 1849 by Friedrich Whistling, that “In der Fremde” made its appearance as the opening song. In revisions to the song, Schumann changed Eichendorff ’s poem slightly to improve his melody, adding the “ach” in m. 10 and changing the last line of the poem from “Und keiner mehr kennt mich auch hier” to “Und keiner kennt mich mehr hier.”27 Schumann’s setting begins with a flowing accompaniment that continues throughout the song. Although there is no evidence that Schumann referred to Eichendorff ’s novella in the course of setting this poem, some character istics of the music seem to fit the image portrayed there of a woman singing to her own accompaniment on the guitar. The running ar peggios in a relatively low register are typical of guitar music, and the melody is folk-like in its simplicity. The first five measures present a thoroughly straightforward FS minor, using only tonic and dominant. When the melody is repeated in mm. 6– 9, the har monization becomes a bit r icher with the fully diminished seventh chords of mm. 6 and 7, but the basic har monic framework established in the opening measures remains intact. Beginning in m. 10, however, there is a shift toward A major, and the sound br ightens considerably as the higher register of the piano is called into service for the r inging B4-FS4 fifth of mm. 10 – 11. A proper ar rival on the I⁶ of A in m. 13 is thwarted by the melody’s temporary escape to E5, and when the outer-voice sixths are retraced in mm. 14– 15 (as shown in ex. 6.7), the har mony at the point of arrival is changed to the dominant of B minor (that is, FS major) rather than the tonic of A.28 This not only

sources are cor related with the manuscripts at the Deutsche Staatsbibliothek Berlin in Reinhold Brinkmann, Schumann und Eichendorff: Studien zum Liederkreis Opus 39, Musik-Konzepte, 95 (Munich: Edition Text + Kr itik, 1997), 80 – 86. See also Herwig Knaus, Musiksprache und Werkstruktur in Robert Schumanns “Liederkreis”: Mit dem Faksimile des Autographs, Schriften zur Musik, 27 (Munich: Emil Katzbichler, 1974). 26. “Der frohe Wandersmann” and why Schumann may have included it in the 1842 edition of the Liederkreis are discussed in Jon W. Finson, “The Intentional Tourist: Romantic Irony in the Eichendorff Liederkreis of Robert Schumann,” in Schumann and His World, ed. R. Larry Todd (Princeton, N.J.: Princeton University Press, 1994), 156 – 70. 27. A compar ison of the two versions is given in Wolff, Lieder Robert Schumanns, 56– 57; the revisions are not given in the facsimile provided in Knaus, Musiksprache und Werkstruktur in Robert Schumanns “Liederkreis.” 28. In my analysis, I have emphasized the sense of departure evoked by mm. 10 – 14— that is, the firm motion away from minor and the implied cadence on A major. In a compelling analysis of “In der Fremde,” David Ferris discusses Rufus Hallmark’s reconstruction of one of Schumann’s earlier versions of the song; in this version Schumann does indeed cadence on A major. See Ferris, Schumann’s Eichendorff Liederkreis and the Genre of the Romantic Cycle (New York: Oxford University Press, 2000), 111– 13. Working from a strongly Schenkerian perspective, Ferris also makes a convincing argument that, in ter ms of large-scale tonal structure, the move to A major in the final version of the song is, in fact, illusory and is subordinate to an expansion of the subdominant of FS minor (pp. 98– 106). Although Ferris’s reading makes sense of Schumann’s overall har monic and contrapuntal plan, it does not preserve the sense that with the ar rival on FS major the promised cadence on A major has been subverted. It is this sense of subversion that my analysis, focused as it is on a more surface level of harmonic and contrapuntal activity, attempts to capture.

word s, mu s i c, and s ong example 6.7

Linear analysis of mm. 12– 15 of Schumann’s “In der Fremde” 14

12

6

6

10

6

6

6

6

returns the music to minor but also starts the return to FS, accomplished in the latter half of m. 19 when a B minor chord is transfor med into the leading-tone chord of CS. The cadence on FS minor in m. 21 is followed by eight measures with an FS pedal in the bass, over which there are double chromatic neighbors to FS (Gn and ES), as well as a major third (AS). This music, together with Eichendorff ’s text, sets up the CIN diag rammed in figure 6.4. The gener ic space, like that for Klein’s and Schubert’s settings of “Trockne Blumen,” is structured around the notion of two contrasting ontological states. Lacking, however, is the notion that there is a smooth or ready connection between the two states: although there is a sense that they are linked in some larger scheme, they are portrayed as basically incommensurate. Contrast between ontological states in Eichendorff ’s poem is supported by a marvelously subtle shift of conceptual metaphor.When reference is made to the past or the present, a spatial mapping is used: the past is “there” (the “dort” of the fourth line), the present is “here” (the “hier” of the eighth line).When reference is made to the future, an affective mapping is used: the future is “quiet” (the “stille” of the fifth line) and partakes of “forest-solitude” (the “Waldeinsamkeit” of the seventh line). Each of these mappings is further associated with somewhat more diffuse emotions. The spatial mappings of the past and present are connected with the poignant memory of departed parents and the sense of abandonment that comes with disappearing from memory, with the confused or uncomfortable feelings summoned by the red lightning and approaching clouds, and with the loneliness of an anonymous existence. The affective mappings of the future are connected with a sense of rest and of being in the presence of beauty. Contrast between ontological states can also be seen in Schumann’s music. The FS minor music is, for the most part, resolutely secure, yet it is, nonetheless, tinged with chromaticism. Thus, in mm. 1– 9, regular cadences appear, but also the fully diminished seventh chords of mm. 6 and 7. Similarly, mm. 20 – 28 offer the secur ity of the pedal point, as well as the double chromatic neighbors to FS, which render ambiguous the assertion of major in the final measures. The music of mm. 10 – 19 tends to be br ighter (note the higher register in the piano accompaniment that is especially audible in the r ight hand of mm. 10 – 15) and less involved with chromaticism (with the important exceptions of the melodic deflection to AS in m. 15 and the fully diminished seventh chord of m. 17). However, in this same passage, convincing cadences are conspicuous only for their absence.

277

278

analysis and theory

Generic space • contrasting ontological states

Text space • past, present–spatial mappings: abandonment loss, threatening weather • future–affective mappings: forest-solitude, quiet rest

Music space • secure F# minor, tinges of chromaticism • brighter not-F#minor music, higher register, lack of cadence

Blended space • matter-of-fact, melancholy present, temporarily displaced by animated, hopeful future, only to return to melancholy present

figure 6.4

CIN for Schumann’s “In der Fremde”

Correlations between these idealized representations of contrasting ontological states provide an opportunity for the combination of concepts in the blended space. The combination draws on elements of the input spaces to create a portrayal of two worlds, not totally unlike those of “Im Rhein,” but framed in emotional rather than architectural ter ms.

composition

Composition combines the FS minor/major music with the spatially mapped past and present. Evidence that Schumann was aware of the importance of maintaining a consistent musical environment for the first four lines of the poem is provided by his manuscr ipt, for after wr iting a more varied accompaniment for mm. 6– 10 he scratched it out and continued the patter n established in mm. 1– 5.29 The affectively mapped future is first combined with A major and then, with the voice still near the top of its range for the song, B minor.With the repetition of “die schöne Waldeinsamkeit,” however, the melody drops, and we return to FS and the spatially mapped present.

completion

Following the structure of the blend and our knowledge that a single first-person voice is being projected, we could imagine a singer who begins with almost matter-of-fact observations but who gradually becomes more engaged 29. See the unpag inated “Faksimile des Autographs” appended to Knaus, Musiksprache und Werkstruktur in Robert Schumanns “Liederkreis.”

word s, mu s i c, and s ong and more melancholy. This melancholy is then rather abruptly displaced (in m. 10) by more animated and hopeful emotions, leading the singer to a higher register and to sing with a fuller voice (in keeping with the profusion of longer note values in the melody). The hopeful attitude cannot be sustained, however, and solitude once again becomes loneliness, the present that is reasserted in m. 21 effectively vanquishing the br ight promise of the future.

elaboration

The imaginary world of Schumann’s song is one quite different from that of Eichendorff ’s original poem. The song sung by the young woman in the window niche is almost folk-like, its regular meter and stylized emotions disturbed only once, by the metr ical awkwardness of the sixth line. But this momentary shadow of emotional depth passes, and it is possible to imagine the singer jumping up, the guitar and song flung aside, to greet her fr iends. Schumann’s singer will not be so easily released. The almost for mulaic melancholy of the song’s opening reveals itself in the end to be inexorable, pulling the energy and hope from the singer and leaving her hollow and forlor n. Schumann’s song leaves us with a singer for whom eter nity now stretches out as flat and colorless as her present, her spirit struggling as the walls of anonymity close around it.

Brahms’s “In der Fremde” Johannes Brahms was but nineteen when, in November of 1852, he made his setting of “In der Fremde,” published the next year by Breitkopf and Härtel as the fifth of his Sechs Gesänge, Op. 3; the score is given in example 6.8.30 “In der Fremde” was the first of the Op. 3 songs that he composed, and it shows clear debts to Schumann: Brahms adopted Schumann’s version of the text, the key of FS minor, and some important motivic details. Nonetheless, the song is clearly Brahms’s own, and nowhere is this more apparent than in the conceptual blend it sets up. After a short introduction that anticipates the vocal melody without directly stating it (by presenting only elements of the piano accompaniment for the melody), the song proper commences, laid out in four phrases. These phrases have almost identical beginnings, both in har mony and melody, although each ends rather differently. The first touches back upon the tonic at its midpoint (m. 6) and then deflects away to A major. Arrival on A (m. 8) is unsettled by the entrance of the dominant on the second beat (over an A pedal), which supports an echo of the last three notes of the voice part. The second phrase moves at its midpoint to D major (m. 12); its cadence (on the downbeat of m. 13) is as unsettled rhythmically as that of mm. 7– 8, but it gains a bit of stability when the fourth line of the poem is repeated (mm. 13– 15). Deflection toward A major occurs again in the third phrase (m. 19), but the completion of the cadence is delayed by two beats and the vocal line continues, ultimately eliding with the beginning of the fourth phrase in m. 22. The fourth phrase breaks off momentar ily at its midpoint (which, as in all the 30. Brief discussions of the song can be found in Lucien Stark, A Guide to the Solo Songs of Johannes Brahms (Bloomington: Indiana University Press, 1995), 15– 16; and Er ic Sams, The Songs of Johannes Brahms (New Haven, Conn.:Yale University Press, 2000), 36– 37.

279

example 6.8

Johannes Brahms, “In der Fremde,” from Sechs Gesänge, Op. 3 No. 5 Poco agitato

Voice

Aus der a tempo

poco rit.

Piano

5

Hei

mat hin

ter den Bli tzen rot, da

kom men die Wol ken

her.

9

A

ber

Va

ter und Mut ter sind lan ge

tot, es

rit.

13

mehr, kennt

mich dort kei

ner

mehr.

kennt mich dort kei ner

a tempo

Wie

rit.

word s, mu s i c, and s ong example 6.8

(continued)

17

bald, ach wie bald kommt die stil

le

21

Zeit, da

ru

he ich auch und

ü

a tempo

poco rit.

ber mir rauscht

die schö ne Wald ein sam keit,

poco rit.

25

und

sostenuto

dim. e rit.

kei

ner

kennt mich mehr hier, kei

ner

kennt mich

mehr

hier.

dim. e rit.

preceding phrases, is marked by an ar rival on the tonic), and the mode suddenly changes to major on the last beat of m. 23. Brahms then completes the phrase by recalling the melody of m. 12, but this time har monized in FS rather than D.Within this context, the Gn in the melody at m. 25 recalls the end of Schumann’s setting, an association made stronger when the repetition of the last line of the poem in (mm. 26– 28) is set to a melody similar to that which appeared in m. 26 of Schumann’s piano accompaniment. Besides the obvious melodic repetitions engendered by this overall compositional scheme, two additional features bear note. First, the compass of the melody is relatively restricted (from GS4 to G5, the smallest range of any of the Op. 3 songs). Second, the melody is constantly brought back to A4: each phrase begins on A4, it

281

282

analysis and theory

Generic space • discomfort of foreign surroundings

Music space • rhythmic disruptions of phrase and cadence, oppressiveness of F# minor, prevalence of melodic A4

Text space • alienation: mysterious red lightning, anonymity, orphaned by parents and the world

Blended space • restlessness, grudging, uneasy acceptance of predicament

figure 6.5

CIN for Brahms’s “In der Fremde”

marks the ar rival on the midpoint of each phrase, and the second and third phrases end on it (in the latter case, this br ings about the elision of the end of the third phrase with the beginning of the fourth). This music, together with Eichendorff ’s text, sets up the CIN diag rammed in figure 6.5. The gener ic space is structured around the feeling of discomfort attendant on being in alien sur roundings. This space is rather unlike those for the other CINs discussed in this chapter in that it does not lend itself as readily to a nar rative framework. However, discomfort, by its nature, suggests a dynamic situation (to the extent that we want to return to a state of comfort). This may not quite constitute a nar rative in its own right, but it creates an opportunity at least for a minimal story. Eichendorff ’s poem supports this sense of discomfort with the ominous portents of the clouds and red lightning, as well as with the isolation and anonymity noted in the fourth and eighth lines. Discomfort is also summoned, if negatively, through the thought that rest is to be found elsewhere. The discomfort of alien sur roundings is suggested musically by the repeated attempts in mm. 4– 21 to escape the pitch A4 and the key of FS minor. (The accompaniment patter n for the FS minor sections also makes use of an insistent CS4 that starts as a simple bit of rhythmic activation in the introduction, but soon begins to cloy.) Each attempt fails, of course, as it is undercut by insecure cadences and the relentless pull of A4. When a sort of escape is fashioned, at the song’s conclusion, one senses that the forces of oppression have been held in abeyance more than defeated. Although the mode changes to major, the Gn5 summons the b2 that is

word s, mu s i c, and s ong more typical of minor; although the melody ends away from A4, it has not accomplished a structural close on FS4.31 Correlations between these idealized representations of discomfort at alien surroundings provide an opportunity for the combination of concepts in the blended space that draws on the elements of the input spaces to create a portrayal of life “in der Fremde.”

composition

Composition combines the images of isolation and the alien in the first four lines of the poem with two successive musical phrases that begin in the same place but move away to end at a distance from the tonic and with the downbeat destabilized. The combination of the last line of the poem and the concluding music is slightly more tenuous: the return of the voice to the high end of its range and the recall of the end of phrase 2 reinforce the portrayal of discomfort, but the sonorous FS major chords and pedal point also suggest a sort of reconciliation outside of the basic mapping that structures the CIN.32 Although I have not emphasized the failure of elements from the text-space and music-space to combine in my discussions of the process of blending, it is particularly noticeable in the case of lines 5 – 7 of Eichendorff ’s poem and mm. 17– 23 of Brahms’s setting. At this point, the topography of the two spaces is not unifor m— more specifically, the text at this point (concer ned as it is with contemplation of peaceful rest in the embrace of the forest) does not confor m to the structural premises of the gener ic space. Although words and music certainly co-occur here, they do not combine from the perspective of the CIN diagrammed in figure 6.6. This lack of correspondence may be one reason Brahms’s song seems weak here: his text-painting of “über” (as a long, relatively high note that is manifestly “over” the accompaniment) offers rather insufficient compensation for the failure of words and music to work together on a larger scale.

completion

It is through completion of the conceptual blend that Brahms’s song takes on a dynamism that extends beyond the rhythmic disruptions and key-area juxtapositions of the music. As noted, we know that states of discomfort cry out for resolution, whether that is provided by shifting position in our chair or moving away from someone who makes us uneasy.When the music of the first half of each phrase is followed by the contrasting music in the second half, it is easy to hear this as a moving away, a physical adjustment to unpleasant circumstances. The sudden shift to major and return of the higher vocal tessitura at the end of the song suggest not so much a final resolution as an uneasy truce: the struggle of the first twenty-odd measures has yielded results, but they can hardly be called definitive. 31. From a Schenkerian perspective, the lack of a clear descent to 1 (through the melodic progression A–GS–FS) poses interesting, although by no means ir resolvable, problems. 32. It is worth noting that the two lines of the poem most clearly associated with the discomfort of abandonment and alienation — lines 4 and 8— are also the only two that Brahms chose to repeat, thus providing an opportunity to emphasize the composition of elements from the text-space and musicspace.

283

284

analysis and theory

elaboration Entering further into the world of Brahms’s song, we can see that Brahms’s singer is thoroughly within the foreign lands as she sings, and, although her deflections toward major keys suggest an attempt to make herself comfortable in these alien sur roundings, she remains an anonymous stranger — she cannot escape the iron grip of FS minor, just as she cannot escape her isolation. Nonetheless, Brahms’s singer does not despair — at least not yet. Instead, she struggles against her fate, crying out against her anonymity in her highest register, attempting to use her predicament as a lever to gain recognition and a life in this foreign land. Given this text and this music, we can imagine her shaking her fist at fate; if her eyes fill with tears, they are tears of a struggle against destiny. Summary With his setting of “In der Fremde” Brahms clearly wanted to demonstrate his independence as a composer, as well as to pay homage to an important fr iend and mentor.Yet, two other factors are important. The first is raw youth: Brahms at nineteen was no stranger to feelings of alienation and restless energy, and it is hardly surprising that he drew these from Eichendorff ’s poem. The second are the compositional advances made by Schumann in the Liederjahr of 1840: the year bore witness not only to an incredible outpour ing of song but also to a new understanding of how musical syntax could be shaped to respond to the possibilities of poetry. Brahms lear ned the lessons of Schumann’s Liederjahr, as well as the many other lessons taught by the music of his century, and he built on them.Where cadence was still a pr imary articulator of the musical argument for the Schumann of 1840, it became something infinitely more malleable for the Brahms of 1852. Indeed, over the course of Brahms’s “In der Fremde,” there is not one clear cadence; instead, there are cadences disrupted, so understated as to be almost invisible (as the cadence of m. 23), or assembled out of the bits and pieces of traditional cadential for mulae (which is how Brahms br ings the song to a conclusion). Brahms, of course, knew when and how to exploit traditional cadential for mulae, and he did so with g reat success in the years that followed, but his setting of “In der Fremde” shows that, when his understanding of a text demanded it, he could create a new set of syntactic possibilities for musical discourse.

conceptual blending and song As part of his anthropological fantasy on the or igins of language, Jean-Jacques Rousseau imagined the pr imordial world that gave birth to the languages of the temperate south. Around the water wells necessary for life in these ar id lands people gathered, and young men met young women for the first time. Beneath aged oaks, conquerors of years, an ardent youth gradually forgot its ferocity, gradually they tamed one another; through endeavoring to make themselves understood, they learned to explain themselves. There the first festivals took place, feet leaped with joy, eager gesture no longer sufficed, the voice accompanied it with passionate accents; mingled together, pleasure and desire made themselves felt at the same

word s, mu s i c, and s ong time. There, finally, was the true cradle of peoples, and from the pure crystal of the fountains came the first fires of love.33

As Rousseau would have it, the language that developed around these aqueous gathering places was not like moder n language, but a fusion of words and music: Around the fountains of which I have spoken, the first discourses were the first songs; the periodic and measured recurrences of rhythm, the melodious inflections of accents caused poetry and music to be bor n along with language; or rather, all this was nothing but language itself in those happy climates and those happy times when the only pressing needs that required another’s help were those to which the heart gave rise.34

In the myth Rousseau offers, music and language don’t simply cohabitate; they commingle their syntaxes: the per iodic and measured recurrences of rhythm and the inflections of accent are combined in an Ur-language, which, only later, after the Fall or its equivalent, separated into music and language. In the end, Rousseau’s fantasy has more to tell us about the role of language and music in the anthropological speculations of the eighteenth centur y than it does about the possibility that the two media were once one.35 But the conviction that music represents a communicative medium to equal language — a conviction Rousseau shared with his old antagonist Rameau36 — and the idea that the sum of music and language might be g reater than its parts are concepts wr iters like Müller and von Spaun believed were demonstrated, in fairly specific ways, by the nineteenthcentury Lied. While it is possible to dismiss such beliefs as products of overheated rhetor ic, the fascination composers, audiences, and cr itics have had with song cannot be ignored. Conceptual blending offers a way to explain why this fascination has been so endur ing: under certain circumstances, elements and relations from the mental space set up by the music of a song blend with elements and relations from the mental spaces set up by the text to create a new world for the imagination — a world of supernatural char m, noctur nal ter ror, and much, much more. For conceptual blending to occur, the mental spaces that serve as inputs to the blend must have a shared topography. For the songs analyzed in this chapter I have located this shared topography in commonalities between the complete discourse 33. Jean-Jacques Rousseau, “Essay on the Or igin of Languages (c. 1763),” in Essay on the Origin of Languages and Writings Related to Music, trans. and ed. John T. Scott, Collected Writings of Rousseau, 7 (Hanover, N.H.: University Press of New England, 1998), 314. In my comments on Rousseau’s essay, I am more concer ned with the idyllic state he imagines than with the overall context relative to which the image is framed. For a probing discussion of this context, see Lydia Goehr, The Quest for Voice: Music, Politics, and the Limits of Philosophy (Berkeley: University of California Press, 1998), 98– 106. 34. Rousseau, “Essay on the Or igin of Languages,” 318. 35. For more on the role of language and music in speculations about human or igins by French writers of the eighteenth century, see Downing A. Thomas, Music and the Origins of Language: Theories from the French Enlightenment, New Perspectives in Music History and Cr iticism (Cambr idge: Cambridge University Press, 1995), chap. 2. 36. Although Rousseau and Rameau both argued that music was the equal to language, for Rousseau this meant melody and for Rameau it meant har mony. This difference of opinion (among other things) was the basis for their debate about musical expression, discussed at the end of chap. 3 in this volume.

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analysis and theory structure set up by the music and the complete discourse structure set up by the text. That such commonalities might exist suggests deep cor respondences between musical and linguistic syntax. To be sure, these cor respondences are, in most instances, of a general sort, outlining as they do constructs like contrasting ontological states (as in the settings of “Trockne Blumen” and in Schumann’s “In der Fremde”), exterior and inter ior domains (as in “Im Rhein”), or discomfort with foreign surroundings (as in Brahms’s “In der Fremde”). And yet, such highly abstract constructs still have their power, for they can find realization in manifold concepts associated with both the emotions and the intellect. Agawu ended his provocative 1992 essay with these words: “We await the development of a syntax of song.”37 The preceding analyses suggest that this syntax is to be found not “in” the song proper, but in the way the constituent media of song — words and music — relate to one another. The syntax of song, then, is a syntax of conceptual blending, through which music breathes life into poetr y and poetry breathes life into music, and together they proceed as song.

37. Agawu, “Theory and Practice,” 30.

chapter seven

Q competing models of music: theories of musical form and hierarchy

idway in her jour ney through Wonderland, Lewis Car roll’s Alice takes leave of the Cheshire Cat and makes her way toward the house of the March Hare. There she finds a tea party under way— a mad, perpetual tea party, attended by the March Hare, the Mad Hatter, and the somnolent Dor mouse. As the party proceeds, Alice’s patience begins to wear thin, tried by turnabout word play and abrogated manners, and is stretched to the limit when she finds out that the Hatter’s riddle — “Why is a raven like a wr iting desk?”— is without solution.

M

Alice sighed wearily. “I think you might do something better with the time,” she said, “than wasting it in asking r iddles that have no answers.” “If you knew Time as well as I do,” answered the Hatter, “you wouldn’t talk about wasting it. It’s him.” “I don’t know what you mean,” said Alice. “Of course you don’t!” the Hatter said, tossing his head contemptuously. “I dare say you never even spoke to Time!” “Perhaps not,” Alice cautiously replied; “but I know I have to beat time when I learn music.” “Ah! That accounts for it,” said the Hatter.“He wo’n’t stand beating. Now, if you only kept on good terms with him, he’d do almost anything you liked with the clock.”1

Exchanges like this are common enough in Wonderland, a place inhabited by creatures whose logic is often as fantastic as their appearance. Nonetheless, the game Carroll is playing at here is less a matter of labyrinthine logic and more a matter of different ways to structure what is putatively the same domain. Alice uses two different cross-domain mappings to reckon with time: time as something to be saved or wasted (mapping from the domain of commodities or substances onto the domain of time); and time as a set of regular motions (mapping from the domain of physiologically defined space onto the domain of time). For the Hatter’s cockeyed contr ibution, Carroll exploits a traditional character ization of time as a human 1. Lewis Carroll, The Annotated Alice: Alice’s Adventures in Wonderland and Through the Looking Glass, intro. and with notes by Martin Gardner, illustrated by John Tenniel (New York:W.W. Norton, 2000), 72. The tea party is the topic of chap. 7 of Alice’s Adventures in Wonderland.

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analysis and theory agent (as in Father Time, or the New Year as a diapered baby), an anthropomor phic mapping that exploits conceptual blends like those discussed in the latter portion of chapter 2. The mer ry confusion of mappings that results is part and parcel of the imaginary world Car roll constructed — indeed, Wonderland is a maze of interfiliated conceptual blends. However, the scene at the tea party also throws into relief a fundamental conflict between Alice’s world and that of Wonderland, which comes to a head in the final chapter. There, Alice responds to the Queen of Hearts’s peremptory “Off with her head!” (“Sentence first— verdict afterwards”) by dismissing the entire court and courtroom with “Who cares for you? You’re nothing but a pack of cards!” At this, Wonderland disappears, and Alice wakes to find herself lying on the bank of the river, with her head in the lap of her sister.2 A confusion of mappings similar to the one apparent in Alice’s dialogue with the Hatter often ar ises in music theory. The result, while not quite as entertaining as a turn in Wonderland, can have some of the same flavor. Theorists appear to be talking about the same thing, but they structure their understanding of it in very different ways. Two examples are taken up in this chapter. The first involves musical form, the second musical hierarchy. During the eighteenth century, the study of musical for m emerged as an important basis for discourse about music. Form was regarded as dealing with the very essence of musical works: how musical mater ials were arranged and cor related over the course of a piece of music. As the study of form developed and was continued through the nineteenth century, theorists worked with two basic — and seemingly opposed — models of musical for m, one static, the other dynamic. Musical for m, viewed from a static perspective, is reminiscent of architecture (a parallel all the more ironic, given Friedrich von Schelling’s character ization of architecture as “frozen music”)3 and typically consists of either a framing structure clad with musical mater ial or relatively abstract containers filled with musical events. Musical for m from a dynamic viewpoint is processive and a bit unpredictable: the musical work emerges over the course of time, and musical mater ials are both the substance of and raison d’être for this emergence. As a further complication, the cross-domain mappings that activated these two models changed dur ing the nineteenth century. Consequently, there are two levels of mapping involved, both of which can breed confusion about just what is meant by musical for m: a gener ic level associated with the two basic models (one inter preting for m as static, the other as dynamic); and a specific level associated with the cross-domain mappings that activate the gener ic models. In the first section that follows, I explore static and dynamic models of musical for m that emerged in the eighteenth centur y and the way these models were transfor med by changes in ideology and music education that took place beginning late in that century. 2. Carroll, The Annotated Alice, 124. 3. “Architecture, as the music of the plastic arts, thus necessar ily follows ar ithmetical relationships. Since it is music in space, however, in a sense, solidified music, these relationships are simultaneously geometric relationships.” Friedrich Wilhelm Joseph von Schelling, Philosophy of Art, ed., trans., and intro. Douglas W. Stott, with a foreword by David Simpson, Theory and History of Literature, 58 (Minneapolis: University of Minnesota Press, 1989), 165. See also, on p. 177, the passage that begins “If architecture is indeed solidified music . . .”

competing mode ls of mu s i c The two models of musical hierarchy I deal with in the second of the two sections that follow are a somewhat different matter, for these models were first developed to apply to domains other than music. It was only in the early nineteenth century that they were applied to music, and then to two rather different aspects of musical organization. The first model views hierarchy as a matter of control: each level in a hierarchy (with the exception of those at the extremes) controls the nextlower level and is itself controlled by the next-higher level. This model stretches back at least to the Middle Ages and is most often used to account for tonal organization. The second model of hierarchy relies on a more componential approach: the elements of level A of the hierarchy combine to make up individual elements at the next-higher level (level B of the hierarchy); the elements of level B then combine to make up individual elements at the next higher level (level C of the hierarchy), and so on, until the account of structure is exhausted. This model emerged during the seventeenth century and is most often used to explain music’s metr ical structure. When confronted by a maze of mapping like those I have just outlined, mappings that yield contradictor y accounts of quite basic musical mater ials, our inclination may be to throw up our hands and shout the equivalent of “Who cares for you? You’re nothing but a pack of cards!” But problems of musical understanding are rarely so easily dismissed. Instead, we must enter into the mad tea party that is music theory, where music theor ists from different nations and different histor ical periods gather around the table to discuss and dispute musical concepts. If we are to make sense of the conversation there, we need to understand how cross-domain mapping shapes this discourse— indeed, as I suggested in chapter 2, how it makes music theory possible.

two models of musical form There was a certain enviable simplicity to the study of music in the fin de siècle Anglo-Amer ican musical world, due in no small part to its near-complete subjugation to the Ger man musical world.4 Music teachers in Anglo-Amer ican circles were either Ger man or trained in Ger many, the repertoire studied was almost entirely German, and the theoretical models — developed exclusively with respect to German musical practice — had been for mulated by German music theor ists of the nineteenth century. Thus the beginning Anglo-Amer ican music student of the late nineteenth and early twentieth century learned a tradition of musical study that was almost entirely Ger man. This is not to say, however, that the tradition they assimilated was completely unified. Consider, for instance, the account of musical motives offered by Ebenezer Prout, a prominent music educator in England during the late nineteenth century. Having distinguished between phrases (which end with a cadence) and sections (subphrase units that do not necessar ily end with a cadence), Prout makes one further subdivision: Every section contains at least two [metric] accents, and can be separated into smaller parts, containing only one accent each. Such parts are called motives, and cor respond 4. By “German musical world,” I mean the Ger man-speaking countr ies of Europe.

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analysis and theory exactly to the feet in poetry. Here we have what (to bor row a scientific ter m) we may call the “protoplasm”— the germ out of which all music springs. A thorough knowledge of the nature of the motive is therefore indispensable to anyone who would understand the fundamental pr inciples of musical for m.5

Important for Prout’s character ization of a motive are the dynamic context provided by metrical accentuation — he will later define motive as composed of a strongly accented note preceded by at least one unaccented note6 — and the somewhat more abstract notion of a motive as the seed of a musical organism. Rather different is the approach to motive taken some ten years later by Percy Goetschius, born in New Jersey but educated in Stuttgart, where he first taught. Goetschius situates the motive in an explicitly grammatical context: The smallest unit in musical composition is the single tone. The smallest cluster of successive tones (from two to four or five in number) that will convey a definite musical impression, as miniature musical idea, is called a Figure. Assuming the single tone to represent the same unit of expression as a letter of the alphabet, the melodic figure would be defined as the equivalent of a complete (small) word;—pursuing the comparison further, a series of figures constitutes the melodic motive, equivalent to the smallest group of words (a subject with its article and adjective, for example); and two or three motives make a Phrase, equivalent to the complete, though comparatively brief, sentence (subject, predicate, and object).7

In contrast with Prout’s dynamic account of musical for m, Goetschius relies on a highly schematized g rammar of musical elements. So formalized is this g rammar that it ultimately reduces to a matter of counting measures: “Melodic motives differ in length from one to four measures; by far the most common extent, however, is two measures, and the student will do wisely to accept this dimension and analyze accordingly, unless there is unmistakable evidence to the contrary.”8 What we have in these excer pts, then, are two markedly different approaches to musical for m, voiced through character izations of motive.9 Prout’s is the more dynamic: music is likened to some sort of organism, and the motive is the seed from which it spr ings. Goetschius’s approach, by contrast, is rather more static: music is but prose in tones, and the motive is simply the smallest intellig ible syntactic unit.

5. Ebenezer Prout, Musical Form (London: Augener, 1893), 26. 6. Prout, Musical Form, 31. 7. Percy Goetschius, Lessons in Music Form: A Manual of Analysis of All the Structural Factors and Designs Employed in Musical Composition (Bryn Mawr, Penn.: Oliver Ditson, 1904), 19. 8. Goetschius, Lessons in Music Form, 23. 9. Although I have chosen to highlight the differences between Prout’s and Goetschius’s approaches to musical for m, Robert Gjerdingen has reminded me that the two theor ists knew each other’s work and exchanged dedications of their texts. Moreover, not all theor ists within the Anglo-American tradition agreed on the importance of motive. For instance, Stewart Macpherson, whose book on for m supplanted that of Prout and who was mightily suspicious of overly thorough analyses, wrote, “As an example of a too mathematical conception of analysis may be instanced the stress laid by some theor ists upon an arbitrary dissection of the music into certain metr ical fragments called motives, a dissection of which usually conveys little or nothing to which the musical sense can respond.” Macpherson, Form in Music: With Special Reference to the Designs of Instrumental Music (London: Joseph Williams, 1908), 39. A footnote makes clear that in referring to “some other theor ists,” Macpherson actually meant Prout.

competing mode ls of mu s i c However, two related factors complicate these seemingly neat constructions. First, neither Prout nor Goetschius eschews entirely the approach of the other. Prout is perfectly capable of rendering a crushingly static account of musical for m, and Goetschius knows how to enliven his account to make music seem more like an organism than a dr y recitation. Second, both of these models of form originate in mappings between language and music (a mapping more obvious in the excer pt from Goetschius, but evident as well in Prout’s reference to poetic feet). To untangle matters, we need to begin with theor ies of musical for m developed dur ing the Enlightenment. From there we must proceed to explore how these theor ies were subsequently reformulated in the first half of the nineteenth centur y under the influence of political and ideological pressures that transfor med the way music was taught.

Grammar, Rhetor ic, and Musical Form in the Eighteenth Century Mappings between music and language go back at least to the Middle Ages. For instance, the ninth-century Musica enchiriadis opens with an analogy that anticipates Goetschius by over a thousand years: “Just as the elementar y and indivisible constituents of speech (vox articulata) are letters, from which syllables are put together, and these in tur n make up verbs and nouns, and from them is composed the fabric of a complete discourse, so the roots of song (vox canora) are phthongi [musical notes], which are called soni in Latin. The content of all music is ultimately reducible to them.”10 In the eighteenth centur y, mappings between language and music flourished and — as an almost inevitable consequence — became more manifold and more complicated. Enlightenment preoccupations with the or igins of language and the place of music within systems of human communication led to a number of proposals for how language and music did, or did not, relate to one another.11 The continued growth of print culture made it increasingly common for music and language to intersect — as score and text — on the printed page, a phenomenon exploited by author-pr inters such as Samuel Richardson.12 Finally, a growing middle class fueled a demand for music instruction books, and, within these books, mappings between language and music provided a ready frame of reference for the explanation of fundamental musical concepts. During this per iod, two mappings from the domain of language onto the domain of music became particularly important for accounts of musical for m: the first mapped from grammar onto music, the second mapped from rhetor ic onto music.

10. Musica enchiriadis and Scolica enchiriadis, ed. Claude V. Palisca, trans. Raymond Erickson, Music Theory Translation Ser ies (New Haven, Conn.:Yale University Press, 1995), 1. 11. For a discussion centered on eighteenth-century France, see Downing A. Thomas, Music and the Origins of Language: Theories from the French Enlightenment, New Perspectives in Muisic History and Cr iticism (Cambr idge: Cambridge University Press, 1995). 12. Richardson’s insertion of a musical score into the text of a novel is discussed by Janine Barchas in “The Engraved Score in Clarissa: An Intersection of Music, Narrative, and Graphic Design,” EighteenthCentury Life 20 (1996): 1– 20.

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analysis and theory

g rammar and music

Mappings between grammar and music were based on the assumption that music was language-like in its organization — that is, it had structural features analogous to those of language and a nor mative syntax. The mapping also relied on a familiar ity with and respect for grammar acquired through the thorough grounding in the subjects of the Classical tr ivium— rhetoric, grammar, and logic— that was a common feature of early education in the eighteenth century. Just as every verbal construct, whether spoken or wr itten, can be divided up into clauses, sentences, and paragraphs, the thinking went, so can musical works. This was the basis of Johann Mattheson’s account of musical grammar, first proposed in his Kern melodischer Wissenschaft of 1737 and subsequently expanded in his Der vollkommene Capellmeister of 1739.13 Mattheson began his discussion with vocal music, showing how the grammar of music had to be in rapport with that of the text: each of the significant divisions in the text had to be supported by analogous divisions in the music. This led Mattheson to a discussion of what things made for effective musical divisions (typically, cadence was the main articulative event) and how such divisions were graded from the barely noticeable to the emphatic.14 In a subsequent chapter of Der vollkommene Capellmeister, Mattheson argued that knowledge of this sort was even more important for knowing how to wr ite instrumental music. He illustrated his discussion with the minuet shown in example 7.1.15 Mattheson analyzes the whole as a parag raph, made up of two per iods (or Sätzen; mm. 1– 8 and 9 – 16), which are divided into a clause (marked by the colon below m. 4), a subclause (marked by the semicolon below m. 12), and phrases (marked by the commas below mm. 2, 6, and 10). Lacking, however, is any explanation for how these analytical decisions were made — why, for instance, mm. 1– 4 constitute a clause, while mm. 9– 12 constitute a subclause. The reader is left with a clear sense of the importance of grammatical structure to musical works — that grammar is, in fact, a self-evident property of musical works— but with only a few hints as to how the grammatical divisions in music are deter mined. A more complete methodology for analyzing musical grammar was provided some fifteen years later by Joseph Riepel in his Grundregln zur Tonordnung insgemein of 1755 (the second volume of his Anfangsgründe zur musicalischen Setzkunst). Using a thoroughly schematic and comparatively systematic approach to musical organization (wr itten in the dialogue style common in pedagogical treatises of the day), Riepel made explicit connections between grammatical components and musical passages, illustrated through hundreds of examples drawn from or applicable to 13. Johann Mattheson, Kern melodischer Wissenchaft (Hamburg: C. Herold, 1737; repr. Hildesheim: Georg Olms, 1976); idem, Der vollkommene Capellmeister (Hamburg: C. Herold, 1739; repr. Dokumenta musicologica, 1. Reihe, Druckschr iften-Faksimiles, 5, ed. Margarete Reimann [Kassel: Bärenreiter, 1954]). 14. Mattheson, Der vollkommene Capellmeister, 180 – 95; Ernest C Har riss, Johann Mattheson’s Der vollkommene Capellmeister: A Revised Translation with Critical Commentary, Studies in Musicology, 21 (Ann Arbor, Mich.: UMI Research Press, 1981), 380 – 404. 15. Mattheson, Der vollkommene Capellmeister, 223– 25; Harriss, Mattheson’s Der vollkommene Capellmeister, 451– 53. For a discussion and analysis of this passage, in a slightly different context, see Ian Bent, ed., Fugue, Form and Style (vol. 1 of Music Analysis in the Nineteenth Century), Cambridge Readings in the Literature of Music (Cambr idge: Cambridge University Press, 1994), 5– 6.

competing mode ls of mu s i c example 7.1 Minuet analyzed by Johann Mattheson in Der vollkommene Capellmeister, part 2, chap. 13

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Fine

D.C. al fine

∴

∴

11

:

’

6

instrumental music.16 Riepel based his analysis of the grammatical function of a musical passage on har monic structure and on the assumption that subdivision of the phrase into even-numbered units was the nor m in instrumental music. Although his references to the grammatical structure of speech are explicit, they are also relatively few in number. Subphrase units (which Riepel called Einschnitte, and which were usually less than four measures in length) were marked by incomplete harmonic progressions — that is, they ended inconclusively. In contrast, the phrase (the Satz or, more frequently, the Absatz) was a four-bar unit that provided a complete har monic progression: it had a conclusive ending. Each Absatz was further character ized on the basis of whether it ended on tonic, on the dominant, or in some other key.17 By this means, Riepel was able to give an exhaustive (and at times exhausting) account of the different sorts of grammatical structures that might be evinced by music, based on the ways various components could be fit together and modified. Riepel’s approach to musical grammar was adopted by Heinr ich Chr istoph Koch in his Versuch einer Anleitung zur Composition (1782 – 1793), but Koch began his account by returning to the model of speech. After noting the importance of “certain more or less noticeable resting points of the spir it” to those fine arts that attain their goal through speech — namely, poetry and rhetor ic— Koch then draws the connection to music. Speech . . . breaks down into various sentences [Perioden] through the most noticeable of these resting points of the spir it; through the less noticeable the sentence, in turn,

16. Joseph Riepel, Grundregln zur Tonordnung insgemein (vol. 2 of Anfangsgründe zur musicalischen Setzkunst) (Regensburg: Johann Leopold Montag, 1755), 32– 56; idem, Sämtliche Schriften zur Musiktheorie, ed. Thomas Emmer ig,Wiener musikwissenschaftliche Beiträge, 20 (Vienna: Böhlau, 1996), 138 – 62. 17. For further discussion of Riepel’s approach, see Justin London, “Riepel and Absatz: Poetic and Prosaic Aspects of Phrase Structure in 18th-Centur y Theory,” Journal of Musicology 8 (1990): 505 – 19; Nola Reed Knouse, “Joseph Riepel and the Emerg ing Theory of Form in the Eighteenth Centur y,” Current Musicology 4 (1986): 46– 62; and John Walter Hill, “The Logic of Phrase Structure in Joseph Riepel’s Anfangsgründe zur musikalischen Setzkunst, Part 2 (1755),” in Festa musicologica: Essays in Honor of George J. Buelow, ed. Thomas J. Mathiesen and Benito V. Rivera, Festschrift Ser ies, 14 (Stuyvesant, N.Y.: Pendragon Press, 1995), 467– 87.

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analysis and theory breaks down into separate clauses [Sätze] and parts of speech [Redetheile]. Just as in speech, the melody of a composition can be broken up into per iods by means of analogous resting points, and these, again, into single phrases [Sätze] and melodic segments [Theile].18

However, Koch also saw limits to the applicability of mapping from the grammar of speech onto the grammar of music. After a long and thoughtful passage in which he pursues the notion that musical phrases are organized around subjects and predicates as are those of speech, Koch tur ns away from the model. He writes, “I am abandoning this compar ison because, as already mentioned, subject and predicate cannot be differentiated enough in melodic sections. We must content ourselves with learning how to deter mine, through feeling, the presence or absence of resting points of the spir it and the nature of sections with regard to their completeness.”19 As did Riepel, Koch assumes subdivision of the phrase into even-numbered units to be the nor m. He uses har monic structure— specifically, the har mony with which each phrase ends20— to deter mine the divisions of musical grammar. And he builds larger musical structures by modifying and concatenating musical phrases. Mappings between grammar and music of the sort evident in the work of Mattheson, Riepel, and Koch allowed writers in the eighteenth centur y to give detailed accounts of musical organization and to indicate how composers manipulated musical mater ials to create unique musical statements that nonetheless conformed to certain basic syntactic pr incipals.21 The mapping yields a character ization that emphasizes the static rather than the dynamic — what Koch came to call the “mechanical” aspect of music in the introduction to the second volume of his Versuch.22 Each unit of musical grammar can be contemplated and discussed separately,

18. Heinrich Chr istoph Koch, Introductory Essay on Composition: The Mechanical Rules of Melody, Sections 3 and 4, trans. Nancy Kovaleff Baker, Music Theor y Translation Ser ies (New Haven, Conn.: Yale University Press, 1983), 1. The source from which Baker’s translation is drawn is the second volume of Koch’s Versuch einer Anleitung zur Composition (Leipzig: Adam Fr iedrich Böhme, 1787; repr. Hildesheim: Georg Olms, 1969). I have adapted this and the following quotation to restore Koch’s somewhat unwieldy locution “resting points of the spir it” (“Ruhepuncte des Geistes”), which preserves the subjective aspect of determining music-grammatical divisions. 19. Koch, Introductory Essay on Composition, 6, translation adapted. In a note to this passage, Koch explains that he abandoned str ict compar isons between the phrases of speech and melody because his treatise is intended for beg inning musicians who wish to lear n composition, and “these seldom have either grammatical knowledge of speech or familiar ity with that part of logic which explains the different types of phrases and their closures.” 20. Koch wr ites, “The essential difference between an inter nal phrase and a closing phrase depends on nothing more than the essential difference of ending for mulas.” Koch, Introductory Essay on Composition, 7. 21. As noted in chap. 2, it is through mappings such as these that theor ists br ing an integrated system of terms and structural relations to bear on particular problems of musical understanding. In chap. 2, the problems discussed had to do with ways to character ize tonal organization. Here the problems relate to how musical mater ials should be organized to create meaningful utterances. 22. Nancy Kovaleff Baker and Thomas Chr istensen, eds. and trans., Aesthetics and the Art of Musical Composition in the German Enlightenment: Selected Writings of Johann Georg Sulzer and Heinrich Christoph Koch, Cambridge Studies in Music Theor y and Analysis, 7 (Cambridge: Cambridge University Press, 1995), 140.

competing mode ls of mu s i c and each can be fit together with other such units to create a complete statement at the level of a paragraph or higher. The perspective, then, is inherently constructivist: mapping grammar onto music isolates the building blocks of music and describes how they fit together to create coherent structures. The account of musical for m produced by this mapping is one that tends to emphasize complete, free-standing structures, as well as a synoptic view of such structures.23 What is incomplete is ungrammatical; what is ungrammatical is incomplete. This is a view of basic mater ials well suited to pedagogy— mappings from grammar to music are invariably connected with lessons in composition — but one that has little to say about the process of constructing grammatical statements that are both complete and compelling.

rhetoric and music

One of the principal uses of mappings from rhetoric to music dur ing the eighteenth century was to descr ibe how to go about composing music and the laying-out of musical mater ials in particular. Mattheson, in his Das neu-eröffnete Orchestre of 1713, offers the following analysis: “A [musical] composition compr ises three things: Inventio (Erfindung), Elaboratio (Ausarbeitung), [and] Executio (Ausführung or Aufführung), which seem to display a close relationship to oratory or rhetor ic. The last two things can be lear ned; the first has no competent master.”24 Of course, Mattheson is being somewhat disingenuous here, since the three techniques he mentions — and, for that matter, the very term “composition”— are all der ived from the teaching of Classical rhetor ic and were only secondarily applied to music. Twenty-six years later, in Der vollkommene Capellmeister, Mattheson expanded this plan to include a total of five stages: Inventio (Erfindung), Dispositio (Einrichtung), Elaboratio (Ausarbeitung), Decoratio (Schmückung or Zierde), and Executio (Ausführung or Aufführung).25 In this more extensive application of rhetoric to music, Mattheson also drew on the structural categor ies of rhetor ical theory to character ize the parts of a musical work (as distinct from the process of creating the work). These he identified as the Exordium (Eingang), Narratio (Bericht), Propositio (Antrag), Confirmatio (Bekräfftigung), Confutatio (Wiederlegung), and Peroratio (Schluß). Mattheson then used these categor ies to analyze the music of a da capo aria by Benedetto Marcello, but the result was at best a mixed success:

23. As I understand it, this synoptic view of the musical work does not recover what Michel Foucault calls the “simultaneity” of thought: musical works, whether “paragraphs” or “chapters,” must still unfold in the temporal ser ies specified by their grammar. The synoptic function instead reflects the taxonomy of forms basic to grammatical systems. There is an immediacy to such taxonomic units— be they phrases or parag raphs, books or symphonies — that is independent of the time it takes to traverse the individual syntactic components they compr ise. On the simultaneity of thought, see Foucault, The Order of Things: An Archaeology of the Human Sciences (New York:Vintage Books, 1973), 83. 24. “Es gehören sonst zu einen Composition dreyerley: Inventio, (Die Erfindung) Elaboratio, (Die Ausarbeitung) Executio, (Die Ausführung oder Aufführung) welches eine ziemliche nahe Verwandschafft mit der Orator ie oder Rhetor ique (Rede-Kunst) an den Tag legt; Die beyden lezten Stücke können erlernet werden; zum ersten hat sich noch kein tüchtiger Maitre.” Johann Mattheson, Das neu-eröffnete Orchestre (Hamburg: Printed for the author, 1713; repr. Hildesheim: Georg Olms, 1993), 104. 25. Mattheson, Der vollkommene Capellmeister, 235; Harriss, Mattheson’s Der vollkommene Capellmeister, 470.

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analysis and theory the ar ia simply did not provide an adequate target for mappings from the traditional structure of oratory.26 Where Mattheson’s mappings between grammar and music pointed to a fruitful model for character izing musical organization, his proposed mappings between rhetoric and music never flour ished in the same way. One problem was that the structural model of an oration used in Classical rhetor ic was simply too r igid for music— indeed, there was every sign that it was coming to be regarded as too r igid for speech as well.27 Another problem was that the flexibility of musical semantics made it difficult to develop hard and fast rules for what counted as a Propositio, a Confirmatio, or any of the other elements of an oration: it was clear to Mattheson and other theor ists that music had meaning, but just how this meaning cor responded with the figures and processes of Classical rhetor ic proved difficult to specify.28 The account of the process of composition afforded by rhetor ic was given new promise when it was incor porated into the theor y of aesthetics promulgated by Johann Georg Sulzer in his Allgemeine Theorie der schönen Künste, first published in two large volumes in 1771 and 1774. Sulzer drew on Classical rhetor ic to develop a general character ization of the creative process, reflecting his belief that art shared with rhetor ic the goal of moral improvement. According to Sulzer, the artist first discovers the ideas necessary to a work of art through invention. After the ideas have been discovered, the artist then realizes them through a three-stage process: Anlage (layout), Ausführung (realization), and Ausarbeitung (elaboration).29 Of these, the latter two stages are identical with those identified by Mattheson in Das neu-eröffnete Orchestre. Sulzer’s first stage cor responds with the second stage — Dispositio (Einrichtung)— of the expanded plan presented in Der vollkommene Capellmeister. (Of Sulzer’s treatment of Mattheson’s first stage — Inventio — more presently.) The approach to composition outlined by Sulzer, while promising, was also very 26. Mattheson’s analysis is in Der vollkommene Capellmeister, 237– 39 (pp. 472– 76 of the Harriss translation). For discussion, see Mark Evan Bonds, Wordless Rhetoric: Musical Form and the Metaphor of Oration, Studies in the History of Music, 4 (Cambridge, Mass.: Harvard University Press, 1991), 82– 90; and Peter Hoyt, “Review of Mark Evan Bonds, Wordless Rhetoric,” Journal of Music Theory 38 (1994): 127 – 29. 27. For further discussion of the limitations of rhetorical models, see Hoyt, “Review of Wordless Rhetoric,” 130 – 33. 28. The problem is, if anything, more intractable at the level of individual rhetor ical figures, as is evident in the complicated and occasionally redundant system set up by Joachim Bur meister in the early seventeenth century; see Bur meister, Musical Poetics [1606], trans. Benito Rivera, Music Theory Translation Series (New Haven, Conn.:Yale University Press, 1993). For his part, Mattheson attempts no formalization of rhetor ical figures, preferring to descr ibe a few of them, indicate the applicability of many more, and then move on; see Der vollkommene Capellmeister, 243– 44 (pp. 482– 84 of the Harriss translation). Although locating the specifics of rhetor ical structure in musical discourse is challenging, the importance of rhetor ic for all manner of thought and expression — even beyond the eighteenth centur y— should not be underestimated. For a discussion of the importance of rhetor ic in scientific discourse, for instance, see Jeanne Fahnestock’s recent Rhetorical Figures in Science (New York: Oxford University Press, 1999). 29. My summary of Sulzer’s aesthetic theory and translation of the Ger man ter ms for the stages in the compositional process are taken from Thomas Chr istensen’s introduction to Sulzer’s writings in Baker and Chr istensen, Aesthetics and the Art of Musical Composition, 3– 24.

competing mode ls of mu s i c abstract, and it lacked specifics where music was concer ned. These were supplied by Koch in the second and third volumes of his Versuch, in which he endeavored to show how Sulzer’s three-stage process could be implemented with musical mater ials.30 Where Sulzer was vague, having attempted to give an account of composition adequate for all the fine arts, Koch was specific, providing a detailed account of just what was involved at each stage of the compositional process, which he illustrated with an analysis of an ar ia from Carl Heinr ich Graun’s highly popular cantata Der Tod Jesu of 1755.31 Making Sulzer’s framework for the compositional process specific for music also provided a further justification for the technical language of musical grammar developed by Koch, for Koch believed it was by the conscious manipulation of this grammar that the beg inning composer could create an aesthetically satisfying final work. Mappings between rhetor ic and music allowed music theor ists like Mattheson and Koch to descr ibe the compositional process in ter ms of distinct stages, which made it possible to give specific advice about how the novice composer should proceed along the way. Inasmuch as this process was construed as analogous to that undertaken in other art forms, music was placed on a parallel with sister arts to which it had for merly been but a poor cousin. Mapping from rhetor ic to music also allowed music — more specifically, untexted music — to be regarded as a medium with persuasive powers similar to that of orator y. Although the trope of music as oratory was common at least since the Renaissance, preoccupations with the relationship between language and music dur ing the Enlightenment revivified the analogy and put into relief the dynamic aspect of music: here was a type of oratory that not only unfolded over time but also was conducted in the pure language of tones — what Mattheson called Klang-Rede (sound-speech). The view of the compositional process and its product afforded by mapping from rhetor ic to music also highlighted the essential mystery of musical creation. This is plainest in the quotation from Mattheson’s Das neu-eröffnete Orchestre — “invention is the process that knows no competent master”— but it is also evident in Sulzer’s discussion of invention in the Allgemeine Theorie and in Koch’s adaptation of that discussion in his Versuch. At first Sulzer maintains that invention is a capacity that can be improved through diligent and careful practice: “The power of invention, like the power of judgment, is a natural and inbor n faculty that all men possess in proportion to their own genius. And just as one may turn to reason to aid one’s power of judgment, so can one’s talent for invention be augmented, in as much as it might be treated, like logic, as a part of philosophy.”32 Sulzer’s initial suggestion for accomplishing this augmentation is to tur n to rhetor ic, urging the artist to exploit the rules and methodology that rhetor icians had developed for the express

30. Koch’s realization of Sulzer’s plan is discussed in Ian Bent, “The ‘Compositional Process’ in Music Theory 1713 – 1850,” Music Analysis 3 (1984): 29– 55; and by Nancy Kovaleff Baker in her introduction to Koch’s wr itings in Baker and Chr istensen, Aesthetics and the Art of Musical Composition, 111– 43. Koch was apparently unaware of Sulzer’s work when he prepared his first volume, published in 1782. 31. Koch’s analysis of Graun’s ar ia can be found in translation in Baker and Chr istensen, Aesthetics and the Art of Musical Composition, 163– 76. 32. Baker and Chr istensen, Aesthetics and the Art of Musical Composition, 56.

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analysis and theory purpose of discovering useful ideas. But as attractive as such an orderly process is for the ever-moralizing Sulzer, he ultimately realizes that it is not the most productive where invention is concer ned. Better to be constantly occupied with one’s art, for one will surely stumble upon good ideas this way. As Sulzer ruefully admits, The most important inventions probably do not ar ise through the first deductive manner descr ibed above, but rather by the second way: the main subject appears only dimly at first to the artist; he recognizes its importance and takes time to think about its contents so it can be set in its proper light. This is how a famous composer told me he worked. He had more than once saved mater ial that he heard by chance to use as a theme or subject for a composition. He never could have invented anything as good had he decided ahead of time to look for something having the identical character of expression.33

In this Koch agrees, writing, “Theory will never be able to invent a truly effective means to indicate just how the beg inning composer should contr ive that a beautiful melody ar ises in his soul.”34 However, once inspiration str ikes and invention has commenced, the composer must work with haste to capture the whole in a plan of the sort Koch developed for Graun’s aria. The plan in place, the composer may then proceed to the more mechanical side of musical composition. The mystery surrounding invention, together with the focus on purely musical meaning afforded by mapping the structures of rhetor ic onto music, suggests an independence for music adumbrated by Koch’s reflections on the value of theory. Music, now more than simply mater ials to be manipulated, is something that ar ises in the soul of the composer. Although the full flowering of the idea that music was an autonomous medium would have to wait until the tur n into the nineteenth century, we can see its seeds in eighteenth-centur y mappings from rhetor ic to music. These provided a view of music as a powerful and highly dynamic medium with the potential to shape the thought of those who listened to it.35

g rammar, rhetoric, and musical form

It has been traditional and convenient to think of grammar and rhetor ic as separate subdomains of language. Of the two, grammar is the simpler and more basic, necessar y for proper communication but not the stuff to tur n heads. Grammar, reckoned this way, is thus pure syntax, a careful if static ordering of linguistic units. By compar ison, rhetor ic is more complex and subtle, persuasive because it has true semantic force. As the means by which the passions can be moved, it is truly dynamic.36 Nonetheless, the 33. Baker and Chr istensen, Aesthetics and the Art of Musical Composition, 61. 34. Baker and Chr istensen, Aesthetics and the Art of Musical Composition, 186. 35. For a discussion of the emergence of the idea that music was an autonomous art form, see Lydia Goehr, The Imaginary Museum of Musical Works: An Essay in the Philosophy of Music (Oxford: Clarendon Press, 1992), chap. 6; and Bellamy Hosler, Changing Aesthetic Views of Instrumental Music in 18th-Century Germany, Studies in Musicology, 42 (Ann Arbor, Mich.: UMI Research Press, 1981). 36. When Michel Foucault sought to character ize the distinct functions of rhetor ic and grammar, he seemed rather deliberately to invert this traditional perspective, arguing that rhetor ic is spatial and that grammar distr ibutes that spatiality in time — that is, rhetor ic is static and grammar is dynamic (Foucault, The Order of Things, 84). However, “spatial” here refers to the simultaneity of thought — to its essential and ongoing polyphony. Grammar distr ibutes this spatiality in time only by freezing fragments of it so

competing mode ls of mu s i c distinctions between the two are hardly as clear-cut as this traditional perspective would have it, and nowhere is this more evident than when they are mapped onto music. Returning briefly to Riepel, his classification of cadence types provides a case in point. In distinguishing between an Absatz that ends with a “garbled cadence” (verstümmelter Schluß ) and one that ends with a “complete cadence” (vollständiger Schluß ), Riepel uses the rhetor ical ter m “enthymeme” for the first, and “syllogismus” for the second.37 Descending momentar ily into the labyrinth of rhetorical ter ms, we can discover that enthymeme refers to an incomplete syllogism, one in which either the major or minor premise of the syllogism is left implied. A syllogismus, by contrast, calls on the audience to draw an obvious conclusion, the major and minor premise having been stated.38 Although the mapping between these two terms and the musical phenomena to which Riepel would have them apply is less than perfect, what is important is the implication that each of the grammatical components is imbued with semantic value — syntax has its semantic function. Indeed, as I argued in chapter 4, the manipulation of musical syntax is one of the principal means by which musical semantics is created. Careful attention to the grain and texture of discourse about music is thus necessary to deter mine which of these metaphor ical mappings is used to structure a given theory of music. Generally speaking, eighteenth-century writers used grammar to emphasize things that do not change in music — suitably defined, an Einschnitt is always an Einschnitt, an Absatz always an Absatz. The same wr iters used rhetor ic to emphasize how music functions in time, either in the challenges it presents a composer attempting to deploy musical mater ials or in the reaction of a listener persuaded by a musical argument. Grammar gave a view of musical for m that was static, and rhetor ic gave a view of musical for m that was dynamic. Significant, however, is the context relative to which these character izations were made. As the dynamic view offered by rhetor ic began to be more important for those who thought about music, and as the cultural context for thinking about music changed, mappings from language began to give way to other possibilities for conceptualizing music.

Formal Theory in the Nineteenth Century Over the course of the nineteenth centur y, the two basic models of musical for m that emerged in the eighteenth century remained in place. Musical works could be regarded as manufactured things that compr ised discrete — and inherently static — components, or as instances of quasi-abstract communication that unfolded dynamically in time. However, explicit mappings from language to music faded as they

that they can be ordered, much as musical mater ials, isolated from their becoming, are transfor med into basic building blocks for the beginning composer. 37. Riepel, Grundregln zur Tonordnung insgemein, 59; idem, Sämtliche Schriften zur Musiktheorie, 153. 38. These definitions are drawn from Gideon Burton’s online Silva Rhetoricæ, at http:/humanities. byu.edu/rhetor ic/silva.htm.

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analysis and theory were absorbed into musical nomenclature or replaced by other mappings that served a similar pur pose. Instrumental in this process were the context within which music was taught and the intellectual framework relative to which music was conceptualized. Beginning in the final years of the eighteenth centur y, music instruction was taken over by institutions concer ned as much with the advancement of the state as with education. In consequence, the move toward a complete and comprehensive curriculum that arose in furtherance of the for mer objective brought with it the development of integrated courses of study that employed both static and dynamic accounts of music. At around the same time, music came to be thought of in organicist ter ms, and, as a result, even the most basic and isolated of musical materials were imbued with dynamic character istics. Hence, the conceptual metaphors for musical for m established in the eighteenth century— form as static, or form as dynamic — remained in place, but they were activated by a number of different linguistic metaphors.

the paris conservatoire and the berlin university

During the eighteenth century, music education in the French- and Ger man-speaking countr ies was car ried out in a diffuse manner. Students typically studied with a local music master or at a school associated with a church, and there were few if any efforts at centralized music instruction. As a result of various political upheavals, this situation began to change in the late eighteenth centur y, and music education, together with instruction in other topics, began to be more closely controlled by the state. The circumstances of music education changed most rapidly in France. After the 1789 revolution, numerous educational reforms were proposed, focused largely on efforts to create a utilitar ian educational system and to promote deductive reasoning for the arts and sciences; some of these were at least partially enacted.39 As a consequence of the diminishing role of the church after the revolution, the system of maîtrises — the music schools associated with the major cathedrals — collapsed, leaving two principal options for music instruction: the School of the National Guard (a product of the revolution) and the Old Regime’s School of Singing (founded in 1784 with the intent of providing a reliable supply of singers for the Académie Royale de Musique, known familiarly as the Opéra). To realize the goal of conserving a French national music that was free from the influence of Italy and Germany, the Republic in 1795 consolidated the faculty and power of these two schools and for med the Conservatoire National de Musique et de Déclamation. The institution, as or iginally envisioned, was to provide free training for musicians (especially those destined for militar y service or the Opéra). It was also to serve as official arbiter of music used for state functions or music that was to be sanctioned by the state. The Conservatoire also became the source of the first national music theory, for its or iginal charter included the provision that the texts used therein would be wr itten by its faculty. Because of the political power that eventually 39. A thorough account of changes in music education after the French revolution is given in Cynthia M. Geselle, “The Institutionalization of Music Theory in France: 1764– 1802” (Ph.D. diss., Princeton University, 1989), 235– 306.

competing mode ls of mu s i c accrued to the Conservatoire, the texts that it adopted became the core of a national music cur riculum. The first texts adopted by the Conservatoire were models of practicality, simplifying those notions that were deemed unnecessar ily complex and str iving toward uniformity of method. As time went on, however, the faculty went beyond the highly utilitar ian education envisioned by the or iginal reformers and developed a sophisticated pedagogy that embraced virtually all aspects of musical thought. As an example, the pedagogy created by Antoine Reicha, who was appointed professor of counter point at the Conservatoire in 1817, extended from his Traité de mélodie of 1814 through the Cours de composition musicale (?1816 – 18) to the Traité de haute composition musicale of 1824 – 26.40 In these texts, Reicha, with the zeal of a geometer and the passion of an artist, strove to provide a systematic approach that extended from the most basic aspects of musical structure— expressed through a grammar of music analogous to that of Koch— to a full account of the largest for ms. Thus was institutionalized an approach to music that began with isolated components and culminated in large for ms conceived as dramas enacted in sound.41 Within this course of study, musical for m was presented as both static and dynamic. In the early stages of the pedagogical plan, form was static, consisting of various components that could be assembled to create musical compositions. In the later stages, it became thoroughly dynamic, as this perspective yielded to one that accommodated, even if it did not completely sanction, the artistic license necessary to create works such as Mozart’s Overture for the Marriage of Figaro.42 Changes to the Ger man universities were not as sudden as those that led to the formation of the Conservatoire, but they were motivated by pragmatic and political concer ns similar to those that shaped France’s new educational system. There had developed in Ger many over the course of the eighteenth centur y the perception that a university education served no useful pur pose. This notion, together with efficiencies imposed by French rule and the growing financial burden presented by universities whose traditional sources of financial support had begun to erode, contributed to the disappearance of over half the Ger man universities dur ing the Napoleonic era.43 As a way of counter ing this general disintegration, a delegation of professors from the University of Halle, which had been suspended by Napoleon in 1806, approached King Fr iedrich Wilhelm III in the late summer of 1807 and asked 40. Reicha’s Cours de composition musicale ultimately replaced Charles-Simon Catel’s Traité d’harmonie, which had been approved by the General Assembly of the Conservatoire in 1801 as the Conservatoire’s main har mony text. 41. For a discussion of affinities between Reicha’s account of the grande coupe binaire (now conventionally called sonata for m) and drama, see Peter Hoyt, “The Concept of Développement in the Early Nineteenth Centur y,” in Music Theory in the Age of Romanticism, ed. Ian Bent (Cambr idge: Cambridge University Press, 1996), 141– 62. 42. For a discussion of the range of Reicha’s analytical perspective, which included the Overture from the Marriage of Figaro, see Ian Bent’s commentar y on one of the analyses from Reicha’s Traité de haute composition musicale, in Music Analysis in the Nineteenth Century, 1: 152– 53. 43. Theodore Ziolkowski, German Romanticism and Its Institutions (Princeton, N.J.: Princeton University Press, 1990), 228. My account of the history of German universities owes much to chap. 5 of this book, which is given over to a consideration of the institution of the university dur ing the time of German Romanticism.

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analysis and theory that their university be reestablished in Berlin. The king was apparently receptive to the idea and is reported to have responded that “the state must replace through intellectual powers what it has lost in the way of physical powers.”44 Loosely modeled on the ideals associated with the University of Jena when Fr iedrich Schiller, Johann Gottlieb Fichte, and Fr iedrich von Schelling lectured there, the University of Berlin was conceived as an institution combining faculties in the sciences, medicine, and the humanities. It was to be unified by a central faculty of philosophy professing an “encyclopedic” approach to knowledge. The university for mally opened in October 1810 with a faculty that included Fichte and Fr iedrich Schleiermacher. By the time the composer and music theor ist Adolph Ber nhard Marx was offered a chair at Berlin in 1830, much of the spirit of the Romantic university had faded to a memory.45 What remained were a faculty that included Hegel in its ranks (who began lectur ing at Berlin in 1818) and the notion that the university was an institution by, of, and for the state. Marx’s encyclopedic approach to music theory resembled Reicha’s sweeping attempt to provide a complete account of musical knowledge in his three treatises. In 1837, Marx published his four-volume Die Lehre von der musikalischen Komposition, praktisch-theoretisch. This comprehensive tract, which went through six full or partial editions dur ing Marx’s lifetime, presented a graduated course of study that began with the simplest of musical mater ials and forms and proceeded to the most complex.46 However, where the pedagogy of Reicha’s treatises was conceptualized around the models of language and drama, Marx adopted a different model, one closely associated with the same Romantic idealism that had shaped the structure of the University of Berlin. This was the model of organicism.

organicism

As has often been noted, organicist models, which map features from principally vegetative domains onto inorganic or artificial domains, flourished among early Romantic philosophers and wr iters.47 The model was, however, also in use dur ing the late eighteenth century. Our friend Sulzer, as part of his more practical remarks on invention, advises the artist faced with an intractable situation to put the work to one side for a short while. Gradually, solutions will present themselves, until a way is found where none was thought to exist.

44. Ziolkowski, German Romanticism, 287. 45. An account of Marx’s place at the University of Berlin can be had in Scott Bur nham’s introduction to Adolph Ber nhard Marx, Musical Form in the Age of Beethoven: Selected Writings on Theory and Method, ed. and trans. Scott G. Burnham, Cambridge Studies in Music Theor y and Analysis, 12 (Cambridge: Cambridge University Press, 1997), 5– 6. 46. For overviews of the content of Marx’s Die Lehre and discussions of the educational context within which it was embedded, see Burnham’s introduction to Musical Form in the Age of Beethoven, 7– 11; and Mark Spitzer, “Marx’s ‘Lehre’ and the Science of Education: Towards the Recuperation of Music Pedagogy,” Music and Letters 79 (1998): 489 – 526. 47. A thorough account of the role of organicist models in theor ies of invention dur ing the eighteenth and nineteenth centur ies (framed in ter ms of the memorable phrase “vegetable genius”) can be found in Meyer Howard Abrams, The Mirror and the Lamp: Romantic Theory and the Critical Tradition (Oxford: Oxford University Press, 1953), 198 – 225.

competing mode ls of mu s i c It is one of many remarkable secrets of psychology that apparently clear thoughts can, when one tur ns to them for deeper contemplation, refuse to be developed or comprehended in a clear way. But when they are left alone they will by themselves grow in greater clar ity, much as that per iod in which plants ger minate unnoticed and all at once burst into full bloom. Some concepts will gestate little by little in our mind, so to speak, and extract themselves from the mass of obscure ideas into the clear light. Every artist must rely upon such fortunate moments of genius, and if he cannot always find what he diligently seeks, he must await with patience that moment when his thoughts r ipen.48

Here the mystery of invention, which Sulzer also connected with rhetor ic, is explained in ter ms of an organicist model: ideas are seeds, and, given time and a little care, they will put forth complete and fully articulated intellectual constructs — the flowers of invention — that could never be produced by more mechanical means. The perspective evident in Sulzer’s account of unconscious psychology had a profound effect among Ger man thinkers of the late eighteenth and early nineteenth centur ies. These proponents of “nature philosophy,” including Fichte, Schelling, Jean Paul Richter, and August Wilhelm Schlegel, embraced the newly emerging biological sciences, finding in them a source of concepts that could replace those derived from Cartesian or Newtonian mechanics. It was this model that Marx absorbed and adapted for the character ization of musical for m. In the first volume of Die Lehre, after a few preliminar ies, Marx begins the journey that would culminate in a consideration of the most exalted compositional forms of his day with a br ief contemplation of the relationship between a major scale and its tonic. He observes that no note within the scale provides the sense of repose that the tonic does: pausing on any other note is unsatisfying and demands further motion. This observation leads Marx to a pr inciple basic to all music, the main ter ms of which are placed in typographical relief on the page: In this we have found the opposition that thoroughly per meates all of music: Rest and Motion Tonic and Scale.49 Marx extended this opposition to apply to all aspects of musical for m, formulated as the dynamic impulse rest — motion — rest. For Marx, this basic patter n is truly comprehensive: it governs the modest four-measure phrase, as well as the entire expanse of sonata for m.50

48. Baker and Chr istensen, Aesthetics and the Art of Musical Composition, 63. 49. “Hierin haben wir einen durch die ganze Tonkunst wirksam hindurchgehende Gegensatz, Ruhe und Bewegung Tonika und Tonleiter gefunden.” Adolph Bernhard Marx, Die Lehre von der musikalischen Komposition, praktisch-theoretisch, 4th ed. (Leipzig: Breitkopf and Härtel, 1841– 47), 1: 27. 50. This character ization is from Bur nham’s introduction to Marx, Musical Form in the Age of Beethoven, 9.

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analysis and theory It was in locating a source for this impulse that Marx tur ned to an organicist perspective that resonated not only with his era but also with the character ization of invention that had been offered by Sulzer some sixty-five years earlier. However, where for Sulzer the idea is the seed, for Marx it is the motive: “The motive is the primal configuration [Urgestalt] of everything musical, just as the ger minal vesicle, that membranous sac filled with some fluid element (or perhaps with solid bodies), is the pr imal configuration of everything organic — the true primal plant or pr imal animal. The motive, this conjunction of two tones or some other unities, simply is.”51 Marx’s mapping from the organic domain to the musical domain makes possible an account of form that extends from little more than a pair of notes to entire symphonies. Evident throughout is an approach to musical for m that is not only dynamic (through the progression rest — motion — rest ) but also motivated by the forces latent within the most basic of musical mater ials. According to Marx, the motive, as the essential organic entity, offers something that can connect with the composer’s spirit. Should the spir it adopt the motive, the composer’s intellect will then come into play, shaping the motive to create works of art.52 The organicist perspective that Marx employs thus serves as a way to character ize the dynamic aspect of musical for m and as a launching point for the pedagogy of composition. It also fulfills the promise of eighteenth-centur y theor ists who first suggested that music was an independent domain of meaning and expression: in the organicist perspective of the early nineteenth centur y, the fully autonomous work of music is born.53 As heady as was the intellectual environment associated with the organicist perspective basic to his conception of form, Marx’s Die Lehre was, as its full title announced, both theoretical and practical. In his discussion of the basic elements of musical for m, Marx notes a certain confusion regarding the notion of a per iod, which is for med from two fundamental elements (the Gang and the Satz) derived from the motive: “If, in my compositional method, I associated the per iod with the fundamental for ms, it was only for reasons of method, in order to keep this important and ubiquitously hard-working for m constantly before the student’s eyes from the very beginning.”54 Marx’s pedagogy, shaped by the practical exigencies of a system of education intended to work the will of the state, had its static building blocks, as well as its dynamic idealism. Although Marx could always trace these building blocks back to their organic or igins, they nonetheless represented basic components of a student’s education and, at least for the beg inner, of the musical work. 51. Marx, Musical Form in the Age of Beethoven, 66. This passage is from Marx’s 1856 essay “Form in Music.” 52. Marx, Musical Form in the Age of Beethoven, 66– 67. 53. Although my inter pretation of the or igin of the fully autonomous work of music is somewhat different from that of Lydia Goehr, this is due mostly to the somewhat different focus of my approach. I am concer ned here not simply with the idea of a fully autonomous work but with the complex of ideas represented by organicism that allowed music theor ists to articulate the notion of an autonomous work on both a practical and a theoretical level. Goehr’s interpretation can be found in The Imaginary Museum of Musical Works, 159– 75. 54. Marx, Musical Form in the Age of Beethoven, 68.

competing mode ls of mu s i c That the high abstraction of Marx’s theory caused problems, at least for some theorists, is suggested by the approach to motive taken by Hugo Riemann. Riemann, as editor of the ninth edition of Marx’s Die Lehre (which appeared in 1887), was well acquainted with Marx’s conception of a motive. Nonetheless, in his MusikLexikon of 1882, Riemann began his definition of a motive by mapping from yet another domain: “Motive means in music, as it does in architecture, the most basic character istic parts of an artistic structure.”55 Riemann goes on to distinguish between rhythmic motives, melodic motives, and har monic motives, all conceived in architectural ter ms. Although the dynamic impulse basic to Marx’s conception of motive would appear to have vanished, in other of his works it is evident that Riemann has simply transfer red it to metr ic structure, which he construed as having, as its essence, the impulse upbeat-downbeat.56 This construal gave Riemann a way to represent the musical dynamism that Marx had developed through an organicist metaphysics in more concrete ter ms. To the extent that the student or reader understands the basic exper ience of musical rhythm, so will he or she understand the dynamic impulse basic to music.

models of musical form

To all appearances, Ebenezer Prout and Percy Goetschius are a bit like Alice and the Mad Hatter (although I shall not venture to say which theor ist takes which role), seeming to talk about the same thing but doing so in very different ter ms. But where Alice and the Hatter are engaged with the elusive topic of Time, Prout and Goetschius are dealing with the rather more humble matter of Motive. And where the Hatter is as surely a denizen of Wonderland as Alice is not, Prout and Goetschius draw their ideas about motive and form from the same pool of German music scholarship. As we can now see, Prout’s approach is infor med by the work of Marx and Riemann: he conceives of motive in ter ms of both metr ical accentuation and organicism, although in the end it is the for mer that is foregrounded in his theory while the latter remains safely in the backg round. Goetschius, in contrast, conceives of motive in almost exclusively grammatical ter ms. His approach resembles, first and foremost, that of Reicha (whose three treatises were translated into Ger man by Carl Czerny and published in a four-volume French-Ger man bilingual edition in 1832). To a lesser extent, it resembles that of Koch (whose work was not as widely known in the nineteenth centur y). Thus, Goetschius’s method is shaped not only by a grammatical approach to musical for m but also by a pedagogy that was thoroughly pragmatic. Just as Reicha’s theory of form was part of a larger program of complete instruction in music for a nation intent on building its musical identity, so Goetschius’s manual was part of a ser ies of texts intended to fulfill the same function in the New World. Beyond being able to sort out the lineages of Prout’s and Goetschius’s ideas 55. “Motive nennt man in der Musik wie in der Architektur die letzten charakter istischen Glieder eines Kunstgebildes.” Hugo Riemann, Musik-Lexikon (Leipzig: Verlag des Bibliographischen Instituts, 1882), 605. 56. Hugo Riemann, System der musikalischen Rhythmik und Metrik (Leipzig: Breitkopf and Härtel, 1903), 13– 18.

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analysis and theory about motive and for m, however, we now also have a better grasp on the different sorts of conceptual work done by the mappings they employ. Mappings that yield a static account of musical for m put into relief the explicitly conceptual side of music: they rely on our ability to isolate musical events or ser ies of musical events and put them into categor ies. Members of the categor ies can then be compared with one another, as can the categor ies themselves. The view that results is of music as mater ial that can be shaped and manipulated, whose meaning is neatly contained in discrete packages. Mappings that yield a dynamic account of musical for m put into relief the exper iential side of music: music as something to be lived through, which may move us or not, but which in all cases resists packaging into neat conceptual containers. Here meaning is at best only imperfectly contained and is in constant danger of overflowing the crude boundar ies of ontological necessity. As the examples drawn from the ways musicians character ized for m in the eighteenth and nineteenth centur ies show, the cross-domain mappings we use in our theories of music are more than simple cur iosities of language, for these mappings have everything to do with our understanding of how music is organized, along with what counts as music in the first place.

two models of musical hierarchy As I attempted to show in the preceding pages, descriptions of musical for m have occasioned a number of cross-domain mappings, operating on both the specific and generic level. The situation with musical hierarchy is somewhat different, in part because hierarchy was not deemed an attr ibute of musical works as such but was instead used to character ize the organization of musical mater ials. Consequently, explicit discussions of hierarchy rarely appear in accounts of works of music but instead for m the context for those accounts. As an example, let us consider three contemporary analyses of the same passage: the first eight measures of the theme from the opening movement of Mozart’s Piano Sonata in A major K. 331. All three analyses deal with the rhythmic structure of the passage (the score appears in ex. 7.2). example 7.2 mm. 1– 8

W. A. Mozart, Piano Sonata in A major K. 331, first movement, theme,

Andante grazioso

5

competing mode ls of mu s i c Edward Cone’s analysis of the theme appeared in his Musical Form and Musical Performance of 1968. The analysis comes just after the introduction of a str iking metaphor for the melodic and har monic shape of a musical phrase: Cone likens the shape of a phrase to a game of catch: If I throw a ball and you catch it, the completed action must consist of three parts: the throw, the transit, and the catch. There are, so to speak, two fixed points: the initiation of the energy and the goal toward which it is directed; the time and distance between them are spanned by the moving ball. In the same way, the typical musical phrase consists of an initial downbeat (/), a period of motion ( ¯ ), and a point of arrival marked by a cadential downbeat (\).57

This metaphor then provides the framework for his analysis of the rhythm of Mozart’s theme, a portion of which is given in example 7.3. Cone rejects a simple alternation of strong and weak measures of the sort posited by Riemann on the basis of harmony. Cone asserts, rather, that the first and fifth measures of the period should be considered strong because of the fir m statement of tonic. The fourth and eighth measures should also be deemed strong because of the emphasis provided by the cadences. A consideration of the motivic structure of the per iod enables Cone to refine this analysis. The first phrase consists of two individual sequential measures followed by a two-measure unit. The shape of the two-measure unit duplicates the shape of the phrase in miniature: it consists of two half-measure units followed by a full measure. As we see in example 7.3, the internal dynamic of the two-measure unit is the same as that of the complete phrase. The second phrase begins with the same sequential measures as the first, but in m. 7 the compression that prepares the closing cadence br ings the r ise from A4 to CS5 into prominence. Cone’s hearing of this rise as a third member of the sequence prompts him to assign it the same rhythmic symbol as the second member of the sequence, heard in m. 6.Voice-leading concerns and the forward energy of the sforzando cause Cone to group the final eighth note of m. 7 with the cadential mater ial of m. 8; this constitutes the closing downbeat. Although Leonard Meyer’s analysis of this theme appeared after Cone’s (he presented it first in one of the Ernest Bloch lectures he gave at the University of California at Berkeley in 1971), his methodology is essentially the same as that which he had developed with Grosvenor Cooper over a decade earlier. Cooper and Meyer understood rhythmic structure to be perceived as “an organic process in which smaller rhythmic motives, while possessing a shape and structure of their own, also function as integral parts of a larger rhythmic organization.”58 Rhythmic relationships are analyzed as patter ns of beats, in which a stable accent and one or more weak beats are grouped together in different ways; these low-level, foreground patter ns combine with one another in various ways to for m more extended rhythmic groupings. In this way the musical surface gives rise to a hierarchy of rhythmic groupings.59 57. Edward T. Cone, Musical Form and Musical Performance (New York:W.W. Norton, 1968), 26– 27. 58. Grosvenor W. Cooper and Leonard B. Meyer, The Rhythmic Structure of Music (Chicago: University of Chicago Press, 1960), 2. 59. Leonard B. Meyer, Explaining Music: Essays and Explorations (Berkeley: University of California Press, 1973; repr. Chicago: University of Chicago Press, 1978), 27– 28. Meyer’s Bloch Lectures of 1971 form the basis for Explaining Music.

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analysis and theory example 7.3 Edward Cone’s analysis of the opening theme of Mozart’s Piano Sonata K. 331, mm. 1– 8

I

I

V

Meyer’s analysis of the opening per iod of Mozart’s theme is given in example 7.4. The first level of the analysis starts at the half-measure level of the music, impor- patterns of the first two measures of each phrase do tant for Meyer because the Ωdçç much to deter mine the grouping and accentual patter n of the complete bar. In mm. 3 and 4, Meyer’s analysis on level 2 cor responds closely with Cone’s reading: although the symbols are slightly different (Meyer’s indication for a retrospectively weak accent replacing Cone’s symbol for an initial downbeat), on this level as well as the third and fourth, the analyses for the most part agree. The main difference between the two is that Cone starts his analysis at what for Meyer is the third level of a rhythmic hierarchy. In his article “The Theory and Analysis of Tonal Rhythm” (1978), Robert Morgan noted that, although both Cone’s and Meyer’s work reflected the influence of Schenker’s theory of tonal music, their analyses of Mozart’s theme were still beholden to certain aspects of metrical dogma. For his part, Morgan proposed considering the theme from a more consistently Schenkerian viewpoint. Morgan noted that Schenker’s theory supplied a method for locating points at which structural motions or iginate and ter minate; his idea was to cor relate these points of structural origin and ter mination with the points of principal accent through which the larger rhythm of a passage is regulated. In Morgan’s analysis, the first phrase of the theme

competing mode ls of mu s i c example 7.4 Leonard B. Meyer’s analysis of the opening theme of Mozart’s Piano Sonata K. 331, mm. 1– 8 A antecedent

a m

m'

n p

Andante grazioso

p'

q

1. 2. 3. 4.

consequent m

a' m'

n'

5

is governed by the overall motion from CS5 and A3, in m. 1, to B4 and E3 in m. 4 (see ex. 7.5, level 3). This overall motion is articulated on the next level (level 2 of ex. 7.5) by a motion down to A4 and FS3 in m. 3. Although the A could be seen as the completion of a third span from CS5, the bass FS3 and the acceleration away from A4 to B4 on the second beat of m. 3 prevent closure. Up to this point, Morgan’s analysis agrees, in most respects, with the analyses by Cone and Meyer. Morgan does not, however, believe the first beat of m. 4 should be heard as accented relative to the second beat. The acceleration of m. 3 continues into m. 4, in his view, carrying the music forward to the ar rival of the bass on the dominant on the second beat. This ar rival, according to Morgan’s analysis, serves as the rhythmic goal and closing accent of the phrase. From Morgan’s perspective, then, the rhythm of this phrase is not a matter of strong and weak beats or strong and weak measures; it is created rather by an articulated tonal process that moves between the two points defined by the outer-voice frame.60 The acceleration in the first phrase is answered by an even greater acceleration 60. Robert P. Morgan, “The Theor y and Analysis of Tonal Rhythm,” Musical Quarterly 64 (1978): 446.

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analysis and theory example 7.5 Robert Morgan’s analysis of the opening theme of Mozart’s Piano Sonata K. 331, mm. 1– 8

1

2

3

in the second, for the consequent phrase must go through the dominant to ar rive on the tonic. That ar rival gives a different character to the closing accent of the second phrase; for Morgan, it is the difference in character between the two closing accents, and not some analogy to two large beats, that is responsible for the upbeatdownbeat effect created by the pair ing of antecedent and consequent. Implicit in this analysis is the notion that accent refers to a point of emphasis, which also leads Morgan to reject Cone’s and Meyer’s reading of the rhythm of mm. 3 and 4 as a diminution of the overall rhythm of mm. 1 through 4. If mm. 3 and 4 supply the downbeat for mm. 1 and 2, they must represent an ar rival, but in fact the point of arrival occurs only at the end of the unit. Morgan does not believe m. 3 can simultaneously be both an ar rival and a departure. Although these three analyses converge on a number of points, their divergences reflect two different models of musical hierarchy. The first model, which gives r ise to what I call chain-of-being hierarchies, does a good job of capturing the har monic and scale-degree dependencies typical of the har monic organization of instrumental music of the late eighteenth centur y. The second model, which gives rise to what I call atomistic hierarchies, does a good job of capturing the regularity and nesting of accentual patter ns typical of musical meter dur ing the same per iod. Because both models are associated with what appears to be a common set of structural relations — called “hierarchy”—we might be misled into thinking that they are simply variations of each other. Such is not the case, however, for these models developed at different times in history, and with reference to different domains. These differences are reflected in the structure of the models and also in the ways they have been applied to music.

competing mode ls of mu s i c Histor ical Models of Hierarchical Organization The principal mark of chain-of-being hierarchies is a conception of the universe as a precisely ar ranged system of interdependent levels or degrees of existence extending from a Supreme Being down to the lowliest organism. Although this concept is part of an incredibly rich collection of ideas — one wr iter has suggested that the history of chain-of-being hierarchies is, in reality, a history of Occidental thought61 — only a few central aspects need concer n us here. The ingredients for this complex of ideas came from Plato and Aristotle; Aristotle’s connection of “powers of the soul” with levels of being in De anima proved particularly influential. It was in Neoplatonism, however, that these ideas first appeared fully organized into a coherent general scheme.62 Crucial to this organization was Plotinus’s idea that the perfection of the One included a superabundance which, overflowing, was the source of the Many. According to Plotinus, this generation of the Many from the One could not come to an end as long as any possible variety of being in the descending ser ies was left unrealized. One of the principal ways the Neoplatonic cosmology was transmitted to the Middle Ages was through Macrobius’s Commentary on the Dream of Scipio (which dates from the late fourth to early fifth centur ies a.d.). In a passage expanding on the revelation presented to Scipio that minds are given to man out of the eter nal and divine fire of the stars, Macrobius wr ites: Accordingly, since Mind emanates from the Supreme God and Soul from Mind, and Mind, indeed, forms and suffuses all below with life, and since this is the one splendor lighting up everything and visible in all, like a countenance reflected in many mirrors arranged in a row, and since all follow on in continuous succession, degenerating step by step in their downward course, the close observer will find that from the Supreme God even to the bottommost dregs of the universe there is one tie, binding at every link and never broken. This is the golden chain of Homer which, he tells us, God ordered to hang down from the sky to the earth.63

61. C. A. Patrides, “Hierarchy and Order,” in Dictionary of the History of Ideas: Studies of Selected Pivotal Ideas, ed. Philip P.Wiener (New York: Charles Scr ibner’s Sons, 1973), 2: 434. 62. Concer ning the complex of ideas associated with the g reat chain of being and Neoplatonism, see Arthur O. Lovejoy, The Great Chain of Being: A Study of the History of an Idea (Cambridge, Mass.: Harvard University Press, 1936), 61; concer ning De anima, see p. 58. 63. Ambrosius Aurelius Theodosius Macrobius, Commentary on the Dream of Scipio, ed. and trans. William Har ris Stahl (New York: Columbia University Press, 1990), 145. It is also in Macrobius (pp. 185– 200 in the Stahl translation) that we find a detailed discussion of the har mony of the spheres, as well as the legend of Pythagoras and the blacksmith’s shop. The connection between har mony and order found in Macrobius was an important one, and it may have contr ibuted to the application of a metaphor ical chain-of-being hierarchy to music. However, it is also str iking that the image of a ladder is used in both domains. In the Middle Ages, the hierarchical organization summoned by the Great Chain of Being was commonly represented by Jacob’s Ladder; see Paul G. Kuntz, “A Formal Preface and an Infor mal Conclusion to The Great Chain of Being: The Universality and Necessity of Hierarchical Thought,” in Jacob’s Ladder and the Tree of Life: Concepts of Hierarchy and the Great Chain of Being, ed. Marion Leathers Kuntz and Paul Gr imley Kuntz, American University Studies, Ser.V, Philosophy, 14 (New York: Peter Lang, 1987), 6. Also, some early mnemonic diagrams show the gamut as notes on a ladder; see Karol Berger, Musica Ficta: Theories of Accidental Inflection in Vocal Polyphony from Marchetto da Padova to Gioseffo Zarlino (Cambridge: Cambridge University Press, 1987), 9– 10.

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analysis and theory The notion of a Great Chain of Being proved a concise and powerful model through which humans could give order to their universe. It also provided a model through which the distr ibution of power could be accomplished and justified. The model is quite evident in ecclesiastical hierarchies: power flows from the top down, in the same way that being and soul flow from the Godhead down through the various levels of being, from highest to lowest. Inherent in the Neoplatonic scheme is a tension between the self-sufficiency of the One and the multitudinous abundance of creation it gives rise to: it is a paradox that the One needs nothing else and yet produces everything else. Giordano Bruno, writing in the sixteenth centur y, reveled in this paradox.64 Yet it was also Bruno who, by combining the concept of atomism with the comprehensive organization provided by the Neoplatonic scheme, inspired a way of thinking about hierarchical organization that would eventually compete with the Great Chain of Being. For Bruno, atomism was a metaphysical pr inciple that provided the basis for a demonstration of the underlying unity of all nature.65 This view was especially influential in England, where Bruno lived from 1583 to 1585 and where two factors combined to transfor m his vague, metaphysical scheme into a compelling account of order. The first factor came in the for m of a challenge to the model for the distribution of power provided by the application of a chain-of-being hierarchy to the social sphere. In a social chain-of-being hierarchy, the power of any individual is linked, as an essential property, to the level occupied by that individual within the system: the higher the level, the greater the power over others. A refutation of this model can be seen in Thomas Hobbes’s Leviathan of 1651. Hobbes argued that all humans were basically equal in the faculties of body and mind: all had approximately equal power over others. Because of this equality, the natural state of individual humans was one of competition. Only by imposing a social order on humans from without, in the for m of a common power “to keep them all in awe,” was it possible to overcome the natural state of virtual or actual war.66 Thus the properties ascribed to each member of a society (which result in equal measures of power for all members) are different from those according to which societal order should be established (which result in unequal measures of power): the properties of the individual are independent of the properties of the system. The second factor important in the development of an alter native view of hierarchical organization was the increased presence of mechanical devices in people’s lives.67 These machines provided thinkers of the time with practical models of the organization of nature. Among the most important of these was the mechanical clock. As Gideon Freudenthal has observed: “In the construction of the mechanical clock it was possible to produce complicated movements by an appropriate disposition of gears and a dr iving force. The task of science [in the seventeenth and eighteenth centur ies] can be inter preted as the attempt to discover in a limited area 64. Lovejoy, The Great Chain of Being, 120. 65. Robert H. Kargon, “Atomism in the Seventeenth Centur y,” in Dictionary of the History of Ideas: Studies of Selected Pivotal Ideas, ed. Philip P.Wiener (New York: Charles Scr ibner’s Sons, 1973), 1: 133. 66. Thomas Hobbes, Leviathan, or the Matter, Forme, and Power of a Common-Wealth Ecclesiasticall and Civill (London: Andrew Crooke, 1651), chap. 13. 67. Kargon, “Atomism in the Seventeenth Century,” 1: 132.

competing mode ls of mu s i c and to a limited extent the pr inciples of construction of the divine clock.”68 The model of a clock is one that appears consistently in the dispute between Isaac Newton and Gottfr ied Wilhelm Leibniz on the ultimate nature of matter. Of particular interest are the different methodological approaches used by Newton and Leibniz. Leibniz held to what had become, by the early eighteenth centur y, a traditional Baconian methodology: scientific inquir y should seek to disassemble the divine clock, piece by piece, never speculating beyond what could be observed. Although Newton was in sympathy with this methodology, it was inadequate for a purely mechanical account of physics, since the ultimate workings of the clock — its atomic structure— could not be observed. Newton’s solution, given in the final Query appended to the fourth edition of his Opticks, was a practical one that divided scientific theor izing into two halves.69 The first half is analysis: “This Analysis consists in making Exper iments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against Conclusions, but such as are taken from Exper iments, or other certain Truths.”70 The second half is synthesis or composition, in which the various inductive generalizations produced by analysis are organized into a logical system based on a limited number of essential pr inciples. In the case of the divine clock, synthesis of necessity played a larger role than analysis (which led Leibniz to accuse Newton of arguing from hypothesis rather than from observation). However, Newton believed this exception to his overall methodology was justified by the potential results: To derive two or three general Pr inciples of Motion from Phænomena, and afterwards to tell us how the Properties and Actions of all cor poreal Things follow from those manifest Pr inciples, would be a very great step in Philosophy, though the Causes of those Pr inciples were not yet discover’d: And therefore I scruple not to propose the Principles of Motion above-mention’d, they being of very general Extent, and leave their Causes to be found out.71

In other words, the scientist simply had to assume that the general pr inciples produced by synthesis held, even on levels that could not be directly observed: the mechanical workings of the divine clock were assumed to be consistent throughout. When combined with the independence of elemental and systemic properties proposed in the social sphere, this approach developed into a new conception of hierarchical order, which I call an atomistic hierarchy. In contrast to a chain-ofbeing hierarchy, an atomistic hierarchy can be built from the bottom up, its organization governed by a set of general pr inciples that obtain no matter what the

68. Gideon Freudenthal, Atom and Individual in the Age of Newton: On the Genesis of the Mechanistic World View, trans. Peter McLaughlin, Boston Studies in the Philosophy of Science, 88 (Dordrecht: D. Reidel, 1986), 63. Sulzer also used the analogy of a clock, but to character ize the unity of a work of art; see Baker and Chr istensen, Aesthetics and the Art of Musical Composition, 43– 46. 69. R. I. G. Hughes, “Reason and Exper iment in Newton’s Opticks: Comments on Peter Achinstein,” in Philosophical Perspectives on Newtonian Science, ed. Phillip Br icker and R. I. G. Hughes (Cambridge, Mass.: MIT Press, 1990), 177. 70. Isaac Newton, Opticks, or a Treatise of the Reflections, Refractions, Inflections and Colours of Light, 4th ed. (London: W. Innys, 1730; repr. New York: Dover, 1952), 404. 71. Newton, Opticks, 401– 02.

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analysis and theory specific attr ibutes of a given level. It is a concise and concrete account of organization, and one that, through applications in physics, chemistry, and biology, has had an enor mous influence on how humans view their world.

Structural Features of Chain-of-Being and Atomistic Hierarchies Each of these models of hierarchy offers a different view of how the world is organized. The fundamental conceit of chain-of-being hierarchies is to regard a domain as a huge organism pervaded by a force, the or igins of which are mysterious.72 “Being” and “political power” are both examples of such forces. The mysterious force behind any chain-of-being hierarchy manifests itself as properties instantiated in varying degrees by the elements of the domain. In a traditional Great Chain of Being, for instance, a rock has the property of substance, a tree has the properties of substance and life, and an insect has the properties of substance, life, and mobility. The domain can be organized into a hierarchy in which any given level is distinguished by a specific set of properties that embody aspects of being. These properties include all of the properties that distinguished lower levels, plus properties unique to the given level: trees include substance and add life; insects include substance and life and add mobility. Inclusion within the hierarchy is thus of properties, but not elements. The fundamental conceit of atomistic hierarchies is to regard a domain as an extended mechanism operating according to a limited set of general pr inciples. The laws of classical physics are an example of one such set of principles. All of the actions and properties of elements within the domain, from the smallest to the largest, and from the most simple to the most complex, follow these general pr inciples. Thus subatomic particles and planets both confor m to the same pr inciples. Classes of elements may be distinguished according to common confor mance with the general pr inciples of the system. The actions and properties of electrons, protons, and neutrons on the atomic level are by no means identical, but they can be distinguished from the actions and properties of atoms on the molecular level. In addition, all of the elements within a given class have the shared property of combining into units: electrons, protons, and neutrons combine to for m atoms, and atoms combine to for m molecules. The domain can be organized into a hierarchy in which each level is a confor mance class whose elements combine into units that constitute the elements of the next higher level in the hierarchy. This process continues recursively until the limits of the system are reached. Inclusion within the hierarchy is thus of elements, but not properties. The unique features of each of these models of hierarchy can be character ized in terms of relationships that are established between the general, abstract property of “energy” and the container schema. “Energy” takes for m as either the mysterious 72. While the parallels with the ideology of organicism that blossomed in the late eighteenth century are intriguing, it should be remembered that the organicism associated with chain-of-being hierarchies dates back at least to the Middle Ages. Accordingly, the mysterious or igins of the power behind chain-of-being hierarchies is somewhat different from the mystery associated with Romantic organicism since the for mer is an essential property of the model where the latter would be better descr ibed as accidental.

competing mode ls of mu s i c force of a chain-of-being hierarchy or the power that dr ives the mechanism of an atomistic hierarchy. For both models, the container schema provides the basic internal structure of the levels that make up the hierarchical system. In a chain-of-being hierarchy, the energy proper to the system (that is, “being” or “political power”) is distr ibuted unequally throughout the system. Systemic organization is consequently based on the amount of energy (inter preted as “properties of being” or “extent of political power”) each element of the system has. The containers (or hierarchical levels) that articulate this organization g roup elements according to their amount of energy (or systemic properties). Although chain-ofbeing hierarchies often offer vivid and dynamic accounts of organization, hierarchical structure (based on the contents of the containers that make up the hierarchy) is, in fact, relatively abstract. In an atomistic hierarchy, energy is distr ibuted throughout the system according to a fixed set of general pr inciples. Systemic organization is consequently based on the way different elements of the system manifest these pr inciples. The containers (or hierarchical levels) that articulate this organization group elements according to common confor mance with the general pr inciples. The generality of the organizing principles of atomistic hierarchies means that the pr inciples can seem somewhat removed from actual exper ience, although hierarchical structure (based on the contents of the containers that make up the hierarchy) is, in fact, relatively concrete. Given these structural attr ibutes, each model has a slightly different potential as a source domain. A chain-of-being hierarchy will map these predicates onto a target domain: • The target domain is pervaded by a mysterious force. • This force manifests itself as properties instantiated to varying degrees by the elements of the domain. • The domain can be organized into a hierarchy, in which each level is distinguished by a unique set of properties. • Each level of the hierarchy includes all of the properties of the next lower level and adds new properties unique to that level. • The higher levels of the hierarchy more completely manifest the mysterious force (and are thus more perfect) than the lower levels of the hierarchy. Because chain-of-being hierarchies have often been used to structure natural and human domains, applying the model to other domains may suggest that elements of that domain have natural or anthropomorphic aspects, even though these are not necessary entailments of the mapping.73 An atomistic hierarchy will map these predicates onto a target domain: • The target domain is analogous to an extended mechanism. • This mechanism operates according to a limited set of general pr inciples. • All of the actions and properties of elements within the domain follow these general pr inciples. 73. As the analyses at the end of chap. 2 suggest, factor ing anthropomorphism into the application of chain-of-being hierarchies to different domains would quickly lead to a dense and highly interconnected network of correlated domains.

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analysis and theory • Classes of elements may be distinguished according to common conformance with the general pr inciples and the shared property of combining into units. • The domain can be organized into a hierarchy, in which each level represents a confor mance class. • The elements on each level of the hierarchy combine to for m units; these units constitute the elements of the next higher level in the hierarchy. • The recursive combination of elements into units continues until the limits of the system are reached. Because atomistic hierarchies have often been used in scientific explanations, applying the model to other domains may suggest that a “scientific” approach is being used, even though this is not a necessary entailment of the mapping. Given the different structural attr ibutes each model of hierarchy will map onto a target domain, it follows that each provides a different model for reasoning about the target domain. Nowhere is this clearer than in the first thoroughgoing applications of these models to the domain of music dur ing the early nineteenth century.

Mapping Models of Hierarchy onto Music

chain-of-being hierarchies and tonal theory

Early in his Cours complet d’harmonie et de composition of 1806, Jérôme-Joseph de Momigny presents a C major scale ar ranged as two symmetr ical tetrachords: G

a

b

C C

d

e

F

Momigny reminds his readers that the three main notes of the scale are G, C, and F. He goes on to stress the centrality of tonic, providing a telling image in the process: “The tonic tr iumphs over all the other notes. It is [tonic] who plays the premier role in le Ton. It is the center of gravity, the purpose of all purposes, the end of all ends; in a word, it is to [tonic] that the scepter of the musical empire is entrusted.”74 At the beginning of the chapter in which this passage occurs, Momigny linked his concept of Ton to that of hierarchy;75 with his image of tonic holding the scepter, he leaves no doubt as to what sort of hierarchy he has in mind. 74. The complete passage is as follows: “J’ai déjà dit que ce sont là les trois Notes pr incipales du Ton. La tonique l’emporte sur toutes les Notes. C’est elle qui joue le premier rôle dans le Ton. Elle est le centre de gravité, le but de tous le buts, la fin de toutes les fins; en un mot, c’est à elle que le sceptre de l’empire musical est confié.” Jérôme-Joseph de Momigny, Cours complet d’harmonie et de composition, d’après une théorie neuve et générale de la musique (Paris: Chez l’auteur, 1806), 1: 47. The image is used again on p. 81 of the same volume. Although the early nineteenth-century notion of Ton can be considered to be approximately equivalent to the modern notion of “key,” there are also differences between the two concepts; specifically, Ton has a dynamic quality lacking in “key.” For this reason, I shall not use the latter as a translation of the former. 75. “Ton is the hierarchy, the order established between the notes of a genus and a mode.” [“Le Ton est la hiérarchie, l’ordre établi entre les Notes d’un genre et d’un mode.”] Momigny, Cours complet d’harmonie et de composition, 1: 47.

competing mode ls of mu s i c A similar, if less colorful, image may be found in the fuller explanation of order in music that he offered twelve years later in the second music volume of the Encyclopédie méthodique. This order, which Momigny claims is purely metaphysical, consists in a natural hierarchy of seven notes that are arranged according to the authority of the one called tonic.76 As Renate Groth has noted, this is essentially the same definition of order given over two decades later by François-Joseph Fétis; the most important difference is that Fétis assigned it the name tonalité.77 By mapping a chain-of-being hierarchy onto the domain of music, Momigny creates a very specific notion of Ton. The origin of Ton is mysterious — Momigny never gets more specific than claiming that it is “metaphysical.”78 The notes organized by Ton occupy different levels, according to their directive force; Momigny establishes these levels through various musical propositions. Perhaps most important, notes are regarded as agents with powers proportional to their status within the hierarchy: the properties character istic of Ton increase as one ascends toward tonic. Thus, even though Momigny identifies dominant as the generator of the scale (based on the presence of a minor seventh in the overtone ser ies), he argues that it must be regarded as subservient to tonic, for the author ity of tonic cannot be challenged.79 The conception of tonal organization produced by mapping a chain-of-being hierarchy onto music was a powerful one.We see it not only in Momigny’s early formulation of the concept of Ton but also in the persuasive account of tonal organization presented in the first and third volumes of Heinrich Schenker’s Neue musikalische Theorien und Phantasien. As presented in Schenker’s Harmonielehre of 1906, the mysterious force that pervades the domain of music is that of nature, manifested through the overtone ser ies. Earlier, in chapter 3, in a discussion of conceptual models as the basis for theor ies, I quoted a central passage from the Harmonielehre on Schenker’s organicist approach to the overtone ser ies and pursued its application to his approach to musical analysis. The same passage and related discussion is directly relevant to our present concer ns, and we turn to them again here. In Schenker’s conception, every tone within the musical domain is possessed of the urge to produce endless overtones, much as living beings have procreative urges.80 Beginning with a single tone, Schenker creates a community of tones ar ranged in 76. Jérôme-Joseph de Momigny, “Musique,” in Musique, Series 36 of Encyclopédie méthodique, ou par ordre de matières, ed. Nicolas Étienne Framéry, Pierre Louis Ginguené, and Jérôme-Joseph de Momigny (Paris: Chez Madame veuve Agasse, 1818), 2: 179. 77. Renate Groth, Die französische Kompositionlehre des 19. Jahrhunderts (Wiesbaden: Franz Steiner, 1983), 58. 78. On this use of “metaphysical” (which can also be seen in the work of Fétis), see Thomas Chr istensen, “Fétis and Emerging Tonal Consciousness,” in Music Theory in the Age of Romanticism, ed. Ian Bent (Cambridge: Cambridge Univesity Press, 1996), 37– 56. 79. Momigny, Cours complet d’harmonie et de composition, 1: 49– 51, 47– 48. 80. “It is self-evident that the urge to produce unending generations of overtones belongs to every tone in equal measure. One might also compare this urge to that of animals, for it appears in fact to be in no way infer ior to the procreative urge of a living being.” [“Es ist selbstverständlich, daß den Trieb, Generationen von Obertönen ins Unendliche zu zeugen, jeder Ton in gleichem Maße besitzt. Man darf, wenn man will, auch diesen Trieb einem Animalischen vergleichen, denn er scheint in der Tat dem Fortpflanzungstr ieb eines Lebewesens durchaus nicht nachzustehen.”] Heinr ich Schenker, Harmonielehre, Neue musikalische Theor ien und Phantasien, 1 (Stuttgart: J. G. Cotta’sche, 1906), §14, p. 42.

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analysis and theory hierarchical order, with the notes closest to the source-pitch having priority over those more remote.81 The tonal system that results is a manifestation of the desire of the source tone to rule over others and to extend this rule as far as possible.82 In Der freie Satz, from 1935, Schenker retained this conception of tonal organization and, by emphasizing the organicism latent in this conception, built from it an account of the coherence of entire works of music. He did this by proposing that the transfor mation of the musical source (now the Naturklang, or chord of nature) proceeded through discrete levels from background to foreground. The background represented an abstract, initial working-out of the tendencies of the chord of nature through the Ursatz, or fundamental structure; the foreground represented the musical work as we conventionally think of it.83 Schenker makes clear that this foreground emanates from and is controlled by the background.84 Thus the hierarchical organization of music is not restricted to the ordering of single tones into a scalar system, but manifests itself as a ser ies of transfor mations that steadily enr ich musical content. In Schenker’s vision of the relationship between structural levels, a version of the Neoplatonic cosmogony central to the or iginal Great Chain of Being continues to echo: “Between fundamental structure and foreground there is manifested a rapport much like that ever-present, interactional rapport which connects God to creation and creation to God. Fundamental structure and foreground represent, in terms of this rapport, the celestial and the ter restrial in music.”85

81. Schenker, Harmonielehre, §§17 – 18, pp. 54– 55. 82. “But now, what does ‘relationship’ mean in the life of the tone and what in this context would be implied by the intensity of living life to the fullest? The relationships of a tone are its system. Once the egoism of the tone manifests itself in such a way that the tone (rather like a human) might rule over its fellow-tones rather than be ruled by them, then these very systems provide the means for satisfaction of this egoistic love of power. A tone rules over others when it subjugates them to the relationships outlined in the systems above.” [“Nun aber, was soll denn Beziehung heißen im Leben des Tons und was soll hier wohl Intensität des Sichauslebens bedeuten? Beziehungen des Tones sind seine Systeme. Äußert sich der Egoismus des Tones dar in, daß er, hierin einem Menschen ähnlich, lieber über seine Mittöne herrscht, als daß er von ihnen beher rscht wird, so sind ihm zur Befr iedigung dieser egoistischen Herrschsucht eben in den Systemen die Mittel zur Her rschaft geboten. Ein Ton her rscht über die andern, wenn er sich dieselben nach den in den Systemen geschilderten Verhältnisse unterwirft.”] Schenker, Harmonielehre, §38, pp. 106– 07. 83. Robert Snarrenberg has recently pointed out what I would character ize as competing conceptual models in the usual translations of Schenker’s terms (e.g., “fundamental structure” for “Ursatz”); see Snarrenberg, “Competing Myths: The Amer ican Abandonment of Schenker’s Organicism,” in Theory, Analysis and Meaning in Music, ed. Anthony Pople (Cambr idge: Cambridge University Press, 1994), 45– 52. 84. “All the foreground diminutions, including the apparent ‘keys’ arising out of the voice-leading transfor mations, ultimately emanate from the diatony in the background.” Heinrich Schenker, Free Composition (Der Freie Satz), ed. and trans. Ernst Oster, New Musical Theor ies and Fantasies, 3 (New York: Schirmer Books, 1979), §4, p. 11. [“Ist doch alle Vordergrund-Diminution, einschließlich der scheinbaren Tonarten aus den Stimmführungsvervandlungen, zuletzt eben aus der Diatonie im Hinterg rund erflossen.”] Heinr ich Schenker, Der freie Satz, Neue musikalische Theor ien und Phantasien, 3 (Vienna: Universal-Edition A. G., 1935), §4, p. 32. 85. Schenker, Free Composition, 160 (Passage E). “Aehnlich wie von Gott zum Geschöpf zu Gott eine Fühlungnahme waltet, stets ineinanderlaufend, stets gegenwärtig, wirkt sich eine Fühlungnahme auch zwischen Ursatz und Vordergrund aus als gleichsam einem Jenseits und Diesseits in der Musik.” Schenker, Der freie Satz, 18.

competing mode ls of mu s i c

atomistic hierarchies and metrical theory

A rather different view of musical order is presented by Gottfr ied Weber in his Versuch einer geordneten Theorie der Tonkunst, which appeared in a number of editions in the early nineteenth century. In the course of introducing this particular view,Weber focused not on the organization of pitches but on the organization of musical rhythm. For Weber, rhythm depends on regularity, and the mechanical nature of this regularity is revealed in his breathless definition: If . . . a symmetrical measured division of the times is found in a piece of music, i.e. the time is distr ibuted into exactly equal general divisions, and these are again divided into equal parts, and the latter are farther separated into equal smaller quotas or proportional parts, &c. and the duration of the tones in relation to one another is exactly measured according to such divisions of time, so that a general division always appears as a symmetr ically ar ranged group of several smaller portions of time, and these taken together as a smaller subordinate group of yet smaller parts, and the accent is also symmetr ically apportioned amongst all these divisions of time— then the music is measured and rhythmical.86

This mechanical notion of rhythm is accompanied by a mechanical notion of timekeeping: Weber emphasizes the importance of inventions like the metronome and devotes a lengthy footnote to instructions for constructing a pendulum that will accomplish the same thing.87 Weber follows his digression into the mechanics of time-keeping with a detailed account of the rules by which musical measures are constructed, first dividing the measure into its constituent parts and then building measures according to symmetrical patter ns of accent. He then proceeds to further levels of rhythmic organization: But there is still a higher symmetry than this. That is to say, as parts of times taken together for m small groups, so also can several groups taken together be presented as parts of a larger group, of a greater or a higher rhythm, of a rhythm of a higher order. We may go still farther, and to such a greater rhythm we may annex moreover a second and a third, so that these two or three together constitute again a still higher rhythm. Thus, e.g. in the following passage, two measures taken together constitute a small rhythm, two of these, taken together, constitute again a rhythm of a higher species, and again two of the latter taken together, constitute a capital or pr incipal rhythm.88

The construction of the members of the larger rhythms is a symmetry proceeding more by the great; it is perfectly similar to that involved in the structure of measures, except that it is simply on a larger scale. As a measure consists of two or three parts, 86. Gottfr ied Weber, Theory of Musical Composition, Treated with a View to a Naturally Consecutive Arrangement of Topics, ed. John Bishop, trans. James F.Warner (London: Robert Cocks, 1851), 1: 62 [§47]. 87. Weber, Theory of Musical Composition, 1: 68– 71 [§51]. 88. Weber, Theory of Musical Composition, 1: 85 [§68].

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analysis and theory so two or three measures form the parts of a greater rhythm, and several such rhythms are again parts of a still higher group. Hence the measures are distinguished from one another in such higher rhythms, in respect to their g reater or less inter nal weight or accentuation, in the same way the parts of the measure are distinguished among themselves; i.e. the heavy or accented measures assume a prominence above the lighter, as do the heavier parts of the measure above the lighter.89

What Weber has descr ibed, of course, is an atomistic hierarchy of metrical groups: beats combine into measures, measures combine into groups of measures, and so on up through a ser ies of hierarchical levels. Mapping an atomistic hierarchy onto the domain of musical rhythm emphasizes the regularity of accentual patter n often associated with the concept of meter. By turning rhythm into a machine,Weber can descr ibe its organization with three basic principles: (1) all units of rhythm are either accented or unaccented; (2) these units are grouped into cyclic patter ns of accent that for m symmetr ical groups; (3) the groups of one level constitute the units of the next higher level. All of the objects within this domain must confor m to these pr inciples, but not necessar ily in exactly the same way. Although accent or nonaccent applies to both beats and g roups of measures, with beats, the property lasts for but an instant, whereas with groups of measures, the property lasts for the duration of the group. No limit is specified for the hierarchy that results, although Weber does not develop levels beyond those shown in his example. The approach to musical rhythm proposed by Weber became standard during the nineteenth century, although subsequent theor ists often added interesting complications. Moritz Hauptmann, for instance, imposed a Hegelian inter pretation on metrical groupings, which per mitted him to frame the basics of meter and har mony in the same ter ms.90 By the time of Riemann’s System der musikalischen Rhythmik und Metrik, the hierarchical structure represented by Weber’s “capital or pr incipal rhythm” was presented as the nor mative framework (normatives Grundschema) of rhythmic organization: beats for med measures, which in tur n formed duple groups, which combined into two half-phrases of four measures each, which joined to create the eight-measure phrase.91

Reasoning about Music through Chain-of-Being and Atomistic Hierarchies Chain-of-being and atomistic hierarchies developed at different points in the history of Western thought to explain two different domains of human exper ience. These differences are reflected in the basic structure of each type of hierarchy, and they result in two distinct models for reasoning about the world.When these mod89. Weber, Theory of Musical Composition, 1: 87 [§69]. 90. Moritz Hauptmann, The Nature of Harmony and Metre, trans. W. E. Heathcote, 2nd ed. (London: Sonnenschein, 1893; repr. with a new forward by Sigmund Levarie, New York: Da Capo Press, 1991), 189– 91. 91. Riemann, System der musikalischen Rhythmik und Metrik, 196– 98.

competing mode ls of mu s i c els are mapped onto music they yield different inferences about how musical materials are organized, which lead to different ways to analyze music. If our reasoning is guided by a chain-of-being hierarchy, we infer that each musical work constitutes a domain pervaded by a mysterious force. Musical analysis consists in explicating the way different musical elements embody this mysterious force. By this means, the proper place of these elements in the musical hierarchy can be deter mined and an account of musical structure can be produced. If our reasoning is guided by an atomistic hierarchy, we infer that each musical work operates like an extended mechanism. Musical analysis consists in identifying the basic components of this mechanism and explicating the pr inciples according to which it works. The view of musical structure that results is of a hierarchy of distinct yet inter related substructures that, combined, constitute the musical work. With these two models for reasoning in mind, let us now return to the three analyses of the rhythmic organization of Mozart’s little theme discussed at the opening of this section and consider in more detail how these two models of hierarchy condition and constrain musical analysis.

Conceptual Models and Music Theory According to the Schenkerian paradigm Robert Morgan adopts, tonality is characterized by the property of control: within a tonal composition, every pitch controls or is controlled by other pitches. Pitches located at the foreground have only the property of being controlled. Pitches located at middleground levels control pitches at lower levels and are themselves controlled by pitches at higher levels. Pitches located at the backg round level are governed only by restrictions placed on the Ursatz by the chord of nature. Morgan’s cor relation of rhythmic organization with this account of tonal organization has two important entailments for the conception of musical rhythm. First, rhythm becomes a matter of motion between structurally significant events. The initiation and completion of each rhythmic motion is marked by the appearance of the pitches that control a given span; the character of the rhythmic motion will reflect relationships between these controlling pitches. Thus the first rhythmic motion of Mozart’s theme begins with the Kopfton in m. 1 and ends with the appearance of 2 in m. 4; the motion has the character of an antecedent because a complete motion from 3 to 1 has not yet been achieved (see ex. 7.5). Second, the type of accent assigned a g iven musical moment will tend to be unequivocal. Emphasis, as an articulation of rhythmic motion, follows from hierarchical structure: emphasized pitches will be those located at higher levels of the tonal hierarchy. Because the location of a given pitch within the hierarchy is not equivocal, the emphasis it receives will not be equivocal. Thus m. 3 cannot have both an upbeat accent and a downbeat accent at the same time but must be given a rhythmic reading that matches the overall tonal structure. Although Leonard Meyer’s treatment of Mozart’s theme certainly takes account of tonal structure, his rhythmic analysis begins, as noted, at the musical surface. The accentual g roups of the first (surface) level of the hierarchy become the elements of the second level of the hierarchy, the accentual g roups of the second level

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analysis and theory become the elements of the third level, and so on up through four levels of hierarchical organization (see ex. 7.4).92 From Meyer’s perspective, rhythmic organization, insofar as it is metr ical, is independent of tonal organization, since the elemental patter ns of metrical accent can be specified in the absence of pitch. The overall rhythmic character of a passage results from an interaction between tonal organization and patter ns of metrical accent occur ring on a number of hierarchical levels. The emphasis accorded a given musical event can only be reckoned in context. On level 2 of Meyer’s hierarchy, m. 3 is (as a whole) accentually weak; on level 3, it is one component of a strong accent; and on level 4, it is a subcomponent of a weak accent. The property of accent is consequently different on each hierarchical level, since the accent proper to each level pertains to different spans of musical events. The differences between these two accounts of the rhythmic structure of Mozart’s theme follow in part from the way each model of hierarchy constrains reasoning about music. From the perspective of a chain-of-being hierarchy, the musical surface is the least important of all levels. Given the way musical events are assigned to hierarchical levels, any polysemous reading of such events is little more than analytical dither ing. From the perspective of an atomistic hierarchy, there can be no grand plan of musical organization that does not or iginate with the simplest and most readily apprehended of musical mater ials. Nonetheless, there is a bit more to the story. The constraint these models impose on our reasoning goes beyond the inferential possibilities provided by their relational structure and penetrates to the very core of what counts as relevant phenomena for theor izing and analysis. Indirect evidence for this constraint is supplied by the way each model of hierarchy is mapped onto music. Chain-of-being hierarchies have been mapped almost exclusively onto the domain of musical pitch — they have generally not been mapped onto the domain of musical meter. Atomistic hierarchies, on the other hand, have been most often mapped onto the domain of musical meter — mapping them onto the domain of pitch has not met with wide acceptance.93 Explaining how this constraint works requires that we briefly revisit the procedures of cross-domain mapping discussed in chapter 2, with particular attention to the Invariance Pr inciple. According to this pr inciple, for those portions of the source and target domains involved in a cross-domain mapping, the mapping preserves the image-schematic structure of the target domain, and it imports as much of the image-schematic structure from the source domain as is consistent with this preservation. Mapping a model of hierarchy onto music will preserve aspects of our musical exper ience and structure these by importing the relationships between 92. In the complete analysis Meyer actually adds two additional levels of hierarchy, although the sixth and final level is somewhat speculative; see Meyer, Explaining Music, 39. 93. Eugene Nar mour’s recent attempts to map an atomistic hierarchy onto pitch have met with only limited success, and the application has not been widely adopted. See the in-depth treatment of the issue in Nar mour, “Some Major Theoretical Problems Concer ning the Concept of Hierarchy in the Analysis of Tonal Music,” Music Perception 1/2 (1983 – 84): 129– 99; Narmour discusses mm. 1– 8 of the first movement of Mozart’s Piano Sonata in A, K. 331, on pp. 160 – 98. In some recent analyses, Narmour reads musical structure as only quasi-hierarchical and thus better dealt with in ter ms of networks. See Narmour, The Analysis and Cognition of Basic Melodic Structures: The Implication-Realization Model (Chicago: University of Chicago Press, 1990).

competing mode ls of mu s i c “energy” and the container schema embodied by this model. When we take a chain-of-being hierarchy as the source domain, we preserve our sense that some aspects of music are more important than others, and we import a model of systemic organization in which energy is distr ibuted unequally and hierarchical levels group elements according to their amount of energy. This mapping works well for the asymmetr ical pitch relations typical of tonal music but less well for the measured domain of metrical rhythm. When we take an atomistic hierarchy as the source domain, we preserve our sense that some aspects of music are regular and recurring, and we import a model of systemic organization in which energy is distr ibuted equally and hierarchical levels group elements according to common confor mance with general pr inciples. This mapping works well for the measured domain of metrical rhythm but less well for the asymmetr ical pitch relations typical of tonal music. Thus the image schemata that g round our conceptual models also facilitate mapping these models onto novel domains, subject to the limitations of the imageschematic structure of both domains. Additional evidence for the part played by image schemata in conceptual models and cross-domain mapping is suggested by Edward Cone’s analysis of Mozart’s theme, which combines aspects of the approaches demonstrated by Morgan’s and Meyer’s analyses. For Cone, as for Morgan, musical rhythm involves motion between points of tonal stability. The first and fifth measures of the theme should be strong because of the fir m statement of tonic; the fourth and eighth measures should also be strong because of the emphasis provided by arrivals on important harmonies. However, Cone, like Meyer, is also interested in the contr ibution of the musical surface to our understanding of musical rhythm as a whole. Cone’s overall interpretation of the rhythmic structure of the opening eight measures is thus shaped by meter, motivic structure, and surface accents. What guides Cone’s analysis is his concept of musical energy — it was this that prompted his compar ison of a musical phrase to a game of catch. The path of energy that marks the transit of the ball in the game of catch is the analogue for the path of musical energy constituted by a given passage in a work of music. Starting with the concept of energy rather than with a model of hierarchy allows Cone to tap into both models of hierarchy and draw from each what he needs. By this means, he can forge a single account of musical rhythm that recognizes both hierarchic paradigms but which is restricted to neither. Thus, Cone’s analysis demonstrates a conceptual blend, the gener ic space of which focuses on the notion of energy common to both models of hierarchy. According to the approach I have developed here, the discrepancies between these three analyses of Mozart’s theme reflect the role of conceptual models in theories of music. At work are two different models of hierarchical organization. One maps a chain-of-being hierarchy onto music and highlights one set of aspects of the musical domain. The other maps an atomistic hierarchy onto music and highlights a different set of musical aspects. Two of the analyses — those by Robert Morgan and Leonard Meyer— rely on relatively straightforward mappings, one from each model of hierarchy.Where the structure of the models of hierarchy diverge, there the musical analyses based on these models will also diverge. The third analysis, by Edward Cone, blends the two mappings by focusing on commonalities between their image-schematic structure. By focusing on these commonalities, Cone puts

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analysis and theory some distance between his inter pretation and notions about hierarchical organization and produces yet a third analysis of Mozart’s theme. The discrepancies between the three analyses are thus not the result of different opinions about what constitutes the theme of the first movement of Mozart’s sonata, nor are they a consequence of analytical inconsistencies. Rather, they follow from the structure of these two conceptual models and the way they are employed in accounts of music.

competing models of musical form and hierarchy The foregoing represents an attempt to sort out why musicians — reasonable, highly experienced musicians — disagree about such things as musical for m and musical hierarchy. As I have endeavored to show, such disagreements can be traced to competing models of musical structure. Much as Alice and the Hatter have different ideas about what time is, so music theor ists have different ideas about the properties of musical for m and the structure of hierarchical relationships. The analyses I offer should help explain why this is so. If one is thinking about musical for m in ter ms of grammar or building blocks, it may not be immediately evident how music achieves its rhetor ical effects or seems to g row from within. If one is thinking about musical relationships in ter ms of dominance and control, musical meter may appear to be something of a cipher, for meter provides only weak demonstrations of these properties. More interesting, however, is the way these models reflect back on the theor ists who employ them, much as Alice’s models of time reflect the world of a seven-yearold girl in Victorian England, while the Hatter’s model of time reflects the world of Wonderland. Theorists who focus on a static model of musical for m are almost invariably occupied with a very basic level of music pedagogy. Dynamic models only start to make real sense once a level of artistry has been achieved— that is, once the student can speak and understand the language of music with some fluency. Not surprisingly, then, the two models begin to overlap and intertwine in confusing and interesting ways in the early nineteenth century, for the institutionalization of music education required a bit of both perspectives. Nation building required the mechanisms of rationalized instruction and of artistic exegesis, the first to guarantee a future, the second to celebrate a past. Similarly, theorists who focus on atomistic hierarchies are convinced that we enter music from its surface and only later can penetrate to its depths by understanding the general laws that connect them both. Theorists who make recourse to chain-of-being hierarchies, on the other hand, are convinced that surfaces are illusions — the real truth of music lies hidden in mysterious powers that guide compositional creation like an unseen hand. These summaries are too reductive, of course, but they make in br ief the point toward which this chapter has argued at length: the models we choose for our character izations of music tell us at least as much about ourselves as they do about music.

conclusion

Q cognitive structure, theory, and analysis

et us return to Proust’s A la recherche du temps perdu and to the encounters between listener and music descr ibed within. The introduction to this volume was framed around the moment when Charles Swann first hears the Andante of a sonata for violin and piano byVinteuil at the bourgeois salon of the Verduins. As that moment unfurled, Swann moved from vague and unfor med impressions to active understanding: he began to conceptualize music. Now, a year later, Swann again encounters the same fictitious composition, this time at a soirée at the Marquise de Saint-Euverte’s. Over the course of this year, Swann has become obsessed both with the Andante — especially as represented through the fragment he calls “the little phrase”— and with Odette, the courtesan whom he had also first come to know at the Verduins. At the moment we find him, Odette has left him, and he finds himself surrounded by people who, if they knew of his love for her, would only trivialize it. Then, unexpectedly, the musicians commence the sonata, and Swann finds himself enraptured once more. Where in his first encounter the sonata had amounted to not much more than pleasant sensations, it is now a full-fledged discourse, speaking in a beautiful and paradoxical language: “Ever since, more than a year before . . . the love of music had, for a time at least, been bor n in him, Swann had regarded musical motifs as actual ideas, of another world, of another order, ideas veiled in shadow, unknown, impenetrable to the human mind, but none the less perfectly distinct from one another, unequal among themselves in value and significance.”1 The ideas that enthrall Swann — distinct yet shadowy, perfectly clear yet impenetrable— are musical concepts; the discourse to which he attends is musical discourse. What began as a sketchy, provisional transcr ipt has blossomed into a theory of musical organization that is robust enough to reach out to the transcendental. The process that led to this transfor mation (as descr ibed in chap. 1) begins with categories of musical events, of which the motifs (or motives) upon which Swann focuses are a good example. Musical motives show a number of similar ities to basic-

L

1. Marcel Proust, Swann’s Way (vol. 1 of Remembrance of Things Past), trans. C. K. Scott Moncr ieff and Terence Kilmartin (New York:Vintage Books, 1981), 379 – 80.

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conc lu s i on level categor ies, offering an effective compromise between efficiency and infor mativeness. The variability of motives, as they are shaped to the exigencies of musical context and compositional process, matches perfectly the variability of Type 1 categories; our impression that there is a motive reflects the conceptual models around which such categor ies are organized. Of course, motives of the sort typical in late nineteenth-centur y music, of which the little phrase is intended to be a paragon, represent only one possibility for musical categor ies. Categories might also be organized around a har monic structure or a g round bass, around a two-voice contrapuntal patter n or a persistent rhythmic figure. As the analysis of atonal music has suggested, musical categor ies might even involve relatively abstract relationships, which are obscure at first but which emerge with repeated listenings.2 As I proposed in chapter 1, we can construe musical concepts as equivalent to musical categor ies. Although such concepts may be affiliated with language, language is not necessary for their creation or maintenance. The paradox presented by Proust — that musical ideas are “ideas veiled in shadow, impenetrable to the human mind, but none the less perfectly distinct from one another”— is simply a reflection of the limits of language. Musical concepts are of another world, another order, because they extend into a domain that is beyond words. One of the principal ways musical concepts are related to other concepts — musical and otherwise — is through the process of cross-domain mapping. A bit before the passage quoted above, the little phrase is first a kind of superhuman agent transfor med into sound (whose presence is itself likened to the perfume of a flower), then the words this spir it speaks, then an almost cor poreal lover, and finally once again a comforting spir it: Swann felt its presence like that of a protective goddess, a confidante of his love, who, in order to be able to come to him through the crowd and to draw him aside to speak to him, had disguised herself in this sweeping cloak of sound. And as she passed, light, soothing, murmurous as the perfume of a flower, telling him what she had to say, every word of which he closely scanned, regretful to see them fly away so fast, he made involuntar ily with his lips the motion of kissing, as it went by him, the har monious, fleeting for m. He felt that he was no longer in exile and alone since she, who addressed herself to him, was whisper ing to him of Odette.3

This dense field of overlapped mappings cannot, of course, quite summon the acoustic reality of the little phrase (which exists, after all, only in Proust’s imagination), but it does select certain aspects of the musical domain as targets. The little phrase is distinct enough from the sur rounding mater ials that it can be likened to a person emerg ing from a crowd; it has a measure of delicacy about it, both in its

2. I am thinking especially here of the work of David Lewin, who has a knack for discovering intriguing musical relationships, character izing them through impressively abstract for mulations, and managing to create analyses of compelling immediacy. On the possibility of hearing these for mulations, Lewin comments, “One should not ask of a theory, that every formally true statement it can make about musical events be a perception-statement. One can only demand that a preponderance of its true statements be potentially meaningful in sufficiently developed and extended perceptual contexts.” Lewin, Generalized Musical Intervals and Transformations (New Haven, Conn.:Yale University Press, 1987), 87. 3. Proust, Swann’s Way, 378.

cog n i t ive st ruc ture, th e ory, and analys i s overall aesthetic shape and in its lack of assertiveness; despite this delicacy, the substance of its communicative force is such that it evokes response not simply in words but in deeply intimate gestures. If, after this descr iption, the little phrase still remains elusive, we can nonetheless generate a fairly clear sonic picture of what it involves. Proust’s mappings have thus constructed an image of this imaginary music, selecting musical concepts — vague and ill for med, to be sure, but convincing nonetheless — from the general field of possible musical constructs. It is through similar, if more prosaic, mappings that we structure our understanding of music, building up the integrated systems of terms and relations through which we descr ibe our exper ience with and conceptions of music. Such crossdomain mappings have their ultimate g rounding in embodied exper ience (as we observed in chap. 2). In tur n, our exper iences with music allow us, on occasion, to map from the musical domain onto other domains. For instance, in the passage just cited, music (as represented by Vinteuil’s sonata) provides a model according to which a succession of fleeting impressions — the movement of a person’s body, the scent of a flower, the brush of a kiss, a scatter ing of forms— can be construed as constituting an indivisible whole. Just as the sonic mater ials proper to a musical work appear and disappear and yet always remain part of “the work,” so the fleeting impressions noted by Swann are, in truth, but some of the disparate threads out of which his love for Odette is woven.4 The possibility of mapping structure both to and from the musical domain contributes to the process of conceptual blending, in which elements from two cor related mental spaces are blended together in a third mental space. This offers a further inter pretation of Swann’s encounter with the little phrase, for what appears before him is a blend of features drawn from the human and sonic domains — a protective goddess who has disguised herself in a sweeping cloak of sound. Just such a blend seems to have been intended by Proust, who goes on to wr ite that Swann “had no longer, as of old, the impression that Odette and he were unknown to the little phrase. Had it not often been the witness of their joys? True that, as often, it had warned him of their frailty.”5 As the story continues, the little phrase becomes fully personified, engaging in dialogue with Swann, offering sage advice, and leading him to transports of the spir it.What Proust is relying on, of course, is the sort of anthropomorphic blend he also employed in his descr iption of Swann’s lilac trees, and which Tovey employed so strategically in his analysis of Beethoven’s Sixth Symphony (both discussed in this volume in the latter portion of chap. 2). The musical concepts produced by categor ization and the structural relationships produced by cross-domain mapping come together in conceptual models, which provide the basis for reasoning about music. Swann relies on two models. Of these, the first yields a view of music as a type of discourse structure: musical motives are regarded as ideas that are shaped into a communicative medium by the way they are organized in time and with respect to other musical ideas. The sec4. This is particularly apparent because Proust’s allusion to “the perfume of a flower” is anticipated a few pages earlier by Swann’s detailed recollection of the chrysanthemum Odette gave him early in their romance. 5. Proust, Swann’s Way, 378.

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conc lu s i on ond model yields a view of the nonlinguistic as super natural. Words, as proper to human discourse, are necessar ily mortal; those things that escape words are consequently immortal; things that are immortal exist only outside the natural world. These models are then combined into a theor y of music appropriate to Swann’s moment of clairvoyance, following the perspective developed in chapter 3. According to this theor y, musical discourse is a suprahuman mode of communication, something evident as the two musicians conclude the perfor mance that had summoned the little phrase and Swann’s rapture. Swann dared not move, and would have liked to compel all the other people in the room to remain still also, as if the slightest movement might imper il the magic presence, supernatural, delicious, frail, that was so soon to vanish. But no one, as it happened, dreamed of speaking. The ineffable utterance of one solitary man . . . breathed out above the rites of those two hierophants, sufficed to ar rest the attention of three hundred minds, and made of that platfor m on which a soul was thus called into being one of the noblest altars on which a super natural ceremony could be perfor med.6

This is a theor y of music rather different from the others I have discussed, not the least because where specifics are wanted we find only sweeping generalities. Nonetheless, the theory of music that Swann has developed in his efforts to understand the effect of Vinteuil’s sonata is in truth but a manifestation of a portion of the broader theory of aesthetics Proust sought to develop in A la recherche du temps perdu. Within this theor y, music was to occupy the same place accorded it by Schopenhauer: as a pure expression of the will.7 Necessary to this perspective is the conceit that absolute music somehow exists outside the domain of human cognition. The perspective relative to which I have framed this book, of course, is that music,“absolute” or otherwise, is wholly within the domain of human cognition. In making this argument, I have focused not on the most basic aspects of musical cognition — the level where raw data is taken in by the auditory processing system and transfor med into electro-chemical infor mation within the brain — but on a relatively high level of cognition accessible to our conscious thoughts. My emphasis has been on how general cognitive capacities (like those for categor ization, crossdomain mapping, and the construction and maintenance of conceptual models and theories) are specified for music. Indeed, understanding something as music— as opposed to the hammer ing of a woodpecker, or an ag reeable if not particularly interesting succession of sounds, or just noise — is intimately bound up with directing these general cognitive capacities to the specific task of making sense of patterned sound. This approach to music cognition makes it possible to give a fairly detailed account of how M. Swann (and M. Proust, for that matter) conceptualize music. It also provides a perspective on broader problems of musical understanding, four of which I treated at length in the second part of this book.

6. Proust, Swann’s Way, 383. 7. On this point, see Jean-Jacques Nattiez, Proust as Musician, trans. Derrick Puffett (Cambr idge: Cambridge University Press, 1989), chap. 4.

cog n i t ive st ruc ture, th e ory, and analys i s

musical syntax

The idea that musical works could be woven from relatively limited bits of musical mater ials — motives— was one that gained cur rency around the time that composers became increasingly interested in the resources of purely instrumental music — that is, around the middle of the eighteenth centur y. As such, the idea that motives are important for musical discourse is hardly a new one, even if it did not assume prominence in music theory treatises until the mid–nineteenth century.Viewing a motive as a cognitive category has the practical benefit of explaining why we construe diverse motive forms as “the same,” despite their manifold differences. The perspective becomes really interesting, however, when we start to consider relationships among the members of a category of motives, for these offer a way to explain the way the musical syntax specific to a given work emerges over time. As the composer deploys now more, now less typical members of the categor y, we not only develop a more complete sense of the structure of the category but also come to see how typicality cor relates with overall compositional design. This syntactic strand could be woven together with those spun from har monic and for mal syntax to create a r ich, multileveled discourse (as we saw in the analyses of works from the eighteenth century presented in chap. 4). The same approach also provides a way to explain how the musical topics so important in eighteenth-centur y instrumental music emerged. As we saw in the first movements of two Beethoven str ing quartets, categor ies of motive forms were distinguished by how they were used in the course of a movement. In the case of a motivic categor y used only for beg innings, for instance, this property then becomes part of the conceptual model for the categor y of motive forms: in addition to its other attr ibutes, the category now acquired the attr ibute “used only for beginnings.” This change has the consequence of giving the categor y a semantic value: within the context of this movement, the motive means “this is a beginning.” As a result, a musical topic, even if of a very local and restricted sort, has been bor n. For eighteenth-centur y music, this process is of interest chiefly for answering the r iddle of how musical topics were created in the first place and for understanding the interplay between locally generated signs and established topics. For music with a less-clearly defined tradition, such as that of the twentieth century, the process is of rather more interest, for it offers a way to explain how each individual piece generates a semiotic system. Indeed, it is in part through establishing and manipulating categor ies of musical events that composers of the twentieth centur y create musical meaning. We can also see the part this process plays in helping us understand an unfamiliar repertoire: by attending to the specifics of musical syntax, we can begin to understand the process of meaning construction of which this syntax is a part. In a manner of speaking, music teaches us how we should listen to it. The dynamic approach to musical syntax made possible by consider ing relationships among the members of musical categor ies (and among categor ies themselves) is one that is well suited to developing an account of large-scale rhythm — that is, rhythm at the phrase level or above. The challenge of theorizing large-scale rhythm has been to develop a model that is more than simply an adaptation of metric theory or a reinterpretation of large-scale har monic theory. One way to develop such a model is to construe relationships among categor y members in dynamic terms. For instance, if we return to the compositional strategies discussed in chapter

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conc lu s i on 4, we could use cross-domain mapping to cor relate the typicality of category members with stability, and atypicality with instability. Applied to the opening measures of the Allegro from Mozart’s “Dissonance” Quartet, what emerges is a large-scale pattern that begins with stability (in mm. 23– 26), moves to instability (beginning in m. 27), returns to stability (in mm. 31– 34), moves somewhat more quickly to instability (beginning in m. 35), returns (after a br ief hiatus) to stability (in m. 44), and then finally dissolves into instability (after m. 48).8 The patter n could be further applied to each subsequent episode involving the motive, producing a dynamic account of the movement as a whole.

musical ontology That an exploration of musical ontology might yield significant insights into the structure and character of cultural knowledge might at first seem sur prising, for as common as music is, it is still not the central business of human culture. However, because music is resolutely ephemeral, knowledge of it is, in most cases, preserved only in human cognitive structure. We can know what Greek potter y of the fifth centur y b.c. was like, because some of it has been preserved into the present era. The same cannot be said of Greek music. Theoretical and other wr itings give us hints about the character of Greek music, but direct exper ience of it is impossible. Music, where it is not preserved through some artifactual means, exists solely in the conceptual models and theor ies of the members of a musical community. In consequence, giving an account of the basis for determinations of musical identity — what it means for something to be considered an instance of music — means giving an account of the cultural knowledge upon which such deter minations are based. Although it is easy to hold up the Western preoccupation with “the score” as the acme of musical objectification, the notion of a musical object is not a consequence of artifacts like scores but is instead an offshoot of the conceptual models we use to structure our understanding of what we hear. Because these models are, for the most part, completely transparent, we take them for the way things are: conceptual models are part and parcel of what counts as reality (as noted in chap. 3). Our impression that “music” is an objective category, and that there are musical objects, is simply a consequence of the cognitive efficiency conceptual models represent. In that the conceptual model relative to which we make deter minations of musical ontology captures the things our culture deems most important about patter ned sound (or the place patter ned sound occupies in our culture), our theor ies of music are consequent to these models: what counts as “music” determines what counts as “music theory.” One prominent example of this was provided by the Greek music theories of antiquity discussed in the introduction. However, more subtle examples are available as well: for Rameau, “music” meant French music, and it was relative to that national tradition of musical expression that his theory was framed. Similarly, 8. The changing patter n of stability and instability I have outlined very much resembles the patter n that occurs at the level of the beat, specifically in the context of what Harald Krebs calls metr ic dissonance. The principal difference is that the patter n as I have described it is expanded to encompass entire musical phrases. This theory of metric dissonance is most fully worked out in Krebs, Fantasy Pieces: Metrical Dissonance in the Music of Robert Schumann (New York: Oxford University Press, 1999).

cog n i t ive st ruc ture, th e ory, and analys i s for Schenker “music” meant music from the Ger man-speaking world, and it was to this repertoire that his theor y was directed. This conception of musical ontology can be extended to other repertoires, like jazz (as noted in chap. 5). There we observed that certain jazz musicians of the 1950s and 1960s regarded the har monic possibilities of a tune (that is, the potential for the har monic template of the tune to be reconstituted through the modification or substitution of harmonies) and its overall affect as more important than the bare pitch structure of its melody or the basic syntax established by its har monies. In consequence, the theory of music that issued from this practice — a theory woven throughout the interviews and quotations that for m the fabric of Paul Berliner’s Thinking in Jazz — was centrally concerned with ways to create and layer the multiple musical discourses made possible by a particular har monic patter n.9 For this music, it was far less important to develop an explanation of the imperatives of melodic or har monic syntax, since these were assumed to be almost totally dependent on local context.

music and other domains

According to at least some definitions, language and music are quite separate domains. The distinction is eminently sensible: when we want to know if supper is ready, we expect a response in words, not a musical phrase ending with a deceptive cadence. Nonetheless, inasmuch as both language and music are products of human cognitive processes, it also seems sensible that they will rely on some of the same cognitive capacities. For example, evidence from conceptual blending suggests that they both employ similar discourse strategies. Admittedly, these strategies, as represented by the gener ic space of a conceptual integration network, are rather abstract, so elemental as to be almost simplistic. And yet there is strong evidence that such simple stor ies are basic to human cognition and communication — indeed, as we observed in chapter 2, Antonio Damasio has argued that they are involved with consciousness itself .10 In situations where linguistic discourse and musical discourse are simultaneous and structured by the same basic strategy, concepts from the mental spaces set up by each can combine in a third mental space: a conceptual blend. Situations of this type were demonstrated by the analyses of songs in chapter 6. And, as we saw with Brahms’s “In der Fremde,” if a unifor m topography between the constituent spaces in a conceptual integration network is lacking, conceptual blending will not occur. The combination of words and music in such cases may be pleasant enough, but it will not realize the full potential of these conjoined media. A basic conceptual blend involves four coordinated mental spaces (as noted in chaps. 2 and 6). However, as Tovey’s analysis of Beethoven’s Sixth Symphony shows, conceptual blending may involve any number of mental spaces. It is fairly easy to imagine songs that might involve multiple spaces — for instance, if the song makes 9. Paul F. Berliner, Thinking in Jazz: The Infinite Art of Improvisation, Chicago Studies in Ethnomusicology (Chicago: University of Chicago Press, 1994). 10. For an overall account of the importance of abstract discourse structures to human cognition, see Mark Turner, The Literary Mind (New York: Oxford University Press, 1996). The approach Antonio Damasio takes in his The Feeling of What Happens: Body and Emotion in the Making of Consciousness (New York: Harcourt Brace, 1999) is notable for the empir ical evidence and level of neurophysiological detail that he br ings to bear.

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conc lu s i on reference to a well-known myth, or if, as in the case of Schubert’s “Trockne Blumen,” there are strong parallels between the situation descr ibed in the words and details of the composer’s life.11 Even more intr iguing are the possibilities offered by opera, which can easily engage — and often revels in — simultaneous musical, linguistic, theatr ical, gestural, and scenic discourse.Various kinds of musical multimedia — music and film, music and dance, music and visual images — offer further possibilities for explor ing conceptual blends involving multiple spaces. In each case, where a unifor m topography between the spaces set up by these media obtain, conceptual blending can occur.What is potentially intr iguing about the blends that can be set up by the coordination of these diverse media are the views of discourse structure that will result, so that the syntax of music will shed light on the syntax of other media, and they on music.While differences between the media are essential to the exper ience of multimedia, as Nicholas Cook has suggested, the deep commonalities between the discourse structure of various media offer new ways to think about musical structure.

competing models of musical structure The theory of music developed by Charles Swann, while useful for making a reconciliation with what he imagined to be the end of his love affair, offers hardly any explanation for why the little phrase works the magic that it does or how Vinteuil’s sonata can hold three hundred Parisian socialites enthralled. Where we long to discover more about its syntax, or its place within a tradition of similar works, or the means by which it sprang forth from the mind of its creator, Swann’s theory gives us only obscurantism and effusion. That this should be so is a direct consequence of the conceptual models his theory employs. Given the assumption that music is a type of discourse structure (rather than, say, some sort of organism or mechanism), Swann’s theory places an emphasis on the message rather than the medium and on temporal constraint as an essential element of musical exper ience. Music has things to tell us, but the disappearance of these messages is practically coincident with their emergence. Given the assumption that nonlinguistic discourse is super natural (rather than something humans make use of regularly), we cannot expect to make much sense of the things music tells us; we can only be grateful that we have been able to hear them at all. Of course, Swann’s— and Proust’s— theory of music is a product of a particular cultural and histor ical moment, one that sought to explain how humans could participate in the divine even while they were forever shut off from it. Other cultural and historical moments — including our own— will seek other explanations, employing the categor ies, cross-domain mappings, conceptual models, and theor ies that resonate with them most deeply and constructing a vision of music that best fits with their vision of the world as a whole. Theories of music, then, are not so much about truth as about a particular perspective on what aspects of patterned sound are rewarding or important to attend to; they are equally concer ned with the integration of this perspective into a larger 11. Although this biographical cor relation does not figure in my consideration in chap. 6 of Schubert’s song, I touch on these parallels in Lawrence Zbikowski, “The Blossoms of ‘Trockne Blumen’: Music and Text in the Early Nineteenth Century,” Music Analysis 18 (1999): 340.

cog n i t ive st ruc ture, th e ory, and analys i s view of human society and culture. Similarly, music does not offer us an unmediated vision of the truth — despite what M. Swann believes— but a truth assembled from the possibilities of patterned sound and human cognitive capacities. Most of my discussion has focused on cognitive structure and theory, and I have had relatively less to say about analysis — especially analysis as the object of a separate domain of inquiry. The reason for this apparent imbalance, as mentioned in the introduction to this volume, is that while analysis is essential for making claims about musical structure explicit, it is not independent of theory: every analysis relies on some theor y of music.12 For that matter, I am somewhat doubtful about making a meaningful distinction between descr iption (as a more or less passive reporting of the relevant features of a work) and analysis (as a thorough contextualization of aspects of musical structure), since decisions about what counts as “relevant features” and “musical structure” rely equally on some theoretical understanding about music. It seems more promising to distinguish between ad hoc theor ies and extended theor ies, as I did at the end of chapter 3. This distinction is based on the kind of problems a theor y engages, its place within a tradition of inquiry, and the degree to which it is rendered systematic. Generally speaking, descriptions or analyses based on extended theor ies are more interesting than those based on ad hoc theories, for extended theor ies draw much more deeply on our cognitive capacities and cultural knowledge. Although analysis has been a bit of a dark horse, it has hardly been out of the running. Indeed, it has been present throughout the course traced by the preceding pages: in the analyses by Schoenberg, Tovey, Rameau, Schenker, Mattheson, Meyer, Cone, and Morgan I have discussed, and in the analyses I myself have presented. In the case of earlier wr iters, I have been most interested in what their analyses have to say about their theor ies of music. My own analyses, of course, are based on the theor y that our understanding of music is shaped by our cognitive capacities and that these are visible at every turn in our encounters with music. Through our theor ies and analyses, we thus shed light not just on music but on the fascinating mysteries of human thought. The abiding mystery I have sought to explain is the one embodied in M. Swann’s first encounter with Vinteuil’s sonata: how it is that we can make some sort of sense of an unfamiliar music almost immediately and yet have this same work provide continued reward in our further exper iences with it. Music, as revealed by Proust’s vignette, is thus simultaneously immediate and complex, transparent and opaque. The solution I have offered is that our understanding of music relies on cognitive capacities that we use throughout our daily lives. The cognitive processes behind categor ization, cross-domain mapping, conceptual models, and theor ies would all be operational had we never heard a note of music. Doubtless, our lives would be immeasurably impoverished had this unlikely tur n of events transpired, 12. Among the first to draw this distinction was Edward T. Cone in “Analysis Today,” Musical Quarterly 46 (1960): 172 – 88. This essay can also be found in Paul Henry Lang (ed.), Problems of Music Analysis: The Princeton Seminar in Advanced Musical Studies (New York:W.W. Norton, 1960), 34– 50; and Cone, Music, a View from Delft: Selected Essays (Chicago: University of Chicago Press, 1989), 39– 54.

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conc lu s i on but not only because we would have never been exposed to what Proust characterized as “another world, another order, ideas veiled in shadow, impenetrable to the human mind, but none the less perfectly distinct from one another.” We would also have never had these cognitive capacities stretched and transfor med by the challenge of listening to the play of patterned sound. Nor would we have taken what we learned in our encounters with that domain back to our understanding of the world as a whole. And we would never have had the opportunity to extend our conceptualization of music into theor ies of music — theories that, in the webs of relations they build both within and without music, offer their own topic for intellectual investigation. Conceptualizing music, seen in this way, is thus both a celebration and an exploration of the means by which our minds go out to meet the world.

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b i bl i og raphy Red Nichols and His Five Pennies. “I Got Rhythm.” In Rarest Brunswick Masters, 1926–1931: Red Nichols and His Five Pennies. MCA Records, [LP] MCA 1518, 1982. Red Norvo and His Swing Sextette. “I Got Rhythm.” In Red Norvo. Time-Life Records, [LP] STL-J14, 1980. Sidney Bechet and the New Orleans Feetwarmers. “Shag.” In Sidney Bechet. Time-Life Records, [LP] STL-J09, 1980.

index

Page numbers in italics indicate that a musical example appears on the given page. Page numbers in boldface indicate substantial analytical discussions with numerous musical examples and figures. Abelson, Robert P., 112 Absatz, 293, 299 Académie Royale de Musique. See Opéra Agawu,Victor Kofi, 51n45, 244 – 45, 286 Aldwell, Edward, viii analysis, musical and music theory, 19, 134 – 35, 333 analysis of song, 18, 244 – 45 and conceptual blending, 254 – 55, 264 – 65, 285 – 86, 332 Anlage, 296 Anstieg, 130, 261 anthropomor phism, 79– 81, 91– 95, 113, 127n59, 248, 315, 327 Antrag (Propositio), 295 Aristotle, 10, 311 Aristoxenian music theory, 7, 12– 14, 16 Aristoxenus, 10 – 12, 14, 63 Arom, Simha, 217 Aufführung (Executio), 295 Ausarbeitung (Elaboratio), 295 – 96 Ausführung (Executio), 295– 96 Austin, Gene, 231– 32 “Baby Face” (by Harry Akst and Benny Davis), 234 Bach, Johann Sebastian, 126 Bakhtin, Mikhail Mikhailovich, 18, 204, 224 – 25, 227–29 Bali. See pitch relations, descriptions of Bamberger, Jeanne research on musical understanding, 96– 99 work with Jeff, 17, 99– 101, 103– 7 Barker, Andrew, 63

Barsalou, Lawrence W., 41, 69 Bechet, Sidney, 210 Beethoven, Ludwig van, 18, 27, 48, 59, 169, 201– 3, 242 Fifth Symphony (Symphony No. 5 in C minor, Op. 67), first mvmt., 34, 35 – 40, 42– 44, 46– 48 Ninth Symphony (Symphony No. 9 in D minor, Op. 125), 120 piano sonatas, 120 Sixth Symphony (Symphony No. 6 in F major, Op. 68; “Pastorale”), 89– 94, 327, 331 String Quartet, Op. 18 No. 1, first mvmt., 177– 91, 191– 94, 196, 198, 200, 329 String Quartet, Op. 18 No. 1 [first version], first mvmt., 177, 191– 97 String Quartet, Op. 18 No. 6, first mvmt., 169 – 77, 199, 329 Bekräfftigung (Confirmatio), 295 Bericht (Narratio), 295 Berlin, Brent, 32, 115 Berliner, Paul F., 220, 331 Boethius, Ancius Manlius Severinus, 15 Brahms, Johannes, 126, 279 compositional technique, 25, 57– 58, 284 “In der Fremde” (Op. 3 No. 5), 279–84, 286, 331 Sextet in Bf major, first mvmt., Op. 18, 26, 26– 27, 28 Brailoiu, Constantin, 216 – 17 Brechung, 127 Brown, Roger, 31, 33 Bruckner, Anton Sixth Symphony, 57– 58

353

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i nde x Bruno, Giordano, 312 “Bye Bye Blackbird” (by Mort Dixon and Ray Henderson), 18, 203 – 4, 219, 223 – 25, 229 – 39, 240 racial associations, 223 – 24, 239 – 40 recording history, 230 – 39 cadence, 121, 151– 52, 284 complete (vollständiger Schluß ), 299 garbled (verstümmelter Schluß ), 299 perfect authentic, 61 Cage, John 4' 33", 242 Cantor, Eddie (Edward Israel Iskowitz), 235 Carroll, Lewis (Charles Dodgson) Alice’s Adventures in Wonderland, 287 – 88, 305, 324 Through the Looking Glass, 169 categor ies, 12, 16, 326, 332– 33 artificial (see categor ies: Type 2) basic-level, 31– 33 basic-level, and musical motives, 34, 36 classical (see categories: Type 2) natural (see categor ies: Type 1) Type 1, 39– 42, 44, 48– 49, 61n59, 149, 326 Type 2, 40 – 41, 48, 61n59 typicality effects in, 36– 40 typicality effects in, and musical motive, 43– 44, 46– 49 categor ies, musical, 59– 62, 168, 176, 242, 326 and compositional strategy, 139 – 40, 150 – 52, 159, 167, 191, 199 – 200 and musical ontology, 203, 213, 222 – 23 typicality effects in, and compositional strategy, 47, 50 – 51, 149, 153, 200 categor ies, musical motives as, 34, 43– 44, 46– 52, 58– 59 in Beethoven’s String Quartet Op. 18 No. 1, 177, 179 – 80, 182 – 84, 186, 188 – 89, 191, 193 – 94, 196, 198 in Beethoven’s String Quartet Op. 18 No. 6, 169, 171– 74, 176 in Mozart’s String Quartet K. 465, 155, 158 – 60, 164, 166 – 67 categor ization, 12– 17, 24, 30 – 33, 37, 43– 46, 48– 49, 51, 58, 60 – 61, 77, 102, 108, 203 – 4, 222, 327 – 28, 333 and compositional strategy, 139, 199 – 200 research on, 30 – 31, 108 Catel, Charles Simon, 301n39 Chambers, Jack, 224 Chambers, Paul, 223, 239 changes (i.e., harmonic progressions; in jazz performance), 211n21 Charlie and His Orchestra, 234

Chomsky, Noam, 4 chorus (in jazz perfor mance), 210 CINs. See conceptual integration networks cognitive capacities, 328, 331, 334 cognitive domain, 110n20 cognitive linguistics, 5, 17, 64, 66, 138 – 39 cognitive structure, 4– 6, 17, 19, 108, 111, 119, 133 – 34, 330, 333 cognitive theory, 19 Coleman, Linda, 226, 242 Colston, Herbert L., 69 Coltrane, John, 223 – 25, 239 – 40 competence, linguistic, 4 competence, musical, 4 compositional strategy, 47, 54, 138 – 41, 148 – 49, 152 – 54, 159, 167 – 68, 177, 180, 184, 191, 198 – 200, 264, 329 and musical syntax, 138 – 40, 148, 153 – 54, 167, 198 – 200, 264 concepts, 108 – 9 categories and, 60 – 61 musical, 17, 64, 102, 326– 27 (see also categories, musical) conceptual blending, 17– 18, 288, 323, 331 in Brahms’s “In der Fremde,” 284 in Klein’s “Trockne Blumen,” 254, 256, 264–65 in Müller’s “Trockne Blumen,” 248 – 49 and program music, 89– 94 role in text painting, 65, 82– 84, 87– 89 in Schubert’s “Trockne Blumen,” 263 – 65, 286 in Schumann’s “Im Rhein,” 270 – 72 in Schumann’s “In der Fremde,” 278 – 79 theory of, 77– 82 See also analysis of song conceptual domains, 103, 108 – 9 basic features of, 112 – 13 and mental spaces, 113 and theor ies, 113 conceptual integration networks (CINs), 78– 80, 82, 331 for anthropomorphism, 91– 92 for Brahms’s “In der Fremde,” 282 for Klein’s “Trockne Blumen,” 253 – 56 for Palestr ina’s text painting, 82– 83 for Schubert’s “Trockne Blumen,” 262– 63 for Schumann’s “Im Rhein,” 270 for Schumann’s “In der Fremde,” 277 topography of, 79– 80, 254, 265, 272, 283, 285–86 for Tovey’s analysis of Beethoven’s Sixth Symphony, 92– 93 for Wert’s “Tirsi mor ir volea,” 87– 88 conceptual models, 14– 17, 102, 108 – 9, 324, 327, 332–33

i nde x basic features of, 109 – 12 cross-domain mapping and, 71– 72 global, 46– 48, 50, 59, 62, 72, 74, 76, 112, 167, 218, 221– 22 idealization of, 111 Jeff ’s development and use of, 101– 2, 104– 7, 109, 218 local, 48, 50, 59, 62, 112, 218, 221– 22 and music theory, 332 musical motives and, 46– 48, 50 – 52, 57– 58 and musical notation, 221– 22 and musical ontology, 203, 213 – 14, 242, 330 and musical perfor mance, 216– 23 negotiation of, 219– 22 representing, 112 role in categor ization, 44– 48 and theor ies, 15– 17, 62, 98– 99, 102– 3, 107– 9, 111, 125, 131, 133, 317, 323 – 24 conceptual models for musical categor ies for Beethoven’s Fifth Symphony, 46– 48 for Beethoven’s String Quartet Op. 18 No. 1, 179 – 80, 184, 187, 198 for Beethoven’s String Quartet Op. 18 No. 6, 171– 72 for “Bye Bye Blackbird,” 233, 235, 238 – 39 for “I Got Rhythm,” 212 – 16 for Mozart’s String Quartet K. 465, 155, 160, 167 conceptual slippage, 105 – 6, 112, 159, 183 – 84 conceptualization of music, 12, 14, 59– 61, 67, 334 concords, 8– 9, 11, 13, 15 Cone, Edward T., 333 analysis of Mozart Piano Sonata K. 331, 307– 10, 323– 24 on motivic der ivation, 27– 28, 54n48, 59 Confir matio (Bekräfftigung), 295 Confutatio (Wiederlegung), 295 Conservatoire (Conservatoire National de Musique et de Déclamation), 300 – 301 consonant intervals. See concords Cook, Nicholas, 245, 265, 332 Cooper, Grosvenor W., 307 corps sonore, 123, 127n59 Cowdery, James R., 217 Crawford, Richard, 204n7, 210, 214, 222 cross-domain mapping, 13– 17, 19, 71, 73, 287– 89, 291, 295– 97, 326– 27, 332– 33 accounts of music and, 64, 76 between grammar and music, 291– 92, 294 – 96, 299, 301 between language and music, 291– 92, 299 between rhetor ic and music, 295, 297 – 99 image-schema theory and, 68– 69 metaphor theory and, 65– 66

music theory and, 72– 76 and musical categor ies, 330 role in conceptual models, 109– 10 See also hierarchy; metaphor: contemporary theory of cultural knowledge, 109 – 10, 115 – 16, 202 – 4, 219– 20, 222– 23, 240 – 42 cultural model, 110n20 cultural theory of information exchange, 225 – 29 Czerny, Carl, 305 Dahlhaus, Carl, 23– 24, 49, 57– 58 Damasio, Antonio R., 70, 108n16, 331 Davis, Miles, 223 – 25, 239 – 40 Davis, Ruth, 222 Debussy, Claude Reflets dans l’eau, ix Decoratio (Schmückung or Zierde), 295 Dever,William E., 223 diezeugmenon, 6 discords, 8– 9, 11, 13, 15 Dispositio (Einrichtung), 295– 96 dissonance, 25, 121 dissonant intervals. See discords Dixon, Mort, 229 Dorsey, Jimmy (James), 210, 213 – 16 double-voiced discourse, 204, 224 – 25, 227 – 29, 239–41 Dylan, Bob (Robert Allen Zimmer man), 139n73 Eco, Umberto, 137 – 38, 154, 168 – 69, 199 Edelman, Gerald M., 60, 69, 108 Eichendorff, Joseph Freiherr von “In der Fremde,” 272 – 73, 276 – 77, 279, 282–84 Viel Lärmen um nichts, 272 – 73, 276 Eingang (Exordium), 295 Einrichtung (Dispositio), 295 – 96 Einschnitt, 293, 299 Elaboratio (Ausarbeitung), 295– 96 embodied exper ience. See image schemata enthymeme. See cadence: garbled Erfindung (Inventio), 295 ethnobotanical classification, 32, 115 – 16 Executio (Aufführung or Ausführung), 295– 96 Exordium (Eingang), 295 fake books, jazz, 209 Fantasia (Walt Disney movie), 94n47 Fauconnier, Gilles, 78, 82 Feld, Steven, 67, 116 Ferris, David, 276n28 Fétis, François-Joseph, 317 Fichte, Johann Gottlieb, 302 – 3 Fingerle, Marlene, 234

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i nde x Finnegan, Ruth, 220 Fisher, Freddie “Schnickelfritz,” 234 Fitzgerald, Ella, 236 Fodor, Jerry A., 29, 60n53 form, musical, 18, 288. See also grammar, and musical for m; sonata for m; theories of musical for m Förster, Friedrich, 246 Forte, Allen, 132 Foucault, Michel, 295n23, 298n36 frames, 41– 44, 110n20 Freudenthal, Gideon, 312– 13 Friedrich Wilhelm III (king of Prussia), 301 games, musical, 139 – 40 Garland, Judy (Frances Gumm), 212 Garland, Red (William M.), 223, 239 Gates, Henry Louis, Jr., 18, 204, 224, 228 Geertz, Clifford, 111, 201– 2, 241– 42 German universities, 301– 2. See also music education: German Gershwin, George, 204, 209, 213 – 16. See also “I Got Rhythm” Gershwin, Ira, 204 Gibbs, Raymond W., Jr., 69 Girl Crazy (George and Ira Gershwin musical), 204 – 6, 212, 213n25 Gjerdingen, Robert O., 43n33, 168 Goetschius, Percy, 290 – 91, 305 Goodman, Benny (Benjamin), 212 – 15 Goodman, Nelson, 203n5 Gopnik, Alison, 117 – 18 grammar and music, 290, 292– 95, 297– 99. See also cross-domain mapping: between grammar and music grammar, and musical for m, 298– 99 Graun, Carl Heinr ich Der Tod Jesu, 297 Greater Perfect System, 6– 7, 10 – 13 Greek music, 6, 12, 330 theories of music, 6– 16, 330 Griffin, Donald R., 60 Groth, Renate, 317 Guarini, Giovanni Battista, 84 Hammerstein, Oscar, 224 “Happy Birthday” (“Good Mor ning to All,” by Mildred J. and Patty Smith Hall), 97– 98 Harris, Paul L., 118n39 Hauptmann, Moritz, 320 Haydn, Joseph, 154, 174 head (in jazz perfor mance), 210n15 Hegel, Georg Wilhelm Friedrich, 302

Heine, Heinrich “Im Rhein,” 265 – 66, 272 Lyriches Intermezzo (1823), 265, 272 Henderson, Fletcher, 210 Henderson, Ray, 229 Hensel, Luise, 246 Hensel, Wilhelm, 246 hierarchy atomistic, 310, 313, 320 mapping on to music, 320 – 23 structure of, 314 – 16 chain-of-being, 310 – 13, 320 mapping on to music, 316– 18, 321– 23 structure of, 314 – 15 models of, 289, 310, 314, 316, 324 musical, 18– 19, 59– 60, 120, 128, 131, 306– 8, 323–24 Hobbes, Thomas, 312 Hockenberry, John, 73n21 Hofstadter, Douglas R., 105 Holland, Dorothy, 109 – 10 Hood, Mantle, 220 “Hot Cross Buns” (folk song), 99 Hutchins, Edwin, 9n9, 115 Hypate hypaton, 6, 10 Hypate meson, 6, 10 hypaton, 6 hyperbolaion, 6 “I Got Rhythm” (by George and Ira Gershwin) 18, 203, 204 – 12, 213 – 16, 218 – 22, 231, 233, 238 recording history, 205– 6, 208– 12 “Rhythm changes,” 211, 331 tunes der ived from, 210 “I Know That You Know” (by Vincent Youmans), 234 “I’m a Little Blackbird Looking for a Bluebird” (by Grant Clarke, Arthur Johnston, George W. Meyer, and Roy Turk), 237 idealized cognitive model, 110n20 “Im Rhein.” See Heine, Heinrich; Schumann, Robert image schemata, 68– 71, 314 – 15, 322 – 23, 327 and rhetor ical figures, 138 – 39 theory of, 68– 70 “In der Fremde.” See Brahms, Johannes; Eichendorff, Joseph Freiherr von; Schumann, Robert India, music theory of, 13 intervals. See pitch relations, descriptions of Invariance Principle, 70 – 71, 322 – 23 Inventio (Erfindung ), 295 invention (process of ), 295– 97, 302– 3

i nde x Jackendoff, Ray, 59 Java. See pitch relations, descriptions of Jeff (experimental subject). See Bamberger, Jeanne: work with Jeff Johnson, Mark, 65– 66, 68 Johnson, Robert “Cross Road Blues,” x–xi, 74n22 Jones, Philly Joe (Joseph Rudolph Jones), 223, 239 Kaluli (Papua New Guinea). See pitch relations, descriptions of Kay, Paul, 226, 242 Keats, John “Ode to a Nightingale,” 66 Keller, Hans, 61n57 Kerman, Joseph, 169, 176 Klein, Bernhard, 243 “Trockne Blumen,” 249 –57, 264 – 65, 286 knowledge structures, 110n20 Koch, Heinrich Chr istoph, 148, 152, 293– 94, 297 – 98, 301 Kopfton, 127, 129– 30n64, 261, 321 Kramer, Lawrence, 244 Krueger, Bennie, 230 – 32 Kuhn, Thomas S., 118 Kurth, Ernst character ization of tonality, 76 Lakoff, George, 65– 66, 70, 111 Langer, Suzanne, 244 language and music, 5, 17, 61, 64, 84, 89, 220, 245, 285, 297, 326, 331. See also cross-domain mapping: between language and music language, origins of, 284– 85, 291 Lee, Peggy (Nor ma Delor is Egstrom), 224, 236– 40 Leibniz, Gottfried Wilhelm, 313 Leidensmotiv. See Wagner, Richard: Leidensmotiv from Tristan und Isolde Lerdahl, Fred, 59 Levy, Janet, 174, 177, 191 Lewin, David, ix, 98, 326n2 Lichanos hypaton, 6 Longinus, 138 – 39 Louis, Rudolf, and Ludwig Thuille character ization of tonality, 74– 76, 83 Lully, Jean-Baptiste, 120 recitative from Armide, 120, 123 McClary, Susan, x–xi, 59, 74n22 McNeill, David, 69 Macpherson, Stewart, 290n9 Macrobius, Ambrosius Aurelius Theodosius, 311 Maddox, Johnny, 236

Mahler, Gustav, 242 Marcello, Benedetto, 295 Marx, Adolph Bernhard (A. B.), 48, 177, 302 – 5 definition of musical motive, 304 Die Lehre von der musikalischen Komposition, 302–5 Mattheson, Johann, 292, 294 – 97, 333 analysis of anonymous minuet, 292, 293 Meltzoff, Andrew, 117– 18 Melvin and Howard (Jonathan Demme movie), 239n78 mental models, 110n20 mental spaces, 78, 80, 82, 89, 331. See also conceptual domains: and mental spaces Merman, Ethel (Ethel Agnes Zimmer man), 204– 5, 213 Mese, 6 meson, 6 metaphor conceptual, 66– 70, 300 contemporary theory of, 14, 17, 65– 70, 108 linguistic, 66, 300 Meyer, Leonard B., 307– 10, 321– 23, 333 Milne, A. A. (Alan Alexander), 77 Minsky, Marvin, 112 modular ity, theory of, 29– 30 Momigny, Jérôme-Joseph de theory of tonality, 316 – 17 Monson, Ingrid, 220, 224– 25, 240 Montessor i bells, 96 Morgan, Robert P., 50n43, 52n47, 54nn48 – 49, 333 analysis of Mozart K. 331 theme, 308– 10, 321, 323 motif. See motive, musical motive, musical, 3, 16, 18, 325 as category, 16 as dynamic construct, 289 – 90, 305 Goetschius’s definition of, 290 Marx’s definition of, 304 and musical for m, 289– 91 and process of derivation, 27– 29 Prout’s definition of, 289 – 90 Riemann’s definition of, 305 as static building block, 290 See also theories of musical motive Mozart,Wolfgang Amadeus, 18 Marriage of Figaro, Overture, 301 musical game (see Musikalisches Würfelspiel ) Piano Sonata in A major, K. 331, first mvmt., 306–10, 321– 24 String Quartet K. 465 (“Dissonance”), first mvmt., 154–68, 199, 330 Müller,Wilhelm, 243, 285 Die schöne Müllerin, 246 – 47, 272 “Trockne Blumen,” 247 – 49

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i nde x music education demand for instruction books, 291 French, 300 – 301, 305 German, 289, 302, 304 – 5 institutionalization of, 324 Musica enchiriadis (anonymous treatise), 291 musical notation, 67, 72, 330 Jeff ’s development of, 100 – 101, 103– 4, 106– 7 and the negotiation of conceptual models, 221– 22 musical ontology, 18, 202– 4, 214, 222, 241– 42, 330 Musikalisches Würfelspiel (attributed to W. A. Mozart), 140 – 54 organization of game, 141– 43, 145, 148 template for compositional strategy, 149 – 54 “My Favorite Things” (by Oscar Hammerstein and Richard Rodgers), 224 – 25, 240 Napoleon I (Napoleon Bonaparte), 301 Narmour, Eugene, 62n60, 322n93 Narratio (Bericht), 295 Naturklang, 127, 131, 318 navigation in Polynesia and Micronesia, 115 – 16 Neoplatonic cosmology, 311– 12, 318 Neoplatonism, 311 Newton, Isaac, 313 Nichols, Red (Ernest Lor ing Nichols), 206, 213– 15 Nicomachus of Gerasa, 8– 9 Norvo, Red (Kenneth Norville), 213 – 15 notation, musical. See musical notation obligate Lage, 130 – 31 Odette (from Proust’s A la recherche), 19, 325– 27 Opéra (Académie Royale de Musique), 300 organicism, 113, 127, 130 – 31, 300, 302 – 5, 314n71, 317 – 18 Palestr ina, Giovanni Perluigi da Pope Marcellus Mass, Credo, 63–64, 73, 82– 83 use of text painting, 63– 64, 73– 74, 77, 82– 84 Parhypate hypaton, 6 Parker, Charlie (Charles), 211, 213– 15 Pastoral Symphony. See Beethoven, Ludwig van: Sixth Symphony perceptual symbols, 70, 111n21 Peroratio (Schluss), 295 Pete Kelly’s Blues (Jack Webb movie), 236 pitch relations, descriptions of Aristoxenus, 11, 14, 63 Bali, 67– 68, 71– 72 basis in image schemata, 69 Greek, 14, 63, 67 Java, 67– 68, 71– 72

Kaluli (Papua New Guinea), 67– 68, 116 – 17 Suyá (of the Amazon basin), 68 pitch relations, musical notation and, 67, 72 pitch-event, 101– 5, 107, 110, 112 Plato, 10, 311 Plotinus, 311 Pollard-Gott, Lucy, 43n33 Porter, James, 217 Powers, Richard, 218n34 Propositio (Antrag), 295 Proslambanomenos, 6, 10 Proust, Marcel, 16 A la recherche du temps perdu, 3–4, 81– 82, 325 – 27, 334 aesthetic theory, 328 Prout, Ebenezer, 289 – 91, 305 Ptolemy, 15 Pythagoras of Samos, 7– 9, 12, 311n62 Pythagorean music theory, 7– 8, 10, 12– 14, 16 Quinault, Philippe, 120 Quinn, Naomi, 109 – 10 Rama Indians (Nicaragua) snakebite cure, 115 – 16 Rameau, Jean-Philippe, 17, 119, 285, 330, 333 analysis of recitative by Lully, 120 – 24 theory of music, 121– 24, 132, 148 theory of music as a cognitive theory, 124 – 26 ratio (applied to music), 8– 10, 13, 15 epimeric, 13, 15 epimoric, 13, 15 multiple, 13, 15 Ratner, Leonard G., 168 – 69, 179 – 80, 200 Redman, Don, 208, 213– 15 Reicha, Antoine, 301– 2, 305 Réti, Rudolph theory of motive, 26– 27 rhetor ic, 139n74, 225, 228, 292– 93, 303 and music, 296 – 98 musical, 288– 89, 324 and musical for m, 298– 99 See also cross-domain mapping: between rhetor ic and music rhetor ical figures, 138– 39, 295– 96, 299 Rich, Fred, 208, 213 – 15 Richardson, Samuel, 291 Richter, Jean Paul, 303 Riemann, Hugo, 305 character ization of tonality, 76 definition of musical motive, 305 theory of meter and rhythm, 320 Riepel, Joseph, 148, 152, 292 – 94, 299 Robertson, Jeanne, 217 Rodgers, Richard, 224

i nde x Rooney, Mickey (Joe Yule, Jr.), 212 Rosch, Eleanor, 16, 32– 33, 41 Rousseau, Jean-Jacques analysis of recitative by Lully, 122 on the or igins of language, 284 – 85 Saint-Saëns, Camille Le Carnaval des animaux, 71 Satz, 48n40, 293 Schachter, Carl, viii Schank, Roger S., 112 Schelling, Friedrich von, 288, 302 – 3 Schenker, Heinrich, 17, 119 – 20, 331, 333 analysis of Schubert’s waltz Op. 77 No. 1, 128 – 30 theory of hierarchy, 317 – 18 theory of music, 127 – 30 theory of music as a cognitive theory, 130 – 32 theory of musical motive, 26– 27 Schiller, Friedrich, 302 Schlegel, August Wilhelm, 303 Schleier macher, Friedrich, 302 Schluss (Peroratio), 295 Schmückung (Decoratio), 295 Schoenberg, Arnold, 242, 333 character ization of tonality, 76 theory of musical motive, 25– 27, 30, 34, 42, 57– 59, 139, 154 Schöll, Adolf, 273 Schopenhauer, Arthur, 328 Schubert, Franz, 243, 332 “Der Wanderer” (Op. 4/1, D. 489), 28, 29 “Trockne Blumen,” from Die schöne Müllerin (D. 795), 257– 64, 265, 332 Valses nobles, Op. 77 No. 1, 128 –29, 130 Wanderer Fantasie (Op. 15), 27– 28, 29 Schumann, Robert, 265, 272 – 73, 279 “Der frohe Wandersmann” (Op. 77 No. 1), 276 Dichterliebe (Op. 48), 265 “Im Rhein” from Dichterliebe, 266–72, 278, 286 “In der Fremde” (Op. 39 No. 1), 273 – 79, 281, 286 Liederjahr of 1840, 265, 284 Schutt, Arthur, 234 Sectio canonis (anonymous treatise), 13, 15 Seeger, Charles, 221 semantics, musical, 17– 18, 138, 199 – 200, 329 musical syntax and, 54, 199 – 200, 299, 329 semiotics, musical. See semantics, musical Short, Bobby, 237 – 39 Signifyin(g), 18, 224, 229, 240 – 41 Skolsky, Sidney, 235 Sleepless in Seattle (Nora Ephron movie), 239n78 sonata for m, 152 – 53 Spaun, Joseph von, 243, 285

Stägemann, Friedrich August von, 246 Stägemann, Hedwig von, 246 Sulzer, Johann Georg, 296 – 98, 302 – 4, 313n67 Suyá (of the Amazon basin). See pitch relations, descriptions of Swann, Charles (from Proust’s A la recherche), 3– 5, 16, 18– 19, 61, 81, 325 – 28, 333 theory of music, 332 Sweetser, Eve E., 225 – 27, 242 syllogismus. See cadence: complete symbols, 72, 103, 106. See also perceptual symbols synaesthesia, 89n38 syntax, musical, 17– 18, 52, 54, 75, 95, 132 – 33, 137 – 38, 140, 199 – 200 in Beethoven’s String Quartet Op. 18 No. 1, 189, 191, 196, 198 in Beethoven’s String Quartet Op. 18 No. 6, 172 – 73, 176 dynamic approach to, 329 formal, 143, 167, 199, 329 harmonic, 124 – 25, 130, 146, 153 – 54, 198 – 200, 329, 331 melodic, 140, 154, 159, 167 – 68, 331 in Mozart’s String Quartet K. 465, 154, 159, 167–68 multiple levels of, 198 musical categor ies and, 51– 52, 54, 61– 62, 329 and the Musikalisches Würfelspiel, 151– 54 Rameau’s theory of music and, 121– 22, 124–25 and rhetor ic, 54n48 Schenker’s theory of music and, 127 – 28, 130 – 31 and song texts, 254 – 55, 284 – 86 thematic, 198, 200 Talmy, Leonard, 69 tetrachords, 6 tetraktys of the decad, 9 text painting, 17, 63– 65, 73– 74, 77, 82– 84, 87– 88, 95 theme, musical conceptual models and, 47– 48 theories, 5, 15– 17, 62, 98– 99, 102 – 3, 108 – 9, 119, 125, 131, 133, 317, 332 – 33 ad hoc, 132 cultural, 114 – 17 extended, 132 function and structure, 106 – 7, 111, 113 – 14 implicit, 116 – 17 scientific, 113 – 14, 117 of very young children, 117 – 19 See also conceptual models: and theor ies theories of meter and rhythm, 307 – 10, 319–23

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i nde x theories of music, 5, 15, 121– 24, 127– 30, 132, 148, 323 – 24, 332, 334 as cognitive theory, 119, 124– 26, 130 – 34 of early India, 13 Greek, 6– 16 Jeff ’s development of, 101– 2, 104– 7 and syntax, 121– 22, 124 – 25, 127 – 28, 130 – 31 See also Aristoxenian music theory; Pythagorean music theory theories of musical for m, 300 – 306 theories of musical motive, 25– 30, 34, 42, 57– 59, 139, 154, 289 – 90, 304 – 5 theories of tonality, 74– 76, 83, 316– 18 Thompson, William (Big Bill), 223 Thuille, Ludwig. See Louis, Rudolf, and Ludwig Thuille Ton, 316– 17. See also Momigny, Jérôme-Joseph de: theory of tonality tonality character izations of, 76 as metaphysical, 317 See also theories of tonality topics, musical, 168, 174, 176 – 77, 184, 198, 200, 329 topography. See conceptual integration networks (CINs) Tovey, Donald Francis, 90 – 94, 327, 331, 333 “Trockne Blumen.” See Klein, Bernhard; Müller, Wilhelm; Schubert, Franz Tunisia, music of, 222 Turner, Mark, 70, 78 on rhetor ical figures, 138 – 39 “Twinkle, Twinkle Little Star” (folk song), 100 Jeff ’s work with, 99– 108

University of Berlin, 302 University of Halle, 301 University of Jena, 302 Urlinie, 127, 130 – 31 Ursatz, 127 – 31, 318, 321 Verwandlung, 128 Vinteuil’s sonata (from Proust’s A la recherche), 3– 4, 16, 18– 19, 325, 327– 28, 332– 33 Wagner, Richard compositional strategy, 49– 51, 58 Leidensmotiv from Tristan und Isolde, 49– 52, 54, 57– 59, 62, 138 Sehnsuchtsmotiv from Tristan und Isolde, 49 Tristan und Isolde, 23– 24, 24, 49–58 Webb, Chick (William Henry Webb), 209, 213–15 Webb, Jack, 236 Weber, Gottfr ied, 319– 20 Welker, Robert L., 43n33 Wert, Giaches de “Tirsi mor ir volea,” 84, 85–86, 87– 89 Wieck, Clara, 273 Wiederlegung (Confutatio), 295 Will, Richard, 90 Wittgenstein, Ludwig, 30 Wolzogen, Hans von, 49 work of music. See musical ontology Young, Lester, 211, 213– 15 Zemlinsky, Alexander von, 25 Zierde (Decoratio), 295