The Philosophy of Rhythm: Aesthetics, Music, Poetics 0199347778, 9780199347773

Rhythm is the fundamental pulse that animates poetry, music, and dance across all cultures. And yet the recent explosion

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The Philosophy of Rhythm

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The Philosophy of Rhythm Aesthetics, Music, Poetics Edited by

P E T E R C H EY N E , A N DY HA M I LT O N , A N D M A X PA D D I S O N

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3 Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America. © Oxford University Press 2019 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. Library of Congress Cataloging-​in-​Publication Data Names: Cheyne, Peter. | Hamilton, Andy, 1957– | Paddison, Max. Title: The philosophy of rhythm : aesthetics, music, poetics / edited by Peter Cheyne, Andy Hamilton, and Max Paddison. Description: New York, NY : Oxford University Press, [2019] | Includes bibliographical references. Identifiers: LCCN 2019004326 | ISBN 9780199347773 (cloth) | ISBN 9780199347780 (pbk.) | ISBN 9780199347896 (oxford scholarship online) Subjects: LCSH: Musical meter and rhythm. | Music—Philosophy and aesthetics. | Musical perception. | Music—Psychological aspects. Classification: LCC ML3850 .P55 2019 | DDC 781.2/24117—dc23 LC record available at https://lccn.loc.gov/2019004326 1 3 5 7 9 8 6 4 2 Paperback printed by Marquis, Canada Hardback printed by Bridgeport National Bindery, Inc., United States of America

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“This remarkable collection of essays brings together philosophical and empirical approaches to the significance of rhythm across the arts. The approach is refreshingly interdisciplinary. Anyone concerned with the place of rhythm and metric structure in the arts, and—more generally—within the wider domain of human practices will find this an extraordinarily helpful volume.” —Robert Kraut, Professor of Philosophy, The Ohio State University “Fascinating and mysterious, rhythm is at the heart of music, dance, poetry, sociology, and neuroscience. This inspired volume engages, enlightens, and is the first to explore rhythm across a broad range of philosophical, aesthetic, and perceptual domains. This book is required reading for anyone concerned with time and rhythm in contemporary life.” —Peter Nelson, University of Edinburgh “This wonderful collection considers questions about rhythm from a wide variety of angles, perspectives, and disciplines—among them analytic and continental philosophy, musicology, art history, poetics, and neuroscience. Like the dialogue that opens the book, The Philosophy of Rhythm supports no particular line of thought or argument but enormously deepens our understanding of a topic so palpable and yet so mysterious.” —Christoph Cox, Hampshire College

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Preface This project began in the mists of time, as a collaboration between Andy Hamilton and Will Montgomery. Will had to pull out and Max Paddison took his place—​but Will remained as a contributor and his essay on rhythm in poetry is invaluable. Max has worked on musical time since his contributions to the 2004 special edition of Musicae Scientiae on spatialization and temporality in music, while Andy’s first publication on rhythm was for Proceedings of the Aristotelian Society in 2011. Max’s expertise in Continental philosophical traditions has been a necessary corrective to Andy’s more analytic background, and they organized a workshop in Durham in 2013, at which many contributions were presented. Besides his contributed essay, Peter Cheyne has been involved in an editorial role from an early stage. He reorganized the material, making it thematic rather than discipline-​centered, and closely edited each chapter. Acknowledgments are gratefully given to Laura Dearlove for diligently checking the style of several chapters; Anthony Parton for advice on artwork permissions; Suzanne Ryan, Jamie Kim, and Dorian Mueller at OUP for their work in helping to bring the volume to press; the anonymous reader for careful criticisms; Brian Marley for invaluable assistance in helping compile the index; and Durham University and the British Society of Aesthetics for their support for the workshop. Later-​stage work was supported by JSPS Kakenhi grant number 19K00143. Finally, a sincere apology is due to the patient contributors. This volume has taken much longer in preparation than was originally anticipated.

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Illustrations 8.1. Sulzer’s Schlagfolge 127 8.2. Koch’s Schlagreihe 128 8.3. Koch’s Schlagreihe with resting points (Ruhepuncten) 129 8.4. Model of the drift from rhythm to punctuation

129

8.5. Koch’s schema of a sonata-​form exposition

133

8.6. Mozart, String Quartet in C major, K. 465, “Dissonance,” bars 23–​6

135

8.7. Mozart, bars 67–​97

136

8.8. Introduction, bars 1–​4

137

9.1. Michael Jackson, “Billie Jean,” cabasa, drums, bass guitar, and synthesizer, timing c.00:20–​00:24

144

9.2. The double backbeat

146

11.1 Kanizsa triangle, organized array (left panel); disorganized array (right panel)

172

11.2. Beat interpolation in the opening theme of Brahms’ Symphony No. 4 in E-​minor, Op. 98

177

11.3. A “metrically malleable” melody notated in (a) 4/​4, and (b) 9/​8, showing alternate listening construals

178

11.4. The “Standard Pattern” (or “Bell Pattern”) timeline found in many styles and genres of African music. Upper system: construed as a three-​(or six-​) beat pattern. Bottom system: construed as a four-​beat pattern

178

15.1. Keats, “Hymn to Pan,” first stanza (from Endymion, Book 1, lines 232–​46), annotated. 236 15.2. The two sides of “projection”

242

15.3. One version, among many, of the nursery rhyme “Humpty Dumpty” as an illustration of the determinacy of tetrameter (and also as an example of the pattern long-​long-​short-​short-​long) 244 15.4. The first line said as strict iambic pentameter (five isochronous beats each of the form “weak-​strong”) in obvious violation of the line’s complexity

245

15.5. The first line said as five more or less isochronous beats, but now allowing for complexities of “weak” and “strong”

246

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xiv   List of Illustrations 15.6. The first line said as five “flexibly isochronous” beats whose flexibility or variability is determined (or “controlled”) by higher levels of complexity

246

15.7. Beat-​to-​beat projections in which each new event is focally aware simply of its immediate predecessor

249

15.8. A representation of projective complexity showing the resistance of a five-​beat line to the determinacies of four, or rather two, beats (Attridge’s “doubling”). NB: this diagram is not meant to represent the complexity of most “pentameter” lines where a reduction to two is not an issue. (Indeed, in some “pentameter” nine-​or ten-​syllable lines there are four beats, but these situations are hardly “square.”)

250

18.1. Husserl’s structure of time-​consciousness

297

19.1. Sonia Delaunay, Rythme coleur n° 1076 (1939). Centre national des arts plastiques. © Pracusa S.A./​Cnap/​Photograph: Yves Chenot

310

19.2. Dactyl illustration (Creative Commons)

313

19.3. Raphael, The Miraculous Draught of Fishes (1515–​16), bodycolour over charcoal underdrawing, mounted on canvas, 320 x 390cm, Victoria and Albert Museum. © The Royal Collection, HM The Queen/​Victoria and Albert Museum, London

314

19.4. Nicholas Dorigny, The Miraculous Draught of Fishes (1719), etching and engraving on paper, 51 x 65cm, Victoria and Albert Museum. © Victoria and Albert Museum, London

316

19.5. Joseph-​Marie Vien, St. Denis Preaching in Gaul (1767), oil on canvas, 660 x 393cm, Église Saint-​Roche, Paris. © The Art Archive

322

19.6. Ten percent of all saccades of forty viewers (twenty art experts and twenty non-​experts) beholding Vien’s painting for two minutes each. Adapted version © Laboratory for Cognitive Research in Art History, University of Vienna

323

19.7. Visualization of frequent saccadic transitions between fixation clusters for Vien’s St. Denis Preaching in Gaul (average of forty viewers, twenty art experts and twenty non-​experts, whilst viewing for two minutes each). Adapted version © Laboratory for Cognitive Research in Art History, University of Vienna 324 19.8. Visualization of frequent saccadic transitions between fixation clusters for Doyen’s The Miracle of St. Anthony’s Fire (average of forty viewers, twenty art experts and twenty non-​experts, whilst viewing for two minutes each). Adapted version © Laboratory for Cognitive Research in Art History, University of Vienna

325

21.1. Opening lines of John Milton’s Paradise Lost displayed as prose in David Charles Bell and Alexander Melville Bell’s Standard Elocutionist (London, 1878), 426

352

21.2. Graphic record of various rhythmical sounds, from Edward Wheeler Scripture, Elements of Experimental Phonetics (New York, 1902), 509

356

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Abbreviations bpm EDM fMRI HKB OED

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beats-​per-​minute electronic dance music functional magnetic resonance imaging Haken–​Kelso–​Bunz [equation] Oxford English Dictionary

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Notes on Contributors Aili Bresnahan is Associate Professor of Philosophy at the University of Dayton (USA). She specializes in aesthetics, particularly in applied philosophy of dance, improvisation, interpretation, and the philosophy of mind and motor cognition as it relates to the performing arts. She is also the founder and moderator of Dance Philosophers, an interdisciplinary research and networking Google group. More information can be found on her professional website: https://​www.artistsmatter.com. Contact:abresnahan1@ udayton.edu. Peter Cheyne is Associate Professor at Shimane University, and Visiting Fellow in Philosophy at Durham University. He is leading two international projects, one on the Aesthetics of Perfection and Imperfection, the other on the Seventeenth-​to Nineteenth-​Century Philosophy of the Life Sciences. Published in journals including Intellectual History Review and the Journal of Philosophy of Life, and editor and co-​author of Coleridge and Contemplation (OUP, 2017), he recently completed a monograph on Coleridge’s Contemplative Philosophy (OUP, forthcoming 2020). Martin Clayton is Professor in Ethnomusicology at Durham University. His publications include Time in Indian Music (OUP, 2000)  and Experience and Meaning in Music Performance (OUP, 2013, co-​edited with Laura Leante and Byron Dueck). He is currently pursuing research on entrainment in musical performance within Durham’s Music and Science Lab (https://​musicscience.net). Víctor Durà-​Vilà is Lecturer at the University of Leeds. In aesthetics, he works on Humean aesthetics, aesthetic experience, ethics and aesthetics, aesthetic cognitivism, as well as on interdisciplinary projects in music and dance. Other research interests include applied ethics (parental obligations; autonomy and paternalism) and philosophy of physics. His work has been published in journals such as Analysis, Journal of Value Inquiry, Journal of Aesthetics and Art Criticism, and British Journal of Aesthetics. Jason Gaiger is Associate Professor of Contemporary Art History and Theory at the Ruskin School of Art and a Fellow of St. Edmund Hall at the University of Oxford. His principal research interests are in aesthetics and art theory from the mid-​seventeenth century through to the present day; he also works on theories of depiction and visual meaning, and on twentieth-​century and contemporary art practice and theory. Ted Gracyk teaches philosophy at Minnesota State University Moorhead, and is co-​editor of the Journal of Aesthetics and Art Criticism. He is the author of several philosophical books on music, including Rhythm and Noise: An Aesthetics of Rock Music (Duke University Press, 1996), Listening to Popular Music (University of Michigan Press, 2007), and On Music (Routledge, 2013). With Andrew Kania, he co-​edited The

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xviii   Notes on Contributors Routledge Companion to Philosophy and Music (Routledge, 2011). Most recently, he co-​authored Jazz and the Philosophy of Art (Routledge, 2018). Garry L. Hagberg is James H.  Ottaway Professor of Philosophy and Aesthetics at Bard College. Author of numerous papers at the intersection of aesthetics and the philosophy of language, his books include Art as Language: Wittgenstein, Meaning, and Aesthetic Theory (Cornell University Press, 1995), and Describing Ourselves:  Wittgenstein and Autobiographical Consciousness (OUP, 2008). He is editor of Art and Ethical Criticism (Wiley Blackwell, 2008); Fictional Characters, Real Problems (OUP, 2016); and Wittgenstein on Aesthetic Understanding (Palgrave Macmillan, 2017). Editor of the journal Philosophy and Literature, Hagberg is currently writing Living in Words: Literature, Autobiographical Language, and the Composition of Selfhood. Jason David Hall is Associate Professor of English at the University of Exeter. He has written the books Seamus Heaney:  Poet, Critic, Translator (Palgrave Macmillan, 2007), Seamus Heaney’s Rhythmic Contract (Palgrave Macmillan, 2009), and Nineteenth-​ Century Verse and Technology: Machines of Meter (Palgrave Macmillan, 2017), and is contributing author and editor of Meter Matters: Verse Cultures of the Long Nineteenth Century (Ohio University Press, 2011) and Decadent Poetics: Literature and Form at the British Fin de Siecle (Palgrave Macmillan, 2013, with co-​editor Alex Murray). Andy Hamilton teaches Philosophy at Durham University, UK. He specializes in aesthetics, philosophy of mind, political philosophy, and history of nineteenth-​and twentieth-​ century philosophy, especially Wittgenstein. His books are Aesthetics and Music (Continuum, 2007), The Self in Question: Memory, the Body and Self-​Consciousness (Palgrave Macmillan, 2013), and Routledge Philosophy Guidebook to Wittgenstein and On Certainty (Routledge, 2014). He also teaches aesthetics and history of jazz at Durham, and published Lee Konitz: Conversations on the Improviser’s Art (University of Michigan Press, 2007). Christopher Hasty is Walter W. Naumburg Professor of Music at Harvard University where he teaches music theory. His research interests center on questions of time and rhythm understood from perspectives of process and event formation. Recent publications include essays in Thought and Play in Musical Rhythm: Multidimensional Perspectives on African, Asian, and EuroAmerican Musics (co-​edited with Richard Wolf and Steven Blum, OUP, 2019) and an essay on “Time” in The Oxford Handbook of Western Music and Philosophy (ed. McAuley, Nielsen, and Levinson, OUP, 2020). John Holliday has a PhD in philosophy from the University of Maryland and is currently Lecturer in the Philosophy Department at Stanford University, where he supports Stanford’s initiative in Philosophy and Literature. His research centers on issues of literary value and has appeared in the British Journal of Aesthetics and the Journal of Aesthetics and Art Criticism. Salomé Jacob holds a PhD on philosophy from the University of Durham. Her research lies at the intersection between philosophy of perception, aesthetics, and phenomenology. She focuses on the nature of musical movement. Jenny Judge is PhD candidate in philosophy at NYU. She also holds a PhD in musicology from the University of Cambridge, as well as degrees from University College Cork

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Notes on Contributors  xix and the Cork School of Music. Her research explores the resonances between musical experience and the philosophy of mind. Her doctoral dissertation defends and elaborates the thesis that music represents attitudes. Judge is also an active musician. Justin London is Andrew W.  Mellon Professor of Music, Cognitive Science, and the Humanities at Carleton College (USA). He received his PhD from the University of Pennsylvania where he worked with Leonard Meyer. His research interests include rhythm and timing in non-​Western music, beat perception, sensorimotor synchronization and joint action, and musical aesthetics. He has served as President of the Society for Music Theory (2007–​9) and President of the Society for Music Perception and Cognition (2016–​18). David Macarthur is Associate Professor at the University of Sydney. He has published articles on liberal naturalism, pragmatism, metaphysical quietism, skepticism, common sense, Wittgenstein’s philosophy of language, perception, and philosophy of art—​especially concerning architecture, photography, and film. He has co-​edited three collections of papers with Mario De Caro:  Naturalism in Question (Harvard University Press, 2004); Naturalism and Normativity (Columbia University Press, 2010); and Philosophy in an Age of Science (Harvard University Press, 2012); and recently edited Hilary and Ruth-​Anna Putnam, Pragmatism as a Way of Life (Harvard University Press, 2017). Will Montgomery teaches contemporary poetry at Royal Holloway, University of London. He is the author of The Poetry of Susan Howe (Palgrave, 2010); co-​edited (with Robert Hampson) Frank O’Hara Now (Liverpool University Press, 2010); and co-​edited (with Stephen Benson) Writing the Field Recording (Edinburgh University Press, 2018); and has published numerous articles on contemporary and twentieth-​century poetry. His monograph on short form in American poetry is forthcoming. He has a long-​standing involvement in experimental music and field recording and has released several CDs. Matthew Nudds is Professor of Philosophy and Chair of the Faculty of Social Sciences at the University of Warwick. His work is principally in the philosophy of perception and he has a particular interest in the non-​visual senses and auditory perception. Max Paddison is Emeritus Professor of Music Aesthetics at the University of Durham. He works in critical theory, philosophy, contemporary music, and popular music. His publications include Adorno’s Aesthetics of Music (CUP, 1993), Adorno, Modernism and Mass Culture (Kahn & Averill, 1996), and Contemporary Music: Theoretical and Philosophical Perspectives (co-​edited with Irène Deliège, Ashgate, 2010). He has recently contributed essays to The Palgrave Handbook of Critical Theory (Palgrave Macmillan, 2017), The Routledge Companion to the Frankfurt School (Routledge, 2018), and The Oxford Handbook of Western Music and Philosophy (forthcoming 2019). Deniz Peters is Professor for Artistic Research in Music at the University of Music and Performing Arts Graz, Austria, where he also directs the Doctoral School for Artistic Research. His research concerns philosophical questions, such as the concept of musical expression, listening modes, ensemble empathy, and the epistemic potential of artistic research through music. His explorative pianistic practice is part of his research method.

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xx   Notes on Contributors Peter Simons is Professor Emeritus of Philosophy at Trinity College Dublin. He is the author of the monograph Parts (OUP, 2000) and some 300 essays on pure and applied ontology, philosophy of language, logic and mathematics, the history of early analytic philosophy and of Central European philosophy (mainly Austrian and Polish) in the nineteenth and twentieth centuries. He is a member of the British, European, Irish, and Polish Academies. Michael Spitzer is Professor of Music at the University of Liverpool and Editorial Chair of the Society for Music Analysis. He inaugurated the International Conferences on Music and Emotion (Durham, 2009), and co-​organized the International Conference on the Analysis of Popular Music (Liverpool, 2013). His publications explore interactions between music theory, philosophy, and psychology, and include Metaphor and Musical Thought (Chicago University Press, 2004); Music as Philosophy (Indiana University Press, 2006); A History of Emotion in Western Music (OUP, forthcoming 2020); and The Musical Human (Bloomsbury, forthcoming 2021). Roger Squires works in areas opened up by the mid-​twentieth-​century revolution in philosophy of mind brought about by Wittgenstein and Ryle. Publications include: “Depicting,” Philosophy, 44 (1969); “Memory Unchained,” Philosophical Review, 77.2 (1969); “On One’s Mind,” Philosophical Quarterly, 20 (1970); “Silent Soliloquy,” Understanding Wittgenstein, Royal Institute of Philosophy Lectures, 7 (1973); “The Problem of Dreams,” Philosophy, 48 (1973); “Mental Arithmetic,” Ratio, 1 (1994). Alison Stone is Professor of European Philosophy at Lancaster University. She is the author of Petrified Intelligence: Nature in Hegel’s Philosophy (University of Notre Dame Press, 2004), Luce Irigaray and the Philosophy of Sexual Difference (CUP, 2006), An Introduction to Feminist Philosophy (Polity, 2007), Feminism, Psychoanalysis and Maternal Subjectivity (Routledge, 2011), and The Value of Popular Music (Palgrave Macmillan, 2016). She edited the Edinburgh Critical History of Nineteenth-​Century Philosophy (Edinburgh University Press, 2011)  and co-​ edited the Routledge Companion to Feminist Philosophy (Routledge, 2017). Michael Tenzer is Professor of Music at the University of British Columbia. His books include Gamelan Gong Kebyar: The Art of Twentieth Century Balinese Music (Chicago University Press, 2000) and the edited volumes Analytical Studies in World Music (OUP, 2006) and Analytical and Cross Cultural Studies in World Music (OUP, 2011, with co-​ editor John Roeder). His compositions are available on New World and Cantaloupe Records. Recent articles include the cross-​cultural study of world “Polyphony” in the Oxford Handbook of Critical Concepts in Music Theory (OUP, 2018). Matthew Tugby is Associate Professor at Durham University. He has published on a range of topics in contemporary metaphysics and co-​ edited  Metaphysics and Science (OUP, 2013). Rebecca Wallbank is PhD candidate in the Philosophy Department at Uppsala University, specializing in aesthetics and the philosophy of art. In addition to research on rhythm and the philosophy of literature she also has strong interest in the philosophy of trust and its relation to aesthetic testimony. She is Editorial Assistant to the British Journal of Aesthetics.

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Notes on Contributors  xxi Udo Will is Professor of cognitive ethnomusicology at The Ohio State University. He has studied music, sociology, and neuroscience, holds a PhD in both musicology and neurobiology, and his research focuses on cognitive aspects of music performances in oral cultures. He leads projects on physiological entrainment to music, on cultural effects on cognitive processing of prosodic components in music and language in Asian and African tone language cultures, and on cross-​cultural studies of rhythm perception, movement and the concept of time. Rachael Wiseman is Lecturer in Philosophy at University of Liverpool. She works on Wittgenstein, early analytic philosophy, and philosophy of mind, action, and ethics, and wrote the Routledge Guidebook to Anscombe’s Intention (Routledge, 2016). Her articles have been published in the Journal of Philosophy, American Catholic Philosophical Quarterly, and Philosophical Topics.

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Introduction Philosophy of Rhythm Peter Cheyne, Andy Hamilton, and Max Paddison

This volume brings together philosophical and empirical approaches to offer critical perspectives on the philosophy of rhythm. The editors have not imposed theoretical or interpretational prescriptions, except that contributors should examine concrete manifestations of rhythm in the various arts and in human activity. Our aim is to locate fruitful questions and stimulate lively discussion of them. Contributors offer definitions and theories of rhythm in music and prosody that are often opposed, referring to meter, pulse, stress, and accent as constituent elements of rhythm, or at least as key concepts in understanding it; lines of dispute are examined from different perspectives throughout the book. As well as examining the case of music, essays explore possibilities or hypotheses of rhythm in non-​musical and non-​ prosodic (non-​poetic) arts. As the essays are generally contemporary in scope, Section 1 outlines some key points in the history of rhythm in philosophy, not in the pretence of providing a comprehensive survey in such a short space, but to offer some historical precedents for the problems addressed. Section 2 discusses the extent of recent attention to rhythm and the puzzling neglect of the field, especially in philosophy. Section 3 gives an outline of the chapters, describing the conceptual space of the book.

1.  Historical Considerations Recent neglect notwithstanding, philosophical traditions have long acknowledged the importance of rhythm across the arts and in everyday life. However defined, it is readily agreed that rhythm is fundamental to those arts that directly involve duration and temporality:  dance, music, drama, and recited poetry. These arts were closely associated in classical Greece. They all include rhythm, the animating, flowing factor it is the purpose of this book to explore, along with the associated phenomena of movement, measure, pattern, and repetition. Before Parmenides and Plato, Heraclitus ascribed to rhythm a universal significance in holding that “everything flows [panta rhei].” This stream of thought Peter Cheyne, Andy Hamilton, and Max Paddison, Dialogue on Rhythm In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.001.0001

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2   The Philosophy of Rhythm continues in contemporary process philosophy, influencing thinkers, including some in this book, who employ the concept of rhythm as flow. Less cosmic, more socio-​cultural, Plato’s consideration of rhythm, in contrast, focuses primarily on music and its effects on culture and mood. In the Republic, he has Socrates discuss the various rhythms and regulations of meter as modeling different virtues (courageous, self-​controlled, active, graceful) and vices (lamenting, drunken, idle, graceless), reprising the theme in his later dialogue, the Laws. It is also in the Laws—​in a discussion of the ability to control and order one’s bodily movements and speech—​ that Plato has “the Athenian” give the definition by which: “Order within movement is called ‘rhythm.’ ”1 A core motivation for this collection of essays is to explore rhythm across the arts. Connections between the different arts are addressed in Aristotle’s Poetics via three related concepts: mimēsis, metaphora, and poiēsis. Aristotle saw mimesis as a dynamic, performative impulse to “mimic” actions, processes, emotions, and gestures through different media and art forms. Mimesis, he said, “is natural to us,” and in the opening pages of the Poetics he specifically refers to rhythm as a medium for mimesis: the medium of imitation [mimēsis] is rhythm, language, and melody, but these may be employed either separately or in combination. For example, music for pipe and lyre . . . uses melody and rhythm only, while dance uses rhythm by itself and without melody (since dancers too imitate character, emotion and action by means of rhythm expressed in movement).2

Clearly, Aristotle describes our capacity for an embodied mimesis that enables us to move rhythmically in space and move together in time with others. His discussion links music, poetry, and dance and anticipates the theory of entrainment discussed in several contributions to this volume. Another theme in this book is the contemporary debate between proponents of the dynamic thesis, who hold that music literally moves, and those on the other side, who conform to the thesis that movement in music is metaphorical. We return to this debate in Section 2, but should note here the three categories of rhythm distinguished by Aristides Quintilianus in his Peri musikês: The term ‘rhythm’ is used in three ways. It is applied to bodies that do not move, as when we speak of a statue having ‘good rhythm’; to anything that moves, as when we speak of someone walking with ‘good rhythm’; and it has a specific application to sound . . . . [viz.] a systēma of durations [chronoi] put together in some kind of order.3

1 Plato, Republic, Bk 3, 397a–​401a; Laws, Bk 7, 798d–​802e; Laws, Bk 2, 665a. 2 Aristotle, Poetics,  3–​4. 3 Aristides, On Music, Bk 1, Ch. 13.

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Introduction  3

For Aristides, then, rhythm applies to proportionality in static objects, physical movement, and music. Distinguishing rhythm in things that move from rhythm in music, it seems he stands on the movement-​as-​metaphor rather than the dynamic side of the debate. Philosophical theories of rhythm in the modern era include Rousseau in the eighteenth century, with his entry on rhythm in Diderot and d’Alembert’s Encyclopedia (1751), and his later Dictionary of Music (1768).4 In the Encylopedia he states that: Rhythm can be defined generally as the proportion that the parts of a measure, parts of a movement, or even parts of a whole have with each other: in music it is the difference in movement which results from speed or slowness, from respective length or brevity of the notes.5

In 1802 (though published posthumously, another half-​century later), Schelling proposed that art first “breaks through into the world of representation” via the expression in music of “the primal rhythm of nature.”6 It is, he claimed, “through rhythm” that humans “impose variety or diversity onto everything,” thereby finding pleasure in “an entire unity within a particular multiplicity,” often transforming “an essentially meaningless succession into a meaningful one.”7 Schelling thus argued that with rhythm music transforms the atomic or disparate into the organic, its basic units forming larger groups which in turn cohere in a variegated whole. In its articulative capacity to transform experience, rhythm is, in Schelling’s view, the dominant of the three powers in music—​rhythm, melody, and modulation. Because articulating or “informing . . . unity into multiplicity” is for him the essence of music, and since rhythm effects “this informing within music itself,” he concludes that “Rhythm is the music within music.” Nietzsche’s early lecture “Rhythmic Researches” (1870–​2) distinguished what he saw as Greek mathematical rhythms from the fluid, living rhythms of the body, anticipating his influential Apollonian–​ Dionysian distinction.8 Influenced by Schopenhauer, who distinguished music as “entirely apart” from all other arts in reaching further than mimetic representation and into a “serious and deeper significance . . . referring to the innermost essence of the world and of our selves,”9 Nietzsche finds the primality of will in rhythm and dance. Thus this philosopher, for whom “Without music life would be an error,”10 affirms the Dionysian necessity of rhythm: one must dance to enter fully, bodily, into the life of the world. Thus too he declared: “I would only believe in a god who knew how to dance.”11

4 Rousseau, Dictionnaire. 5 Rousseau, “Rhythme.”

6 Schelling, Philosophy of Art, 17.

7 Schelling, Philosophy of Art, 110–​11.

8 Elaine P. Miller, “Harnessing Dionysus.”

9 Schopenhauer, Will and Presentation, 306.

10 Nietzsche, Twilight of the Idols, 10 (“Epigrams and Arrows” §33).

11 Nietzsche, Thus Spake Zarathustra, 29.

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4   The Philosophy of Rhythm Drawing from such nineteenth-​century sources, Bergson’s distinctly modernist writings on time, duration, and continuity had a remarkable influence on music and philosophy in France from the 1890s up to the 1930s. The phenomenologist Gaston Bachelard’s The Dialectic Of Duration (1936; revised 1950), for example, arose from a critique of Bergson’s concepts of duration and continuity. Against Bergson’s notion of continuity, and indeed against the tradition that since the ancient Greek philosophers has regarded musical rhythm and melody as “flow,” Bachelard argues that “music’s action is discontinuous; it is our emotional resonance that gives it continuity.”12 Bachelard regards continuity and duration in music as an elaborate metaphor “reconstructed in reverse” by the experiencing subject.

2.  Recent Times: Attention and Neglect Given its importance in ancient and modern philosophy, the neglect of rhythm as an area of inquiry in contemporary philosophical aesthetics is puzzling. This lack of interest is not only from aesthetics, however. Poetics is also marked by a neglect of rhythm; there is a corresponding lack of interest from prosody, the area of linguistics concerned with patterns of stress and intonation. In the case of musicology, the neglect has been relatively less evident but nevertheless noticeable, given that, in contrast to popular music, rock music, and jazz, the dominant focus in the theory and analysis of Western art music has tended to be on the parameter of pitch in relation to harmony, as opposed to rhythm as such. Grosvenor Cooper and Leonard B. Meyer’s groundbreaking work on rhythmic structure commented on the “moribund state” of its topic.13 Subsequently, Christopher Hasty, in an ambitious work, analyzed the experience of music as an irreducibly temporal phenomenon, as opposed to the spatialized representation assumed by many theorists and by ordinary thinking.14 Philosophically influenced by William James, phenomenologists such as Edmund Husserl, and process thinkers such as Henri Bergson and A.  N. Whitehead, Hasty argued that music should be regarded as a process of becoming rather than a record of what has become, rejecting the image of meter as an artifact of a system of representation—​that is, of notation. There has also been a neglect of the relationship of rhythm and larger-​scale form and structure. Aspects of this relationship occur in the work of Heinrich Koch in the eighteenth century, as Michael Spitzer has observed.15 In non-​Western music theory and practice, however, notably that of North Indian classical music, rhythm and its relation to extended improvisation has an ancient and long-​standing,



12 Bachelard, The Dialectic of Duration, 124.

13 Cooper and Meyer, Rhythmic Structure of Music. 14 Hasty, Meter as Rhythm.

15 Spitzer, Metaphor and Musical Thought, 69, further discussed at 243–​59.

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Introduction  5

fundamental significance, as has been emphasized by Martin Clayton’s work on the relation of meter, duration, and structure in this tradition.16 In English-​language philosophy, John Dewey, Leonard B. Meyer, Roger Scruton, Andy Hamilton, and Andrew Kania are among the small number of philosophers to address rhythm to any great extent. This blind spot is particularly unfortunate because rhythm is a phenomenon that is immediately evident to everyone, and is a topic on which philosophical progress can be made without expert technical knowledge. The need for greater attention to rhythm provides a major motivation for this volume, which sets out to rectify the oversight. We have sought to do this not only through commissioning contributions from philosophical aesthetics, but also—​ albeit with a philosophical perspective—​from other disciplines like neuroscience, psychology, musicology, ethnomusicology, poetics, literary studies, dance, and art history. In taking an interdisciplinary approach, this volume facilitates lines of inquiry that investigate whether rhythm (and related concepts including meter and duration) should be restricted to music, dance, and poetry, or, by contrast, should be extended to non-​poetic literature and theatre, as well as painting and the visual arts, and also architecture. The attempt to apply the concept of rhythm across the arts raises problematic philosophical issues, and the term “metaphor” is often employed rather loosely. It is, in any case, hard to define. Might there remain in all the arts something—​perhaps even some dimension, such as movement, the immediately spatial, or the immediately temporal—​that can only be discussed in metaphorical terms? This suggestion raises a number of interesting further questions in relation to rhythm and has led to much recent debate. Music is a time-​based art and has duration, but can we say that music really moves, and if so, what does talk of “movement in musical space” mean? The debate arises among those who hold movement in music to be metaphorical—​ such writers include Roger Scruton, who draws from Victor Zuckerkandl. Scruton concludes that the sense of movement is, though vastly important, only metaphorical in terms of the physical space in which bodies move, that is, the sounds of music “are ordered in space only apparently, and not in fact.”17 Zuckerkandl’s position involves the further sophistication that while, as he concludes, music transcends physical and geometrical space, it does not transcend spatiality completely, for it testifies to a space that remains in the absence of physical objects and geometry.18 What can be said today of rhythm in arts besides music? In the case of poetry—​ and indeed literature in general—​one can say that duration is involved, in that it takes time to read it, but, as with music, what might be meant by movement in poetic or literary space? The visual arts of painting, sculpture, and architecture, which literally occupy space, also endure through time, and take time to view and walk around or within—​but are they generically different in terms of temporality from



16 Clayton, Time in Indian Music.

17 Scruton, Aesthetics of Music, 14.

18 Zuckerkandl, Sound and Symbol, 292.

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6   The Philosophy of Rhythm artworks that take time to unfold in their entirety, such as performed music and recited poetry? These questions are taken up in a number of essays in this volume. Simply to say that we can discuss an “absent dimension” only metaphorically is also to underestimate the importance of metaphor in its relation to mimesis and poiesis (creative, artistic production), whether in our experience of the arts and of nature (which has traditionally been the domain of aesthetics), in our attempts to understand, explain, and interpret the arts (which is the domain of hermeneutics), or in the making of art (which was traditionally the domain of poetics). As Aristotle says: “A metaphor is the application of a [word] which properly applies to something else.”19 He refers to metaphor as a “transference” from one sphere to which it belongs to another where it is not normally encountered. Thus this collection aims to provide both an overview of an often neglected but vital aspect of aesthetic experience, and an examination of formal affinities between historically interconnected fields of music, dance, poetry and literature, and also the visual and spatial arts, addressing key concepts such as embodiment, movement, entrainment, and performance. We have attempted to avoid an over-​ emphasis on music, and have sought also to stress structural parallels between different art forms and their aesthetics. An essential aim has been intelligibility across disciplines. While the volume draws on a wide range of disciplines, contributors were encouraged to present their ideas non-​technically as far as possible, and to engage in cross-​disciplinary dialogue, in part through the insights of philosophical aesthetics.

3.  Outline of Chapters Enhancing its interdisciplinary ambition, this book is organized not territorially, into academic disciplines, but thematically, into aspects and questions concerning rhythm. With this arrangement, the editors not only encourage connections between the disciplines and a closer exchange of perspectives, but also see a conceptual map of the philosophy of rhythm taking shape. The five thematic parts that make up the volume arose naturally, as the project progressed, revealing a spread of concerns among current scholars regarding rhythm, suggesting also the shape of the conceptual space itself. Part One, “Movement and Stasis,” addresses conceptual questions that include: Does rhythm necessarily involve movement, or is this a matter of metaphor only? Is rhythm as a literal phenomenon restricted to human activities and actions, or does it extend to natural and mechanical phenomena such as ocean waves and the sound of a train on a track? How is rhythm experienced through the senses—​is it recognized or projected?



19 Aristotle, Poetics, 34.

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Introduction  7

The opening chapter, collated and edited by Andy Hamilton, is a dramatized dialogue in the long philosophical tradition of that form. The debate poses the dynamic conception—​that rhythm involves movement—​against the view that nothing relevant in the music moves literally, that is, spatially. Hamilton’s dynamic conception characterizes rhythm as “[a primitive] order within human bodily movement or movement-​in-​sound,” and opposes static accounts in terms of order-​in-​time and Scruton’s metaphorical conception. Most dialogue participants support a dynamic conception of some kind, but Macarthur denies that rhythm “moves in a literal but non-​spatial sense.” Squires and Wiseman develop Hamilton’s account, arguing that the movement criterion should be expressed as a capacity and not a disposition. Matthew Nudds’ “Rhythm and Movement” continues this theme, arguing that we can experience literal movement in rhythm. The argument depends on the claim that our experience of musical grouping involves experiencing sounds as produced by extra-​musical events that include movement, and that musical grouping is central to our experience of rhythm in music, hence our experience of rhythm involves the experience of movement. The view defended rejects the suggestion that movement can only be heard in music in a metaphorical sense. In “The Ontology of Rhythm,” Peter Simons defends, in contrast, a static conception of rhythm. Investigating its complex ontology, he sets out the types of entity on which rhythm is founded and their relationships with rhythm itself. No single characterization will work, Simons argues; rather, a series of types branches off from simple paradigms. Rhythm in music is characterized in its simplest form by a repetitive temporal pattern, which forms the basis for variations generating the whole range of musical rhythms. In music, but not rhythm in general, this range is limited (though not constituted) by anthropological constraints concerning pitch, tempo, volume, and complexity. Jenny Judge’s chapter on “ ‘Feeling the Beat’ ” argues that the experience of musical meter is multimodal: it involves the binding to a common sensory individual of auditory and proprioceptive content. One hears the beat, and feels it, too. She further claims that a consideration of this multimodal content undermines the seeming necessity of the appeal to “metaphorical perception” as a way of accounting for the experience of movement in the case of musical meter. Next, in “Dance Rhythm,” Aili Bresnahan proposes a theory of dance rhythm as distinct from rhythm in dance. Distinguishing natural from intentional rhythm, she defends this account by exploring musical and non-​musical connections between rhythm and dance. She argues that dance rhythm can arise in conjunction with music; follow music; set the musical rhythm; or be completely independent of music, though natural or internal bodily rhythms can underpin both. Finally, she asserts the existence of dance that might be naturally rhythmic, but not in a way essential to dance qua dance. Part Two, “Emotion and Expression,” considers the relation of rhythm to human feeling and covers topics including:  the deep significance of rhythm deriving from its being “a universal scheme of existence”; the use of rhythm in empathetic

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8   The Philosophy of Rhythm communication and composition; rhythm at the base of cognitive and linguistic meaning; the creativity involved in bodily responding to musical rhythms such as those found in popular music; and entrainment and the recognition of expression in music. In “Theories of Rhythm,” Garry Hagberg poses the question: Why does rhythm speak to us so deeply? Patterns of percussive sound that move us are meaningful, yet we find it hard to say what associations or connotations create that meaning. What is required is something more elemental and universal than personal or idiosyncratic associations. Hagberg argues that John Dewey’s Art as Experience has important insights on this question. Focusing on examples from jazz improvisation, Hagberg suggests that both player and listener are very like Dewey’s broader conception of the live organism interacting within its environment. Deniz Peters’ “Rhythm, Preceding its Abstraction” takes a non-​reductive approach to the understanding of musical rhythm based on reflections on his musical practice, arguing that, preceding its abstraction, rhythm centrally resides in “doings” and “happenings” in our bodies and interactions between each other. Further, it resides in our somatic and cognitive awareness of these “doings” and “happenings” by way of experience and attention. The line of thought Peters develops stems from a number of related observations concerning how “lived rhythm,” unlike “represented rhythm,” comes into being via interpersonal-​and self-​attention. In “Mozart’s ‘Dissonance’ and the Dialectic of Language and Thought in Classical Theories of Rhythm,” Michael Spitzer discusses Mozart and eighteenth-​century theories of rhythm. Challenging the abstract conception of musical rhythm, Spitzer argues for its intrinsic expressiveness, supporting his claim with reference to a rich eighteenth-​century tradition. He argues that eighteenth-​century rhythmic theory was cognitive, in tune with the cognitive qualities of classical music. Another expressive aspect of classical rhythm was its linguistic character. It imitated the nature of primitive grammar as imagined by contemporary linguists. Spitzer concludes by showing how these ideas can enhance our understanding—​and hearing—​of a piece by Mozart. Next, in “Rhythm and Popular Music,” Alison Stone explores how rhythm functions and affects us in popular music. She considers explicit rhythm as a constant layer of percussion that has no precise pitch. Relative to this layer, the rhythmic qualities the other layers of sound are heightened, emphasizing beats that fit in or pull against those emphasized by the percussion. Referring to Michael Jackson’s “Billie Jean,” Stone discusses how this pronounced rhythmic character of popular music appeals to our bodies to move in time with the emphases sounded in different layers. In “Rhythms, Resemblance, and Musical Expressiveness,” Ted Gracyk argues for the plausibility of entrainment accounts of musical expression in holding that the ability to hear expressiveness in rhythmic sounds is logically prior to hearing some musical patterns as expressive gestures. Although Gracyk does not endorse arousalism as a general account of musical expression, understanding the role of

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Introduction  9

rhythm in expressiveness supports a combination of the “resemblance” and “contagion” accounts of musical expressiveness, blending what are often treated as mutually opposed accounts. Part Three, “Entrainment and the Social Dimension,” expands on the concept of entrainment raised in Gracyk’s chapter and discusses rhythm in psychology, neuro-​ science, and biology. They aim less to make a particular scientific contribution, than to assess the nature and viability of scientific approaches to rhythm. Justin London begins Part Three with “Metric Entrainment and the Problem(s) of Perception,” discussing the limits and mechanisms of our perceptual faculties for auditory rhythm. His consideration reveals that the perceptual process is not a linear chain of information from the external world, but an active interplay between mind and world. Yet while considering our senses as cross-​modal perceptual systems solves some problems of perception, it creates other, perhaps deeper ones, he argues. In music, our rhythmic percepts are often non-​veridical, as we add accents, beats, and grouping structure to otherwise undifferentiated stimuli. Martin Clayton’s “Entrainment and the Social Origin of Musical Rhythm” discusses the social nature and origin of musical rhythm. The argument draws on Halbwachs’ idea of rhythm as a social rather than a natural phenomenon, and Schütz’s critique of Halbwachs in his famous essay “Making Music Together.” Clayton argues that rhythm in fact emerges spontaneously both in individuals and (crucially) in interactions between them, and that it is therefore both natural, in the sense of physiological, and social in origin. Michael Tenzer’s “How Many Kinds of Rhythm Are There?” offers an ethnomusicological perspective on the indefinite varieties of rhythm, examining the contrasts between musical and linguistic rhythm, anthropological categories, perception, and technology. Partitioning the universe of rhythm typologically, Tenzer views the potential of rhythm along various continua: via comparison with language; in the development of human culture; in the life of an individual’s experience, perception, and cognitive prowess; and in the non-​human natural world. Udo will considers the physiological, psychological, and social origins of rhythm in “Temporal Processing and the Experience of Rhythm: A Neuro-​Psychological Approach.” Reviewing data from Australian Aboriginal music, he argues for dynamic neural models that challenge abstract conceptions of rhythm. Will holds that instrumental rhythms and vocal rhythms in speech and music derive from different ways of interacting with our environment and are controlled by different temporal mechanisms. Thus, he argues, instrumental music should be considered in parallel to vocal music, not as derived from it. Part Four, “Time and Experience: Subjective and Objective Rhythm,” considers subjective and objective conceptions of time; phenomenological, process philosophy, and empiricist perspectives; rhythmic duration; and—​reprising the main theme of Part One for this experiential point of view—​whether movement is a necessary criterion for rhythm. In “Complexity and Passage: Experimenting with Poetic Rhythm,” Christopher Hasty begins by treating rhythm as the shaping of

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10   The Philosophy of Rhythm events and their succession, rather than as a pre-​existent order of isochronous division. He argues for rhythm as flow, as the fluid, active, and characterful creation of things or events, rather than of a homogeneous substance (“time”). He relates this concept to poetry by reading the opening of Keats’s “Hymn to Pan,” analyzing the continuing “life” of the vocal impulse along the lines and through the word-​sounds taken as “mouth events”—​a reading after the manner of M. H. Abrams (2012). Peter Cheyne defends an unprioritized ontology regarding the subjectivity and objectivity of rhythm in “Encoded and Embodied Rhythm:  An Unprioritized Ontology,” and thus argues against writers such as Christopher Hasty and Nicholas Cook, who prioritize the subjectivity of rhythm as flow. Cheyne argues that because rhythm is perceived through the senses as patterned temporality evoking emotional response, it has both objective and subjective qualities according to Lockean criteria. He further argues that the intricacy of actual rhythm neither excludes its description in objective form, nor its subsequent performance by other skilled performers who are present and listening attentively. In “Time, Rhythm, Subjectivity:  The Aesthetics of Duration,” Max Paddison argues that rhythm must be considered in relation to time and subjectivity, understood within a larger concept of “rhythmicized duration” as form. Drawing on Bachelard’s phenomenology of duration, he argues that aesthetic concepts of temporality, movement, and rhythm in music and the performing arts are subject to change, development, and displacement, and have functioned normatively and metaphorically in different historical periods. He concludes that our experience of rhythm as structured duration is both subjectively experimental and historically contingent. Salomé Jacob examines the implications of Husserl’s model of temporal consciousness on the experience of musical rhythm in “Husserl’s Model of Time-​ Consciousness, and the Phenomenology of Rhythm.” Husserl’s framework, when applied to rhythm, suggests that listeners retain the just-​past sounds and anticipate the sounds-​to-​come in the light of what has been heard. Besides, Husserl’s model helps to frame a rich embodied phenomenology of rhythm. One’s experience encompasses the perception of musical rhythm but also a bodily awareness of one’s own movements, where both aspects share the same temporal structure. In “Pictorial Experience and the Perception of Rhythm,” Jason Gaiger considers whether a painting can have a rhythm. Rhythmic structure unfolds in time, but if rhythm is essentially durational, he asks, how can a static configuration of marks and lines be rhythmic? Gaiger argues that although viewing a picture takes place in time, and thus is successive, it cannot be temporally structured in a sufficiently determinate manner to sustain the attentional focus required for the communication of even simple rhythmic patterns. Graphic art is non-​sequential and this has important consequences for picture perception. Víctor Durà-​Vilà then engages Gaiger’s essay in “Soundless Rhythm,” to develop a notion of rhythm that is independent of sound and can include all senses. Durà-​Vilà argues against the theoretical proposal that music is required

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Introduction  11

to conceptualize rhythm. Moreover, he contends that rhythm in painting can be experienced in a non-​metaphorical way. Finally, he examines some potential implications of his thesis for incipient art practices involving senses other than sight and hearing. Part Five, “Reading Rhythm,” addresses the role of rhythm in reading and thus focuses on poetry and prose. The stressed–​unstressed model of metrical analysis, and its variants, now seems obsolete as a means of describing the patterns of emphasis in poetry. However, although in the twentieth century verse loosened its relationship to meter, these essays show how rhythm remains an essential, though less easily described, feature of literary language. Jason Hall presents a genealogy of metrical abstraction in nineteenth-​and twentieth-​century literature in “Rhythm, Meter, and the Poetics of Abstraction,” surveying approaches to metrical abstraction that have shaped the modern metrical imagination, taking abstract meter as their starting point. Hall examines the early twentieth-​century return to theories that tried to avoid the complications introduced by emphasizing voiced particularities of rhythm; these theories resisted earlier syntheses of meter with music. For the New Critics, at least, the reader is in “a better position” to offer a rhythmically “meaningful” reading if he or she “recognizes the meter.” In “The Not-​So-​Silent Reading . . . ,” Rebecca Wallbank asks: What does it mean to say that we appreciate rhythm in literature? By raising this question, she aims, first, to illuminate the modes of attention to rhythm in literature, and second, to call for a re-​evaluation of certain common assumptions concerning literary aesthetic experience and appreciation. She analyzes the impact of different forms of attention within aesthetic experiences, and through this aims to expose and illuminate the overlooked roles of rhythmic auditory-​imagining within our experiences of literary works. Will Montgomery shows in “Leaving it Out:  Rhythm and Short Form in the Modernist Poetic Tradition,” how in the modernist era rhythm was no longer a stable background pattern, but became part of the overall acoustic texture of the poem—​with short-​form poetry the most powerful vehicle for rhythmic innovation. Montgomery focuses on the Poundian line of influence, with particular emphasis on the writing of the American poet Robert Creeley. Montgomery argues that brevity and ellipsis are integral to a modernism best approached through the modernist dictum Dichten = condensare (to poetize is to condense). Finally, in “Hearing it Right:  Rhythm and Reading,” John Holliday addresses the neglect of sound and rhythm within prose literature, arguing that poetry is not more rhythmic than prose. He argues that works of prose have rhythm, to which the pauses, inflections, stresses, and pronunciation of its language all contribute. As such, prose literature, like poetry, should be considered musical. While poetry is lineated and prose is not, Holliday argues that this distinction does not result in poetry being more rhythmic. He concludes that rhythm in prose literature generally deserves attention for the different roles it plays.

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12   The Philosophy of Rhythm

Works Cited Abrams, M. H., The Fourth Dimension of a Poem, and Other Essays (New York, 2012). Aristides Quintilianus, On Music (c.350?), tr. R. P. Winnington-​Ingram, in Greek Musical Writings II: Harmonic and Acoustic Theory, ed. Andrew Barker (Cambridge, 1989). Aristotle, Poetics (c.335 bc), tr. Malcolm Heath (London, 1996). Bachelard, Gaston, The Dialectic of Duration, tr. Mary McAllester Jones (Manchester, 2000). Clayton, Martin, Time in Indian Music: Rhythm, Metre and Form in North Indian Rag Performance (Oxford, 2000). Cooper, Grosvenor and Leonard B. Meyer, The Rhythmic Structure of Music (Chicago, 1960). Hasty, Christopher, Meter as Rhythm (Oxford, 1997). Nietzsche, Friedrich, Twilight of the Idols (1889), tr. Richard Polt (Indianapolis, 1997). Nietzsche, Friedrich, Thus Spake Zarathustra:  A Book for All and None (1883–​92), tr. and ed. Adrian del Caro, co-​ed. Robert B. Pippin (Cambridge, 2006). Miller, Elaine P., “Harnessing Dionysus: Nietzsche on Rhythm, Time, and Restraint,” Journal of Nietzsche Studies, 17 (1999), 1–​32. Plato, The Republic (c.380 bc), tr. G. M. A. Grube, rev. C. D. C. Reeve, in Complete Works, ed. John M. Cooper (Indianapolis, 1997). Plato, The Laws (c.360 bc), tr. Trevor J. Saunders, in Complete Works, ed. John M. Cooper (Indianapolis, 1997). Rousseau, Jean-​Jacques, “Rhythm” (1765), The Encyclopedia of Diderot & d’Alembert Collaborative Translation Project, tr. Valerie Porcello (Ann Arbor, 2005):  http://​hdl.handle.net/​2027/​spo. did2222.0000.491. Rousseau, Jean-​Jacques, Dictionnaire de la musique (Paris, 1768). Schelling, F. J.  W., Philosophy of Art (1802–​3; published 1859), tr. and ed. Douglas W. Stott (Minneapolis, 1989). Schopenhauer, The World as Will and Presentation, tr. and ed. Richard E. Aquila (London, 2008). Scruton, Roger, The Aesthetics of Music (Oxford, 1997). Spitzer, Michael, Metaphor and Musical Thought (Chicago, 2004). Zuckerkandl, Victor, Sound and Symbol:  Music and the External World, tr. Willard R. Trask (Princeton, 1956).

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1 Dialogue on Rhythm Entrainment and the Dynamic Thesis Andy Hamilton, David Macarthur, Roger Squires, Matthew Tugby, and Rachael Wiseman (compiled and edited by Andy Hamilton)

The advantages of the dialogue form—​in particular, the advantage of openness—​ have been neglected in post-​eighteenth-​century philosophy. Unlike the currently dominant journal article form, the present dialogue neither arrives at, nor seeks to impose, a definite conclusion. Debate is left open. Knowledge in philosophy is dialogical. As love of wisdom, philosophy pursues truth via challenging dialogue, knowing that it needs opposing views to approach its aim. That aim is to arrive at truth, and the most fruitful debate can help one get there. In Plato’s Socratic dialogues, Socrates is regarded as the bearer (or at least a “midwife”) of truth. We can infer that Plato endorses—​though perhaps does not defend—​the viewpoint voiced by Socrates. In these earlier dialogues his main positive contribution is the Socratic elenchus, a method of eliminating incoherent beliefs from the set that his interlocutor holds. It is this method, rather than particular philosophical claims, that Plato endorses through Socrates. By the time of the Republic, however, Socrates is more like Plato’s mouthpiece, and his view seems to prevail. With Hume, the dialogue form is more open. He used it to evade religious censorship, leaving it unclear whose view the author was advocating—​though in the Dialogues Concerning Natural Religion it is clear that one character, Demea the deist, does not represent Hume. In the twentieth and twenty-​first centuries, the dialogue form is more rare—​Brecht’s Messingkauf Dialogues and Beckett’s more imaginative Dialogues with Georges Duthuit are two very different philosophical dialogues on artistic questions. This “Dialogue on Rhythm” is based on contributions from Andy Hamilton, David Macarthur, Roger Squires, Matthew Tugby, and Rachael Wiseman. The “Dialogue” is neither a creation by a single author—​as the classic dialogues by Plato, Berkeley, and Hume were—​nor verbatim transcription of actual conversation. Text was passed back and forth, and the final result agreed. Here, no one view prevails, though characters modify their views in the light of criticism. Debate is left open,

Andy Hamilton, David Macarthur, Roger Squires, Matthew Tugby, and Rachael Wiseman (compiled and edited by Andy Hamilton), Dialogue on Rhythm In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0002

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16   The Philosophy of Rhythm even to the extent that the alternative positions are not entirely clear—​but progress in clarifying them has been made. Andy Hamilton

Dramatis Personae skepticus = David Macarthur dynamicus = Andy Hamilton metaphysicus = Matthew Tugby analyticus = Roger Squires vitalia = Rachael Wiseman

Summary This dialogue debates the common philosophical assumption that nothing relevant in the music moves literally, that is, spatially—​physical movements of performers, or air molecules, are not relevant. It addresses Andy Hamilton’s critique of this assumption, and his dynamic conception of rhythm as order-​in-​movement or order-​in-​movement-​in-​sound, defended in his article “Rhythm and Stasis.” On that account, rhythm is characterized as “[a primitive] order within human bodily movement or movement-​in-​sound,” and it is suggested that this order “involves a non-​spatial yet literal sense of movement.”1 This dynamic account opposes both Budd’s and Simons’ static accounts in terms of order-​in-​time, and also Scruton’s metaphorical conception of sonic rhythm as movement in space.2 While Macarthur (Skepticus) and perhaps Tugby (Metaphysicus) oppose or resist it, the other participants support some kind of dynamic conception. Macarthur rejects the dynamic–​static distinction as Hamilton (Dynamicus) presents it, while Tugby offers a metaphysical account of non-​spatial movement in terms of quality-​ space—​a view of which both Macarthur and Hamilton are skeptical. Macarthur criticizes Hamilton’s original claim that music moves in a literal but non-​spatial sense; Hamilton concedes the point, but responds that something relevant does move literally:  musicians and audience share a rhythmic, dance-​like response. Drawing on aspects of Macarthur’s account, and discussion by Squires (Analyticus), he argues that this dance-​like response is a participatory manifestation of musical understanding; there is an internal relation between music and movement, such that rhythm constitutes an order of movement. As Ezra Pound said, “music begins 1 Hamilton “Rhythm and Stasis,” 29, 40. 2 Budd “Musical Movement,” 209–​23; Simons, “Ontology of Rhythm”; Scruton, Aesthetics of Music.

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to atrophy when it departs too far from the dance . . . poetry begins to atrophy when it gets too far from music.”3 Music, dance, and poetry originated as an integrated practice. Macarthur insists that the dynamic account rests on an implausible view of literal movement in music; Hamilton responds that the non-​movement assumption rests on sonicism—​the view that music is a strictly sonic art, that does not essentially involve bodily and visual experience.4 On his view, rhythm as order-​in-​ movement does not require an implausible notion of non-​spatial literal movement. Squires and Wiseman (Vitalia) develop the movement criterion, arguing that it should be expressed as a capacity, not a disposition.

1.  Projection, rhythm, and proto-​rhythm (palace green, durham) skepticus: Good morning, Dynamicus! I hope you are enjoying the fine weather today. What brings you to Palace Green so early this spring morning? Though surely there is no pleasanter time of day, or more delightful season of the year. dynamicus: In fact, my thoughts were taken up with the philosophical problem we discussed recently, and I found it hard to sleep. I decided to take some early morning exercise—​perhaps its rhythmic nature prompted further ideas. skep: Yes, these issues are absorbing. I find myself in sympathy with your philosophical humanist approach, that treats music both as a sounding, vibrating phenomenon, of changing patterns of intentionally produced sound in time, and a performing art or entertainment. Like you, I want to reject both an abstract, Platonic conception, and also the sub-​personal standpoint of neuro-​ philosophy. I want to insist, with you, that rhythm is essentially a felt person-​level phenomenon. dy: Yes, a humanistic approach has important implications for the understanding of rhythm. So you agree with my view that rhythm is intentional, while creatures or artifacts that do not have or express intentions can produce only proto-​rhythms? skep: Not entirely, Dynamicus. My view is that while a rhythm might be experienced as if it were intentional and meaningful, it may, in fact, be either non-​ intentional or intentional, meaningful or meaningless. Musical rhythm is intentional and apparently meaningful. But it seems obvious to me that there are non-​intentional meaningless rhythms, such as a train running on a track, a heartbeat, or the drip of a leaky tap. We might call these natural rhythms and distinguish them from human rhythms like music and dance, without denying that making rhythms is natural to us.

3 Pound, ABC of Reading, 14. 4 This issue arises with other contributions in this volume, such as Gaiger and Durà-​Vilà.

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18   The Philosophy of Rhythm

But let me turn to your argument that in the case of music or poetry, rhythm is imparted by performers, and “imaginatively projected” by listeners.5 Music, poetry, dance and human bodily movement are paradigms of rhythm, you say, understood as the “imposition of accents on sequences of sounds or movements, creating non-​periodic phenomena usually within a periodic repetitive (metrical) framework.”6 And you stress that rhythm is humanly-​produced—​a genetic claim about a sound’s causal origins that, I take it, may not be evident to a listener. dy: I would qualify what you are saying, Skepticus. I  am not claiming that all rhythms are humanly-​produced. A drum machine produces rhythms, and these are only indirectly humanly-​produced—​if they’re sampled, or given that the machine itself is humanly-​produced. I meant rather that human producers of rhythm, and the human practices of music, poetry, and dance in which rhythm is embedded, draw on and incorporate natural sounds, and later mechanical and electronic sounds—​often regarding these sounds as in themselves proto-​ rhythmic, or rhythmic. skep: I see. However, I take your more fundamental point to be that rhythm, in its primary manifestations, is an intentional phenomenon. And as you say, the rhythms associated with music, dance, and poetry constitute “an intentional order.”7 An immediate emendation is to limit the realm of rhythm to intentional bodily movement rather than bodily movement in general. dy: That might be acceptable, Skepticus. skep: Let us say that, on your view, rhythm is primarily an intentional phenomenon, whose expression we can and often do perceive in various human activities. It is thus an aspect of the human world—​a claim that seems to fit well with your humanist inclinations. Rhythms produced by inanimate things, such as a dripping tap, you call “proto-​rhythms” and treat them as secondary phenomena. dy: Yes, that is my view. skep: Now, turning to the question of projection, you seem to want to distinguish perceiving intentional or “true” rhythm, from projecting “proto-​rhythm,” the latter being a phenomenon of natural or non-​intentional orders of stressed and unstressed accents in time, such as a heartbeat, waves on the shore, or a horse’s gallop. Indeed sometimes you speak of rhythms themselves as both being perceived and projected. dy: “Pulse” would be an alternative term, to capture what you are calling “stressed and unstressed accents.” skep: But what we must remember is that the data for philosophizing here involve a range of experiences of rhythm in both human and natural phenomena. So 5 Hamilton, “Rhythm and Stasis,” 29: “A humanistic account treats rhythm as an order distinctive of human movement or movement-​in-​sound, an order imaginatively projected onto processes that do not literally possess it.” 6 Hamilton, “Rhythm and Stasis,” 38, 26. 7 Hamilton, “Rhythm and Stasis,” 30.

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I do not find the distinction between rhythm and proto-​rhythm helpful. Perhaps it has this to be said for it: the intentional case structures both non-​intentional and intentional rhythm at the level of phenomenology. Rhythm, however it is produced, can often seem intentional and meaningful, even where it is not. But for present purposes, let us follow your restricting the term “rhythm” to human-​ produced phenomena. We can therefore ask, is “projection” needed to explain our experience of rhythm? dy: You believe it is not? skep: Indeed. Your account appeals to projection principally to explain how we hear rhythm in “proto-​rhythmic” phenomena—​heartbeats, waves, trains. You argued that in these non-​intentional, naturally recurring patterns of stressed and unstressed sound, we cannot avoid projecting rhythm—​as I recall, citing La Monte Young’s composition “ ‘X’ for Henry Flint” (1960), where the performer has the impossible task of producing an absolutely uninflected pulse without meter. You said that this piece shows both how the performer cannot help creating rhythm, and how the listener cannot avoid projecting it. dy: Yes, that is a good summary. skep: Well, there is a problem I believe, with the idea that rhythm is “projected.” Projection presupposes a something that one projects onto. This can happen literally: images are projected onto a screen from a film-​reel, or sounds are projected into a space from a source; or figuratively: as when one’s joy is projected onto the world at large. In the case of perceived rhythm—​something experienced as a feature of bodily movement or sound—​projection implies one has access to some subjective state of mind whose “projection” can plausibly account for our experience of it as “in” the movement or sound. But what is this inner something that we experience as outer? dy: I am not sure there has to be an “inner” something—​but pray continue. skep: There does if the notion of projection is to make any sense. Perhaps the idea is that rhythm is like color in this respect. Color is often thought by philosophers to be a mental projection onto an essentially colorless world. But I reject the coherence of this way of thinking. We have no genuine explanation of color in projective terms insofar as we have no coherent idea of how color could be a feature of the inner realm from whence it is supposedly projected. The failure of projectivism here—​one rarely noticed in projectivist discussions of color in modern philosophy—​is attributable to our having no coherent definition of what we might call, pleonastically, a “color sensation.” dy: This is very interesting, my dear Skepticus. However, you seem to assume that my view is like Schütz’s well-​known position. He argues that communication rests on a “mutual tuning-​in relationship” in which individuals come to share their experience of “inner time.”8 In his view, rhythmic coordination is prior to any collective agreement. This is not my view. The “inner” in “inner time” is 8 Schütz, On Phenomenology, 212.

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20   The Philosophy of Rhythm redundant. I favor instead Clayton’s view of rhythm emerging spontaneously in individuals and in interactions between them, and so being both natural (physiological) and social in origin.9 This is the currently popular concept of entrainment, discussed by music psychologists in this volume, which I think captures the idea that rhythm is essentially a felt phenomenon.10 I differ from Clayton and colleagues, however, in insisting that entrainment is an elucidation, not a scientific explanation. skep: Pray enlighten us, Dynamicus. dy: I agree with the psychologists that entrainment is essential to music, and that one responds to rhythm by getting in sync. So rhythm is essentially social. What I object to is their view that natural processes themselves entrain. I also object to their apparent denial that a human being can initiate rhythm, on the grounds—​ they say—​that one always entrains to something inner. Entrainment is no more fundamental than rhythm itself.11 skep: Be that as it may, I still maintain that projection is an otiose explanation of genuine rhythm and an unnecessary explanation of proto-​rhythm. Suppose, Dynamicus, we follow you and say that the primary experience of rhythm is as intentional temporal movement—​leaving aside for now the question of what distinguishes mere temporal ordering from rhythmic movement. On the view under discussion, rhythm is constituted, not merely caused, by intentional stresses imposed on sequences of sound. It is a genuine feature, a perceptible order or pattern that characterizes a range of human bodily movements and sounds—​one that allows for ignorance, error, and discernment. But as you argued concerning “ ‘X’ for Henry Flint,” the explanation of our experience of rhythm is over-​determined:  the performer “cannot help imposing rhythm and . . . the listener cannot avoid projecting it.”12 Is it not redundant to say that one apprehends the rhythm created and imposed by the performer, and that one also projects it? dy: You have correctly characterized my view, Skepticus, though I’m not sure there is over-​determination. skep: Surely all we need to say is that the performer cannot help imposing a rhythm, an (apparently) intentional ordering, on the basic pulse for which they are responsible. We can translate your infelicitous claim that we cannot avoid projection of rhythm onto pulse, as the inevitability of experiencing rhythm in a pulse even when there was no intention of producing a rhythm. dy: I am not entirely persuaded, Skepticus. I would say that in the case of proto-​ rhythm, there is projection. By “projection,” I  mean just that rhythm is not entirely an intrinsic feature of the sounds, but also of how they are heard. However, rather than using the metaphor of projection, I would be happy to

9 Clayton, “Entrainment.”

10 Clayton, “Entrainment”; London “Metric Entrainment.” 11 Further discussed at Section 4.

12 Hamilton, “Rhythm and Stasis,” 34.

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talk of the listener interpreting or hearing-​as—​a metaphor that does seem more appropriate in the case of rhythmic or metrical ambiguity, where there is genuine rather than proto-​rhythm. An excellent example is Debussy’s “Des pas sur la neige” from his Preludes.13 I understand hearing-​as on the model of Wittgenstein’s seeing-​as, and Wollheim’s seeing-​in.14 But can I propose an adjournment of our discussion to a nearby café?

2.  The movement in music (bean social café, durham) skep: To return to our topic, Dynamicus. I have been pondering your characterization of rhythm as “order within human bodily movement or movement-​in-​ sound.” You went on to claim that “there is a primitive order underlying” these, “an order that involves a non-​spatial yet literal sense of movement.”15 dy: Yes, that is correct. skep: Well, I must say that this view seems highly problematic. Your aspiration to provide an overarching account of rhythm applicable both to a certain kind of bodily movement—​such as dance—​and a certain kind of sound, for instance African drum music, is ambitious. But the problem arises with your account of movement itself. As we know from the OED, one definition of “movement” is that it is “an act of changing physical location or position or of having this changed.” So your proposal seems to equivocate by combining a literal and a figurative use of the term “movement”—​literal regarding bodily movement, and figurative regarding sound. Whilst sound does move through space at a certain rate, that is not the relevant phenomenon here. Rather, you seem to advocate the more radical and paradoxical idea that bodily rhythm and sound rhythm both manifest “a non-​spatial yet literal sense of movement.” But how could this be? dy: Slow down Skepticus, you are losing me! You find my account incoherent? skep: Yes. Movement is a spatial notion, so to speak of a “non-​spatial movement” is to use movement as a metaphor for a non-​spatial phenomenon. In appealing to movement literally in this context, you hallucinate a new sense. The only available options are a literal (hence spatial) use of the term, or a figurative use of the term which may (but need not) be applied to non-​spatial phenomena. Of course you can give “movement” a new sense, but this must be a reasonable extension from one of its existing senses. 13 Discussed in Cooper and Meyer, Rhythmic Structure of Music,  171–​4. 14 See Hamilton, Aesthetics and Music, Ch. 4, sec. 5. 15 Hamilton, “Rhythm and Stasis,” 29, 40. Zuckerkandl, Sound and Symbol, 292 refers to movement in a more or less Kantian space more fundamental than, and comprehensive of, the space of geometry and that of physical objects.

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22   The Philosophy of Rhythm   To speak of the rhythm of a line drawing, for example, is to use the figure of movement to describe something spatial and static, according to which one’s experience of the (fixed) line imaginatively engages with an idea of the movement required to create (or retrace) it. And to experience the rhythm of a philosopher’s thought, is to use the metaphor of movement to describe the changes and development of a connected series of thoughts, where the comparison is with the way one travels to a destination passing through various places on the way. Here we have a metaphorical appeal to movement to describe a non-​spatial phenomenon, viz. thought. dy: Your objection is certainly a strong one, Skepticus. skep: I will develop it further, Dynamicus. Your two suggested models of “non-​ spatial movement” are based on confusions. Firstly, you say that the term “rapid” means both “happening in a short time” and “happening at a fast pace” (OED), and you then appeal to the first of these as an example of non-​spatial movement. But “rapid” in this sense is a purely temporal notion and not a form of movement at all. We might conjecture that it was, perhaps, once a spatial metaphor—​ based on the comparison with moving between or past various places in a short time—​that has ossified into a literal purely temporal (non-​spatial) use with no connection to movement. dy: I see. skep: Second, you suppose that “non-​travelling movement around a point” is not spatial because it doesn’t involve movement to a new location.16 But movement need only be relative, not absolute, change in location. Consequently, it does not require “travel” in your sense. Rotations around a point, as well as oscillations to and from a point, both count as spatial changes in location, and hence as movements.   As Scruton and others have noted, experiencing rhythm in sound is not an experience of change of location. It is a non-​spatial experience of an order of changes in time that we can describe metaphorically, as in the case of the line drawing, in terms of the movement required to create (or recreate) it; or perhaps in terms of a comparison with the rhythm of various forms of ordered movement. Scruton’s account of musical rhythm in terms of a metaphorical appeal to movement survives your assault upon it. dy: These are indeed serious objections, Skepticus. Perhaps our friend Metaphysicus, who I see just arriving, will help me respond. Good morning, Metaphysicus, how are you? What brings you here on this fine day? metaphysicus: Good morning to you both. I felt the need to escape the oppressive atmosphere of my study for some air to refresh my thoughts. skep: Very understandable, Metaphysicus. We are engaged in a discussion on rhythm, with which I believe you are familiar. Dynamicus has put forward some puzzling claims that I am questioning. In particular, I believe that movement is

16 Hamilton, “Rhythm and Stasis,” 40.

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essentially a spatial notion, and so his idea of non-​spatial movement, in music and other rhythmic phenomena, must be metaphorical. Yet he denies this, suggesting that rhythm is a literal non-​spatial movement. meta: Evidently you are unhappy with Dynamicus’ strongly dynamic model of rhythm, Skepticus. Let’s backtrack a little, to recall the views of Boghossian and Budd. According to their static conception, talk of movement in relation to rhythm is both metaphorical and dispensable, while Dynamicus’ view is closer to Scruton’s dynamic view.17 But controversially, while Scruton regards talk of movement in music as purely metaphorical though essential, Dynamicus suggests that music literally moves. Given that music clearly does not move in the ordinary spatial sense, the upshot is a notion of real but non-​ spatial movement—​a much more radical form of dynamism than Scruton’s. For Scruton, rhythm in music is dynamic merely insofar as it necessarily involves the metaphorical projection of movement by the listener, the source of which is the listener’s bodily movement. But for Dynamicus, music moves in a literal (metaphysical) rather than figurative (metaphorical) sense.18 dy: That seems a fair summary of one of my proposals. meta: In defense of Dynamicus, there is a way of responding to the worry about incoherence, which involves holding that movement is spatial, but insisting that the notion of space is broader than it may at first seem. This view concedes that it is a conceptual truth that movement must take place in a space. But according to the strategy I will explore, there are two different metaphysical notions of space. The first is what I call geographical space, the ordinary three-​dimensional physical space we are all familiar with. The second and less familiar notion is what we may call quality space—​the kind of space represented by, say, the color gamut chart. Of course, it is natural to assume that there is only a “color space” in a metaphorical sense. However, there is a position in metaphysics that takes a realist stance toward various quality spaces, as a means of understanding and analyzing properties. skep: These are unfamiliar notions to me, Metaphysicus—​can you please explain? Doesn’t the color spectrum occur in physical space? meta: As I  say, when Dynamicus suggests that ordered movement-​in-​sound is literal but non-​spatial, I take him to mean that it does not involve movement in the ordinary geographical sense. But this leaves open the possibility that movement-​in-​sound is movement in quality space, or some other real, metaphysically defined space.   A realist about qualitative properties, such as sound, can endorse this “quality space” view. So, Skepticus, you are wrong to dismiss a literalist view of

17 Boghossian, “Music in the Sound”; Budd, “Musical Movement”; Scruton, “Thoughts on Rhythm.” 18 Similarly, Zuckerkandl argues that music moves in a metaphysical, Kantian sense of space, even though nothing relevant in the music physically or geometrically moves.

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24   The Philosophy of Rhythm rhythmical movement simply on the grounds that it involves a metaphysically incoherent notion of movement. dy: These are interesting suggestions, Metaphysicus. meta: My proposal agrees that it is an analytic truth that movement takes place in space, but holds that as well as geographical space, there is also quality space, which contains the dimensions of determination along which qualitative properties lie. According to this proposal quality space is just as real as geographical space—​that is, talk of quality space is not merely metaphorical. Geographical space is familiar to anyone with ordinary perceptual faculties; quality space is revealed only through metaphysical and scientific reflection. But if there are good reasons for positing quality space, and if sounds are qualitative, as seems plausible, then rhythm could involve distinctive kinds of literal movement in quality space. dy: This is an intriguing view, Metaphysicus, although Peter Cheyne comments that rather than only people trained in metaphysical or scientific reflection, aural quality space is surely revealed to anyone who can hear movement in music. Such hearers might not be able to explain aural quality space articulately, but it is nonetheless revealed to them. skep: Dynamicus, I fear that you are being seduced by metaphysical speculation! dy: My dear Skepticus, it seems that you belong with those anti-​metaphysicians who urge us to “just say no”—​as President Reagan did in the case of drugs—​ when asked to engage in metaphysical debate. skep: That is a parody of my position, Dynamicus, as you well know! I say that it is wise to adopt a skeptical attitude to the metaphysician’s claims to explain appearances in terms of some supposedly fixed, “fundamental” or “absolute” notion of “reality”—​where the appearance–​reality distinction invoked has nothing to do with the everyday grammar of these terms. In the present case I am skeptical that Metaphysicus has provided a new sense of “movement” with regard to quality space. dy: Pray continue, my good Metaphysicus. meta: Let me illustrate quality space by means of color properties. Color can be represented as a 3D space with dimensions of hue, saturation, and brightness. Colors can then be considered regions in this quality space, with determinate colors being proper sub-​regions of the determinable colors they fall under—​so that, for instance, scarlet would be a proper sub-​region of the redness region. And the most determinate specification of a color will correspond to a single point on 3D color space. Note that color and sound cases are plausibly isomorphic, since sounds are also specified across three dimensions—​pitch, timbre, and loudness. dy: Yes, I can see structural similarities between sound and color. But where does movement enter the picture? meta: Well, if movement must take place within a space, and if quality space is as real as any other space, there may be literal yet non-​geographical movement—​as

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Dynamicus posits in the case of rhythm. For quality-​space theorists, such a notion allows us to analyze qualitative change. Not only do things exemplify qualitative properties, they also change them. Indeed, music itself can be understood as an artistically created sequence of changes of sound over time, what Dynamicus calls “an art of temporal process.”19 Thus some realists about quality space appeal to the notion qualitative movement.20 dy: This is a proposal I must ponder, Metaphysicus. But what do you make of the temporal model of rhythmic movement, which I thought quite promising? meta: This is meant to be a non-​spatial model that falls naturally out of the view of music as an “art of temporal process.” Recall your example of a rapid sequence of gunshots. Since the succession in this case is purely temporal, and given that the notion of rapidity has connotations with motion, you suggested this may be a case of literal but non-​spatial movement. dy: That is correct. meta: Now, I would say that in one sense, movement uncontroversially must have a temporal dimension. For even in cases of ordinary spatial movement, as when a physical body changes from occupying one physical location to another, such movement necessarily takes time. However, whether there can be a purely temporal notion of movement is much more controversial. To resolve these disputes, we need principled metaphysical reasons for thinking there can be non-​spatial, or what I  call non-​geographical, movement—​and the quality-​ space proposal provides them. These reasons involve general considerations about the nature of qualitative properties. Rhythm can then be seen as one among several cases of qualitative movement, rather than a unique case of it—​though still a distinctive form, through the humanistic and intentional aspects of Dynamicus’ theory. The quality-​space strategy places this theory on firmer metaphysical ground. skep: I doubt that, my dear Metaphysicus. dy: Enough of your sarcasm, Skepticus! My feeling about Metaphysicus’s proposal is that movement in quality space needs to be close enough to ordinary spatial movement to express how close music is to that. But it challenges me to think more carefully about the point of insisting that music literally moves—​that, for instance, it makes people want to move (in dance, say). I need to ponder further in what sense it moves—​and what the “it” is that does not literally move. It seems to me that proponents of this view assume that music is exclusively a sonic art, neglecting bodily and visual dimensions. meta: Indeed. But whatever view one takes on these questions, there are many independent theoretical reasons for favoring my view, which is increasingly popular among realists about properties. For Funkhouser, quality space theory 19 Hamilton, “Rhythm and Stasis,” 41. 20 Thus Cowling, “Instantiation as Location,” 673, n. 16, advocates “locationism,” treating change as motion through quality-​space; he assumes realism about quality space, so the “motion” he speaks of is understood literally. See also Mumford and Anjum, Causes from Powers, 23.

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26   The Philosophy of Rhythm can be applied to all properties, including geometrical, causal, and functional properties; it allows us to analyze how things fall under kinds, and also the distinction between determinable properties such as redness, and determinate properties such as being scarlet.21 Quality space is used to analyze property instantiation as a species of occupation, or the operation of causal powers.22 dy: Skepticus looks unconvinced. meta: It is not just realist metaphysicians who should appreciate my arguments. In natural science, abstract notions of space are used to represent the states of systems such as configuration or phase spaces in physics. Like quality space, such spaces are not spatial in the ordinary sense, since they typically have many more than three dimensions. But some scientists and philosophers of science regard such spaces as more than representational mathematical tools that correspond to nothing in reality. The notion of non-​geographical space should not be dismissed too quickly. dy: Thank you, Metaphysicus, for raising these important issues, worthy of further investigation. meta: My good wishes for your project, Dynamicus. I have to leave now for a workshop. So I wish you good-​day, colleagues, and hope to see you soon.

3.  Meaningful order (later that day, palace green, durham) skep: Dynamicus—​when we consider the proposal of Metaphysicus, I hold that “space” in “quality space” is being used in a metaphorical sense.23 A  quality space of colors, smells, tastes and so on is an abstract mathematical representation of qualities, modeled by a spatial array of qualities ordered along various dimensions by their similarities and differences, with degree of proximity representing degree of similarity. dy: I am inclined to agree, Skepticus. I appreciate the current popularity of realist metaphysics, but that is not our path, I think. skep: Metaphysicus’ proposal does not capture what you call “literal non-​spatial movement,” I  feel. There is no movement in an abstract quality space unless movement is being used figuratively to refer to changes in qualities in time. However, you stressed the familiar sense of movement when you linked the humanistic account of rhythm to “an order distinctive of human movement.” And you argued that one should reject, as a “static” conception, the idea of rhythm



21 Funkhouser, Logical Structure, 25.

22 Cowling, “Instantiation as Location”; Mumford and Anjum, Causes from Powers. 23 See Nussbaum, “Musical Perception.”

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as a mere pattern of different sound qualities that change in time: what you call “simply order [of qualities]-​in-​time.”24 dy: Indeed, Skepticus. skep: It is worth pausing to observe that the notion of changes of qualities in time surely deserves the label “dynamic” no less than a phenomenon that (literally) moves. The term “dynamic” need not ordinarily imply movement even if movement can be properly be described as dynamic. For this reason I reject the static–​ dynamic distinction as you are using it, Dynamicus. If musical rhythm is, as I think, a pattern of changes of qualities in time, then it is dynamic in a perfectly ordinary sense, without being a form of movement. Furthermore, your description of my conception of rhythm as “static” seems to me to imply that you take a block-​universe conception of time and deny that time involves genuine change. The question is, ultimately, about one’s view of time. dy: I would not want to commit myself here, Skepticus. But I do want to maintain an ordinary sense of “dynamic” according to which it refers to movement and not just change. That is the sense in which I have always used it. skep: I see. But you agree that Metaphysicus’ proposal assumes a metaphysical conception of movement at odds with your humanist conception of rhythm embedded in human behavior and practices? dy: Indeed. The proposal is ingenious, but I would regard its non-​humanistic conception as static, involving merely order-​in-​time. skep: In my view, this speculative metaphysics is not sufficiently sensitive to the human situation—​to reiterate, realist metaphysics should be supplanted by the enterprise of describing the conceptual landscape that we actually inhabit.   Leaving aside the static–​dynamic issue, I want to argue that rhythm is experienced as meaningful—​intentional or purposive, whether it is or not—​and that it is part of the phenomenology of rhythm that it seems meaningful or humanly significant.   One might call this an “as-​if intentional” or “phenomenologically intentional” account which we can deepen by exploring the notion of meaningfulness in this context. Some intentional phenomena are communicative, such as speech or art, and some not—​compare somebody walking down the street, in an ordinary unreflective way, with the walk of a flaneur, trying to attract people’s attention. Central cases of humanly-​produced rhythm are not merely intentional movements; they are intentionally communicative movements—​ where the claim of communication is distinguished from that of empirical support, that is, whether the phenomena in question can be considered a reliable symptom or good evidence for various further claims. Just as human gestures intentionally but wordlessly communicate gestural meanings so, too, most human rhythms—​ excepting language and song—​ intentionally but wordlessly communicate rhythmic meanings in bodily movements and sounds.

24 Hamilton, “Rhythm and Stasis,” 26, 29.

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28   The Philosophy of Rhythm dy: This picture seems persuasive, Skepticus. skep: The non-​intentional rhythm of a moving train or windscreen wipers cannot be said to communicate any meaning, but can be heard as if they did. This is the main motivation for my saying that such phenomena are cases of rhythm, since what is being apparently experienced is a meaningful (hence intentional) order in time. We have a natural tendency to find meaning in a rhythmic order, just as we tend to find fear in a fly struggling in a spider’s web, or awareness of sunlight in a plant that turns towards it. Animistic beliefs and rituals in human societies treat natural phenomena such as storms, volcanic eruptions, and the cycles of the stars and moon as bearers of meaning. Of course in all these cases I am talking about apparent meaningfulness, something consistent with meaninglessness non-​intentional phenomena. dy: I find much of this argument convincing, Skepticus. skep: Understanding rhythm as communicative is a fruitful way of challenging Malcolm Budd’s account, which denies that rhythm involves contact with intentions or meanings. Since your account of rhythm as temporal order-​in-​ movement faces difficulties in sustaining the claim that the movement in question is both literal and non-​spatial, perhaps the appeal to movement is not the right ground for criticism of Budd.25 I agree with him that rhythm is an order of changes in time and not a form of movement—​though movement through space can provide an analogy for this order-​in-​time, which is related to the fact that we can measure time by movements in space, such as the moving hands of a clock. dy: I do regard rhythm as order-​in-​movement, as we shall see. But pray continue with your account of meaningfulness in rhythm, Skepticus. skep: We must contrast two kinds of temporal ordering, one where the elements merely follow one another in time—​as on Budd’s account—​and one where they follow from one another, and so can be read as meaning-​giving structures, as developments or variations or resolutions. The first conception is of a bare order of sounds in time; the second is of a meaningful (or apparently meaningful) order of sounds in time. The vital distinction is not between static and dynamic, but between meaningless and meaningful. dy: Well, I think we disagree here. skep: Consider Wittgenstein’s remark: “Understanding a sentence is much more akin to understanding a theme in music than one may think.”26 For him, a musical theme has an apparent meaning or significance, and so there is such a thing as an understanding of what music is in terms of it. We speak of a piece of music as having an opening, making various statements, restatements, parenthetical comments, and perhaps a recapitulation before coming to a conclusion.



25 Hamilton, “Rhythm and Stasis,” 37: “movement is the most fundamental conceptualization of music.” 26 Wittgenstein, Philosophical Investigations, §527.

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Understanding here is like understanding a sentence—​it involves a meaningful development of notes, akin to a meaningful development of thoughts. dy: I am very sympathetic to this idea, Skepticus—​as shown by my characterization of music as “thinking in sound.”27 skep: I am glad to hear it, Dynamicus. Logicians regard thought as non-​temporal, abstracting from time and psychology to focus on relations of implication—​the structural and conditional question of whether truth is transmitted from premises to conclusion. But if “thinking” means “reasoned change in view,” it must be time-​bound and embedded in psychology.28 Understanding a sentence and understanding a musical theme, then, both depend on understanding the rhythms of thought that they express; both are governed by a sense of necessity, a “logic.” Scruton talks of a “virtual causality that governs musical movement . . . one note in a melody is heard to bring its successor into being.”29 But rather than invoking the concept of causation, I suggest, the relation between notes or tones is better understood as a virtual necessity, the normativity of meaning, of what logically must follow from what. dy: These are very insightful and persuasive arguments, Skepticus—​though I think that by “virtual causality,” Scruton offers a helpful synonym for “necessity.” I agree with you that humanly-​produced rhythm is an intentional, communicative, meaningful activity, and that there is a logic to its expression in music, dance, and poetry. However, I think that these considerations lend support to my view concerning music and movement. I am indebted for this line of thought to my old teacher Analyticus, whom I see striding towards us. Good day, Analyticus! analyticus: Good day, Dynamicus and Skepticus! What is your topic today? dy: Rhythm of course! We are discussing how people respond to music, as Scruton stresses, and are not just caused to move by it. “Response” in such cases has a logical relation to “call,” as in “call and response”—​not the purely causal sense of scientific psychology. I was agreeing with Skepticus’ view that a rhythm is meaningful. ana: Yes, that seems plausible, Dynamicus. Grasping a rhythm involves repeating and developing it in different melodies or harmonies, and recognizing it in different contexts—​a matter of comprehension, not just perception. Rhythm is something one grasps—​it involves cognitive achievement. And one criterion of having grasped it, is moving rhythmically. Such movements are controlled responses, not (mere) effects, though they involve a pre-​cognitive capacity of the body-​subject. dy: This is a promising suggestion, Analyticus—​though some melodies of the most banal commodified pop music seem too simple to require “grasping.” At a



27 Hamilton, Aesthetics and Music, Introduction and Ch. 4. 28 Harman, Change in View.

29 Scruton, “Thoughts on Rhythm,” 229.

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30   The Philosophy of Rhythm certain time of year in Britain, one cannot escape Slade’s pitiful anthem “Merry Xmas Everybody,” with its shockingly bad note-​choice—​if indeed one can call that a melody. skep: Perhaps we should avoid your elitist views on popular culture, Dynamicus. dy: Indeed. The humanist claim is that we would not call various sequences rhythms if people did not react to them in certain typical ways. ana: Yes—​typical ways include continuing or repeating certain sequences or related elements of the sequence, by drumming, singing, or whistling; moving bodily, in time with the sequence, by dancing, or tapping fingers or feet; and noting and demonstrating changes or gaps in the repeated segments of the sequence. So I sympathize with your humanist insight, Dynamicus. Identified naturalistically, the sound sequence would be the same whether we responded to it or not. But if we did not in general respond to it in the ways suggested, it would not be a rhythm.30 skep: I would say not that our response constitutes it as the rhythm it is, but that our response can demonstrate whether we understand the rhythm or not, Analyticus—​at least for intentional or meaningful rhythm. dy: You and I agree that “rhythm” is not a natural kind term, Skepticus—​but from this fact, I conclude that being a rhythm and being called a rhythm amount to the same thing. However, we cannot pursue that deep issue here.31 Setting it aside, it seems to me that Analyticus’ general position is correct. Matching the rhythm of a drum beat is creative in at least a minimal sense, and, more minimally, so is hearing it as a rhythm, as Skepticus stresses. On my account, the paradigm cases of rhythm are human productions, conditioned by natural rhythms. My point is that anyone familiar with music, dance, and poetry is able to initiate rhythms. Music-​making is a social phenomenon. skep: I think here you are confusing what rhythms consist in, with what it is to understand them when they are intentional. Not all rhythms are intentional. The rhythm of a train on its tracks is non-​intentional, even if we naturally respond to it as an intentional order. There is an apparent meaningfulness, akin to seeing a crab’s tracks in the sand that look like a word. Being mere marks there is no word; but we naturally respond as if there is. But let us return to the original question of the relation of rhythm and movement. Again I want to press you—​how do you address my objection that talk of movement in music must be metaphorical and not literal, as Scruton says? dy: Recall Scruton’s argument that “The musical phenomena that we group together under the rubric of rhythm have their counterparts in other areas of human activity”—​speech, dance, physical labour.32 Dance, poetry, and music are conceptually interdependent in that rhythm is essential to each; none can



30 Anscombe, “Linguistic Idealism”; Hamilton, “Rhythm and Movement.” 31 Anscombe, “Linguistic Idealism”; Hamilton, “Rhythm and Movement.” 32 Scruton, Understanding Music, 61.

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be understood independently of rhythm. Hearing musical rhythm does not only involve experiencing music as behaving like a human body; it also involves experiencing the human body, the person, as behaving, moving, musically. skep: What does that mean? How is a temporal phenomenon (music) like a spatial phenomenon (bodily movement) except in an analogical or metaphorical sense? dy: Skepticus, isn’t it begging the question to assume that music is a temporal and not spatial phenomenon? As a performing art, it has many spatial dimensions. I  would characterize the assumption that nothing relevant in the music literally moves as resting on sonicism, the view that music is exclusively a sonic art, or perhaps acousmaticism, the view that music is exclusively an unseen, auditory—​acoustic—​art, focused on sounds without reference to the means of their creation.33 I contrast such views with the conceptual holism of music and dance, according to which music is a cross-​sensory practice and phenomenon. Scruton does not fully appreciate this conceptual holism. The link is stronger than he suggests—​one cannot understand music without understanding dance. skep: I agree with some qualification. I would say something weaker: one cannot understand music without entrainment, i.e., without being able to engage in entrained movement to the music. If such entrained movement counts as dance then your thesis is established—​but perhaps not all entrained movement does so count. dy: That view is close enough to mine, I think. The basic sense of rhythmical movement is dance-​like, I believe—​to hear music as movement is a fundamental way of experiencing and conceiving it. skep: I agree with your invocation of movement as a criterion of understanding musical rhythm, then. But that leaves untouched your original claim that rhythm is literal non-​spatial movement. To say music “moves” is a metaphor or analogue! You still have given no sense to “literal non-​spatial movement.” dy: If one acknowledges that music has essentially spatial dimensions, and affinities with dance, then there is no need for such a notion, which I’ve abandoned thanks to your persuasive objections. But rhythm as order-​in-​movement does not rest on non-​spatial literal movement, and is not refuted along with it—​so I still insist on this idea of an order of movement. The static conception that rhythm is a pattern of sounds and silences is surely refuted by the rhythmic nature of dance—​ how does dance involve a pattern of sounds and silences? A static conception has to make music and poetry the core cases of rhythm, and assert a merely causal connection with dance—​which is not my view. skep: You are simply repeating your earlier, problematic position, Dynamicus. Rhythm is a pattern of sounds and silences, or movements and stillnesses, but one that is apparently meaningful. The static–​dynamic distinction is unhelpful as I have already explained. Why call an order in time “static” anyway? A rhythm changes in time, so it is “dynamic” in a perfectly ordinary sense without being 33 e.g. Malina and Schaeffer, “Concrete Music and Kinetic Art”; Scruton, Understanding Music, 5–​13, 22–​3, 30–​2, 58; Brian Kane, Sound Unseen, passim.

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32   The Philosophy of Rhythm a form of movement. The New Oxford American Dictionary definition for “dynamic” regarding a process is this: “characterized by constant change, activity, or progress.” So change in time counts and there is no requirement of any movement. dy: There may be an ordinary sense in which “dynamic” does not refer to a form of movement, but there is equally an ordinary sense in which it refers to movement rather than change, and that is the sense I am appealing to. Rhythm constitutes what I have termed an order of movement in so far as it implies a conceptual or normative connection between music and dance.   I agree that much work needs to be done in characterizing an “order of movement.” But the idea has a history. Plato in the Laws describes rhythm as “order in movement.”34 Hanslick characterized music as “tonally moving forms,” arguing that music presents the dynamic properties of emotional experience, abstracting from emotional content.35 Messiaen defines rhythm as “the ordering of movement,” which, he says, is “applicable to dance, to words, and to music.”36 Finally, Schütz writes that “Breathing is only one example of rhythmical bodily movement. Others are walking, dancing, knocking and many operations of working . . . rhythm always refers to actual or virtual bodily movements in space.”37   It is significant that so many of the terms used to describe music involve movement, especially dance-​movement:  waltz, march, lullaby, rock ‘n’ roll, sarabande, stomp, swing, thrash, hip-​hop. Your rejection of the dynamic view thus faces a dilemma:  Either “rhythm” has a different meaning in “musical rhythm” compared to “dance rhythm,” or rhythm is not a pattern of sounds and silences—​since that is not an adequate characterization of dance rhythm. And to say that rhythm has different meanings in these cases seems implausible. skep: I reject this dilemma. But as it is getting late, let us resume our discussions tomorrow. dy: Yes indeed, Skepticus.

4.  Entrainment, the movement criterion, and rhythm as “order of movement” (tealicious tearoom, durham) skep: Good morning, Dynamicus and Analyticus. I trust you are both eager for further debate. dy: Indeed we are, Skepticus. Can we begin by considering the phenomenon that we touched on earlier, which psychologists call entrainment—​the tendency of a 34 Plato, Laws, Bk 2, 665a. 35 Hanslick, On the Musically Beautiful, 29. 36 Messiaen adds that the definition is “incomplete,” though he doesn’t explain why: Messiaen, Music and Colour, 67. 37 Schütz, “Fragment on the Phenomenology of Rhythm,” in On Phenomenology, 21.

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subject to align their movement to an external auditory pulse? Psychologists define it as two rhythmic processes adjusting towards and eventually “locking in” to a common phase or periodicity.38 Psychological research generally assumes a dynamic but non-​humanistic conception of rhythm, I would argue—​focusing on bodily rhythms such as heart-​beat, blood circulation, respiration, secretion of hormones, and menstrual cycles.   A humanistic conception denies that entrainment in these internal cases is continuous with entrainment on the personal level—​rather, they are distinct phenomena with interesting affinities. On the humanistic view, individuals adjusting their speech rhythms to match each other in conversation, or entraining in musical performance, are categorially different from convergence in circadian or menstrual cycles. Moreover, naturalistic accounts of entrainment offered by psychologists involve a misconception—​they mistakenly regard entrainment as more fundamental than, and explanatory of, rhythm. ana: I agree, Dynamicus. The misconception here is comparable to how psychologists and scientistic philosophers of mind explain human memory through memory traces; we are able to remember, it is claimed, because we store knowledge and information. However, “store” in the relevant sense is itself a memory-​concept, co-​defined with “remember”; it cannot explain the operation of memory. dy: Indeed. To argue that human rhythmic abilities arise from an ability to entrain, is to make the same kind of mistake. Entrainment stands to rhythm as storage stands to memory. The capacity to entrain does not explain our rhythmic behavior, but is part and parcel of it; just as “storage” is part and parcel of “remembering.” Indeed, as remembering involves more than storage—​it also involves retrieval—​so rhythmic behavior involves more than entrainment:  it also involves a capacity to initiate rhythm. Only a subject unacquainted with rhythmic behavior—​such as a paralyzed, sense-​deprived individual—​could not create a rhythm spontaneously. But one who is familiar with such behavior can create new rhythms, just as a competent language-​user can create novel sentences. ana: That seems right, Dynamicus. dy: A humanistic conception treats rhythm as essentially a human phenomenon, conditioned by the natural organic phenomena addressed by researchers on entrainment. For humanists, people begin to experience waves on the shore as rhythmic as they begin to create music and dance. The humanistic claim is not that all rhythms are humanly-​produced, but rather—​to reiterate—​that rhythm came into being with, or at least is part and parcel of, human practices of music, poetry, and dance. The producers of music, poetry, and dance drew on and incorporated natural sounds—​and in later eras, mechanical and electronic sounds.

38 Clayton et al., “In Time with the Music,” 2.

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34   The Philosophy of Rhythm ana: The contrasting naturalistic view—​that these sounds already were rhythmic, and that humans developed the capacity to mimic them, thus creating their own rhythms—​also has plausibility, Dynamicus. Conceptual integration of music and life is plausible, because you classify rhythm as essentially musical and stress ubiquity and ineliminability of rhythm in everyday life. dy: I agree that this opposed view has some plausibility—​I favor the humanistic stance, but it is an achievement just to locate the most fruitful dialectic. That is a deep issue. Can we instead pursue the claim of the psychologists that rhythmic ability partly depends on, or arises with, entraining to natural rhythms? This claim seems right, as does the psychologists’ assumption that the musical world is a social one, where rhythms are emulated; rhythmic or metrical behavior involves a common, social response. However, the psychologists are wrong to deny that an individual can produce a rhythm spontaneously, without entraining to anything. Entrainment, as psychologists conceive it, prioritizes responding over creating, and indeed almost makes the latter impossible. Londinium claims that “meter is related to, and may be a complex form of, entrainment behavior.”39 But entrainment and meter are interdependent concepts, and metrical behavior cannot just be a form of entrainment. ana: Indeed. dy: Londinium commented to me that “creating rhythms outside of a social setting is a degenerate case of entrainment—​one half of the two-​oscillator system that entrainment requires.”40 When I make rhythms by myself, he argued, entrainment occurs here too, by a coordination of “central timekeeper” and external rhythms. ana: I don’t understand why Londinium regards initiating a rhythm as a “degenerate” case of entrainment. Talk of “oscillation” sounds like a mechanistic account of what it is to grasp a rhythm. dy: Yes, Analyticus. Entrainment cannot yield a complete explanation of musical rhythm. So against the assumption that nothing relevant in the music moves literally, I  would develop Skepticus’ earlier suggestion concerning entrainment, and argue that something relevant does literally move. Performers and listeners move to the music, sharing a rhythmic, dance-​like response. This is not a merely causal connection, but a manifestation of musical understanding and involvement—​an internal relation between music and movement. As Ezra Pound writes, “music begins to atrophy when it departs too far from the dance . . . but this must not be taken as implying that all good music is dance music or all poetry lyric.”41 The connection is not just with dance, but with human rhythmic activities of all kinds—​marching, laboring, rocking a cradle—​ which music accompanies and informs.



39 London, Hearing in Time, 12. 40 Email communication.

41 Pound, ABC of Reading, 14.

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  Thus we see that music, dance, and poetry arise as an integrated practice, and form a conceptual holism or circle of interdependent concepts. This implies a dynamic conception of rhythm. Except at the least dynamic end of the spectrum, as in plainchant, music creates an urge to move in response that shows that one recognizes it as music, and recognizes the rhythm. skep: You admit, then, that since there is no coherent notion of a literal non-​spatial movement, music involves no such thing. dy: I have retracted that claim, or modified it to say “There is something relevant that moves literally—​the listener or performer moving to the music.” I  am arguing that music, dance, and rhythmic bodily movement (leaving aside poetry and prose in the current discussion, though perhaps they could be included too) belong to an order of movement a stronger claim than that made by proponents of metaphorical accounts such as Scruton. I am suggesting that to make and respond to music is to be disposed to move rhythmically. skep: This is the entrainment issue we discussed some time ago; I  think it is a condition of understanding musical rhythm, not just a matter of what one is disposed to do. dy: To speak of “understanding musical rhythm” makes it seem too much like a conceptual matter, but it might not be: infants respond at a very young age to rhythm, emotionally and physically—​is that a matter of understanding? However, it looks like we agree on what I will call the movement criterion. The movement involves bobbing one’s head, tapping fingers or feet, gestures such as punching the air or leaping, as well as dancing. Inconsolable grief or sexual arousal can dispose people to move rhythmically, but although neither requires musical accompaniment, they invite it. ana: What do you make of this objection to the movement criterion: that the disposition can be overridden by social convention, in classical concerts, or church services? Such prohibitions result in what may be called motionless moving, analogous to silent speech. At a certain point in history, silent reading became the norm; similarly, perhaps, motionless moving became the norm for listening to certain kinds of music. dy: Indeed. The movement criterion is illustrated by children’s unlearned movement to music—​marching to martial music, for instance. There are no societies where one is brought up to understand music without understanding dance, or vice versa. It would be absurd to say that dance might have evolved independently of music. The contrary claim might be tempting, because of how modern concert music has evolved—​but this too would be mistaken, even if certain forms of music are now evolving independently of dance. An individual might be forbidden to move to music, or to dance—​but a whole society? Maybe under the Taliban—​though such societies do not endure. Someone who says, “I am able to move in time with the music, but I never feel like doing so” is someone who does not understand it—​medical conditions and syndromes excepted. An example of the latter is the jazz trumpeter Tom Harrell; blowing and valving

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36   The Philosophy of Rhythm movements aside, he is almost immobile when performing. This striking phenomenon results from treatment for schizophrenia.42   We mentioned kinds of music and poetry to which the criterion seems not to apply. Plainchant tried to exclude the human body from music—​it is unmetrical, though not unrhythmic. Children would not move spontaneously to it, as its rhythm is not dance-​rhythm—​though if asked to move, they might do so appropriately. ana: But what disposition or inclination is involved then, Dynamicus? Might we say, more correctly, that someone who grasps a rhythm could make tracking moves? “Disposition” is ambiguous. “She is disposed to shed tears when listening to music” cites a relative frequency. “She is disposed to jeer at Mick Jagger when she attends his performance tonight” is about her possible intentions on a particular occasion. This is the sense in which a person can feel disposed or inclined to do something; what is done will be intentional behavior, which is not implied by the frequency sense of “disposition.” dy: Doesn’t it have to be a disposition, Analyticus? There is a third sense of disposition in addition to relative frequency and possible intention—​viz., “a response that amounts to a criterion.” An injured person is disposed to exhibit pain-​behavior—​such behavior belongs to an indefinite list including crying out, clutching the affected part of the body, moaning, and so on. This is stronger than the statistical or frequency claim, but weaker, perhaps, than intention. Similarly with music, where defeating factors include social prohibition or stigma, feeling tired, and so on.   The movement criterion shows that something relevant does literally move—​ the listener and performer—​as they respond to the music. And given that such a response is a criterion of understanding, the movement criterion brings together my emphasis on movement, and your emphasis on understanding. skep: It is surely not enough to say that most music naturally inclines one to dance to it, given that we are now interested in explaining how dancing to music contributes to understanding music. dy: I am not sure that there is such an explanation—​it seems more like a conceptual elucidation. I would add that most music naturally inclines one to dance—​ the use of “incline” does not seem to be a philosopher’s weasel-​word. But that claim does not express the conceptual connection between music and dance, that I am trying to elucidate. It’s interesting that proponents of entrainment also make this connection, and that here also it seems to be contingent. For instance, Theodorus Gracykus, in our volume, argues that “The centrality of entrainment explains our near-​universal propensity to interpret music as human gait and comportment”: “we grasp the music’s gait in a preconceptual recognition process. Knowledgeable listeners feel the beat. [The listener who sits]



42 Hamilton, “Review: Koktebel Jazz.”

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still in the concert hall will entrain to the occurrent music, anticipating how to move to it.”43   Moving to the music is a kind of entrainment—​but, to reiterate, entrainment is an elucidation and not, as psychologists suppose, an explanation of the movement. If someone taps their feet to music, no explanation is required—​“Why are you doing that?” would be the kind of question someone high on the autism spectrum or a Martian visitor might ask. skep: I most certainly grant this claim! Indeed I formulated a version of it independently of Gracykus. The truth in your intuition of a deep link between music and dance is not that the experience of music disposes one to dance—​that is causal and non-​normative. Rather, it is that unless one dance or move to the music—​a capacity of following the music, entraining to its rhythm—​then one does not know what the music is, one cannot identify it as the music it is. That’s a conceptual, normative notion—​just what your humanistic account of rhythm requires. dy: That is well put, Skepticus—​I see that I was wrong to insist that the movement criterion involves a disposition rather than a capacity. We agree that there is a deep conceptual connection between music and dance—​yet to return to my earlier claim, you want to say that “rhythm,” as it appears in “musical rhythm” and “dance rhythm,” is ambiguous? skep: It is not ambiguous. For a start one could hold, as you yourself once did, that rhythm is disjunctive, characterizing music in one way (accenting sounds, which do not literally move) and dance in another (accenting bodily movements, which literally move): Rhythm is “order in movement . . . viz. the imposition of accents on sequences of sounds or movements, creating non-​periodic phenomena usually within a periodic repetitive (metrical) framework.”44 This definition of rhythm as “order in movement” is disjunctive, in my view, because it applies to phenomena either literally (dance) or figuratively (music). dy: I do not agree that this definition is disjunctive—​but pray continue. skep: I respect the intuition behind your definition: namely, that there is no requirement to reduce the phenomena of rhythm to a unity. Clarification can be achieved by expansion. Thus rhythm involves hearing or otherwise perceiving accents in sounds—​speech (which is not mere sound), non-​intentional phenomena (heartbeat)—​and in movement—​natural objects (cycles of the moon), artifacts (movement of second hand of a watch or of a train), intentional movement (dance, walking gait). But we can go further, and say that rhythms in music and dance, as well as natural rhythms, have this in common: they are all patterns of changes of qualities in time. That is, a dynamic pattern, if one uses the word “dynamic” to connote change rather than movement—​which is not how you use it, Dynamicus. Dewey

43 Gracyk, “Musical Expressiveness.”

44 Hamilton, “Rhythm and Stasis,” 26.

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38   The Philosophy of Rhythm was right, rhythm is “order in change”45—​though as we have seen in the discussion of meaningful order, that is not the end of the matter. dy: The account that you suggest is certainly not the one I intended. My account aims to be unifying and not disjunctive. A genuinely disjunctive account, such as McDowell’s account of perception, finds little in common between the disjuncts. But we are due to meet our colleague Vitalia shortly, and I think we should ask her how she views the debate.

5.  Human Movement (pink lane coffee, newcastle) vitalia: Good day, colleagues. I’ve overheard some of your discussion on the question of rhythm, and some thoughts on these questions occur to me. dy: Pray enlighten us, Vitalia! vit: First I would agree with Analyticus and Skepticus in rejecting a dispositional account—​and would place their objections in a broader context. Most human adults are not disposed to show pain-​behavior when in pain. “Humans wince and cry out at pain” would be a false empirical generalization, but a true natural generalization. In this context, “disposed” is a philosopher’s weasel-​word. To make a true empirical generalization, featuring a claim about dispositions, one must introduce “normal conditions” and such-​like.   Talk of dispositions loses reference to the subject’s history, and refers only to their current state. Possession of a capacity, in contrast, is associated with culture and practice, and conforms with a humanistic approach. Dynamicus’ claim should therefore be: just as the natural, pre-​linguistic response to pain is pain-​ behavior, so the natural pre-​linguistic response to music is dance-​behavior. Humans can suppress that natural response, or communicate it in a non-​natural, linguistic way. ana: Thank you for your support, Vitalia! dy: These are interesting points that I must ponder. vit: There is a further issue I would raise. It struck me while considering your humanistic view, Dynamicus, that the movement in question is bodily movement. It is the movement of a living self-​conscious being, not those of an inanimate object. dy: Yes, of course—​unlike Skepticus, I limit the realm of rhythm to the intentional or voluntary.

45 Dewey, Art as Experience: “Because rhythm is a universal scheme of existence underlying all realization of order in change it pervades all the arts, literary, musical, plastic and architectural, as well as the dance” (150); “There is a rhythm in nature before poetry, painting, architecture and music exist” (147).

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vit: Indeed. Because of our Cartesian heritage, philosophers often treat bodily movement as movement of a thing that happens to be living. However, “life” is not an accidental property of some objects. It is what, following Anscombe, one can call a “form of description”—​or following Hegel, a “logical category.” Likewise, “human movement” is not movement that is accidentally of a human being. dy: These are sage comments, Vitalia. vit: To describe the movements of a living thing is to invoke a form of description quite unlike that which applies to the movements of inanimate objects. As I understand Dynamicus, human movement shares an order with sound-​patterns that we call rhythmic. To investigate this claim we need to think about what it is for a human body to be moving. The criteria for this are quite different from those for inanimate things. It can, for example, be wrong to talk of human movement in the presence of spatial movement, and right to talk of human movement at a moment when there is no spatial movement—​for example, the moment of stillness in the tango dancer’s body as she executes a voleo atrás. Conversely, someone in traction, in hospital, may have their limbs moved by a pulley, while not moving their body. Thus, the criteria for continuity and unity of movement are quite different for a human being than for a lump of matter. dy: That is very helpful, Vitalia. It seems that you and I agree, against Skepticus, that rhythm is an essentially intentional notion, and indeed involves intentional movement—​and that you agree with my view that that there is an order of movement shared by music, poetry, dance, and bodily movement. vit: Yes, that is well-​expressed, Dynamicus. I was unhappy with your suggestion that music literally moves—​“literal” is a strange term, and is not required by your account of a common order between bodily movement and that of music. That isomorphism makes it apt to describe the music as “moving.” I would therefore argue that it is wrong to describe the ascription of movement as metaphorical, but that equally it is unhelpful to say “the music literally moves.” dy: Do continue, Vitalia. vit: The question “literal or metaphorical?” can be raised only after it has been specified to which language-​game the description “the music moves” belongs. Contrast the everyday and scientific language-​games with “solid.” Is the table literally solid? Nothing falls through it; but physicists explain that solid things are literally full of spaces between atomic particles. If we are describing the movements of a raindrop down a window, it is metaphorical to describe them as indecisive. A dancer’s movements may be indecisive, in contrast, in virtue of her dance involving significant periods of stillness and immobility; this immobility is, in the spatial sense, part of her movement. A performer may have her limbs moved by other performers, while not moving her body. skep: I agree with your first point, Vitalia. I deny that the music moves in any literal sense, but I accept the importance of human movement as a manifestation of understanding music—​and other intentional rhythms—​through entrainment.

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40   The Philosophy of Rhythm Rhythm is an order of changes of qualities in time that strikes us as meaningful—​ it is experienced as if intended to communicate something to the listener, even if it is, in fact, non-​intentional and meaningless like the beating of a heart. But while there is an analogy between literal bodily movement and the way the music changes in time, this is not an isomorphism of movement as you put it Vitalia—​so it is misleading to conclude that the music moves. There may be isomorphism between musical rhythm—​an intentional order of sonic changes in time—​and dance rhythm, an intentional order of changes in bodily movement in time and space. But rhythm itself is not movement. Movement can, of course, have rhythm but that does not mean that rhythm is movement. vit: The nub of our disagreement, Skepticus, seems to be that Dynamicus and myself hold that music and bodily movement share an order of movement, and you do not.46 This leaves you with the problem of the ambiguity of “ ‘rhythm,” as it appears in “musical rhythm” and “dance rhythm.” dy: You deny this common order, Skepticus, because you are committed to what I  called sonicism, which regards music as exclusively an aural art, and musical rhythm as an intentional order of sonic changes in time. Sonicism sharply separates music and dance. skep: There is no ambiguity in “rhythm” on my account. To reiterate, we can say, consistently with Dynamicus’ original definition, that the concept of rhythm is disjunctive, characterizing both music and dance, and, indeed, characterizing both natural rhythms (heartbeat, respiration) and human rhythms (music, dance). But I prefer to say, with Dewey, that what all rhythms have in common is an order of changes in time. My humanism is a matter of holding, in addition, not that rhythms must be intentional—​which is Dynamicus’ view—​but that rhythms are experienced as intentional or meaningful. vit: Thank you for that clarification, Skepticus. It seems that we all agree in rejecting a description of bodily movements as if they were movements of an inanimate object—​as an analogue of the naturalistically identified sound-​sequence. With such a form of description, the concepts of rhythm and dance get no grip. Under this mode of description, any physical pause will be a cessation of movement and any sound-​pause a cessation of sound-​sequence.   However, as Anscombe reminds us, our description of human bodies in purely physiological terms is parasitic on vital forms of description. There would be no movements to identify, were it not for the latter. We do not first identify physical movements, and then on investigation come to apply vital descriptions. Rather, we recognize and produce human movements, then by investigating them, come to these other forms of description.   So, too, with the naturalistic description of sound: we recognize (and produce) rhythmic sound sequences, and by investigating them, we apply this other 46 The idea of an order of movement can be developed through the ideas of Simone Weil, explicated by Winch, Simone Weil, esp. Ch. 4.

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Dialogue on Rhythm  41

form of description. In the vital mode of description, physical-​pause or sound-​ pause does not imply that bodily movement or rhythm has ended. Such pauses are internal to the concept of rhythm and dance. dy: A very congenial line of argument, Vitalia. vit: Thus we avoid the need to invoke dispositions. Dance, music, and rhythm are forms of description that belong to human life. To recognize a musical rhythm—​ a movement-​pattern in sound—​is to apply a description that can be expressed in bodily movement, that is, dance. This need not imply anything about one’s individual psychology and dispositions—​I may be quite indisposed to dance. But if we did not have the concept “rhythm”—​that is, did not hear sounds as rhythms—​“dancing” would not be a possible description of human movement. dy: To assert a conceptual connection between bodily movement and music is to make a stronger claim than Scruton. He holds that the source of the metaphor of musical movement is bodily movement, but in fact—​to reiterate—​they share an order of movement, described in rhythmic terms. skep: When Vitalia refers to “a movement-​pattern in sound,” this cannot be taken literally as relative change in spatial location. Music and bodily movement may share rhythm, but rhythm is not any kind of movement; rather it’s an apparently meaningful pattern of changes in time. Responding to musical rhythm in a dance-​like way and even producing music in a dance-​like way—​which is, at best, all you have established—​are distinct from claiming that “rhythm constitutes an order of movement.” That is the nub of the problem. The constitutive claim is not established by the cognitive or genetic claims. dy: On that we differ, Skepticus. But at this pregnant point, my dear interlocutors, we must curtail our discussion—​our word-​limit has been reached. Our readers must decide whether they favor my still inadequately developed attempt to capture a long-​standing intuition about the connection between music and movement, your incisive critique, or the sage views of our other contributors.

Works Cited Anscombe, G. E. M., “The Question of Linguistic Idealism,” Collected Philosophical Papers, vol. 1 (Minneapolis, 1981). Boghossian, Paul, “On Hearing the Music in the Sound: Scruton on Musical Expression,” Journal of Aesthetics and Art Criticism, 60.1 (2002), 49–​55. Budd, Malcolm, “Musical Movement and Aesthetic Metaphors,” British Journal of Aesthetics, 43.3 (2003), 209–​23. Clayton, Martin, “Entrainment and the Social Origin of Musical Rhythm,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C12. Clayton, Martin, Rebecca Sager, and Udo Will, “In Time with the Music:  The Concept of Entrainment and Its Significance for Ethnomusicology,” European Meetings in Ethnomusicology, 11 (2005), 1–​82. Cooper, Grosvenor and Leonard B. Meyer, The Rhythmic Structure of Music (Chicago, 1960).

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42   The Philosophy of Rhythm Cowling, Sam, “Instantiation as Location,” Philosophical Studies, 167.3 (2014), 667–​82. Dewey, John, Art as Experience ([1934]; New York, 1980). Funkhouser, Eric, The Logical Structure of Kinds (Oxford, 2014). Gracyk, Theodor, “Rhythms, Resemblance, and Musical Expressiveness,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C10. Hamilton, Andy, Aesthetics and Music (London, 2007). Hamilton, Andy, “Rhythm and Stasis: An Almost Entirely Neglected and Major Philosophical Problem,” Proceedings of the Aristotelian Society, 111.1 (2011), 25–​42. Hamilton, Andy, “Review: Koktebel Jazz Party, Crimea” (2014): http://​www.jazzjournal.co.uk/​ magazine/​810/​review-​koktebel-​jazz-​party-​crimea. Hamilton, Andy, “Rhythm and Movement:  Music, Metaphor and Dance,” Midwest Studies in Philosophy (forthcoming).1 Hanslick, Eduard, On the Musically Beautiful, tr. Geoffrey Payzant ([1854]; Indianapolis, 1986). Harman, Gilbert, Change in View (Cambridge, MA, 1986). Kane, Brian, Sound Unseen: Acousmatic Sound in Theory and Practice (Oxford, 2014). London, Justin, Hearing in Time:  Psychological Aspects of Musical Meter ([2004]; 2nd edn, Oxford, 2012). London, Justin, “Metric Entrainment and the Problem(s) of Perception,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C11. Malina, Frank J. and Pierre Schaeffer, “A Conversation on Concrete Music and Kinetic Art,” Leonardo, 5.3 (1972), 255–​60. Messiaen, Olivier, Music and Colour: Conversations with Claude Samuel, tr. E. Thomas Glasow (Portland, 1994). Mumford, Stephen and Rani Lill Anjum, Getting Causes from Powers (Oxford, 2011). Nussbaum, Charles, “Musical Perception,” in Mohan Matthen, ed., Oxford Handbook of Philosophy of Perception (Oxford, 2015), 495–​514. Plato, The Laws (c.360 bc), tr. Trevor J. Saunders, in Complete Works, ed. John M. Cooper (Indianapolis, 1997). Pound, Ezra, ABC of Reading ([1934]; London, 1961). Schütz, Alfred, On Phenomenology and Social Relations: Selected Writings, ed. Helmut R. Wagner (Chicago, 1970). Scruton, Roger, The Aesthetics of Music (Oxford, 1997). Scruton, Roger, “Thoughts on Rhythm,” in Kathleen Stock, ed., Philosophers on Music: Experience, Meaning, and Work (Oxford, 2007), 226–​55. Scruton, Roger, Understanding Music: Philosophy and Interpretation (London, 2009). Simons, Peter, “The Ontology of Rhythm,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C3. Winch, Peter, Simone Weil: The Just Balance (Cambridge, 1989). Wittgenstein, Ludwig, Philosophical Investigations ([1953]; 2nd edn, Oxford, 1958). Zuckerkandl, Victor, Sound and Symbol:  Music and the External World, tr. Willard R. Trask (Princeton, 1956).

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2 Rhythm and Movement Matthew Nudds

I My focus in this chapter is on whether our perceptual experience of rhythm involves an experience of movement. I will argue that it does: that a proper understanding of auditory perception shows that an important element of our experience of rhythm—​our experience of musical grouping—​involves experiencing sounds as produced by extra-​musical events that include movement, and that we can therefore experience literal movement in rhythm. Rhythm is not one process, but many. Lerdahl and Jackendoff make a useful distinction between grouping and meter. When we hear a piece of music, we hear the individual notes or tones that compose it as grouped together and organized into streams or phrases. They suggest that “from a psychological point of view, grouping of a musical surface is an auditory analog of the partitioning of the visual field into objects.” As well as perceiving musical sounds as grouped, “the listener instinctively infers a regular pattern of strong and weak beats to which he relates the actual musical sounds.”1 This regular pattern of beats can be categorized, and constitutes the metrical structure of the music—​the temporal pattern of beats to which the listener relates musical events. The metrical structure of a piece of music can crosscut the grouping of tones so that tones belonging to different groups can contribute to the determination of the metrical structure. Though all musical experience involves the experience of groups of tones, not all music is experienced as having metrical structure. Grouping and metrical structure are therefore distinct elements of rhythm. The metrical structure of a piece of music is determined by the relations between moments of time that may not be occupied by any tone in the music. There may be silence at a moment of time that is an element of the metrical structure. Therefore, the metrical structure of a passage of music is not determined by relations between the actual tones that compose the music. Because the metrical structure is not determined by relations between actual tones, it might be suggested that metrical structure is not, strictly speaking, something that we perceive, but a pattern or framework that is abstracted from what we perceive.2 It is an abstract framework 1 Lerdahl and Jackendoff, Generative Theory of Tonal Music, 36, 12. 2 Lerdahl and Jackendoff describe meter as “induced” in the listener. Matthew Nudds, Rhythm and Movement In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0003

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44   The Philosophy of Rhythm against which what we perceive is heard. The suggestion that meter is not something perceived is further supported by the fact that there is typically a gap between what is notated in a score and what can be directly perceived in a passage of music as performed. The gap exists because performers don’t reproduce a piece of music exactly as it is written. Doing so would produce mechanical sounding, lifeless music. Typically performers introduce small changes to the timing of the notes, changes that have a role in explaining the expressive power of music.3 The metrical structure of the music is the notated structure relative to which these temporal changes are heard. Again, it seems that the metrical structure is abstracted from what is perceived rather than directly perceived in the music. That there is a connection between metrical properties of music and movement is evident in the way we can move to music by, for example, tapping a finger or dancing in time to the meter of a piece of music. Empirical evidence that suggests our capacity to perceive the metrical properties of music is connected to our capacity to move in time with the music. There is evidence, for example, that metrical rhythm perception is influenced by the size and shape of our body, and that body movement can influence our perception of the metrical properties of a passage of music.4 This evidence suggests a constitutive connection between our capacity to perceive the metrical properties of music and our capacities for bodily movement. In asking whether there is a constitutive connection between our perceptual experience of rhythm and movement, however, my interest is not in this metrical component of rhythm, but on the grouping component of rhythm and its relation to movement. Whilst many writers have argued that there is a close connection between music and movement, they been skeptical of the idea that we can literally hear movement in music. This skepticism is grounded in a conception of our experience of music and of the intentional object of that experience.

II Malcolm Budd provides a characterization of music and our experience of it: Music is based upon the human capacity to hear sequences of bare sounds in various ways: to hear a rhythm in a series of sounds; to hear two simultaneous rhythms in a series of sounds; to hear a series of sounds as a melody . . . to hear a rhythm . . . is in each case to be aware of a form of sounds or a form in sound, perceived without anything else being  .  .  .  grasped  .  .  .  than sounds that are

3 Repp, “Patterns of Expressive Timing.” 4 Repp, “Sensorimotor Synchronization,” discusses the connection between tapping and meter. Phillips-​ Silver and Trainor, “Vestibular Influence,” and Trainor et al., “Vestibular System,” discuss the influence of the vestibular system on metrical perception. Chen et al., “Synchronization to Musical Rhythms,” provides brain-​ imaging evidence that implicates the motor system in the perception of meter.

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Rhythm and Movement  45 experienced in that form . . . The experience of music is au fond purely auditory: it consists of interconnected modes of hearing mere sounds . . .5

One consequence of this conception of music is that “music as an art-​form is not based upon music’s capacity to represent or refer to items in the physical world.”6 This conception of music goes together with a common conception of auditory experience as the experience of sounds and sounds alone, of auditory experience as purely auditory. Anything else that can be heard in hearing sounds is not an object of experience, but merely suggested to us by the sounds we hear. Because the experience is purely auditory, the structure and order in our perceptual experience of sounds can be accounted for “without anything else being present to or grasped or thought of by the mind than sounds.” Budd allows that there are connections between music and “non-​musical phenomena,” but these connections are not intrinsic to musical experience. So if there is a connection between music and movement, in particular between rhythm and movement, it is not a connection that is intrinsic to the music. And it is not, properly speaking, a perceptual connection. Roger Scruton views our experience of music similarly in some ways to Budd, arguing that it is acousmatic, such that music is experienced as sounds apart from the circumstances of their production, and attended to as they are in themselves:  “One who experiences these sounds [apart from their physical causes] experiences all that he needs, if he is to understand them as music.”7 According to Scruton, music is made up of “tones,” which he distinguishes from mere sounds. Tones are the “intentional object of the musical perception.”8 These sounds are elements of a musical phrase or group, and are connected together by what he calls “virtual” causality. Virtual causality is the relation that groups sounds together as a musical phrase. Scruton therefore distinguishes music from ordinary sounds in two ways. First, music involves sounds considered acousmatically. Second, music can be distinguished from ordinary sounds through the virtual causality of grouping. It follows that music is autonomous in much the same way it is for Budd: “What we understand, in understanding music, is not the material world, but the intentional object: the organization that can be heard in the experience.”9 Scruton thinks that we do hear movement in music if we hear it as music. However, he argues that this movement must be distinct from the movement of things in the material world. Movement in the material world involves something changing its location within a spatial frame of reference. We can’t make sense of music changing location in this way: “Musical space and musical movement are not even analogous to the space and movement of the physical world.”10 How, then,



5 Budd, Music and the Emotions, x. 6 Budd, Music and the Emotions, x. 7 Scruton, Aesthetics of Music, 3.

8 Scruton, Aesthetics of Music,  19–​20. 9 Scruton, Aesthetics of Music, 221.

10 Scruton, Aesthetics of Music, 51.

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46   The Philosophy of Rhythm can we make sense of musical movement? It’s a sense of movement generated by the structure of tones, but of tones whose structure is not explicable in terms of the structure of events in the material world. Because of the way in which music is distinct from the material world, the movement of music cannot be literal movement, and if the movement is not literal, then it is metaphorical. Before turning to an account of the metaphorical content of our experience of movement in music, it’s worth looking at what connections listeners actually make between music and movement. An insight into this is provided by a series of experiments carried out by Zohar Eitan and Roni Granot, who investigated the relation between change in various musical parameters and motion in space.11 Participants were asked to visualize a cartoon character of their choice. They were then played brief passages of music and had to visualize their character moving in an imaginary short film with the music as the soundtrack. They then completed a forced-​choice questionnaire about the way their imagined character had moved. The answers to these questionnaires were analyzed to reveal associations between properties of the music and the movements of the character. A number of associations were found.12 For example, rises in pitch were associated with spatial ascent, but also with moving away, acceleration, and higher energy movement. Falls in pitch were associated with the opposite kinds of movement: spatial descents, slowing down, lower energy, but not with approaching motion. Changes in inter-​onset intervals (the times between tones) were associated with changes in imagined speed. Increasing and decreasing inter-​onset intervals were associated with ascent and descent. In addition, there were found to be associations between articulation and movement. For example, gradual increases in staccato were associated with moving away. Not all the associations were found to be symmetrical. Dynamics, pitch, and tempo were all associated asymmetrically with movement. For example, diminuendos were associated with descent, but crescendos were not associated with ascent; pitch descents evoked spatial descents, but pitch ascents were not associated with spatial ascents. These experiments show that listeners fairly consistently associate certain features of music and movement. We associate certain patterns or groups of tones with movement and, consequently, hearing those patterns or groups brings to mind the movement. Does that show that our experience of music is connected in some significant way with movement? There are reasons to doubt that it is sufficient to show that. First, associations like those found in the experiments are ubiquitous. Many experiments not involving music have discovered similar kinds of associations, some of which are surprising. For example, when asked “are lemons fast or slow?” people consistently answer that lemons are fast;13 when shown pictures of a spiky 11 Eitan and Granot, “How Music Moves.” 12 There were no significant differences between those with and without musical training: Eitan and Granot, “How Music Moves,” 240. 13 Woods et al., “Fast Lemons and Sour Boulders.”

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Rhythm and Movement  47

object and a bulbous object and asked which is “Bobo” and which is “Kiki,” they consistently say that the spiky one is Kiki.14 The fact that lemons and speed are associated doesn’t in itself show anything interesting about our understanding or experience of lemons. The problem lies partly with the experiment. From the fact that, when prompted, we consistently associate lemons and speed, it doesn’t follow that the association plays any role in our unprompted thought about or experience of lemons. It might be some entirely trivial connection that leads us to say, when forced to choose, that lemons are fast rather than slow. The same is true of the connection between music and movement. The fact that, when prompted, we consistently associate certain properties of music with certain kinds of movement doesn’t show that the association plays any significant role in our thought about or experience of music. Second, there’s nothing right or wrong about such associations. We can’t draw the conclusion from the fact that we make associations between properties of music and kinds of movement that we ought to make those associations. We can’t, therefore, say of someone who doesn’t make the association, or who associates differently, that they have gone wrong or failed to appreciate something that is there in the music. If someone who fails to make an association has not failed to appreciate something that is there in the music, then it is difficult to see how the association can be significant for our appreciation of music. Budd’s suggestion was that only features of the music are significant for our appreciation of music; the existence of associations doesn’t undermine that. Third, if what we are trying to explain is an aspect of our perceptual experience of music, then appeal to these associations don’t help. It doesn’t do so because nothing tells us that the associations reflect a feature or aspect of our perceptual experience of music, rather than something semantic, or simply some cognitive bias that “brings to mind” the association in the light of our perceptual experience of music. The mere fact that we make these associations is not, therefore, significant for understanding our experience of music. So the fact that we make these associations doesn’t tell us much, but doesn’t it imply the existence of an underlying connection between music and movement that explains why we associate them? Isn’t this underlying explanation of the associations significant for understanding our experience of music? Perhaps. However, there are likely to be different underlying connections that explain the variety of different associations, and few of these connections promise to be significant. That there is no single explanation of the fact that we make associations between music and movement is evident from the range of different explanations that have been suggested.15 For example, the idea that the intensity of a stimulus can be matched across modalities. There is a connection between pitch height and the

14 Ramachandran and Hubbard, “Window into Perception.” Spence, “Crossmodal Correspondences,” reviews several such studies. 15 Spence, “Crossmodal Correspondences.”

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48   The Philosophy of Rhythm way music is notated. Lateral pitch position corresponds with the layout of piano keyboards. Further, that we associate high pitch and spatial height may be a consequence of the fact we describe both as “high.” Each of these connections explains a different association. Some are perceptual and reflect a statistical correspondence in our environment (which may be trivial, as in the keyboard example); others are semantic and reflect a fact about language (e.g., uses of the word “high”). None of this rules out the possibility that there is a connection between music and movement that results from some deep fact about auditory perception, and below I’ll outline an account of auditory perception according to which there is such a connection. But before that, I want to look at an account of movement as associated metaphorically with music. Music is often taken to have metaphorical content. Usually this is understood in a linguistic way, involving thought or judgment. Thus understood, metaphor will not help explain any constitutive link between our experience of music—​and in particular, rhythmic grouping—​and movement. But we don’t have to think of metaphorical content as linguistic. Christopher Peacocke has defended an account of perceptual experience, and of our experience of music in particular, that sees metaphoric content as nonlinguistic. I’ll briefly outline his account and then assess whether it can ground a constitutive connection between rhythm and movement. Peacock begins by distinguishing three kinds of content that a perceptual experience can have.16 First, there is the familiar perceptual content: in virtue of experience having this kind of content, we experience the world as being a certain way. For example, in seeing a cat, we have an experience in virtue of which it seems that there is a cat in front of us. Second, there is the kind of content involved when we see a picture: in virtue of experience having this kind of content, we can experience something as the depiction of something else. For example, in seeing a drawing or painting of a cat, we can experience the drawing or painting as a depiction of a cat, distinct from the painting. In such cases it does not seem that we are seeing what is depicted in the painting. In seeing a picture of a cat it does not seem that there is a cat there. But that the picture is a picture of a cat is something that we experience. Finally, there is the kind of content that Peacocke is interested in: metaphorical content. In virtue of our experience having this kind of content, Peacocke suggests, we can experience something metaphorically, as something else. He provides a convincing example: seeing Francisco de Zurbarán’s painting of four pots as people.17 It doesn’t look to someone having this experience that there are people in front of them. It is a depiction of pots that are experienced metaphorically, as people. A group of real pots could also be experienced metaphorically, as people. It is distinctive of Peacocke’s account that metaphorical seeing-​as does not require linguistic understanding, and it is not a matter of thinking or judging that they are people. The metaphorical content is an aspect of the experience.

16 Peacock, “The Perception of Music,” 257–​8.

17 Peacock, “The Perception of Music,” 240, reproduces Zurbarán’s “Still Life with Pottery Jars” (c.1635).

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How is it that we have experiences with metaphorical content? Metaphor characteristically involves an isomorphism between two domains. We experience something metaphorically as something else in virtue of that isomorphism. In the case of Zurbarán’s painting, there is an isomorphism between the appearance of the depicted pots and the appearance of people, and the pots are experienced metaphorically as people under that isomorphism. According to Peacocke, such experiences occur as a result a sub-​personal perceptual process that detects an isomorphism between two domains, setting up a correspondence between mental representations of the items in each of these domains.18 Under the correspondence, some representations of the metaphorically represented domain are copied to some special kind of storage, binding them with their corresponding mental representations in the sub-​personal state underlying an experience that has the metaphorical content. In this way their content enters the metaphorical content of the experience. This account of experiencing metaphorically can be applied to our experience of music. There is a wide range of musical properties that can lead to metaphorical experience, and a wide range that can enter into the content of metaphorical experience.19 Peacocke gives a number of examples. The following two give some sense of the breadth of his account. The first involves hearing a symphony as a certain kind of process: . . . in Beethoven’s Ninth Symphony, one [can hear] the emergence of order, unity, and strength . . . built up from what were previously only fragments scattered in many different places. One may experience this metaphorically, as a process of emotional development. But in hearing it that way, one may also be aware of the process as being of a general type, with many possible instances. A political process, a creative process, an intellectual process may all be instances of the type . . .20

The second involves hearing a single chord as sad. A minor chord by itself sounds sad. According to Peacocke, the relation of the perceived minor chord to its (unheard) major is perceived metaphorically as an instance of the relation sadness has to a non-​sad state of mind: sadness is experienced from the inside as subdued; an ordinary state of mind is not subdued. The relation of states of mind is isomorphic to that between minor and major chords. Sadness enters into the content of the metaphor, which helps specify the content of the auditory perception of the minor triad. This account can explain how our experience of music and rhythm can have metaphorical content concerning movement. There are relationships between musical tones that are sufficient to sustain an isomorphism of the kind Peacocke describes



18 Peacock, “The Perception of Music,” 263–​4. 19 Peacock, “The Perception of Music,” 263. 20 Peacock, “The Perception of Music,” 265.

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50   The Philosophy of Rhythm between music and different kinds of movement, and so to ground experiencing the music metaphorically as movement. A number of the associations between music and movement described in the association experiment could be of this kind.21 To take a simple example, changes in inter-​onset intervals of tones may be isomorphic with changes in the rate of footsteps as someone walks or runs faster, and so may be metaphorically experienced as changes in speed of movement. That suggests that at least some examples of hearing movement in music may be explained in terms of our experiencing the music metaphorically as that movement. It would seem, then, that Peacocke’s account of hearing “metaphorically-​as” provides the basis of an explanation of how movement can be part of the content of an experience of music, and so explains how something extra-​musical can be part of the content of an experience of music. But metaphorical content doesn’t capture anything that is intrinsic to our experience of music. To say this is not to say that the metaphoric content isn’t part of the content of our experience of music, because on Peacocke’s account it is. The problem is that the metaphorical content is something additional to the musical content of the experience. Consider the experience of someone who fails to experience metaphorical content in the music in some way. They will miss something about the music that is there to be appreciated, but they will still experience the music as such; and there’s no reason to think that they couldn’t experience the music as having whatever properties would make the metaphorical content appropriate. They may simply lack the understanding, or the imaginative or other capacities, required to bring to bear the metaphorical content. So metaphorical content is not intrinsic to experiencing the music, even if it is essential to enjoying the full experience that the music can provide. For someone who fails to experience the metaphorical content, what the experience lacks is something extra-​musical. If the connection between our experience of rhythm and movement is metaphorical, then movement is not intrinsic to our experience of rhythm as such. In failing to hear a rhythm as involving movement we would miss something about the rhythm that is available to someone who does hear the movement, but we would still hear the rhythm. So metaphorical content is not intrinsic to our experience of rhythm as such, though it may be essential to a richer experience of the rhythm that involves an appreciation of the metaphorical content made available by the rhythm. The metaphorical content does not help explain features of the rhythm as such, nor does it explain why we experience tones as grouped or what grouping consists in. One kind of explanation of the expressive powers of music appeals to the idea of resemblance. We can recognize a passage of music as resembling a human expression of emotion.22 According to this resemblance account, we experience music as expressive of an emotion because it sounds the same in some respect as a human expression of that emotion. For example, we can perceive music as having a pitch

21 It would be an interesting exercise to show that all the association examples can be explained in this way. 22 Kivy, Sound Sentiment.

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contour that is similar to the pitch contour of a vocal expression of an emotion. A passage from Handel’s Messiah, “Rejoice Greatly, O Daughter of Zion!”, resembles the voice rising in joy.23 The vocal lines of Dido’s lament, in Purcell’s Dido and Aeneas, resemble human vocal expressions of grief and intense loss.24 Our experience of the music comes to have content concerning the emotion in the same way our experience of a vocal expression of the emotion comes to have content concerning the emotion. A passage of music may resemble other kinds of expressive behavior. For example, there may be a structural similarity between music and the expressive motion of the human body.25 This account in terms of resemblance can be extended beyond the expressive. Eric Clarke has suggested that the connection between music and movement derives from the way sounds specify their sources. “The structure of music can and does specify objects and events in the world . . . and kinds of action,” including movements.26 Clarke draws a parallel between music and painting. The pigment in a painting is such that the experience we have when looking at a painting can be like that we have when looking at what is depicted in the painting. He suggests that music can work in the same way, by producing experiences of sounds that are like those produced by events in the world. There is a resemblance between the experiences of music and the experiences we have of sounds produced by events in the world. In virtue of that resemblance, music may create perceptual effects with the disposition of discrete pitches and instrumental timbres in time that reproduce, or approximate to, those that we experience with the continuous acoustical transformation that are characteristic of real world events.27

Clarke argues that there is perceptual information that specifies motion in music that is the same as that involved in the perception of motion in everyday circumstances. The motion is neither real nor metaphorical, but “fictional” in the way a scene in a picture is.28 For example, in everyday circumstances when something approaches it gets larger in the visual field. As a consequence, when something gets larger in the visual field it can seem to be approaching (even when it is not). There are musical equivalents of that looming effect. A musical crescendo can produce sounds that mimic the auditory equivalent of looming in the visual field.29 Another example

23 Kivy, Sound Sentiment, 51. 24 Peacocke, “The Perception of Music,” 269. 25 Kivy, Sound Sentiment, 53–​4. Assuming one may perceive someone’s emotion, this explanation in terms of resemblance is a perceptual account. Someone who rejected that assumption might claim that the resemblance merely puts us in a position to recognize the emotion. 26 Clarke, “Motion in Music,” 217. 27 Clarke, “Motion in Music,” 221. 28 Clarke, “Motion in Music,” 228. 29 Clarke, “Motion in Music,” 223.

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52   The Philosophy of Rhythm Clarke gives is a passage from Fatboy Slim’s “Build it Up, Tear it Down.” Clarke describes the music in detail.30 The perceptual effect of this passage, Clarke says, is of a continuous movement toward an occluded sound source that is progressively revealed. The explanation of the effect is that the music changes in a way that resembles the way our experience of the sound made by an occluded sound source changes as we approach it. The spectral composition of a sound changes with distance: higher frequencies are more effectively occluded by objects and dissipate in the environment more quickly, so at a distance a sound appears darker and to lack higher frequency components. As we approach a sound source the appearance of the sound changes: it becomes brighter in a way that is mimicked by the music. There is something right about this suggestion, particularly the idea that there is perceptual information that specifies motion in music that is the same as that involved in the perception of motion in everyday circumstances. But it’s a mistake to think that music specifies “fictional” rather than real motion (analogously to the way pictures depict). To see why, we need a better understanding of how auditory perception enables the perception of events in the world, including movements. In the next section, I set out an account of auditory perception that shows how that is possible.

III Sounds can be produced by solid objects, by liquids (e.g., flowing water), and by gasses (e.g., the wind).31 Objects produce sounds when they are caused to vibrate by impacts, scraping, rolling, or deformations. Call these events, the events that cause an object to vibrate, “sound-​producing” events. Sound-​producing events are events that we can pick out in ordinary ways (“tapping the desk” picks out a sound-​ producing event). They are individuated in terms of objects and interactions between objects as ordinarily conceived. Sound-​producing events cause vibrations. Consider any relatively reverberant object,32 such as a metal plate or tray. Tapping such an object causes it to vibrate; the vibration continues for a period of time and gradually dies away. The vibration of the object is distinct from the tap that causes the vibration. We can therefore distinguish two events: a sound-​producing event (the tap), and the object-​vibration (the reverberation) caused by the sound-​ producing event. There are different accounts that might be given of the ontology of sounds,33 but most accounts view sounds as vibratory events. In particular, they 30 Clarke, “Motion in Music,” 225. 31 In what follows my discussion will focus on sounds produced by objects, but could be extended to sounds produced in other ways. 32 The distinction that I draw here is clearest in the case of reverberant objects, but it also applies to objects that we would not normally regard as reverberant. 33 Casati and Dokic, “Sounds,” provides a survey of ontology of sound. O’Callaghan, Sounds: A Philosophical Theory, and Casati and Dokic, La philosophie du son, defend the event view. Pasnau, “What is Sound?”, rejects the event view.

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view sounds as the object-​vibrations that are caused by sound-​producing events. So when we experience a sound we experience a vibratory event, an object-​vibration. Objects vibrate along a number of different dimensions according to their shape, size, and material composition, how they were caused to vibrate, and whether they are constrained in any way (by resting on a surface or being otherwise supported). Each dimension of vibration corresponds to a mode of the object’s vibration. Object vibrations cause pressure waves in the surrounding medium—​typically air—​that propagate through the medium to reach our ears. The sound wave that reaches our ears may be the result of more than one object vibration. In order to produce an experience of individual sounds, the auditory system must interpret the sound wave. It does so in such a way as to produce a representation of the sound-​producing events in the environment responsible for the sound wave. This is a process known as “auditory scene analysis.”34 Some aspects of this process of interpretation are relatively well understood. In general terms, the auditory system functions to determine the occurrence of those sound-​producing events in the environment that best explain the pattern of frequency components that make up the sound wave detected by the ears, and it groups together frequency components into individual sounds according to whether they were produced by a single event. Auditory scene analysis groups frequency components both at and over time:  frequency components that are detected simultaneously are grouped according to whether they were produced by the same of different events; and frequency components detected over time are grouped according to whether they are a continuation of a previously detected event or a new event. This process is both bottom-​up and top-​down. For example, frequency components of the sound wave are grouped together in a bottom-​up way on the basis of the temporal, harmonic, and phase relationships between them; frequency components are grouped together in a top-​down way on the basis of past experience of that pattern of components having occurred together. The result of auditory scene analysis is an experience that represents two things: it represents the events in our environment that (are likely to have) produced the sound wave detected by the ears, and it represents sounds corresponding to those events. Given that auditory experience has this structure—​representing both sounds and their sources—​it is possible for it to misrepresent in two different ways:  by misrepresenting sounds or by misrepresenting the sources of sounds. The latter is far more common than the former. When sound waves are produced in ways that are abnormal from the point of view of the auditory system, it may result in a non-​ veridical representation of sound-​producing events. When this happens we have an experience of sounds that seem to have been produced by an event or events that did not in fact produce them. The result is a kind of illusion: a non-​veridical experience of sound sources. We experience this kind of illusion when we listen to stereo loudspeakers. Loudspeakers are designed to produce sound waves that would

34 Bregman, Auditory Scene Analysis.

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54   The Philosophy of Rhythm normally be produced by events of various kinds occurring in our environment—​ by a number of different instruments being played for example. The result is that we experience sounds that seem to have been produced by events—​by the playing of instruments—​that did not in fact produce them. There is a widespread conception of auditory perception that views its function as the perception of sounds. According to this conception, the auditory system functions to tell us what sounds there are in our environment. According to the account I have sketched, the auditory system functions to track sound-​producing events in our environment, rather than the sounds produced. So we should conceive of auditory perception as a perceptual system whose function is the perception of sound sources rather than sounds. That’s not to deny that we experience sounds; it is to claim that we experience sounds as a consequence of perceiving the sources of those sounds. Why think that the auditory system functions to track the sources of sounds rather than sounds? First, it follows from the assumption that the function of perception in general is to promote our survival, and that it does so by telling us about the things in our environment that matter to our survival. It is the ordinary events occurring in our environment—​the snapping of a stick or the footsteps behind me, the running water in the distance—​that can make a difference to our survival; not the sounds produced by these events. It is possible for the auditory system to recover information about these ordinary events, so, from an ecological perspective, it makes sense that the auditory system functions to track them. Second, it is not possible to explain our experience of sounds in terms of a perceptual system that functions to track sounds. Sounds are object-​vibrations, so if the auditory system functions to track sounds it must function to track object-​vibrations. But it cannot have that function. To see why, consider how object-​vibrations could be individuated. There are different ways in which the overall vibration of an object could be individuated. We could simply list each different mode of the vibration and so think of the object as vibrating in many different ways; or we could add together these different modes to produce a single complex vibration, and so pick out the object-​vibration in terms of the single complex vibration that begins at the moment the object is struck, lasting until the object returns to a state of equilibrium. Neither way individuates object vibrations in a way that corresponds to the sounds we hear. A single object can vibrate in such a way that we hear two sounds. For example, a reverberant object that is tapped twice in quick succession produces two sounds. If these sounds are object-​vibrations, then how are those object-​vibrations individuated? It can’t be in terms of the overall vibration of the object. Some of the modes of vibration of the object belong together as one sound, and others belong together as the other sound. What determines which go with which? There are two possible explanations. According to the first explanation, the vibrations are individuated in terms of the experience to which they give rise: there are two vibrations because we experience two sounds. Each experienced sound is causally dependent on only some modes

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of the object’s vibration. So two vibrations can be individuated as the complex sum of the modes of vibration on which each experienced sound causally depends. If this explanation of how we individuate object vibrations is right then we can’t explain why we hear two sounds by appeal to the fact that the auditory system detects two object-​vibrations. Rather, there are two object-​vibrations because we hear two sounds. So the suggestion that the auditory system functions to track object-​ vibrations is undermined. According to the second explanation, the vibrations are individuated in terms of what caused them. There are two distinct events—​two events of tapping the object—​that cause the object to vibrate. Some of the modes of the object’s vibration are caused by one of these events and some are caused by the other. So two object-​ vibrations can be individuated as the complex sum of the modes of vibration caused by each of the events. If this explanation of how we individuate object vibrations is right we can’t explain why we hear two sounds by appeal to the fact there are two object-​vibrations that the auditory system detects; rather we hear two sounds because the auditory system detects two sound-​producing events. Again, the suggestion that the auditory system tracks object-​vibrations is undermined. What picture of auditory perception are we left with? It is one according to which the auditory system functions to represent ordinary sound-​producing events in our environment. It does so by interpreting the sound wave produced by the vibrations caused by those events in such a way as to produce an experience of sounds that correspond to the events whose occurrence would best explain that sound wave. Auditory experience represents both sounds and the sound-​producing events that produced them, both sounds and their sources; and we experience the sounds we do as a consequence of the fact that we perceive their (apparent) sources. Once we recognize that auditory experience represents both sounds and their sources we have the materials for explaining both auditory grouping and the auditory perception of movement. We experience sounds as grouped together in two ways: as temporally extended sounds (whose parts are experienced as grouped in a single ongoing sound), and as grouped sequences of sounds. To experience sounds as grouped in both these ways is for them to seem to have a single source. This is a consequence of the way auditory scene analysis groups frequency components over time. We experience a temporally extended sound as having been produced by a single event, and a sequence of sounds as having been produced by a sequence of events that form part of some ongoing process. It follows that auditory grouping is not explained in terms of a relation—​such as Scruton’s “virtual causality”—​between sounds themselves, but in terms of relations between events in the environment that appear to produce them. If the auditory system represents events in our environment, what properties does it represent those events as having? This is an empirical question and answering it requires empirical investigation. We know that sound waves carry a great deal of information about sound sources: information about the nature of the object, including its size, shape and material constitution; what happened to it that

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56   The Philosophy of Rhythm caused it to vibrate; and about the environment in which it is vibrating. It is reasonable to think that the auditory system recovers this information, and empirical investigation tends to support this. There is evidence that we can, on basis of hearing the sounds produced, perceive the material properties of objects, the force with which an object was struck, and the size and shape of an object.35 In addition, we can recognize a wide variety of events on the basis of hearing them. William Gaver suggests that our capacity to recognize complex events in our environment can be explained on the basis of capacities to recognize more basic events.36 The basic kinds of sound-​producing event that we can recognize include movements. For example, we can recognize the sound of something rolling—​a ball, say—​and tell how fast it is rolling; we can recognize a sound as produced by the dragging or scraping of something across a rough surface; we can hear a sequence of sounds as produced by the footsteps of an animal. The best explanation of our capacities to do this is that auditory experience represents sound-​producing events as events of certain specific kinds and not merely as bare happenings responsible for the sounds we hear. The perception of music is not special. Our experience of music is explained by the operation of the same perceptual processes that explain our experience of sounds in general. That means that the psychological processes that explain our experience of music are continuous with the psychological processes that explain auditory perception. In particular, the organization of sounds in music is explained in the same way it is in auditory perception in general: the grouping of musical sounds is explained in terms of the same processes that explain the grouping of environmental sounds. Therefore, to experience a sequence of musical sounds as grouped is—​as it is for sounds generally—​to experience them as produced by a sequence of events that form part of some ongoing process. That is true even when the experience is non-​veridical. That is, we can explain the grouping of musical sounds in terms of their seeming to have been produced by a single event or process even when they were not so produced. This may happen when different instruments—​ different sound sources—​produce a sequence of sounds, which are such that the auditory system treats them as having a single source because, for example, they are harmonically related. What differences there are between our experience of music and our experience of sounds more generally is a consequence of the fact that musical sounds are produced in a way that is abnormal from the point of view of the auditory system. They are produced by the playing of instruments that are designed and played with the aim of producing harmonically pure sounds with little temporal structure

35 Wildes and Richards, “Recovering Material Properties,” discusses evidence of hearing material properties; Freed, “Auditory Correlates,” likewise for hardness; Kunkler-​Peck and Turvey, “Hearing Shape,” and Lakatos et al., “Simple Geometric Form,” for shape; Li et al., “Walking Sounds” for walking; Houben et al., “Rolling Balls,” for rolling. Carello at al., “Object Properties,” provides general discussion. 36 Gaver, “How do We Hear in the World?” and “What in the World do We Hear?”; McAdams, “Recognition of Sound Sources.”

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(compared to sounds produced by typical environmental events). So in the case of music, although we experience sounds as produced by sound-​producing events, our perception of the events that produce musical sounds is often impoverished and may be illusory. Furthermore, we normally don’t attend to sound-​producing events in listening to music—​we adopt an “acousmatic attitude,” attending to musical sounds apart from the circumstances of their production (unlike environmental sounds where we attend to the source event rather than the sound). This account of auditory perception undermines the account of our experience of music as purely auditory. We saw above that Scruton argues that, since movement in the material world involves something that changes location and since we can’t make sense of music changing location, any musical movement is not analogous to movement in the physical world and so cannot be understood literally. But if the outline of auditory perception that I have sketched is right we can make sense of experiencing a kind of movement in music that is movement in the physical world. Once we allow that our auditory experience, and so our experience of music, has content concerning events in the world, we can make sense of our experience of music involving an experience of movement—​the movement of things in the world—​even if sounds do not themselves move. A difficulty for any attempt to give a literal or perceptual account of movement in music is to explain what it is that is supposed to be moving. “In hearing the subject of a Bach fugue . . . it is not at all clear what is moving or where that movement is taking place.”37 According to the perceptual account I sketched, there are two kinds of movement that may be part of our experience of music. Some of the events that produce musical sounds are movements, and it may be possible to perceive these events as movements. The first kind of movements that may be part of our experience of music are the actual movements involved in producing the music. When a violin is played, the bow moves over the strings. We may perceive the resultant sounds as produced by the bow’s movement, and we may perceive features of the movement—​its speed, how forceful it is, and so on. Not all the events that produce musical sounds are movements. Sounds can be produced by, for example, striking, plucking, or blowing events. Although these events are normally brought about by movements—​by the movements of performers—​they are not themselves movements. It may be that we can perceive musical sounds as produced by these events, but that is not to perceive them as produced by movements. The second kind of movement that may be part of the content of our experience of music is merely apparent movement. When we hear a sequence of sounds it can seem that the sounds were produced by events that did not in fact produce them. A sequence of sounds can seem to have been produced by movement that did not actually produce it. A simple example would be a series of musical sounds which are such that they seem to have been produced by walking. They can seem this way in virtue of having properties that lead the auditory system to represent the series of

37 Gjerdingen, “Apparent Motion in Music?”, 142.

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58   The Philosophy of Rhythm sounds as produced by walking even if they were not in fact produced that way. That a sequence of sounds seems to have been produced by walking is part of the content of the experience, not simply something we imagine or cognize, and not simply a matter of the sounds resembling the sounds made by actual walking. A more interesting example is provided by studies of “expressive timing” in musical performance. When a piece of music is performed, the performer will normally make changes in the detailed timing of the notes so that what she plays deviates from the temporal pattern or structure of the music represented in the musical notation. The changes that performers introduce to timing have been investigated.38 By analyzing the performances of a piece of music by different performers, an average timing profile for a piece of music can be produced. These analyses show that the changes introduced by performers have an archetypal acceleration-​deceleration pattern, and that the shape of the timing curve is analogous to forms of physical or biological motion.39 There is a similarity in the temporal structure of physical motion and the temporal structure of the music as performed. When we hear a sequence of sounds with this timing pattern, the sounds seem to have been produced by a certain kind of movement. We experience the musical sounds as having been produced by a certain kind of movement. It’s not implausible to think that the performer introduces changes to the timing of the music to achieve just this effect. It is plausible that our experience of these events, which actually or apparently produce the sounds we hear, can explain some of the expressive powers of music in a way similar to that suggested by Jerrold Levinson.40 Levinson’s account of the expressiveness of music has two components. An account of what can be heard in music, in particular the idea that we hear the gestures of the performers; and an account of how hearing those gestures can explain our hearing the music as expressive of, e.g., emotion.41 The first component has some affinities with the account I have outlined. Levinson suggests that when we hear a passage of music we imagine the gestures of the performer who produces it, which gestures we take to be responsible for the sounds we hear. The gestures rightly heard in music are only heard in their specificity if the apparent performing gestures behind the sequences of sounds per se are taken into account. For the gestures we are right to hear in musical sequences are those we hear in them when we are cognizant of the instrumental actions understood to generate such sequences.42 The gestures we hear in the music—​the musical gestures—​are a function of the performing gestures and so “are partly determined by what we take performers of the passage to literally be doing in producing it.”43 38 Repp, “Patterns of Expressive Timing.” 39 Friberg and Sundberg, “Model of Final Ritardandi.” 40 Levinson, “Authentic Performance.” 41 On the second component, Levinson says “The expressiveness of music is grounded in the fact that the actions or gestures one hears in a passage of music recall the actions or gestures that serve as behavioral expressions of emotions, which allows us to hear the former as the latter”: “Authentic Performance,” 82. 42 Levinson, “Authentic Performance,” 83. 43 Levinson, “Authentic Performance,” 83.

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My account of auditory perception fits with the idea that we can hear the performers’ gestures in music, but there are two significant points of disagreement with Levinson. The first concerns what it is to hear events in music. On my account, the events we hear are part of the content of our auditory experience. They are events that we experience as the apparent sources of the sounds we hear, not events that we merely imagine, cognize, or associate with the sounds we hear. The second concerns which events we hear in music. According to Levinson, what we hear are the performing gestures “that we imagine as responsible for the sounds we hear.”44 On my account, the events we hear may be the events that are actually responsible for the sounds we hear—​the sound producing events—​and in that case they will be events that were brought about by the performer (it is a further step to say that we hear them as events for which a performer is responsible). But the events we “hear” in music may not be the events that actually produced the sounds. They may simply be events that apparently produced the sounds, and in that case they are not events for which a performer was responsible. The explanation of our hearing music as expressive can appeal to the fact that we hear performers’ gestures in music, whether as a result of experiencing the events that actually produce the sounds or merely appear to do so. An important element of rhythm in music is our experience of musical sounds as sequentially grouped. I have given an account of what it is to experience a sequence of sounds as grouped: it is to experience them as apparently produced by a sequence of extra-​musical events that are related as parts of an ongoing process. Grouping is central to our experience of rhythm in music, so understanding the role of extra-​ musical events in our experience of grouping is central to understanding our experience of rhythm in music. Further, I have suggested that we can experience sounds as apparently produced by movement and that experiencing sounds as produced by movement is part of the content of our experience of musical sounds as grouped, and not something that we simply recognize or judge on the basis of hearing sounds. The movement we hear in music can be literal movement perceived (or apparently perceived) in the music. This account of the content of our experience of music is an account of one element of our experience of music and rhythm. That our experience of music has this kind of content doesn’t rule out its being related to movement in other ways, for example by having metaphorical content concerning movement. Indeed, it might have metaphorical content partly in virtue of having content concerning literal movement.

Works Cited Bregman, Albert S., Auditory Scene Analysis: The Perceptual Organization of Sound (Cambridge, MA, 1990). Budd, Malcolm, Music and the Emotions: The Philosophical Theories (London, 1985).

44 Levinson, “Authentic Performance,” 83.

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60   The Philosophy of Rhythm Carello, Claudia, Jeffrey B. Wagman, and Michael T. Turvey, “Acoustic Specification of Object Properties,” in Joseph D. Anderson and Barbara Fisher Anderson, eds, Moving Image Theory: Ecological Considerations (Carbondale, 2005). Casati, Roberto and Jerome Dokic, La philosophie du son (Nimes, 1994). Casati, Roberto and Jerome Dokic, “Sounds,” in Edward N. Zalta, ed., The Stanford Encyclopedia of Philosophy (2011): https://​plato.stanford.edu/​archives/​sum2011/​entries/​sounds/​. Chen, Joyce L., Robert J. Zatorre, and Virginia B. Penhune, “Interactions between Auditory and Dorsal Premotor Cortex during Synchronization to Musical Rhythms,” Neuroimage, 32.4 (2006), 1771–​81. Clarke, Eric, “Meaning and the Specification of Motion in Music,” Musicae Scientiae, 5.2 (2001), 213–​34. Eitan, Zohar and Roni Y. Granot, “How Music Moves: Musical Parameters and Listeners’ Images of Motion Music Perception,” Music Perception, 23.3 (2006), 221–​47. Freed, Daniel J., “Auditory Correlates of Perceived Mallet Hardness for a Set of Recorded Percussive Events,” Journal of the Acoustical Society of America, 87 (1990), 311–​22. Friberg, Anders and Johan Sundberg, “Does Music Performance Allude to Locomotion? A Model of Final Ritardandi Derived from Measurements of Stopping Runners,” Journal of the Acoustical Society of America, 105.3 (1999), 1469–​84. Gaver, William W., “How do We Hear in the World? Explorations in Ecological Acoustics,” Ecological Psychology, 5 (1993), 285–​313. Gaver, William W., “What in the World do We Hear? An Ecological Approach to Auditory Event Perception,” Ecological Psychology, 5 (1993), 1–​29. Gjerdingen, Robert O., “Apparent Motion in Music?”, in Niall Griffith and Peter M. Todd, eds, Musical Networks: Parallel Distributed Perception and Performance (Cambridge, MA, 1999), 141–​73. Houben, Mark M. J., Armin Kohlrausch, and Dik J. Hermes, “Perception of the Size and Speed of Rolling Balls by Sound,” Speech Communication, 43.4 (2004), 331–​45. Kivy, Peter, Sound Sentiment: An Essay on the Musical Emotions: Including the Complete Text of the Corded Shell (Philadelphia, 1989). Kunkler-​Peck, Andrew J. and Michael T. Turvey, “Hearing Shape,” Journal of Experimental Psychology: Human Perception and Performance, 1 (2000), 279–​94. Lakatos, Stephen, Stephen McAdams, and René Caussé, “The Representation of Auditory Source Characteristics: Simple Geometric Form,” Perception & Psychophysics, 59.8 (1997), 1180–​90. Lerdahl, Fred and Jackendoff, Ray, A Generative Theory of Tonal Music (Cambridge, MA, 1983). Levinson, Jerrold, “Authentic Performance and Performance Means,” in Music, Art, and Metaphysics: Essays in Philosophical Aesthetics (Oxford, 1990), 393–​408. Li, Xiaofeng, Robert J. Logan, and Richard E. Pastore, “Perception of Acoustic Source Characteristics: Walking Sounds,” Journal of the Acoustical Society of America, 90.6 (1991), 3036–​49. McAdams, Stephen, “Recognition of Sound Sources and Events,” in Stephen McAdams and Emmanuel Bigand, eds, Thinking in Sound (Oxford, 1993), 146–​98. O’Callaghan, Casey, Sounds: A Philosophical Theory (Oxford, 2007). Pasnau, Robert, “What is Sound?”, Philosophical Quarterly, 50.196 (1999), 309–​24. Peacocke, Christopher, “The Perception of Music: Sources of Significance,” Modern Schoolman, 86.3–​4 (2009), 239–​60. Phillips-​ Silver, Jessica and Laurel J. Trainor, “Vestibular Influence on Auditory Metrical Interpretation,” Brain and Cognition, 67.1 (2008), 94–​102. Ramachandran, Vilayanur S. and Edward M. Hubbard, “Synaesthesia: A Window into Perception, Thought and Language,” Journal of Consciousness Studies, 8.12 (1990), 3–​34. Repp, Bruno H., “Patterns of Expressive Timing in Performances of a Beethoven Minuet by Nineteen Famous Pianists,” Journal of the Acoustical Society of America, 88.2 (1990), 622–​41. Repp, Bruno H., “Sensorimotor Synchronization:  A Review of the Tapping Literature,” Psychonomic Bulletin and Review, 12.6 (2005), 969–​92. Scruton, Roger, The Aesthetics of Music (Oxford, 1999).

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Rhythm and Movement  61 Spence, Charles, “Crossmodal Correspondences: A Tutorial Review,” Attention, Perception, and Psychophysics, 73.4 (2011), 971–​95. Trainor, Laurel J., Xiaoqing Gao, Jing-​jiang Lei, Karen Lehtovaara, and Laurence R. Harris, “The Primal Role of the Vestibular System in Determining Rhythm,” Cortex, 45.1 (2008), 35–​43. Wildes, R. P. and Whitman A. Richards, “Recovering Material Properties from Sound,” in Whitman A. Richards, ed., Natural Computation: Selected Readings (Cambridge, MA, 1988), 356–​63. Woods, Andrew T., Charles Spence, Natalie L. Butcher, and Ophelia Deroy, “Fast Lemons and Sour Boulders:  Testing Crossmodal Correspondences Using an Internet-​ Based Testing Tethodology,” I-​Perception, 4.6 (2013), 365–​79.

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3 The Ontology of Rhythm Peter Simons

1. Introduction The experience of rhythm is practically universal among humans and so familiar that we rarely think about it. Rhythm is one of the central elements of music in all its forms. But what is rhythm? This, the ontological question, is the one Aristotle taught us to answer first if we wish to know about something. What are we talking about? To answer it turns out to be surprisingly intricate and not as straightforward as one might initially imagine. But that is the task here. The Oxford English Dictionary dates the first usage of “rhythm” in English to 1560, in connection with prosody, and to 1576 in connection with music, with the Latin rhythmus first cited in English in 1531. The word of course goes back to the Greek rhythmós, having to do with dance, and, at its root, flow (rheō). The OED definition of the English word in connection with music reads: The systematic grouping of musical sounds, principally according to duration and periodical stress; beat; an instance of this, a particular grouping or arrangement of musical sounds.

From such a broad lexical description, which aims to capture the spread of usage, we do not expect ontological precision, but the lexicon fixes the general area in which we must investigate. While the term “rhythm” has been used in connection with other areas, such as sedimentation in geology, we shall confine attention to rhythm as perceptibly unfolding in time. We shall also be looking especially, though not exclusively, at rhythm among sounds, and again, in particular, as to be expected, at rhythm in music. However, we should bear in mind that, like the majority of terms in everyday use, the term does not have a precise definition or delimitation, and nor should we expect it to have one. We shall see in fact that one of our more intricate tasks is to indicate the limits of what counts as rhythm. Because of this intricacy, we shall start with very basic considerations and move forward slowly.

Peter Simons, The Ontology of Rhythm In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0004

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2.  Rhythms as Characters of Processes Having determined that we are only interested in rhythms as they pertain to time, this indicates that we should be considering something which is spread or extends over time. Such things are processes. In familiar cases they can be movements such as the swinging of a leg or a pendulum, the jiggling of a foot in time to music, the steps of a dance. They do not have to be musical: the walking of a person, the breathing of a fish and the galloping of a horse are also rhythmical, and not just in sound. Mostly here though we are interested in processes associated with the production (and perception) of sounds, such as the beating of a drum, the tapping of a finger, the clicking of a finger, the sound of a piece of machinery, and so on. These processes are not themselves rhythms, so a rhythm as such is not a process. Rather rhythm, where present, is something that the process has, exemplifies, which characterizes, pertains to, or is inherent in the process. It follows from this that a rhythm cannot exist in isolation, but has to be the rhythm of something. In philosophical terms, this makes a rhythm a property, not a substance. Since I do not want to enter here into the ontological disputes around properties, we shall stick with the more neutral term “character,” which carries little philosophical baggage. So I shall call rhythms characters of processes. At the end I mention briefly my metaphysical position on properties or characters as particulars. To call a rhythm a character of a process is not to render it in any way static or to deny that the rhythmic character unfolds through time. Quite the contrary: because the character concerns a process, taken as it unfolds in time, it is paradigmatically not static, unlike say a graphical pattern.

3.  Rhythms Typically Involve Repetition Not all characters of processes are rhythms: they do not unfold in the right way. For example, one character of a process is its duration. The flight of a projectile, such as a well struck cricket ball, is a process, and it has a certain duration, for example four seconds. But this duration is not a rhythm. Nor is the process’s location, nor is its cause, nor is its perpetrator if it has one. Some processes have no rhythm, the flight of a cricket ball from being struck to coming to rest being a case in point. For a process to have a rhythm there must be some kind of repetition, possibly but not necessarily exact, within the process. A pendulum swings to a rhythm, to and fro. Each swing takes roughly the same amount of time, so talk of a rhythm is appropriate. Each swing, first one way, then the other, resembles earlier and later swings, so there are repetitions. The double swing, to and fro, is a temporal part or subprocess of the longer process of swinging, and these subprocesses come one after the other in a repetitive way, until the process stops or runs down. So it is of the essence of processes with rhythm that there be successive subprocesses of generally like kind. We might at a pinch say that a pendulum which swings only once and is then stopped has a

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64   The Philosophy of Rhythm rhythm, but only by courtesy of our knowledge that it would continue to swing with a certain rhythm if left undisturbed. We shall not then in general count processes without any kind of internal repetition or variation as having rhythm, which rules out the cricket ball flight. However, there are cases of unrepeated (though repeatable) processes where we are reasonably inclined to ascribe a rhythm to the process, even when its internal structure does not consist of exact or approximate repetition of very similar subprocesses. They are on the limit of, but not outside, the extension of the concept of the rhythmical. For this to apply however, there must be some qualitatively discernible internal variation in the process which gives it a kind of unrepeated temporally articulated pattern. A spatial analogy may help. A ploughed field with its repeated furrows is regularly patterned. It is a spatial analogue of the simple pendulum or the heartbeat. A mountain range with its peaks, ridges, shoulders, valleys, cliffs, hollows, etc. is irregular and unrepetitive, but it still instantiates a highly complex pattern of ups and downs, variations in altitude across locations. That pattern may not be repeated, but it could in principle occur more than once. It is the same with an irregular process. However, where the process is completely or nearly homogeneous, we are inclined to deny that it has a rhythm, just as we are inclined to deny that a flat featureless plain has a pattern. The nearly homogeneous flight of the cricket ball has no rhythm.

4.  Repetitive Processes in General Where processes have repetitions, we are inclined to look for rhythms. We do so even when the repetitions are not exactly regular. To take a physiological example, our heart beats in a cyclical way and produces the regular lub–​dub noise familiar to physicians. But heartbeats are not perfectly regular, as the heart speeds up or slows down in response to bodily and environmental conditions. We then describe the rhythm as inconstant or changing, but we do not deny one exists altogether. When a heart fails to contract and beat in a repetitive way, as in ventricular fibrillation, physicians speak of arrhythmia or lack of rhythm, although they also refer to other anomalies of heartbeat as either arrhythmia or dysrhythmia. (Bless the physicians, they have a name for everything.) There are extremely many kinds of repetitive process in nature: they occur at all scales and in all domains. Many are familiar from everyday experience. The rotation of the earth, once per day, is evident from the apparent motions of heavenly bodies, notably the sun. The orbiting of the moon around the earth shows up in the lunar cycle. The orbiting of the earth around the sun shows up in the seasons and in the visible shifts in the heavens. At smaller scales, the rate at which an electromagnetic field oscillates is manifest in different colors of light, different radio wavelengths, and so on. The speed at which material particles vibrate to and fro

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about a mean position manifests itself as sound tones of different pitches. On an intermediate scale, our own heartbeats, rates of breathing and rates of walking or running constitute natural rhythms for our own bodies. What is characteristic of all these repetitive processes is that they consist of a sequence of parts, one succeeding the other, usually without interruption, such that each part is similar in its characteristics to the parts before and after it, where such similarity is frequently itself a matter of succession of like parts. So the diurnal repetition we call day and night follows the same pattern every time: the sun rises in the east, moves across the sky in a smooth arc and sets in the west. During the night, though we cannot see it, the sun continues its cyclical journey around and beneath us to reappear in the east. Of course the cause of this apparent motion of the sun is the rotation of the earth, but it too is a smooth cycle, with the earth rotating anti-​ clockwise as seen from the North Pole and a smooth succession of great semicircles being in the plane in which lie both the line between the poles and the line between the centers of sun and earth.

5.  Perceptible Repetition Not all repetitive processes are perceived by us as repetitive. Some repeat too rapidly, others too slowly. An example illustrates the vague borderline between rhythms we perceive as such and those we do not. A regularly repetitive short noise like a click or the combustion phase of a single-​cylinder engine may be experienced as repetitive and rhythmical if its frequency is roughly between 0.6 Hz and 8 Hz. If it is slower, the perception is of a series of disconnected clicks or bangs, whereas if it is faster it is perceived as a drone or a pitched note. So we do not experience slow-​ frequency repetitions as rhythmical, nor ones whose frequency is too high, even though these are of the same general kind as processes we experience as rhythmical. It has often been remarked that the frequencies we perceive as rhythmical correspond closely to those of the human heart and of a single human step, and no doubt this is not accidental. For the purposes of considering rhythm as it concerns music there is no point served by taking repetitive processes which are not perceived as rhythmical as exhibiting rhythm. For example, the regular vibrations of air molecules that are produced by an oboe sounding a 440 Hz A for orchestral tuning are rhythmical from a physical point of view, but they are perceived as pitch, not rhythm. When we come to consider longer temporal stretches, the upper limit of duration is less clear. Rhythmical combinations such as repeated motifs or melodies are experienced as repetitive, but on the other hand they are often recognized as repetitive rather than as rhythmical. In any case, we are accustomed to discerning rhythmical repetitions lasting several seconds, so we shall not be excessively fussy or precise in looking for an upper bound.

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66   The Philosophy of Rhythm

6.  Coping with Complexity: Clades One of the difficulties facing an ontological account of rhythm is that the term appears so elastic. There are very simple cases of rhythm, such as the one-​two-​three of waltz time, and there are extremely complex cases, such as the irregular rhythms of Stravinsky’s Rite of Spring, the overlaid syncopated rhythms of a Bach fugue, gamelan music, or the polyrhythms of Indian or West African music. In such cases as this there is no prospect of finding a traditional definition giving necessary and sufficient conditions for being a rhythm: there will be examples straying outside the supposed boundary. A second classificatory paradigm also turns out to be unhelpful. This is the idea of a focal or prototypical example. This works well in certain areas where necessary and sufficient conditions are lacking. For example, it works well with basic colors:  samples of red surround the prototypical region of red, which is what humans across the world take as the brightest and reddest red, and something is red to the extent it is similar to this focal case. But there is no focal instance of rhythm making something more or less of a rhythm to the extent that it resembles the focal case. Rather than give a mere pot-​pourri of examples, we will approach the task of saying what rhythm is by adapting a method of biological classification. Biologists classify organisms together only if they share a common ancestor. So sharks, salmon, and dolphins, though they are all streamlined aquatic animals, do not share a recent ancestor, and to find their last common ancestor you have to include with them snakes, mammals, birds, and much else that is very unlike them. By contrast humans, chimps, gorillas and orangutans do share a recent common ancestor. The collection of all the descendants of a single ancestor species is called a clade. Biological systematists work to establish clades. Now in the area of rhythm there are no biological ancestry relations, so this method will not work, but a formal analogue of it may. Consider the idea of number in mathematics. Numbers include the natural numbers 0, 1, 2, 3, . . . ; the negative numbers; the fractions or rational numbers; the real numbers; the complex numbers; and . . . and here we can choose to extend the idea further to quaternions and other field structures such as Clifford algebras, and Conway’s hyperreal numbers; or we can stipulate that numbers will go just up to, say, the complex numbers and no further. There is no absolute fact of the matter saying what is a number and what is not. Rather there are certain properties characteristic of some of them, and then when we move to another sort, we have some properties retained and others lost or replaced. When confined to the natural numbers subtraction does not always give a result, for example when we (try to) subtract 5 from 2; but in the integers, there is a result: −3. With the integers we gain a new property, closure under subtraction. The family of structures starting from the natural numbers and extending further out as properties are allowed to vary (here formal, not empirical properties), constitutes what we can call a formal clade.

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The suggestion then is that, in order to tame the complexity, we treat rhythm as a formal clade. We start with straightforward cases, and then see what transpires as we vary and add complications. The result will, as in the case of number, not be a matter of discerning an antecedently existing essence of rhythm, but will nevertheless be charting variations in a complex landscape. Somewhat more than in the case of number, we will be constrained by empirical limits. Mathematicians are notoriously flexible in what they will accept as a formal structure of interest. We on the other hand ought to remain anchored to the givens of human psychology. It is no use calling something a rhythm because it is a variant, an extension or modification of something else we call a rhythm, if it fails to impinge on our experience. For example, a sonic repetition that is too loud, too quiet, too fast, too slow, or too complex to be even potentially recognizable as a rhythm will not count. A rhythm of five, six, seven, eight beats, with one accented, is perceptible by us; a rhythm of nine beats on the other hand is typically perceived as a compound rhythm of three threes. A rhythm of twenty-​nine beats with one accent would simply not be recognized by us as rhythmic, though physically it is just as good as waltz time. A polyrhythm of 3 against 2 is easily recognizable and perceptible as such as a rhythm, a polyrhythm of 53 against 51 is not, at least not by humans. Maybe other creatures than ourselves could recognize it as such, and if so, good luck to them: to us it would sound just a mess. So we will stick for now with terrestrial and indeed with human limitations.

7.  Beginning with Simple Things: Pulse, Cycle, Tempo, Beat Consider as simple an example as possible: a clock ticking. Assume each tick sounds exactly like every other and that they are regular, that is, evenly spaced. The duration of each tick is short compared with the duration of the silence between ticks, each tick has the same duration as the others, and each silence (or Abklang if the sound dies away perceptibly) has the same duration as the others. This is as repetitive (and indeed monotonous) a process (or sequence of processes; we shall not make a distinction) as can be imagined. Repetitions such as this are rare in music, though not unknown. A modern near-​example is the repeated opening chord of Stockhausen’s Klavierstück IX, which occurs over 200 times (overlooking dynamic changes and microvariations). We call each tick or other sound in such a sequence a pulse, and the aural whole consisting of the pulse and its following silence up to the next pulse, a cycle. Because each pulse and silence is of the same duration, so is each cycle, and the rate or speed of cycles is the repetitive process’s frequency or tempo. Like that of other regularly repetitive phenomena, the frequency can be measured in cycles per second (hertz, Hz), or in cycles per minute, or indeed cycles per other temporal unit, just as the duration can be measured in seconds, minutes, microseconds, or whatever.

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68   The Philosophy of Rhythm A common synonym of “pulse” is “beat.” We shall use the latter term not as a synonym for “pulse” but as indicating either a pulse or a time at which there is no pulse but at which, given the context, we naturally expect a pulse, and which we typically mark mentally as if there were a pulse. A clear example is where we have a regular pulse which occurs three times and then misses once, “skips a beat” as we say, as in the pattern “one two three (and) one two three (and) . . . ,” in musical notation

Counting both the pulses and the pulse gaps as beats gives us a regular sequence of beats again, as there would be if there were only regular pulses, but now we have two kinds of beats: sounding and silent.

8.  Elements of Rhythmic Pattern The example just given illustrates a characteristic feature of rhythms in general, which is that a certain pattern of sounds is (typically) repeated. The case of an unbroken cycle of equally spaced pulses is itself a pattern, but of the most monotonous and uninteresting kind, and there would be no toehold in our thought for the notion of rhythm if that were the only sort of pattern. The pattern of three pulses and a silence, repeated over, is very slightly more interesting. Not every kind of repeated temporal pattern of sounds automatically constitutes a rhythm. A repeated melodic motif or phrase such as

exhibits a temporal pattern but not self-​evidently a rhythmic one. Rhythm in fact abstracts from relative pitch, with a small caveat to be entered presently, whereas a motif such as this is all about relative pitch. Some rhythms may be due to pitch variation alone, but they are a limiting case. Usually, for a repeated pattern to count as a rhythm, there is a contrast between strong, loud, or accented beats on the one hand, and weak, soft, or unaccented beats on the other. This is before we take account of length or duration of sounds. The 3 pulses + 1 silence pattern conforms to this because a silence is the limiting case of an unaccented beat. So the 3 + 1 pattern is a rhythm. An only slightly more complicated rhythm is given by this pattern (omitting fermate):

or its close relative

both of which play prominent parts in Beethoven’s Fifth Symphony. These patterns show up the next level of complexity. One aspect of this is the different durations of

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the pulses, as indicated by the different note values showing the relative durations or lengths of the notes. Typically, in Western music there is an obvious felt or indicated beat such that most (not all) note durations and silences are integral multiples or integral fractions of this, and this is reflected in musical notation. The other is that the groupings constituting patterns or subpatterns may have, or be given, beats which count as beginning a repeating time stretch, or period. In Western music, the first beat of such a period is often stressed, or is regarded as stressed (this can of course be locally overridden), and the periods are marked in Western music by bar lines, as

and depending on the number and type of beats in the bar we get a time signature, so in the case of the Beethoven

and the “numerator” of such time signatures indicates the number of beats in a bar. It is often said of a piece that it is in, say “3/​4 rhythm” or “waltz rhythm,” but this is a waste of a word. It is better to say a waltz is in 3/​4 time. The rhythm of a motif in waltz time, such as the famous motif (ignoring grace notes)

of Johann Strauss Jr.’s “The Blue Danube” is a rhythm that, as in many cases, cuts across the time, the felt “one two three” of waltz time with its stressed first beat of each period. The reason it is not unnatural to talk of “waltz rhythm” is that the unadorned “one two three” is itself a rhythm, and of course it guides the dance, but as the example shows, the actual rhythm of a motif written in waltz time may be very different. The waltz time recurs in every bar, but the “Blue Danube” motif spreads across five bars, starting with an upbeat at the end of the first and finishing on the downbeat of the fifth. Unadorned rhythms like this, which derive from stressing the first beat of a certain time, or of main stress and subordinate stress in compound time such as 6/​8, we call base rhythms. They are a subclass of monorhythms.

9. Monorhythms We now have enough conceptual resources to define a simple rhythm, or as we shall call it, a monorhythm. It is a repeatable (and typically repeated) pattern of

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70   The Philosophy of Rhythm sounds and silences, which may be of different relative lengths or durations, where some of the sounds may be more accented than others. This abstracts away from non-​rhythmical elements such as pitch and timbre. It also abstracts away from tempo: not only can the same rhythm be played faster or slower, but composers have frequently repeated a rhythmical pattern at half or double tempo. We cannot abstract away from tempo completely because as we saw initially, there are fairly narrow limits on how quickly or slowly sounds may succeed one another to be perceived as rhythmical. But within those limits there is flexibility. Also variation in amplitude (loudness) is permissible, provided the sounds remain audible but not deafening (both of these factors being likewise relative to human perceptual capabilities). To specify or notate monorhythms we therefore need only three elements: one to indicate the presence or absence of sound, one to indicate the relative lengths or durations of these sounds or silences with respect to a beat duration taken as basic unit, and one to indicate relative stress or accent. Standard musical notation excels in the first two of these regards, the conventional notation managing relative lengths of notes (sounds) and rests (silences) very well, insofar as these are integer multiples or fractions of some basic beat. Stress and accent are less systematically notated. Partly this is because standard bars or periods intimate a downbeat stress quasi-​ automatically, partly because dynamic markings and accents give other indications of more irregular strong and weak sounds, and partly because such differences tend to be managed “on the fly” by practiced musicians. Note that periods (bars) and bar lines are not a necessary element of rhythm or rhythmic notation respectively, common and convenient as they are. A more systematic notation for stress could theoretically make bar lines unnecessary. Also silences of different lengths could be taken as maximally unstressed “sounds” of those lengths, thereby saving one element, if artificially.

10.  Pattern, Repetition, Abstraction Before moving to more complex rhythms, let us pause to consider some of the ontological implications of what we have found so far. Rhythms, we said, are repeatable patterns in sound and silence. That they are repeatable, that the same rhythm or rhythmical pattern is found now here, now there, gives them the status of universals, not particulars. That they are not simple, but consist in patterns of relationships among different elements, means they are not simple but structural universals. A simple universal is something like being middle C, or having a pure sine wave timbre. By contrast the three shorts and a long Beethoven rhythm requires more. To exemplify or instantiate it faithfully we need to produce three noises of (more or less) equal intensity and length and at equal temporal intervals, and follow them by a fourth noise which lasts a certain multiple of duration

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longer than each shorter noise, and then to repeat the pattern in a regular way, with or without an intervening silence. We must therefore pay attention to the relationships among the different noises and silences. In a spatial analogue to this temporal example, consider molecules of methane. To be a molecule of methane is to consist of five immediate parts: one carbon atom, and four hydrogen atoms, disposed tetrahedrally about the carbon and covalently bonded with it. Likewise, to be an instance of the Beethoven motif is to consist of four parts, three equal and one longer, in specified temporal (serial and durational) relationships to one another. This brings us to the dependent nature of rhythm. There is no such thing as a bare rhythm, on its own and subsisting independently of anything else. A  rhythm is always the rhythm of some complex of sounds in relationship. That was what we meant by saying that rhythm is not a substance. Nor is it the universal or kind of a substance, as for example the kind methane molecule is. A single methane molecule can happily subsist on its own: it is not the methane molecule of anything else. A rhythm is more like a shape, or a speed: a shape is always a shape of something (if only a portion of space), a speed is always a speed of something. It is a kind of temporal pattern, a pattern of some process. What can subsist independently is not the Beethoven motif per se, but the realization of the Beethoven motif in certain concrete sounds (which are themselves in turn dependent, requiring a source and a medium). If we wish to talk about an individual instance of the Beethoven motif—​as found in this particular group of sounds—​then the instance of the motif is a structural trope or property instance, inhering in the sounds and dependent upon them in conjunction with other elements of the sounds which make them as they are—​their pitch, intensity, timbre, tempo, etc.

11.  Compound Rhythm Sometimes a rhythm comes in a sequence of subgroups. Rhythms in 6/​8 time are typically felt and played as consisting of two groups of three, 9/​8 as three groups of three. These are usually marked by stresses every third beat and a strong stress every second or third stress. A common form of rhythmical change in baroque and classical music is the hemiola, in which two groups of three beats are replaced with three groups of two beats (or vice versa), giving the impression or effect of a shift from triple to duple meter or back, without changing the time signature. Bruckner was fond of a two plus three rhythm; the main motif of the first movement, “Ruhig bewegt, Allegro molto moderato,” of his 4th Symphony in E♭ being a prominent case in point (there are many other examples):

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72   The Philosophy of Rhythm A slightly more complex example is the rhythm of Bernstein’s song “America” from West Side Story:

12.  Complex Rhythms A complex rhythm (the term is used here relatively loosely) consists of a series or succession of monorhythms, making a repeatable whole. The Bernstein example just given is a very simple case, another being the “Blue Danube” motif. There is no theoretical upper limit to how many monorhythms can be strung one after another, but as usual there are anthropological limits. For example the whole first movement of C. P. E. Bach’s solo flute sonata in A minor H 56 could be considered as instantiating a single rhythm, but no one ever would take it thus. A more tractable or followable pattern is the Allegro con spirito theme of the first movement of Haydn’s Symphony No. 103 in E♭ major, following the famous drum-​roll and slow introduction:

A piece where a complex rhythm is repeated so often that it soon becomes easily recognized, not to say tedious, is the underlying drum rhythm of Ravel’s Boléro:

A case of slightly greater complexity which is also recognized intuitively as a rhythm, albeit a more exceptional one, based on a sequence of five beats, is the repeated rhythmic figure in the first movement, Mars, of Holst’s suite The Planets:

Examples could be multiplied almost without limit. Complex rhythms which are idiosyncratic enough can be readily recognized and used for fun to ask people to identify the melodic figures they underlie, as in Joseph Cooper’s use of the dummy keyboard in the old British TV quiz show Face the Music. For instance, this figure

is fairly easily identifiable as that of the familiar theme of Paganini’s 24th Caprice in A minor for solo violin, made the subject of many variations, from Paganini himself to Lutosławski.

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13. Polyrhythms When two or more rhythms, in the first instance monorhythms, run simultaneously so that at some point they start together, and the resulting complex pattern repeats itself, or can be repeated, cyclically, then we have a polyrhythm. The simplest polyrhythm widely found is a 3 against 2 polyrhythm

which, if the separate generators sound similar, takes on the appearance of a single complex rhythm

but if they sound differently, is clearly two rhythms overlaid. If the onset of the triple is delayed by a sixth of a measure the different tresillo or Habañera rhythm results:

The next step up is a pattern of 4 against 3:

which begins to stretch most people’s ability to produce: the combined effect strikes me and probably most westerners as rather African:

Polyrhythms of this kind and of greater complexity are characteristic of Latin American and sub-​Saharan music. From here on, polyrhythms with more complex overlays and with overlays of more than two rhythms become increasingly difficult to (re)produce although they can be recognized with some facility. The limits of what is humanly recognizable are fairly narrow: a polyrhythm of 7 against 5 or 6 for example would strike most as somewhat chaotic, although the pattern would be recognized on repetition. As ever, there are no formal limits to how many rhythms and of what kind could be overlaid, but the practical and recognition limits are narrow, the former more so than the latter. Polyrhythms are the natural outcome of several voices or instruments singing or playing together in non-​unison. Even simple overlays of 2 against 1 or 4 against 2,

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74   The Philosophy of Rhythm etc. can sound good when taken by different parts. When several complex rhythms are superimposed, things begin to approach the exalted rhythmic complexity that can be found in the great polyphonic composers such as Gabrieli, Monteverdi, or Bach, or in modern jazz.

14.  Nominalism and Actualism: Two Disputed Philosophical Positions This brief section is for philosophers. As a metaphysical nominalist, someone who believes in the existence of only particulars and denies that there are abstract repeatables, it might seem as though I cut the ground from under my own feet by denying actual repetition:  is not a rhythm something that repeats, a pattern? Certainly that is how we talk, and such talk is both harmless and useful. But the different occurrences of a sound pattern are new individual sound sequences that resemble the old, and we are well able to recognize the resemblances in sound sequences, as we are in other cases of resemblance. To talk in the metaphysically correct way is possible, but it sounds unfamiliar, lengthy, and somewhat barbaric, so I have run with the platonic fox rather than hunted with the nominalist hounds. A  nominalist ontology for music would be in my view the correct one, and that would include rhythm, but to work out its details and provide a suitable vocabulary must be a job for another time. Metaphysically, the only rhythms there are, are rhythms that actually exist, at some time or another. A biological clade consists only of actual organisms, the actual descendants of a common ancestor species, excluding merely possible organisms that did not as a matter of fact arise. Rhythms are like this too: until a certain kind of rhythm is first realized, there was only the mere possibility of its being instantiated. It is another area of philosophical dispute whether unrealized possibilities are in any sense “real.” My own view is that they are not: this is called actualism. It in no way counts as stifling creativity or suggesting there are other than practical limits to what rhythms there might be. It is simply to avoid hypostasizing possibilities.

15.  Summary: The Formal Clade of Rhythms The kinds of rhythms we have identified pass from the simple to the increasingly complex, and we need to ask how this increasing complexity arises and where its limits are. The latter question is easily answered: there are no theoretical limits to how complex a rhythm can become, though there are fairly narrow if ill-​defined limits to what is humanly recognizable, which are toward the lower end of the

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complexity spectrum. As to the modes of complexification, as far as I can tell there are essentially two: sequencing and overlay, giving rise to complex rhythms and polyrhythms respectively. A  rhythm is either a monorhythm or is derived from other rhythms by sequential addition or by superimposing two or more other rhythms. By these modes of combination, all rhythms are formal descendants of pulses, basic rhythms, and monorhythms, and so, I suggest, form a formal analogue of the biologist’s clade.1

1 I am grateful to the participants of the Durham Conference and to Peter Cheyne for valuable comments and suggestions. There will be cases I have not considered and which stretch the concept of rhythm beyond what I have envisaged here, but I would have given them had I thought of them. That I mention pulse should not be taken to imply that all rhythms have or stress pulse, only that many straightforward and obvious ones do. I should also emphasize that the similarities and regularities on which rhythms build can be approximate: exact repetition in music sounds mechanical. Against another criticism, however, I remain firm. There are processes which lack any rhythm. A completely homogeneous sound or a smooth rectilinear motion lacks the internal diversity of parts required for rhythm to gain a hold. If all processes are rhythmical, the concept rhythm is then doing no work. But it does do work. Therefore, not all processes have rhythm.

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4 “Feeling the Beat” Multimodal Perception and the Experience of Musical Movement Jenny Judge

1.  Introduction: The Neglect of Rhythm Philosophers have no rhythm—​or, at least, so a reader becoming acquainted with the philosophy of music might suspect. Discussions of form, ontology, and expression abound, but philosophical treatments of rhythm are rare. This seems extraordinary. While a concern for form, ontology, and expression is, in some sense, common to all the arts, an appreciation of rhythm is uniquely, or at least paradigmatically, musical. An examination is central to understanding how music moves us—​and it moves us quite literally in nightclubs, on treadmills, and even in the privacy of our own kitchens. Its neglect by philosophers requires remedial action. This chapter is an attempt to show that when we turn our philosophical attention to rhythm, many new puzzles emerge, the analysis of which brings the philosophy of music into closer contact with the philosophy of mind and perception. I distinguish meter and rhythm, arguing that meter, like rhythm, contributes to the perceptual experience of music in its own right. I claim that the experience of musical beat—​attributable to musical meter, rather than rhythm—​is multimodal in a stronger sense than happening to involve perceptual content across different senses. The term “perceptual content” is frequently deployed in the philosophy of perception, but it may require some explanation. One can think of the term “content” in two ways. One can talk about the contents of buckets, or cupboards, or handbags; one can also talk about the contents of a newspaper. Content can thus be physical—​ what is literally inside some vessel—​or informational. Hence, the term “perceptual content” could mean either (i) what is “contained” in the mind when one has a perceptual experience, or (ii) what is conveyed to the subject having the perceptual experience. In the philosophy of perception, “perceptual content” usually refers to the latter sense, according to which it is natural to think of the senses as channels through which one may discover things about the world. “Auditory content” refers Jenny Judge, “Feeling the Beat” In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0005

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to that which is conveyed to me when I have an auditory experience, “visual content” picks out whatever I find out about the world through a visual experience, and so on for each sensory modality.1 In this chapter, I argue that the experience of musical meter, or “beat,” involves what Casey O’Callaghan terms “intermodal feature binding,”2 whereby perceptual content arising from different sensory modalities is bound to a common entity (such as when I experience the roundness of a ball through touch and sight). However, the experience of beat is a curious case, as I elaborate. Paradigm cases of intermodal feature binding involve the binding of content across exteroceptive senses that yield information from outside the body. The experience of beat, on the other hand, involves the binding of exteroceptive content (the auditory experience of musical sounds occurring in the environment) and interoceptive content (experiences of one’s own body). Specifically, I shall argue that the experience of beat involves intermodal binding between auditory and vestibular content: that is, content arising from the functioning of the vestibular system, which tracks body orientation, movement, and balance.3 A consideration of the multimodal perceptual content of the experience of “beat,” I go on to argue, yields an appealing perspective on the puzzle of musical movement. Roger Scruton notes that the experience of movement in music, though vivid, is nevertheless paradoxical, because musical sounds themselves are not actually moving, and so movement properties cannot feature in the contents of the perceptual experience of music.4 We have to appeal to something other than perceptual content to explain the experience of movement—​specifically, to “metaphorical perception.” My response is that if the perceptual experience of music encompasses more than the auditory experience of musical sounds, then it doesn’t follow, from the fact that musical sounds fail to have movement properties, that our experience of movement cannot be justified by (extra-​auditory) perceptual content. I will claim that there is, after all, legitimate movement-​related content present in musical experience, in the case of the experience of the beat—​and so there is no need to appeal to metaphorical perception. A note, before I continue: I am targeting a motivation for the appeal to metaphorical perception. I am not targeting the notion itself, nor am I claiming that the perceptual experience of beat, in the bare sense I outline here, is enough to explain the full-​blown experience of movement in musical “space” that Scruton has in mind. I merely want to undermine the seeming inevitability of appeals to metaphorical perception, by directing attention to the rich, multimodal perceptual content involved in rhythmic experience. 1 Siegel, Contents of Visual Experience, gives an overview of the notion of perceptual content, and its surrounding debates. 2 O’Callaghan, “Not All Perceptual Experience,” 139–​46; “Intermodal Binding Awareness,” 82–​97. 3 The vestibular system consists of receptors in the inner ear, and their connections to other parts of the nervous system. 4 Scruton, Aesthetics of Music, 13–​15, 21, 49–​71.

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78   The Philosophy of Rhythm And so, to rhythm. What is it, and more pressingly, what do music theorists mean by “meter”?

2.  Rhythm, Meter, and “Beat”: A Perceptual Account Theorists of music and poetry commonly distinguish between rhythm and meter. On one common view, which Andy Hamilton calls the “abstract” account, one may consider rhythm as the bare temporal patterns present in a piece of music: groups of sounds and silences, or simply “order-​in-​time.”5 Meter, on the other hand, is the pattern of stress in which rhythms are grouped. In a piece of music, meter is usually indicated by the time signature. A waltz, for example, will have “3” in the upper part of its time signature, as in ¾: this means that the piece has three (crotchet) “beats” in each measure or bar. Though two different waltzes may be composed of any number of different rhythms, they have the same triple meter. “The Blue Danube” and “Moon River,” for example, contain different rhythmic patterns, but each piece has three beats per bar, occurring in the pattern strong-​weak-​weak. On this abstract view, meter is thought to be, in Christopher Hasty’s words, “a more or less independent structure that rhythm uses for its own ends.”6 Hasty notes that it is customary to view rhythm as a rich and fully sensuous embodiment of music’s temporal progress and metre as rhythm’s shadowy, schematic counterpart—​ abstract, mechanical, and devoid of any intrinsic expression.7

Rhythm is in the music, it is sometimes implied, but meter is not. Some authors characterize meter as a kind of habitual response to rhythm. For instance, Justin London suggests that meter is “an aspect of our engagement with the production and perception of tones in time”8—​implying that meter is really a way of describing our behavior, rather than a feature of our experience, or of the music itself. If meter is an abstract entity, or even a property of behavior as London suggests, does it really feature in immediate musical experience? The phenomenology of musical listening suggests that it does. We needn’t observe our own periodic behavior in response to Stevie Wonder’s “I Wish,” or infer 5 Hamilton, Aesthetics and Music, 26, et passim, criticizes this “abstract” characterization of rhythm, proposing instead that rhythm is an essentially dynamic, human phenomenon. On Hamilton’s view, rhythm is the product of human action: it is “order-​in-​movement” rather than merely “order-​in-​time.” Rhythms must already possess legitimate movement properties in order to count as rhythms in the first place; they are not, for Hamilton, static and abstract to begin with. This is one valid way to counter Scruton’s appeal to metaphorical perception in order to explain the experience of musical movement. It is, however, a different approach to the one pursued here. Rather than challenging extant “abstract” accounts of rhythm, I focus on musical meter: the experience of patterns of stress within musical rhythms. I address the perceptual content involved in such “beat” experiences; I do not directly address the content of experiences of rhythm, taken generally. 6 Hasty, Meter as Rhythm, 4. 7 Hasty, Meter as Rhythm, viii. 8 London, Hearing in Time, 4.

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patterns of stress when perceiving the first movement of Beethoven’s “Waldstein” Sonata, to become conscious of the regular metrical structure. Hasty thinks that the “abstract” conception of meter is an artifact of musical pedagogy, which distracts from its real experiential import. Meter is key to musical experience, he argues. The experience of stressed beats is so crucial, in fact, that “the layman may well call this phenomenon rhythm pure and simple.”9 Hamilton agrees with Hasty, arguing that the abstract conception of meter ignores “the felt regularity of the underlying pulse or groundbeat.”10 Nevertheless, London suggests that, while meter is best thought of as an abstraction, it does have a phenomenal counterpart in the music itself: the “beat.”11 The beat is what shows up in experience. Meter is “phenomenally manifest” to us, says London, “as our perception of a pattern of accentually differentiated beats.”12 Michael Thaut proposes something similar, arguing that, while meter is best thought of as an abstraction, we detect a series of “pulses” in the music, which are organized in a metrical hierarchy.13 The precise nature of the relationship between “beat” or “pulse” and meter remains, however, somewhat opaque in these discussions. Is “beat,” or “pulse,” identical to meter, or does it stand in some other, weaker relation to it? Neither London nor Thaut elaborates on the issue. In what follows, I will claim that there is a component of the perceptual experience of music—​call it “beat” for clarity—​that depends on meter, rather than on non-​metrical rhythm. “Beat” might turn out to be identical to meter, or it might merely be related to it—​an examination of the relationship between beat and meter is reserved for another occasion. The main point, for present purposes, is that there is an aspect of the immediate, perceptual experience of music that is attributable to meter rather than to rhythm. Meter shows up in the perceptual experience of music in the form of the “beat.” The relationship between experiences of meter and rhythm is akin to that between the experiences of melodies and their parts. Mohan Matthen argues that patterns of sound—​such as the tune of the American national anthem—​manifest in experience in their own right, not solely in virtue of the prior perceptual experience of their components.14 There are, he argues, experimental and phenomenological indicators that a process is automatic and sensory, which melodies satisfy. If a beat satisfies these indicators too, this gives good prima facie reason to suppose that beat is perceived, rather than merely inferred on the basis of the perception of rhythm. First, Matthen argues that separate conditionability is a reliable indicator that a given process is perceptual. If subjects’ behavior can be influenced by an entity, this counts as a reason to suppose that the entity is being perceived. Beat seems



9 Hasty, Meter as Rhythm, 5.

10 Hamilton, Aesthetics and Music, 136.

11 London, “Rhythm and Time in Music.”

12 London, “Rhythm and Time in Music,” 5. 13 Thaut, Rhythm, Music, and the Brain.

14 Matthen, “Diversity of Auditory Objects.”

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80   The Philosophy of Rhythm to be separately conditionable from rhythms and melodies. Indeed, its behavioral effect—​our tendency to move along with it—​is a cornerstone of musical experience. This suggests that meter, or beat, is perceived directly. Constancy is a further indicator to which Matthen appeals. Melodies, he claims, are constant: they are the same from different “points of view,” as it were. A melody remains the same melody, even when transposed into a different key. Rhythm also seems to be constant in this regard, remaining the same with changes in tempo; and a musical beat appears to be constant in the same way. I can recognize an instance of march time, or a waltz, no matter what tempo it is played at, what melodies or individual rhythms feature in it, or what instruments play it. Moreover, new experiences of musical meter satisfy the further constraint of familiarity. Repeat instances of waltzes are readily recognizable as such, and feel familiar, even when we have not heard that particular waltz before. It thus seems that there is good reason to think that musical experience involves meter in an immediate, perceptual way. The “beat” is separately conditionable, constant from different “points of view,” and satisfies the “familiarity” constraint.15 So far I have discussed hearing. Now I want to make the further claim that beat, unlike melody for instance, can be perceived by more than just auditory perception.

3.  The perceptual experience of “beat” is multimodal I now argue that if a beat can be perceived—​that a pattern of metrical stresses in time can show up in perceptual experience in its own right—​then those stresses do not have to arise in auditory perception. They can be tactile impulses, or even vestibular signals. Juan Huang et al. investigated the role of touch in the perception of beat.16 They showed that subjects report experiencing identical heard rhythms, which were ambiguous as to meter, as being in either march-​time or waltz-​time, in accordance with the pattern of tactile stimulus to which they were exposed at the same time. If they experienced a tactile impulse coinciding with every second tone, they heard the rhythm in march-​time (that is, the experienced a strong-​weak pattern in the musical sounds); a tactile impulse on every third tone led to an experience of waltz time (a strong-​weak-​weak pattern). It seems, then, that beat can be felt through tactile perception, and not just heard. The authors observe that the sense of touch is particularly important in performance, but also plays a role for audiences, when listeners tap their hands and feet to a rhythm. However, it is not the only extra-​ auditory factor to consider. I may nod my head along to a beat, without tapping my 15 Again, if “meter” is defined as something existing apart from “pulse” or “beat,” which are considered as its phenomenological counterparts, this does not derail the argument; for, even in that case, something other than rhythm, and related to meter, is experienced perceptually, rather than experienced only in virtue of a perceptual acquaintance with rhythm. 16 Huang et al., “Feeling Music.”

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feet or my hands. It seems plausible that this kind of movement, with no attendant tactile stimulus, could also play a role in beat perception. The set of experiments reported by Laurel Trainor et al.17 suggests that this is indeed the case, because a regular vestibular signal can also contribute to the perception of beat. Trainor and colleagues stimulated the vestibular system directly by putting electrodes behind the ears of immobilized participants, introducing a current to simulate the sensation of the head being moved from side to side. They found that this sensation strongly biased the subsequent beat perception of the adults they tested, none of whom experienced any direct tactile stimulation. As in the Huang et al. studies, subjects were presented with a heard rhythm, which was ambiguous as to meter. This remained the same across presentations, but subjects experienced different metrical structure, in virtue of (and corresponding directly with) variations in the pattern of vestibular signal to which they were exposed. It seems that not only can tactile perception contribute to the experience of beat, but the vestibular system can too. The perceptual experience of musical beat can thus involve content, not only from audition, but also from tactile perception and the vestibular system. It seems to be some kind of multimodal experience. But what kind? Is it just multimodal in that it happens to involve experience in multiple modalities, in the sense that all experience probably does? Or is it multimodal in some deeper sense? O’Callaghan claims that the legitimacy of treating the senses as discrete channels of information is undermined by the existence of perceptually apparent intermodal feature binding.18 When one perceives features as belonging to the same thing, on his account, those features are bound in one’s experience.19 Paradigm examples of this kind of binding awareness are intramodal. I visually experience objects as having both colors and shapes; I hear sounds as having both pitch and loudness. O’Callaghan argues that one may also have experiences of objects that bear features in multiple modalities. There is, for example, a perceptually apparent difference between experiencing a thing’s being red and a thing’s being smooth, on the one hand, and experiencing the same thing as being both red and smooth on the other. In the former case, nothing in the content either of my experience of redness or my experience of smoothness guarantees that I experience the same object as having both redness and smoothness. The experience of intermodal binding cannot be exhaustively explained by appeal to the sum of the experiences in each modality involved, understood as discrete channels, along with the mere fact of their co-​occurrence. O’Callaghan appeals to the notion of multimodal phenomenal content to capture this difference. When I experience a beat, it seems to me that I both hear and feel the same unified beat. This is certainly how listeners are, in general, inclined to report their musical



17 Trainor et al., “Vestibular System.”

18 O’Callaghan, “Not All Perceptual Experience.”

19 O’Callaghan, “Intermodal Binding Awareness.”

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82   The Philosophy of Rhythm experience. It does not seem to me that I am hearing a beat, and simultaneously just happening to tap my foot and nod my head in a coincidentally regular fashion. Rather, I am having an experience of an auditory, vestibular, and tactile event. If asked to describe my experience, I would say that I hear and feel the same beat. A problem surfaces, however. Audition and tactile perception both track objects. The vestibular system, however, does not track objects. It tracks a relation between the subject’s orientation and the gravitational field, but this relation is neither an object, nor experienced as one. We are rarely aware of the operation of our vestibular system at all, apart from in cases where it malfunctions, which experience, that of vertigo, is still not of any kind of sensory object. One might worry that the vestibular system can’t bind features to objects at all, even intramodally. How, then, could it be involved in any experience of intermodal binding? This conceals a further worry: that the vestibular system isn’t really a genuine sense modality. The vestibular system usually functions in the background. If I move my head, I might not be aware of the vestibular signal. I might not even realize that I have moved it. The signal might just play the role of enabling or directing perception in my other, exteroceptive modalities. For example, suppose that I tilt my head, in a way regulated by my vestibular system, the better to see my computer screen. I don’t have to be aware of my vestibular experience to do that; indeed, I don’t even have to have a vestibular experience to do it. So, in normal cases, the vestibular system could just unconsciously guide performance in other modalities. Perhaps this is what happens in the case of the musical beat. It could be that the regular vestibular signal leads to increased auditory attention, for example, at the salient points, and it is this attentional effect that influences the experience of beat. But this seems unlikely, because musical beat is not like most everyday cases of vestibular experience, such as the experience of tilting my head to see my computer screen. The vestibular signal does not recede into the background when we move to a beat: it shows up vividly in awareness. There is a phenomenal contrast, to use Siegel’s term,20 between cases where I only hear a beat, and cases where I hear and feel it, by nodding along. If the effect were merely cognitive, it is unclear why the vestibular component should contribute any phenomenological change. The vestibular system is, I claim, contributing to the direct perception of musical meter. I really do feel the beat, through the movement of my head, when I nod along to the music. I hear and feel the same beat. If audition is perceiving exteroceptively here—​perceiving a beat, understood either as some kind of entity located at a distance from me, or as a property of such an entity—​then the vestibular system is doing so, too. That is, when we feel a beat, the vestibular system is behaving as an exteroceptive modality. We have an interoceptive experience—​we experience the beat “within ourselves,” as it were—​where this experience tracks an event occurring outside our bodies, in the world. Yet we do not experience two beats: one heard,



20 Siegel, Contents of Visual Experience, passim.

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and one felt. We experience one and the same beat—​but that beat is experienced through two sensory modalities simultaneously. I have claimed, then, that the perceptual experience of the musical beat is multimodal, and not just auditory. I now want to suggest that this view opens up a new perspective on the experience of musical movement. Specifically, I argue that a consideration of this multimodal perceptual content undermines the seeming necessity of an appeal to metaphorical perception.

4.  Movement in “beat”: an alternative to metaphorical perception Scruton observes that movement is a central component of musical experience.21 Melodies move up and down; tones follow each other through musical “space”; harmonies shift. To experience music without experiencing this movement would be, as Scruton emphasizes frequently (and rightly), to fail to experience music. All of this musical movement is puzzling, however, because tones move, but their physical components—​sounds—​do not. There is nothing relevant actually moving in the environment, when I listen to music, and yet I hear movement all the same. Paul Boghossian refers to this as the thesis of musical anti-​realism: the idea that “sounds do not literally have the musical properties we hear them as having.”22 This friction—​between the properties that musical sounds actually have, and the properties we experience them as having—​motivates an appeal to “metaphorical perception” in characterizing musical experience.23 The idea is that in musical expression (the target of Peacocke’s “The Perception of Music”), and also in movement (Scruton, The Aesthetics of Music), we have a feature of musical experience that cannot be fully accounted for by appeal to its perceptual content, because the things being perceived auditorially (the musical sounds) do not have the appropriate properties. We must appeal, goes the thought, to a different kind of perception—​namely, metaphorical perception—​to account fully for the content of the experience in question. But what does this mean? How could perception be metaphorical? Peacocke gives a useful account,24 further unpacked by Boghossian,25 which is initially formulated with respect to vision.26 We may distinguish between three types of seeing. Firstly, we may see X as X: I see a group of pots on a table, for instance. Secondly, we may see X as a depiction of Y: I see a painting, say, as depicting a group of pots on a table. The 21 Scruton, Aesthetics of Music, 35. 22 Boghossian, “Explaining Musical Experience,” 122. 23 Scruton, The Aesthetic Understanding; Aesthetics of Music; Understanding Music; Peacocke, “The Perception of Music.” 24 Peacocke, “The Perception of Music.” 25 Boghossian, “Comments on Peacocke.” 26 I am discussing Peacocke’s explication of metaphorical perception (as clarified by Boghossian) rather than Scruton’s, because I find the former account to be clearer—​even though it is Scruton who applies metaphorical perception explicitly to the experience of musical movement.

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84   The Philosophy of Rhythm third kind of perception occurs when we see X metaphorically as Y: I see the pots in the painting as a group of people.27 This is not an instance of depiction: the painting depicts pots, and not people. Yet somehow, I see the pots as people at the same time. This experience is not, goes the thought, grounded by my visual experience in the same way that the first two kinds of experience are; but it is an immediate feature of my experience, for all that. When we see the pots as people, it is not that we have a perceptual experience of pots, and then imagine, in an effortful way, that those pots are people. We just immediately see the people, as we may immediately see a face in the clouds. Peacocke thinks that metaphorical perception can explain our experience of sadness in music. This is not an instance of straightforward hearing: there is nothing that is really sad, currently perceived through audition. Is it a depiction of sadness? It is unclear how a concept can be “depicted,” first of all; and moreover, the music is not a depiction of a sad person, in the same straightforward way that the painting is a depiction of pots. How, then, am I to account for my real, immediate experience of sadness in the music? Peacocke thinks that this must be an instance of metaphorical perception. It is a genuine experience of sadness, and the sadness is experienced as being in the music; but this experience is simultaneously overlaid with the understanding that there is nothing really sad present. Scruton thinks that the same goes for musical movement. We do not actually hear sounds moving, yet we experience movement in the music all the same. Scruton thinks that metaphorical perception is the best way to account for this experience of movement. Metaphorical perception is a function of imagination, he argues; it “is effected at the highest level of rational interest, while being transcribed into the perception itself.”28 It is an experience that only rational beings, possessed of imaginative capacities, can have, he thinks. When we experience musical qualities, as opposed to sonic ones, we are not experiencing secondary qualities; such qualities are “not objects merely of sensory perception.”29 Scruton proposes that these qualities are “tertiary qualities,” which are “neither deduced from experience nor invoked in the explanation of experience. They are perceived only by rational beings, and only through a certain exercise of imagination, involving the transfer of concepts from another sphere.”30 I will not discuss Peacocke’s application of metaphorical perception to musical expression here. Nor will I claim that an account of musical movement—​the experience of tones as rising and falling, traveling quickly or slowly, and so on—​in terms of metaphorical perception cannot succeed. My aim is more modest, but also more radical, because I want to undermine the initial anti-​realist stance—​the claim that,



27 I am referring, here, to the painting Pots, by Zurbaran, which Peacocke also discusses in this context. 28 Scruton, Aesthetics of Music, 87. 29 Scruton, Aesthetics of Music, 94. 30 Scruton, Aesthetics of Music, 94.

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Feeling the Beat  85

since sounds do not literally have movement properties, our experience of those properties cannot arise in virtue of the contents of our perceptual experience. The answer to the question “Do musical sounds really move?” is an unequivocal “No.” However, I want to suggest that “Do musical sounds really move?” is not the question we should be asking. We should begin by describing the perceptual content of musical experience. Instead of asking “Do musical sounds move?” we should ask, “Is there movement-​related perceptual content present in the experience under consideration?” We can answer this question in the affirmative, at least in the case of the beat, because of the presence of content from the vestibular and tactile systems, as I will elaborate shortly. Thus, the motivation for the appeal to metaphorical perception is undermined because, on my account, there really is something in the perceptual experience of beat that grounds the experience of movement. Even if one’s auditory perceptual content on a given occasion is insufficient to ground the experience of movement, this does not mean that one’s perceptual content on that occasion, when described fully, cannot justify the experience. We need not appeal either to depiction, or to metaphorical perception, conceived of as an imaginative process, to justify our immediate experience of movement. There is work to do, however, to establish this claim. In particular, I need to show that there really is movement-​ related content in beat experience. We may distinguish between two cases of beat experience: (1) I hear a beat and move along to it; and (2) I hear a beat but remain completely immobile. In case (1), I am having an occurrent vestibular experience, elicited by my physical movement, which is intermodally bound to my auditory experience. I am having a real experience of movement, then, and this movement-​related content is experientially bound to what I hear. Thus, the need to appeal to metaphorical perception, in accounting for the experience of movement in the beat, is circumvented. But what about the second case? Suppose that I hear the beat, but remain totally immobile. I am not experiencing intermodal binding, in this case. I am just having an auditory experience. And yet I do experience movement in the beat. It seems that we have to resort to metaphorical perception to justify the experience of movement after all. Or do we? Consider, by way of comparison, another case of intermodal binding. Take my experience of the roundness of a ball. My experience of roundness is an experience of something that I can both see and touch. Even if I am only seeing the roundness of a ball on a given occasion, I know that if I were to touch it, I would feel, not just some roundness or other, but the same roundness as the one I see. Roundness itself is a notion that is built out of its visual and tactile components: it seems implausible that I should see roundness while experiencing no connection whatsoever to felt roundness. It would not be roundness that I saw, in that case. So, when I see roundness without feeling it at the same time, it doesn’t follow that my perceptual experience is not characterized, in part, by tactile perception. My visual experience of roundness is not, by contrast, affected by auditory phenomenal character. I don’t see roundness as the kind of thing that I could hear, but I do see it as the kind of thing that I could touch. O’Callaghan refers to this kind of experience as

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86   The Philosophy of Rhythm “cross-​modal perceptual completion.”31 He argues that this kind of perceptual experience has phenomenal character that no “pure” unimodal perceptual experience could have. Perceptual “completion” occurs when I have a perceptual experience as of a complete object, despite the fact that I can only see parts of it. It is usually characterized as an amodal process: a perceptual process that operates across sensory modalities, rather than within any particular one. Suppose I see a cat standing behind a picket fence. Parts of the cat are occluded by the slats of the fence. However, I see the cat’s body as continuing behind the fence; if the cat were to move and reveal itself to be just an assemblage of oblong cat-​parts held together invisibly in space, I would be taken aback. I perceptually experience the cat to continue behind the barrier; the currently invisible parts of the cat make a difference to the phenomenal character of my visual experience. My perceptual experience is of a “complete” cat, in other words, despite the partial nature of the visual stimulus. O’Callaghan suggests that “amodal” completion is not a perfect label here—​rather, this is a kind of intramodal (within vision) completion. Now, given that intramodal completion seems plausible, so too is cross-​modal completion, suggests O’Callaghan. Though I may only be having a visual experience of a ball, the character of my perceptual experience is affected—​or “completed,” in other words—​by its tangible, though currently untouched, features. Cases of cross-​modal completion are cases where “a perceptual experience generated by stimulating only one sensory system presents an object as something that bears features of another modality without presenting those hidden features.”32 Importantly, the phenomenal character of perceptual experience is affected by this cross-​modal completion. For example, a visible surface experienced as that of a solid object may differ phenomenologically from the visible surface experienced as holographic. The experience of beat, when I hear it but do not move along, is, I suggest, an instance of cross-​modal completion. I experience the beat as being the kind of thing that I could move to, just as I saw the ball as being the kind of thing that I could touch. This means that my auditory experience of the beat is vestibular-​and touch-​ involving, even when I am not moving, in the same way that my visual experience of a round ball is touch-​involving when I am not touching it. I claimed earlier that an experience of roundness that was not touch-​involving would not be an experience of roundness. So, too, I want to claim that an experience of beat that was not vestibular-​involving and touch-​involving would not be an experience of a beat. Even when I just hear it, content from my vestibular and tactile experience still plays a role in characterizing the experience. It completes the perceptual experience, just as the unseen parts of the cat complete that perceptual experience. This is how I see the roundness of a ball as something I can touch, and it is also how I hear a beat as something that I can move along to.

31 O’Callaghan, “Not All Perceptual Experience.”

32 O’Callaghan, “Not All Perceptual Experience,” 147.

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Hence, when I am moving to the beat, I experience intermodal feature binding between auditory and vestibular content, and thus my experience has movement-​ related content. When I am listening, but not moving, I do not experience occurrent intermodal feature binding—​but I  do experience cross-​modal completion between audition, tactile perception, and the vestibular system, which means that, even though I am not moving, my experience is affected by movement-​related phenomenal character. The distinction between the two kinds of movement-​related content is what we should expect, given the phenomenal contrast between cases where we move along to the beat, and cases where we feel the beat while remaining still. We can, therefore, account for a sense of movement in music—​albeit a basic one—​by considering the richness, often ignored by purely auditory conceptions of music, of the perceptual experience of a beat. And if we can account for the ultimate experience in terms of the perceptual content involved, the move to metaphorical perception begins to seem avoidable. Three objections should be deflected. The first targets the notion of cross-​modal completion. The completion that happens when I look at a ball, and see it as the kind of thing I could touch, might just be an instance of amodal completion, with no consequences for phenomenal character. That is, I might be having a unimodal visual experience of roundness, which may be better thought of as an amodal property (one not associated with any sense modality in particular). When I look at the ball, it could be that I have some expectations concerning tactile content, but that these expectations do not contribute any character to the visual experience. Hearing the beat, but not moving to it, might be analogous. I might be having a unimodal auditory experience of an amodal feature (the beat). I might also have some expectations concerning movement. But these “movement expectations” may not affect the character of my experience. However, I think that this fails to do justice to the character of the experience of listening to music. It seems elemental to the experience of beat that I frequently feel like I want to move along with it, and tap my toe to it; sometimes, I have to actively restrain myself from doing so (if I am in a concert hall, for instance). It seems to me that we really do have a movement-​involving phenomenal experience when we listen to music but remain immobile. We long to move to it. An account that appeals to expectations that have no consequences for phenomenal character seems somewhat wan. The second objection is the following: Why is vestibular experience, or tactile experience, “movement-​involving” in a way that auditory experience on its own is not? Even the barest auditory experience involves movement in the sense that it was caused by something moving—​specifically, the vibration of an object in a medium. Despite this “movement-​involvement,” auditory experience alone cannot account for the experience of musical movement, as everyone agrees. Why should the appeal to movement-​involvement be effective in the case of multimodal perceptual experience, then? The mere fact that tactile experience, or vestibular experience, is produced by something moving doesn’t prove anything, because auditory experience is produced in the same sort of way. But this is not quite right. Auditory

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88   The Philosophy of Rhythm experience involves movement in a causal way, certainly, but it does not necessarily involve movement-​related content. Notice that the perceptual experience of a sound is not an experience as of motion in the same way that touch, or vestibular experience, are experiences as of motion—​either of one’s own body, or of the environment in relation to one’s own body. One may enjoy genuine auditory experience without ever discovering that vibrating objects are at the ultimate source of one’s experience. Physicists had to conduct empirical investigations, after all, in order to figure out that sounds rely, for their existence, upon the usually invisible vibrations of objects. No scientific discovery is necessary for touch, or in the vestibular case. Movement is present in one’s vestibular experience, and in touch, in a way that it is not in auditory experience. It is unthinkable that one could have a tactile or vestibular experience that one did not already experience as involving movement. The third objection is as follows: My account of content from a given modality being “involved” in an experience in another modality is just metaphorical perception in disguise. I experience something heard as something I could also touch; so, I experience something seen as metaphorically touched, in a sense. This may be so; but if we allow this to count as an instance of metaphorical perception, then the floodgates are opened, and every experience of intermodal binding—​every experience of roundness, hardness, softness, roughness—​now involves the deployment of metaphor on the perceptual level. Perhaps the advocates of metaphorical perception would be happy to bite this bullet, but I suspect otherwise. Metaphorical perception is supposed to be reserved for a special subset of perceptual (often aesthetic) experiences, which are not explicable, it is thought, on ordinary accounts. If intermodal binding involves metaphorical perception, then nearly everything does; and this is, I think, an unpalatable prospect. Back to the experience of beat. I think that the idea that musical experience is movement-​involving, even when we are not moving, is what Scruton is alluding to when he describes musical engagement, as “involving a kind of latent dancing—​a sublimated desire to ‘move with’ the music.”33 Jerrold Levinson picks up on this comment of Scruton’s, speculatively suggesting that music may actually be, rather than merely involve, latent dancing.34 He does not, however, elaborate on this idea, merely noting its appeal. I hope to have been able to give some indication of what might lie behind this intuition, which is an attractive one for many philosophers of music; but more importantly, I hope to have shown that we do not need to appeal to imaginative capacity, or to metaphorical perception, in order to account for it. It is of course possible, or even likely, that a basic sense of stressed beats cannot fully account for the experience of musical movement. It could be that the kind of perceptual experience of musical movement that I have been discussing is not sufficiently detailed to capture musical movement in a more full-​fledged sense: tones moving in musical space, from high to low, speeding up and slowing down, and so

33 Scruton, Aesthetics of Music, 357.

34 Levinson, “Aesthetic Appreciation of Music.”

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Feeling the Beat  89

on. Metaphorical perception might, after all, be required to account for this richer sense of musical movement. And it might also be required, as Peacocke suggests, to explain musical expression. I am happy to concede this as a possibility. I merely want to highlight that we do not have to accept the initial “anti-​realist” claim, which makes the appeal to metaphorical perception seem inevitable in the case of movement. For, at least when it comes to beat, there is movement-​related content in my perceptual experience. I am having a bona fide perceptual experience as of movement, which is both heard and felt. It is not just that I really experience myself as moving, and by some kind of illusory imaginative transfer, the sound is heard as moving, too. Rather, the movement has a heard aspect, and also a felt one. I have been discussing the experience of “beat.” I am not making claims about the experience of rhythm more generally, about musical movement in a richer sense, or about the broad utility of appeals to metaphorical perception. Nevertheless, I am sounding the following note of caution: assuming that music is just a matter of sounds, and of auditory experience, risks making intellectualist accounts of musical experience seem inevitable, when they may not be.

5. Conclusion I began by outlining the distinction between rhythm and meter. I claimed that there is a component of the perceptual experience of music—​the “beat”—​that is attributable to meter. I argued that the experience of beat is multimodal: specifically, that when we “hear and feel” a beat, this experience is an instance of intermodal feature binding, where content in audition is bound to content in tactile and vestibular perception. I went on to suggest that a consideration of this multimodal content offers an alternative, perception-​based explanation of the experience of movement in a musical beat, which deflates the seeming necessity of an appeal to metaphorical perception. Beat experience is not exhausted by auditory experience; it also involves, I argued, vestibular and tactile experience, both of which give rise to movement-​involving perceptual content. This is true, I claimed, whether or not we are actively moving to the beat. Thus, our experience of movement in the “beat” is justified by the perceptual experience itself; the seeming necessity of an appeal to metaphorical perception is thus undermined. An “experience-​first” approach to music, which begins from a consideration of perceptual experience rather than sounds, has at least two consequences for the philosophy of music. First of all, it represents a continuation of the extant challenge, formulated by authors such as Aaron Ridley, Andy Hamilton, and Kathleen Higgins, to the view that music can be adequately theorized in isolation from the cultural, biological, and historical factors that have shaped it.35 The second is, however, more novel, insofar as it undermines the dominant assumption that music is fundamentally about sounds. I hope to have shown that rescuing rhythm and

35 Ridley, Philosophy of Music; Hamilton, Aesthetics and Music; Higgins, Music of our Lives.

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90   The Philosophy of Rhythm meter from the sidelines of the philosophy of music not only makes for a more representative characterization of music, but also challenges the validity of the “unimodal” manner in which music has heretofore been approached. Rhythm is not just a matter of sounds. It is not even just a matter of auditory experience. Aspects of musical experience—​central ones, at that—​are deeply multimodal. Considered in this light, music raises many questions for philosophers of perception, and the door is opened for music to feature prominently in debates beyond the confines of the philosophy of art.

Works Cited Boghossian, Paul, “Explaining Musical Experience,” in Kathleen Stock, ed., Philosophers on Music: Experience, Meaning, and Work (Oxford, 2007). Boghossian, Paul, “The Perception of Music:  Comments on Peacocke,” The British Journal of Aesthetics, 50.1 (2010), 71–​6. Hamilton, Andy, Aesthetics and Music (London, 2007). Hasty, Christopher F., Meter as Rhythm (Oxford, 1997). Higgins, Kathleen Marie, The Music of Our Lives (Philadelphia, 1991). Huang, Juan, Darik Gamble, Kristine Sarnlertsophon, Xiaoqin Wang, and Steven Hsiao, “Feeling Music: Integration of Auditory and Tactile Inputs in Musical Meter Perception,” PLoS ONE, 7.10 (2012). Levinson, Jerrold, “The Aesthetic Appreciation of Music,” The British Journal of Aesthetics, 49.4 (2009), 415–​25. London, Justin, Hearing in Time: Psychological Aspects of Musical Meter (Oxford, 2004). London, Justin, “Three Things Linguists Need to Know about Rhythm and Time in Music,” Empirical Musicology Review, 7.1–​2 (2012), 5–​11. Matthen, Mohan, “On the Diversity of Auditory Objects,” Review of Philosophy and Psychology, 1.1 (2010), 63–​9. O’Callaghan, Casey, “Intermodal Binding Awareness,” in David J. Bennett and Christopher S. Hill, eds, Sensory Integration and the Unity of Consciousness (Cambridge, 2014), 73–​104. O’Callaghan, Casey, “Not All Perceptual Experience is Modality Specific,” in Dustin Stokes, Mohan Matthen, and Stephen Biggs, eds, Perception and Its Modalities (Oxford, 2014), 133–​65. Peacocke, Christopher, “The Perception of Music: Sources of Significance,” The British Journal of Aesthetics, 49.3 (2009), 257–​75. Ridley, Aaron, The Philosophy of Music: Theme and Variations (Edinburgh, 2004). Scruton, Roger, The Aesthetic Understanding:  Essays in the Philosophy of Art and Culture (London, 1983). Scruton, Roger, The Aesthetics of Music (Oxford, 1997). Scruton, Roger, Understanding Music: Philosophy and Interpretation (London, 2009). Siegel, Susanna, The Contents of Visual Experience (Oxford, 2010). Thaut, Michael H., Rhythm, Music, and the Brain: Scientific Foundations and Clinical Applications (London, 2005). Trainor, Laurel J., Xiaoqing Gao, Jing-​jiang Lei, Karen Lehtovaara, and Laurence R. Harris, “The Primal Role of the Vestibular System in Determining Musical Rhythm,” Cortex, 45.1 (2009),  35–​43.

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4 “Feeling the Beat” Multimodal Perception and the Experience of Musical Movement Jenny Judge

1.  Introduction: The Neglect of Rhythm Philosophers have no rhythm—​or, at least, so a reader becoming acquainted with the philosophy of music might suspect. Discussions of form, ontology, and expression abound, but philosophical treatments of rhythm are rare. This seems extraordinary. While a concern for form, ontology, and expression is, in some sense, common to all the arts, an appreciation of rhythm is uniquely, or at least paradigmatically, musical. An examination is central to understanding how music moves us—​and it moves us quite literally in nightclubs, on treadmills, and even in the privacy of our own kitchens. Its neglect by philosophers requires remedial action. This chapter is an attempt to show that when we turn our philosophical attention to rhythm, many new puzzles emerge, the analysis of which brings the philosophy of music into closer contact with the philosophy of mind and perception. I distinguish meter and rhythm, arguing that meter, like rhythm, contributes to the perceptual experience of music in its own right. I claim that the experience of musical beat—​attributable to musical meter, rather than rhythm—​is multimodal in a stronger sense than happening to involve perceptual content across different senses. The term “perceptual content” is frequently deployed in the philosophy of perception, but it may require some explanation. One can think of the term “content” in two ways. One can talk about the contents of buckets, or cupboards, or handbags; one can also talk about the contents of a newspaper. Content can thus be physical—​ what is literally inside some vessel—​or informational. Hence, the term “perceptual content” could mean either (i) what is “contained” in the mind when one has a perceptual experience, or (ii) what is conveyed to the subject having the perceptual experience. In the philosophy of perception, “perceptual content” usually refers to the latter sense, according to which it is natural to think of the senses as channels through which one may discover things about the world. “Auditory content” refers Jenny Judge, “Feeling the Beat” In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0005

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to that which is conveyed to me when I have an auditory experience, “visual content” picks out whatever I find out about the world through a visual experience, and so on for each sensory modality.1 In this chapter, I argue that the experience of musical meter, or “beat,” involves what Casey O’Callaghan terms “intermodal feature binding,”2 whereby perceptual content arising from different sensory modalities is bound to a common entity (such as when I experience the roundness of a ball through touch and sight). However, the experience of beat is a curious case, as I elaborate. Paradigm cases of intermodal feature binding involve the binding of content across exteroceptive senses that yield information from outside the body. The experience of beat, on the other hand, involves the binding of exteroceptive content (the auditory experience of musical sounds occurring in the environment) and interoceptive content (experiences of one’s own body). Specifically, I shall argue that the experience of beat involves intermodal binding between auditory and vestibular content: that is, content arising from the functioning of the vestibular system, which tracks body orientation, movement, and balance.3 A consideration of the multimodal perceptual content of the experience of “beat,” I go on to argue, yields an appealing perspective on the puzzle of musical movement. Roger Scruton notes that the experience of movement in music, though vivid, is nevertheless paradoxical, because musical sounds themselves are not actually moving, and so movement properties cannot feature in the contents of the perceptual experience of music.4 We have to appeal to something other than perceptual content to explain the experience of movement—​specifically, to “metaphorical perception.” My response is that if the perceptual experience of music encompasses more than the auditory experience of musical sounds, then it doesn’t follow, from the fact that musical sounds fail to have movement properties, that our experience of movement cannot be justified by (extra-​auditory) perceptual content. I will claim that there is, after all, legitimate movement-​related content present in musical experience, in the case of the experience of the beat—​and so there is no need to appeal to metaphorical perception. A note, before I continue: I am targeting a motivation for the appeal to metaphorical perception. I am not targeting the notion itself, nor am I claiming that the perceptual experience of beat, in the bare sense I outline here, is enough to explain the full-​blown experience of movement in musical “space” that Scruton has in mind. I merely want to undermine the seeming inevitability of appeals to metaphorical perception, by directing attention to the rich, multimodal perceptual content involved in rhythmic experience. 1 Siegel, Contents of Visual Experience, gives an overview of the notion of perceptual content, and its surrounding debates. 2 O’Callaghan, “Not All Perceptual Experience,” 139–​46; “Intermodal Binding Awareness,” 82–​97. 3 The vestibular system consists of receptors in the inner ear, and their connections to other parts of the nervous system. 4 Scruton, Aesthetics of Music, 13–​15, 21, 49–​71.

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78   The Philosophy of Rhythm And so, to rhythm. What is it, and more pressingly, what do music theorists mean by “meter”?

2.  Rhythm, Meter, and “Beat”: A Perceptual Account Theorists of music and poetry commonly distinguish between rhythm and meter. On one common view, which Andy Hamilton calls the “abstract” account, one may consider rhythm as the bare temporal patterns present in a piece of music: groups of sounds and silences, or simply “order-​in-​time.”5 Meter, on the other hand, is the pattern of stress in which rhythms are grouped. In a piece of music, meter is usually indicated by the time signature. A waltz, for example, will have “3” in the upper part of its time signature, as in ¾: this means that the piece has three (crotchet) “beats” in each measure or bar. Though two different waltzes may be composed of any number of different rhythms, they have the same triple meter. “The Blue Danube” and “Moon River,” for example, contain different rhythmic patterns, but each piece has three beats per bar, occurring in the pattern strong-​weak-​weak. On this abstract view, meter is thought to be, in Christopher Hasty’s words, “a more or less independent structure that rhythm uses for its own ends.”6 Hasty notes that it is customary to view rhythm as a rich and fully sensuous embodiment of music’s temporal progress and metre as rhythm’s shadowy, schematic counterpart—​ abstract, mechanical, and devoid of any intrinsic expression.7

Rhythm is in the music, it is sometimes implied, but meter is not. Some authors characterize meter as a kind of habitual response to rhythm. For instance, Justin London suggests that meter is “an aspect of our engagement with the production and perception of tones in time”8—​implying that meter is really a way of describing our behavior, rather than a feature of our experience, or of the music itself. If meter is an abstract entity, or even a property of behavior as London suggests, does it really feature in immediate musical experience? The phenomenology of musical listening suggests that it does. We needn’t observe our own periodic behavior in response to Stevie Wonder’s “I Wish,” or infer 5 Hamilton, Aesthetics and Music, 26, et passim, criticizes this “abstract” characterization of rhythm, proposing instead that rhythm is an essentially dynamic, human phenomenon. On Hamilton’s view, rhythm is the product of human action: it is “order-​in-​movement” rather than merely “order-​in-​time.” Rhythms must already possess legitimate movement properties in order to count as rhythms in the first place; they are not, for Hamilton, static and abstract to begin with. This is one valid way to counter Scruton’s appeal to metaphorical perception in order to explain the experience of musical movement. It is, however, a different approach to the one pursued here. Rather than challenging extant “abstract” accounts of rhythm, I focus on musical meter: the experience of patterns of stress within musical rhythms. I address the perceptual content involved in such “beat” experiences; I do not directly address the content of experiences of rhythm, taken generally. 6 Hasty, Meter as Rhythm, 4. 7 Hasty, Meter as Rhythm, viii. 8 London, Hearing in Time, 4.

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patterns of stress when perceiving the first movement of Beethoven’s “Waldstein” Sonata, to become conscious of the regular metrical structure. Hasty thinks that the “abstract” conception of meter is an artifact of musical pedagogy, which distracts from its real experiential import. Meter is key to musical experience, he argues. The experience of stressed beats is so crucial, in fact, that “the layman may well call this phenomenon rhythm pure and simple.”9 Hamilton agrees with Hasty, arguing that the abstract conception of meter ignores “the felt regularity of the underlying pulse or groundbeat.”10 Nevertheless, London suggests that, while meter is best thought of as an abstraction, it does have a phenomenal counterpart in the music itself: the “beat.”11 The beat is what shows up in experience. Meter is “phenomenally manifest” to us, says London, “as our perception of a pattern of accentually differentiated beats.”12 Michael Thaut proposes something similar, arguing that, while meter is best thought of as an abstraction, we detect a series of “pulses” in the music, which are organized in a metrical hierarchy.13 The precise nature of the relationship between “beat” or “pulse” and meter remains, however, somewhat opaque in these discussions. Is “beat,” or “pulse,” identical to meter, or does it stand in some other, weaker relation to it? Neither London nor Thaut elaborates on the issue. In what follows, I will claim that there is a component of the perceptual experience of music—​call it “beat” for clarity—​that depends on meter, rather than on non-​metrical rhythm. “Beat” might turn out to be identical to meter, or it might merely be related to it—​an examination of the relationship between beat and meter is reserved for another occasion. The main point, for present purposes, is that there is an aspect of the immediate, perceptual experience of music that is attributable to meter rather than to rhythm. Meter shows up in the perceptual experience of music in the form of the “beat.” The relationship between experiences of meter and rhythm is akin to that between the experiences of melodies and their parts. Mohan Matthen argues that patterns of sound—​such as the tune of the American national anthem—​manifest in experience in their own right, not solely in virtue of the prior perceptual experience of their components.14 There are, he argues, experimental and phenomenological indicators that a process is automatic and sensory, which melodies satisfy. If a beat satisfies these indicators too, this gives good prima facie reason to suppose that beat is perceived, rather than merely inferred on the basis of the perception of rhythm. First, Matthen argues that separate conditionability is a reliable indicator that a given process is perceptual. If subjects’ behavior can be influenced by an entity, this counts as a reason to suppose that the entity is being perceived. Beat seems



9 Hasty, Meter as Rhythm, 5.

10 Hamilton, Aesthetics and Music, 136.

11 London, “Rhythm and Time in Music.”

12 London, “Rhythm and Time in Music,” 5. 13 Thaut, Rhythm, Music, and the Brain.

14 Matthen, “Diversity of Auditory Objects.”

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80   The Philosophy of Rhythm to be separately conditionable from rhythms and melodies. Indeed, its behavioral effect—​our tendency to move along with it—​is a cornerstone of musical experience. This suggests that meter, or beat, is perceived directly. Constancy is a further indicator to which Matthen appeals. Melodies, he claims, are constant: they are the same from different “points of view,” as it were. A melody remains the same melody, even when transposed into a different key. Rhythm also seems to be constant in this regard, remaining the same with changes in tempo; and a musical beat appears to be constant in the same way. I can recognize an instance of march time, or a waltz, no matter what tempo it is played at, what melodies or individual rhythms feature in it, or what instruments play it. Moreover, new experiences of musical meter satisfy the further constraint of familiarity. Repeat instances of waltzes are readily recognizable as such, and feel familiar, even when we have not heard that particular waltz before. It thus seems that there is good reason to think that musical experience involves meter in an immediate, perceptual way. The “beat” is separately conditionable, constant from different “points of view,” and satisfies the “familiarity” constraint.15 So far I have discussed hearing. Now I want to make the further claim that beat, unlike melody for instance, can be perceived by more than just auditory perception.

3.  The perceptual experience of “beat” is multimodal I now argue that if a beat can be perceived—​that a pattern of metrical stresses in time can show up in perceptual experience in its own right—​then those stresses do not have to arise in auditory perception. They can be tactile impulses, or even vestibular signals. Juan Huang et al. investigated the role of touch in the perception of beat.16 They showed that subjects report experiencing identical heard rhythms, which were ambiguous as to meter, as being in either march-​time or waltz-​time, in accordance with the pattern of tactile stimulus to which they were exposed at the same time. If they experienced a tactile impulse coinciding with every second tone, they heard the rhythm in march-​time (that is, the experienced a strong-​weak pattern in the musical sounds); a tactile impulse on every third tone led to an experience of waltz time (a strong-​weak-​weak pattern). It seems, then, that beat can be felt through tactile perception, and not just heard. The authors observe that the sense of touch is particularly important in performance, but also plays a role for audiences, when listeners tap their hands and feet to a rhythm. However, it is not the only extra-​ auditory factor to consider. I may nod my head along to a beat, without tapping my 15 Again, if “meter” is defined as something existing apart from “pulse” or “beat,” which are considered as its phenomenological counterparts, this does not derail the argument; for, even in that case, something other than rhythm, and related to meter, is experienced perceptually, rather than experienced only in virtue of a perceptual acquaintance with rhythm. 16 Huang et al., “Feeling Music.”

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feet or my hands. It seems plausible that this kind of movement, with no attendant tactile stimulus, could also play a role in beat perception. The set of experiments reported by Laurel Trainor et al.17 suggests that this is indeed the case, because a regular vestibular signal can also contribute to the perception of beat. Trainor and colleagues stimulated the vestibular system directly by putting electrodes behind the ears of immobilized participants, introducing a current to simulate the sensation of the head being moved from side to side. They found that this sensation strongly biased the subsequent beat perception of the adults they tested, none of whom experienced any direct tactile stimulation. As in the Huang et al. studies, subjects were presented with a heard rhythm, which was ambiguous as to meter. This remained the same across presentations, but subjects experienced different metrical structure, in virtue of (and corresponding directly with) variations in the pattern of vestibular signal to which they were exposed. It seems that not only can tactile perception contribute to the experience of beat, but the vestibular system can too. The perceptual experience of musical beat can thus involve content, not only from audition, but also from tactile perception and the vestibular system. It seems to be some kind of multimodal experience. But what kind? Is it just multimodal in that it happens to involve experience in multiple modalities, in the sense that all experience probably does? Or is it multimodal in some deeper sense? O’Callaghan claims that the legitimacy of treating the senses as discrete channels of information is undermined by the existence of perceptually apparent intermodal feature binding.18 When one perceives features as belonging to the same thing, on his account, those features are bound in one’s experience.19 Paradigm examples of this kind of binding awareness are intramodal. I visually experience objects as having both colors and shapes; I hear sounds as having both pitch and loudness. O’Callaghan argues that one may also have experiences of objects that bear features in multiple modalities. There is, for example, a perceptually apparent difference between experiencing a thing’s being red and a thing’s being smooth, on the one hand, and experiencing the same thing as being both red and smooth on the other. In the former case, nothing in the content either of my experience of redness or my experience of smoothness guarantees that I experience the same object as having both redness and smoothness. The experience of intermodal binding cannot be exhaustively explained by appeal to the sum of the experiences in each modality involved, understood as discrete channels, along with the mere fact of their co-​occurrence. O’Callaghan appeals to the notion of multimodal phenomenal content to capture this difference. When I experience a beat, it seems to me that I both hear and feel the same unified beat. This is certainly how listeners are, in general, inclined to report their musical



17 Trainor et al., “Vestibular System.”

18 O’Callaghan, “Not All Perceptual Experience.”

19 O’Callaghan, “Intermodal Binding Awareness.”

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82   The Philosophy of Rhythm experience. It does not seem to me that I am hearing a beat, and simultaneously just happening to tap my foot and nod my head in a coincidentally regular fashion. Rather, I am having an experience of an auditory, vestibular, and tactile event. If asked to describe my experience, I would say that I hear and feel the same beat. A problem surfaces, however. Audition and tactile perception both track objects. The vestibular system, however, does not track objects. It tracks a relation between the subject’s orientation and the gravitational field, but this relation is neither an object, nor experienced as one. We are rarely aware of the operation of our vestibular system at all, apart from in cases where it malfunctions, which experience, that of vertigo, is still not of any kind of sensory object. One might worry that the vestibular system can’t bind features to objects at all, even intramodally. How, then, could it be involved in any experience of intermodal binding? This conceals a further worry: that the vestibular system isn’t really a genuine sense modality. The vestibular system usually functions in the background. If I move my head, I might not be aware of the vestibular signal. I might not even realize that I have moved it. The signal might just play the role of enabling or directing perception in my other, exteroceptive modalities. For example, suppose that I tilt my head, in a way regulated by my vestibular system, the better to see my computer screen. I don’t have to be aware of my vestibular experience to do that; indeed, I don’t even have to have a vestibular experience to do it. So, in normal cases, the vestibular system could just unconsciously guide performance in other modalities. Perhaps this is what happens in the case of the musical beat. It could be that the regular vestibular signal leads to increased auditory attention, for example, at the salient points, and it is this attentional effect that influences the experience of beat. But this seems unlikely, because musical beat is not like most everyday cases of vestibular experience, such as the experience of tilting my head to see my computer screen. The vestibular signal does not recede into the background when we move to a beat: it shows up vividly in awareness. There is a phenomenal contrast, to use Siegel’s term,20 between cases where I only hear a beat, and cases where I hear and feel it, by nodding along. If the effect were merely cognitive, it is unclear why the vestibular component should contribute any phenomenological change. The vestibular system is, I claim, contributing to the direct perception of musical meter. I really do feel the beat, through the movement of my head, when I nod along to the music. I hear and feel the same beat. If audition is perceiving exteroceptively here—​perceiving a beat, understood either as some kind of entity located at a distance from me, or as a property of such an entity—​then the vestibular system is doing so, too. That is, when we feel a beat, the vestibular system is behaving as an exteroceptive modality. We have an interoceptive experience—​we experience the beat “within ourselves,” as it were—​where this experience tracks an event occurring outside our bodies, in the world. Yet we do not experience two beats: one heard,



20 Siegel, Contents of Visual Experience, passim.

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and one felt. We experience one and the same beat—​but that beat is experienced through two sensory modalities simultaneously. I have claimed, then, that the perceptual experience of the musical beat is multimodal, and not just auditory. I now want to suggest that this view opens up a new perspective on the experience of musical movement. Specifically, I argue that a consideration of this multimodal perceptual content undermines the seeming necessity of an appeal to metaphorical perception.

4.  Movement in “beat”: an alternative to metaphorical perception Scruton observes that movement is a central component of musical experience.21 Melodies move up and down; tones follow each other through musical “space”; harmonies shift. To experience music without experiencing this movement would be, as Scruton emphasizes frequently (and rightly), to fail to experience music. All of this musical movement is puzzling, however, because tones move, but their physical components—​sounds—​do not. There is nothing relevant actually moving in the environment, when I listen to music, and yet I hear movement all the same. Paul Boghossian refers to this as the thesis of musical anti-​realism: the idea that “sounds do not literally have the musical properties we hear them as having.”22 This friction—​between the properties that musical sounds actually have, and the properties we experience them as having—​motivates an appeal to “metaphorical perception” in characterizing musical experience.23 The idea is that in musical expression (the target of Peacocke’s “The Perception of Music”), and also in movement (Scruton, The Aesthetics of Music), we have a feature of musical experience that cannot be fully accounted for by appeal to its perceptual content, because the things being perceived auditorially (the musical sounds) do not have the appropriate properties. We must appeal, goes the thought, to a different kind of perception—​namely, metaphorical perception—​to account fully for the content of the experience in question. But what does this mean? How could perception be metaphorical? Peacocke gives a useful account,24 further unpacked by Boghossian,25 which is initially formulated with respect to vision.26 We may distinguish between three types of seeing. Firstly, we may see X as X: I see a group of pots on a table, for instance. Secondly, we may see X as a depiction of Y: I see a painting, say, as depicting a group of pots on a table. The 21 Scruton, Aesthetics of Music, 35. 22 Boghossian, “Explaining Musical Experience,” 122. 23 Scruton, The Aesthetic Understanding; Aesthetics of Music; Understanding Music; Peacocke, “The Perception of Music.” 24 Peacocke, “The Perception of Music.” 25 Boghossian, “Comments on Peacocke.” 26 I am discussing Peacocke’s explication of metaphorical perception (as clarified by Boghossian) rather than Scruton’s, because I find the former account to be clearer—​even though it is Scruton who applies metaphorical perception explicitly to the experience of musical movement.

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84   The Philosophy of Rhythm third kind of perception occurs when we see X metaphorically as Y: I see the pots in the painting as a group of people.27 This is not an instance of depiction: the painting depicts pots, and not people. Yet somehow, I see the pots as people at the same time. This experience is not, goes the thought, grounded by my visual experience in the same way that the first two kinds of experience are; but it is an immediate feature of my experience, for all that. When we see the pots as people, it is not that we have a perceptual experience of pots, and then imagine, in an effortful way, that those pots are people. We just immediately see the people, as we may immediately see a face in the clouds. Peacocke thinks that metaphorical perception can explain our experience of sadness in music. This is not an instance of straightforward hearing: there is nothing that is really sad, currently perceived through audition. Is it a depiction of sadness? It is unclear how a concept can be “depicted,” first of all; and moreover, the music is not a depiction of a sad person, in the same straightforward way that the painting is a depiction of pots. How, then, am I to account for my real, immediate experience of sadness in the music? Peacocke thinks that this must be an instance of metaphorical perception. It is a genuine experience of sadness, and the sadness is experienced as being in the music; but this experience is simultaneously overlaid with the understanding that there is nothing really sad present. Scruton thinks that the same goes for musical movement. We do not actually hear sounds moving, yet we experience movement in the music all the same. Scruton thinks that metaphorical perception is the best way to account for this experience of movement. Metaphorical perception is a function of imagination, he argues; it “is effected at the highest level of rational interest, while being transcribed into the perception itself.”28 It is an experience that only rational beings, possessed of imaginative capacities, can have, he thinks. When we experience musical qualities, as opposed to sonic ones, we are not experiencing secondary qualities; such qualities are “not objects merely of sensory perception.”29 Scruton proposes that these qualities are “tertiary qualities,” which are “neither deduced from experience nor invoked in the explanation of experience. They are perceived only by rational beings, and only through a certain exercise of imagination, involving the transfer of concepts from another sphere.”30 I will not discuss Peacocke’s application of metaphorical perception to musical expression here. Nor will I claim that an account of musical movement—​the experience of tones as rising and falling, traveling quickly or slowly, and so on—​in terms of metaphorical perception cannot succeed. My aim is more modest, but also more radical, because I want to undermine the initial anti-​realist stance—​the claim that,



27 I am referring, here, to the painting Pots, by Zurbaran, which Peacocke also discusses in this context. 28 Scruton, Aesthetics of Music, 87. 29 Scruton, Aesthetics of Music, 94. 30 Scruton, Aesthetics of Music, 94.

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since sounds do not literally have movement properties, our experience of those properties cannot arise in virtue of the contents of our perceptual experience. The answer to the question “Do musical sounds really move?” is an unequivocal “No.” However, I want to suggest that “Do musical sounds really move?” is not the question we should be asking. We should begin by describing the perceptual content of musical experience. Instead of asking “Do musical sounds move?” we should ask, “Is there movement-​related perceptual content present in the experience under consideration?” We can answer this question in the affirmative, at least in the case of the beat, because of the presence of content from the vestibular and tactile systems, as I will elaborate shortly. Thus, the motivation for the appeal to metaphorical perception is undermined because, on my account, there really is something in the perceptual experience of beat that grounds the experience of movement. Even if one’s auditory perceptual content on a given occasion is insufficient to ground the experience of movement, this does not mean that one’s perceptual content on that occasion, when described fully, cannot justify the experience. We need not appeal either to depiction, or to metaphorical perception, conceived of as an imaginative process, to justify our immediate experience of movement. There is work to do, however, to establish this claim. In particular, I need to show that there really is movement-​ related content in beat experience. We may distinguish between two cases of beat experience: (1) I hear a beat and move along to it; and (2) I hear a beat but remain completely immobile. In case (1), I am having an occurrent vestibular experience, elicited by my physical movement, which is intermodally bound to my auditory experience. I am having a real experience of movement, then, and this movement-​related content is experientially bound to what I hear. Thus, the need to appeal to metaphorical perception, in accounting for the experience of movement in the beat, is circumvented. But what about the second case? Suppose that I hear the beat, but remain totally immobile. I am not experiencing intermodal binding, in this case. I am just having an auditory experience. And yet I do experience movement in the beat. It seems that we have to resort to metaphorical perception to justify the experience of movement after all. Or do we? Consider, by way of comparison, another case of intermodal binding. Take my experience of the roundness of a ball. My experience of roundness is an experience of something that I can both see and touch. Even if I am only seeing the roundness of a ball on a given occasion, I know that if I were to touch it, I would feel, not just some roundness or other, but the same roundness as the one I see. Roundness itself is a notion that is built out of its visual and tactile components: it seems implausible that I should see roundness while experiencing no connection whatsoever to felt roundness. It would not be roundness that I saw, in that case. So, when I see roundness without feeling it at the same time, it doesn’t follow that my perceptual experience is not characterized, in part, by tactile perception. My visual experience of roundness is not, by contrast, affected by auditory phenomenal character. I don’t see roundness as the kind of thing that I could hear, but I do see it as the kind of thing that I could touch. O’Callaghan refers to this kind of experience as

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86   The Philosophy of Rhythm “cross-​modal perceptual completion.”31 He argues that this kind of perceptual experience has phenomenal character that no “pure” unimodal perceptual experience could have. Perceptual “completion” occurs when I have a perceptual experience as of a complete object, despite the fact that I can only see parts of it. It is usually characterized as an amodal process: a perceptual process that operates across sensory modalities, rather than within any particular one. Suppose I see a cat standing behind a picket fence. Parts of the cat are occluded by the slats of the fence. However, I see the cat’s body as continuing behind the fence; if the cat were to move and reveal itself to be just an assemblage of oblong cat-​parts held together invisibly in space, I would be taken aback. I perceptually experience the cat to continue behind the barrier; the currently invisible parts of the cat make a difference to the phenomenal character of my visual experience. My perceptual experience is of a “complete” cat, in other words, despite the partial nature of the visual stimulus. O’Callaghan suggests that “amodal” completion is not a perfect label here—​rather, this is a kind of intramodal (within vision) completion. Now, given that intramodal completion seems plausible, so too is cross-​modal completion, suggests O’Callaghan. Though I may only be having a visual experience of a ball, the character of my perceptual experience is affected—​or “completed,” in other words—​by its tangible, though currently untouched, features. Cases of cross-​modal completion are cases where “a perceptual experience generated by stimulating only one sensory system presents an object as something that bears features of another modality without presenting those hidden features.”32 Importantly, the phenomenal character of perceptual experience is affected by this cross-​modal completion. For example, a visible surface experienced as that of a solid object may differ phenomenologically from the visible surface experienced as holographic. The experience of beat, when I hear it but do not move along, is, I suggest, an instance of cross-​modal completion. I experience the beat as being the kind of thing that I could move to, just as I saw the ball as being the kind of thing that I could touch. This means that my auditory experience of the beat is vestibular-​and touch-​ involving, even when I am not moving, in the same way that my visual experience of a round ball is touch-​involving when I am not touching it. I claimed earlier that an experience of roundness that was not touch-​involving would not be an experience of roundness. So, too, I want to claim that an experience of beat that was not vestibular-​involving and touch-​involving would not be an experience of a beat. Even when I just hear it, content from my vestibular and tactile experience still plays a role in characterizing the experience. It completes the perceptual experience, just as the unseen parts of the cat complete that perceptual experience. This is how I see the roundness of a ball as something I can touch, and it is also how I hear a beat as something that I can move along to.

31 O’Callaghan, “Not All Perceptual Experience.”

32 O’Callaghan, “Not All Perceptual Experience,” 147.

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Hence, when I am moving to the beat, I experience intermodal feature binding between auditory and vestibular content, and thus my experience has movement-​ related content. When I am listening, but not moving, I do not experience occurrent intermodal feature binding—​but I  do experience cross-​modal completion between audition, tactile perception, and the vestibular system, which means that, even though I am not moving, my experience is affected by movement-​related phenomenal character. The distinction between the two kinds of movement-​related content is what we should expect, given the phenomenal contrast between cases where we move along to the beat, and cases where we feel the beat while remaining still. We can, therefore, account for a sense of movement in music—​albeit a basic one—​by considering the richness, often ignored by purely auditory conceptions of music, of the perceptual experience of a beat. And if we can account for the ultimate experience in terms of the perceptual content involved, the move to metaphorical perception begins to seem avoidable. Three objections should be deflected. The first targets the notion of cross-​modal completion. The completion that happens when I look at a ball, and see it as the kind of thing I could touch, might just be an instance of amodal completion, with no consequences for phenomenal character. That is, I might be having a unimodal visual experience of roundness, which may be better thought of as an amodal property (one not associated with any sense modality in particular). When I look at the ball, it could be that I have some expectations concerning tactile content, but that these expectations do not contribute any character to the visual experience. Hearing the beat, but not moving to it, might be analogous. I might be having a unimodal auditory experience of an amodal feature (the beat). I might also have some expectations concerning movement. But these “movement expectations” may not affect the character of my experience. However, I think that this fails to do justice to the character of the experience of listening to music. It seems elemental to the experience of beat that I frequently feel like I want to move along with it, and tap my toe to it; sometimes, I have to actively restrain myself from doing so (if I am in a concert hall, for instance). It seems to me that we really do have a movement-​involving phenomenal experience when we listen to music but remain immobile. We long to move to it. An account that appeals to expectations that have no consequences for phenomenal character seems somewhat wan. The second objection is the following: Why is vestibular experience, or tactile experience, “movement-​involving” in a way that auditory experience on its own is not? Even the barest auditory experience involves movement in the sense that it was caused by something moving—​specifically, the vibration of an object in a medium. Despite this “movement-​involvement,” auditory experience alone cannot account for the experience of musical movement, as everyone agrees. Why should the appeal to movement-​involvement be effective in the case of multimodal perceptual experience, then? The mere fact that tactile experience, or vestibular experience, is produced by something moving doesn’t prove anything, because auditory experience is produced in the same sort of way. But this is not quite right. Auditory

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88   The Philosophy of Rhythm experience involves movement in a causal way, certainly, but it does not necessarily involve movement-​related content. Notice that the perceptual experience of a sound is not an experience as of motion in the same way that touch, or vestibular experience, are experiences as of motion—​either of one’s own body, or of the environment in relation to one’s own body. One may enjoy genuine auditory experience without ever discovering that vibrating objects are at the ultimate source of one’s experience. Physicists had to conduct empirical investigations, after all, in order to figure out that sounds rely, for their existence, upon the usually invisible vibrations of objects. No scientific discovery is necessary for touch, or in the vestibular case. Movement is present in one’s vestibular experience, and in touch, in a way that it is not in auditory experience. It is unthinkable that one could have a tactile or vestibular experience that one did not already experience as involving movement. The third objection is as follows: My account of content from a given modality being “involved” in an experience in another modality is just metaphorical perception in disguise. I experience something heard as something I could also touch; so, I experience something seen as metaphorically touched, in a sense. This may be so; but if we allow this to count as an instance of metaphorical perception, then the floodgates are opened, and every experience of intermodal binding—​every experience of roundness, hardness, softness, roughness—​now involves the deployment of metaphor on the perceptual level. Perhaps the advocates of metaphorical perception would be happy to bite this bullet, but I suspect otherwise. Metaphorical perception is supposed to be reserved for a special subset of perceptual (often aesthetic) experiences, which are not explicable, it is thought, on ordinary accounts. If intermodal binding involves metaphorical perception, then nearly everything does; and this is, I think, an unpalatable prospect. Back to the experience of beat. I think that the idea that musical experience is movement-​involving, even when we are not moving, is what Scruton is alluding to when he describes musical engagement, as “involving a kind of latent dancing—​a sublimated desire to ‘move with’ the music.”33 Jerrold Levinson picks up on this comment of Scruton’s, speculatively suggesting that music may actually be, rather than merely involve, latent dancing.34 He does not, however, elaborate on this idea, merely noting its appeal. I hope to have been able to give some indication of what might lie behind this intuition, which is an attractive one for many philosophers of music; but more importantly, I hope to have shown that we do not need to appeal to imaginative capacity, or to metaphorical perception, in order to account for it. It is of course possible, or even likely, that a basic sense of stressed beats cannot fully account for the experience of musical movement. It could be that the kind of perceptual experience of musical movement that I have been discussing is not sufficiently detailed to capture musical movement in a more full-​fledged sense: tones moving in musical space, from high to low, speeding up and slowing down, and so

33 Scruton, Aesthetics of Music, 357.

34 Levinson, “Aesthetic Appreciation of Music.”

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Feeling the Beat  89

on. Metaphorical perception might, after all, be required to account for this richer sense of musical movement. And it might also be required, as Peacocke suggests, to explain musical expression. I am happy to concede this as a possibility. I merely want to highlight that we do not have to accept the initial “anti-​realist” claim, which makes the appeal to metaphorical perception seem inevitable in the case of movement. For, at least when it comes to beat, there is movement-​related content in my perceptual experience. I am having a bona fide perceptual experience as of movement, which is both heard and felt. It is not just that I really experience myself as moving, and by some kind of illusory imaginative transfer, the sound is heard as moving, too. Rather, the movement has a heard aspect, and also a felt one. I have been discussing the experience of “beat.” I am not making claims about the experience of rhythm more generally, about musical movement in a richer sense, or about the broad utility of appeals to metaphorical perception. Nevertheless, I am sounding the following note of caution: assuming that music is just a matter of sounds, and of auditory experience, risks making intellectualist accounts of musical experience seem inevitable, when they may not be.

5. Conclusion I began by outlining the distinction between rhythm and meter. I claimed that there is a component of the perceptual experience of music—​the “beat”—​that is attributable to meter. I argued that the experience of beat is multimodal: specifically, that when we “hear and feel” a beat, this experience is an instance of intermodal feature binding, where content in audition is bound to content in tactile and vestibular perception. I went on to suggest that a consideration of this multimodal content offers an alternative, perception-​based explanation of the experience of movement in a musical beat, which deflates the seeming necessity of an appeal to metaphorical perception. Beat experience is not exhausted by auditory experience; it also involves, I argued, vestibular and tactile experience, both of which give rise to movement-​involving perceptual content. This is true, I claimed, whether or not we are actively moving to the beat. Thus, our experience of movement in the “beat” is justified by the perceptual experience itself; the seeming necessity of an appeal to metaphorical perception is thus undermined. An “experience-​first” approach to music, which begins from a consideration of perceptual experience rather than sounds, has at least two consequences for the philosophy of music. First of all, it represents a continuation of the extant challenge, formulated by authors such as Aaron Ridley, Andy Hamilton, and Kathleen Higgins, to the view that music can be adequately theorized in isolation from the cultural, biological, and historical factors that have shaped it.35 The second is, however, more novel, insofar as it undermines the dominant assumption that music is fundamentally about sounds. I hope to have shown that rescuing rhythm and

35 Ridley, Philosophy of Music; Hamilton, Aesthetics and Music; Higgins, Music of our Lives.

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90   The Philosophy of Rhythm meter from the sidelines of the philosophy of music not only makes for a more representative characterization of music, but also challenges the validity of the “unimodal” manner in which music has heretofore been approached. Rhythm is not just a matter of sounds. It is not even just a matter of auditory experience. Aspects of musical experience—​central ones, at that—​are deeply multimodal. Considered in this light, music raises many questions for philosophers of perception, and the door is opened for music to feature prominently in debates beyond the confines of the philosophy of art.

Works Cited Boghossian, Paul, “Explaining Musical Experience,” in Kathleen Stock, ed., Philosophers on Music: Experience, Meaning, and Work (Oxford, 2007). Boghossian, Paul, “The Perception of Music:  Comments on Peacocke,” The British Journal of Aesthetics, 50.1 (2010), 71–​6. Hamilton, Andy, Aesthetics and Music (London, 2007). Hasty, Christopher F., Meter as Rhythm (Oxford, 1997). Higgins, Kathleen Marie, The Music of Our Lives (Philadelphia, 1991). Huang, Juan, Darik Gamble, Kristine Sarnlertsophon, Xiaoqin Wang, and Steven Hsiao, “Feeling Music: Integration of Auditory and Tactile Inputs in Musical Meter Perception,” PLoS ONE, 7.10 (2012). Levinson, Jerrold, “The Aesthetic Appreciation of Music,” The British Journal of Aesthetics, 49.4 (2009), 415–​25. London, Justin, Hearing in Time: Psychological Aspects of Musical Meter (Oxford, 2004). London, Justin, “Three Things Linguists Need to Know about Rhythm and Time in Music,” Empirical Musicology Review, 7.1–​2 (2012), 5–​11. Matthen, Mohan, “On the Diversity of Auditory Objects,” Review of Philosophy and Psychology, 1.1 (2010), 63–​9. O’Callaghan, Casey, “Intermodal Binding Awareness,” in David J. Bennett and Christopher S. Hill, eds, Sensory Integration and the Unity of Consciousness (Cambridge, 2014), 73–​104. O’Callaghan, Casey, “Not All Perceptual Experience is Modality Specific,” in Dustin Stokes, Mohan Matthen, and Stephen Biggs, eds, Perception and Its Modalities (Oxford, 2014), 133–​65. Peacocke, Christopher, “The Perception of Music: Sources of Significance,” The British Journal of Aesthetics, 49.3 (2009), 257–​75. Ridley, Aaron, The Philosophy of Music: Theme and Variations (Edinburgh, 2004). Scruton, Roger, The Aesthetic Understanding:  Essays in the Philosophy of Art and Culture (London, 1983). Scruton, Roger, The Aesthetics of Music (Oxford, 1997). Scruton, Roger, Understanding Music: Philosophy and Interpretation (London, 2009). Siegel, Susanna, The Contents of Visual Experience (Oxford, 2010). Thaut, Michael H., Rhythm, Music, and the Brain: Scientific Foundations and Clinical Applications (London, 2005). Trainor, Laurel J., Xiaoqing Gao, Jing-​jiang Lei, Karen Lehtovaara, and Laurence R. Harris, “The Primal Role of the Vestibular System in Determining Musical Rhythm,” Cortex, 45.1 (2009),  35–​43.

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5 Dance Rhythm Aili Bresnahan

1.  Introduction: The Difference between Natural and Intentional Rhythm Dance encompasses a large range of phenomena including social dance, concert dance, dance as therapy, education, or exercise, political dance, and religious dance. All forms of dance are considered art for the purposes of the discussion to follow, where art refers to any culturally developed and skilled activity. This chapter provides an account of intentional rhythm in dance (“dance rhythm”) where rhythm as it pertains to dance refers to a regular, repeated pattern of beats and emphases in movement.1 Rhythm is then divided into natural rhythm and intentional rhythm found in art. Dance rhythm (intentional rhythm that belongs to a dance that is part of its essential features) is thus distinguished from rhythm in dance (natural rhythm which is not part of a dance’s essence and which occurs due to the natural rhythms of the body). (For the remainder of this chapter these terms will be used according to the meanings provided here.) Natural rhythms include the rhythm of the tides, seasons, the pulse of a heartbeat, and the rhythms of sexual reproduction.2 Natural rhythm is given to us in the world or found to be there. It has not been developed by training and does not necessarily occur in the cultural world in which dance, music, and poetry are distinct practices, each with varying methods of teaching and performance. In the human person, natural rhythm means rhythm at the level of human biology, as Joseph Margolis argues, though he might not agree that what he calls an encultured human person can ever act at the biological level alone.3 Thus rhythm in dance captures the idea that a dance might have natural rhythm from a dancer’s breath or pulse, without this contributing to the dance’s distinctive features. Qua dancer, these do not count as dance rhythms unless they are focused on, or enhanced by, the thought process of an encultured person. This chapter takes its cue from John Dewey’s view of art as intentional transformation, and Margolis’ sense that this transformation is effected by the 1 Sheets-​Johnstone, “Man Has Always Danced,” provides an alternative account of rhythm in dance. 2 Dewey, Art as Experience,  153–​5. 3 Margolis, Historied Thought, Constructed World, 224. Aili Bresnahan, Dance Rhythm In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0006

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92   The Philosophy of Rhythm culture-​influenced self. Dewey considers a child learning to cry on purpose to get a parent’s attention. Since “the relation between doing and undergoing is perceived,” rather than merely a “blind” expression, “there is now art in incipiency.” Thus, he writes, An activity that was ‘natural’—​spontaneous and unintended—​is transformed because undertaken as a means to a consciously entertained consequence. Such transformation marks every deed of art.4

Dewey’s argument is that what makes the new kind of crying art is that it is performed with the agent’s awareness of its role in human intercourse. However, this chapter rejects the thoroughgoing “Intentionality” with a capital “I” that Margolis champions,5 where the actions of persons are understood primarily as those of cultural agents rather than as individuals. The transformation I argue for is a metaphysical one of the natural into the artistic, through awareness and purposes of the artist in a cultural context. It is thus more deeply rooted in artistic practice than Arthur Danto’s “transfiguration of the commonplace.”6 My account also differs from that of Susanne Langer, for whom the ordinary is transformed into art by the creation of symbolic forms of human feeling. By contrast, this chapter acknowledges that social dance involves transformative intentionality as well; dance rhythms occur in both high art dance and in other forms.7 Intentional rhythms are those created by human persons to develop, diversify, or attend to the range of natural rhythms, for purposes reflecting the particular genre of art. Though constructed or person-​made, room is allowed for intentional rhythms of proto-​persons in the animal kingdom. Natural, bodily rhythms are also transformed by dancers into ones serving artistic, social, or other purposes.8 When dance self-​consciously transforms ordinary movement, reflexively listening to, and responding to, natural bodily rhythms, it is showing something implicit, of which audience and dancers are not normally aware. The task dance of the Judson Dance Theater, where a performer came onstage, made and ate a sandwich and walked off, had the rhythm of eating and of walking—​not stylized, but part of the postmodern dance movement, seeking to eliminate the division between art and life. My claim is that the intention of focusing on sandwich-​making as dance transforms mere movement, and transforms natural rhythm into dance rhythm if the dance encourages focus on natural rhythm as dance rhythm. This is what I mean by intentionality—​pragmatism in philosophy, and the postmodern movement in art, has meant that appreciating ordinary experience can transform the natural elements of human life and experience into art. Art may transform an element of life

4 Dewey, Art as Experience, 65.

5 Margolis, Historied Thought, Constructed World, 194–​8, et passim; Bresnahan “Artistic Creativity.” 6 Danto, Transfiguration of the Commonplace. 7 Langer, Feeling and Form.

8 Bond, “Recurrence and Renewal,” 178.

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Dance Rhythm  93

into a unified and heightened experience (Dewey), in an enculturated world with culturally developed capabilities and practices (Margolis), or it may focus attention on the aesthetic value of the ordinary (Danto, and postmodernism). Thus the Judson Dance Theater dance performs no longer just the making of a sandwich and its movement should not be interpreted as such. Rhythms not there to be attended to are rhythm in dance, but not dance rhythm—​for instance, if the intended focus was the sandwich-​making rather than the rhythm of walking to the table. This account of dance rhythm is humanistic in holding that the human act of converting mere movement to dance transforms natural into intentional rhythm. Dance rhythm is thus similar but not identical to Andy Hamilton’s dynamic, humanistic sense of rhythm as “order-​in-​movement,” in which perceivable “accents are imposed on a sequence of regular sounds or movements.”9 The account presented in this chapter separates natural rhythm from intentional rhythm in order to isolate the underpinnings and connections between mere sound and mere movement before they have been transformed into music and dance. There is an organic connection between music and dance at sound and movement levels, and this would be overlooked if natural rhythm were not addressed. We now explore some of the rhythmical connections that exist between music and dance, highlighting the intentional–​natural rhythm distinction.

2.  Musical Connections As dance and music are intimately connected, it is often hard to tell whether there is a dance–​music synthesis, or the dance is following the music, or vice versa. This essay holds that, in all three cases, the type of rhythm is intentional insofar as it occurs in dance and music qua dance and music. Any types of natural rhythm that underlie the dance or music are contingent upon movement and sound, rather than upon movement transformed through human intentionality into dance, or sound similarly transformed into music. First, there are dance–​music syntheses and collaborations where the components are in tandem or in combined practice. To draw from Western traditions, dance occurs frequently with music, illustrated by baroque music and dance, or the waltz. Indeed, Western dance and music were originally integrated, their separation being a later development. Most dance scholars place the origin of Western dance in Ancient Greek rituals that integrated religion, theatre, and music.10 In non-​Western countries such as those in Latin America, dance and music also arose together. Dance–​music syntheses occur in social dance, competition, and in concert dance that emerged from social dance. Samba, tango, and salsa are all heavily intentional rhythm-​infused forms of dance embedded in a clear and identifiable musical style,

9 Hamilton, “Rhythm and Stasis,” 26–​7.

10 Jowitt, “Modernism: Modern Dance”; Hamilton, Aesthetics and Music.

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94   The Philosophy of Rhythm essential to their national cultures.11 In these dance–​music syntheses, rhythm is intentional rather than natural; dancers and musicians have integrated these artforms in a purposeful way. Second, dance is often set to music, and following the music can be an object. As in social dance, a dancer must dance on the beat, and the simplest kinds of dance to perform are to or with music that has a regular, metric, rhythmic pattern (as in a country square dance). Indeed, dancers often choose music that makes them want to dance, and often this is music that has an intentional, recognizable, and repeated structure of beats and emphases in sound. When dance follows this type of music it is certainly dance rhythm as defined above. Following the music is more difficult where complex rhythms, such as those by Igor Stravinsky, John Cage, or Anton Webern, are involved—​as in the choreography of Jiří Kylián who set Symphony of Psalms and Svadebka to Stravinsky, and Stepping Stones to Cage and Webern. Thus, dance that follows music can assist the audience to perceive the intentional rhythms of the music in an enhanced visual rather than auditory way, as well as to see the new dance rhythms that result. Some forms of dance interact with music. In African dance–​music syntheses or collaborations, for example, the master drummer is in charge of leading improvisations, influenced by feedback from the dancers.12 Thus, even when dance follows music, there may be a dynamic relationship. Again, this decision to follow a repeated pattern of beats and emphases is part of the intentionality that is inherent in dance rhythm. Finally, there are also dance–​music syntheses and collaborations, such as in jazz, where the band follows the chorus and tap dancers rather than the other way around.13 Some large, classical ballet companies expect orchestras to follow the dancers. This seems also to be true in the many cases where musicians serve as accompanists to the dancers in a supporting role. The vast majority of dance–​music syntheses and collaborations do feature intentional rhythm, and the idea of a dance–​music piece containing only natural rhythm, but no dance rhythm or music rhythm, strains credulity, especially because music rhythm, as mentioned earlier, may not require that the pattern of beats or emphases repeats. We leave the possibility of non-​musically rhythmic music for another occasion.

3.  Dance Rhythm Need Not Be Connected to Music Dance transforms internal bodily rhythms—​pulse, heartbeat, or breathing, or a natural walking pace—​into dance rhythms, in the way that Dewey and Margolis



11 Chasteen, National Rhythms, African Roots.

12 Malone, Steppin’ on the Blues,  14–​15. 13 Malone, Steppin’ on the Blues, 94ff.

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consider characteristic of art. It also uses natural rhythms such as those of the tides, falling leaves, snow, and rainfall, as in the Native American rain dances that simulate thunder, and the pounding of rain. Contemporary dance often focuses on internal bodily rhythms, developing them into dance movements understood viscerally and kinesthetically. Dance scholar Sondra Fraleigh notes that early twentieth-​century modern dance made much use of breath rhythm, notably through the teaching of Doris Humphrey.14 The rhythm of these natural breaths is transformed into art, into dance rhythm, by focusing on the rising and falling of one’s chest, and representing breaths in movement that encompasses other parts of the body. The regular pulse of a dancer’s resting heartbeat might be the impetus to begin a slow, steady movement that accelerates as she dances, possibly in syncopation with the body. A dancer might set a baseline with her feet that mirrors bodily pulse, and then counter it with the upper body. Likewise, a dancer might breathe in a certain way while still, then accelerate rhythmic movements as his breath quickens. Or they may keep the original rhythm of resting breath in their bodily movements even while their breathing rhythm changes. A dancer might also look for rhythmic inspiration in the ebb and flow of waves against the shore, moving in a pattern that represents the feeling of their movement with their arms and legs, perhaps rolling on the floor in the way the waves collect and roll energy and small stones and shells. Thus the dance might end up as a dance-​rhythmic variation on the natural rhythms of pulse or breath, or the movement of the waves and tides. Dance that focuses on natural or cosmic rhythms has been part of spiritual and religious practice in both Western and non-​Western cultures, and the whirling dance of the Sufi dervishes is a well-​known case in point. Havelock Ellis reports that early Christians danced as part of their religious practice.15 The Indian dance of the Siva seeks to align human dancing with that of the gods, in turn maintaining the movement of the cosmos.16 One might ask how a dancer can know or intuit the rhythm of the cosmos and the gods in order to align with them, but dance creation is often a mystical process. Planetary movement might be represented in a rhythmic 360-​degree rotation of torso, arms, head, and legs. In music and poetry too, transformation of internal bodily rhythms can create music rhythm and poetic rhythm. Music transforms the energy of waves and the sound they make when they break upon the shore. In poetry, the rhythm of speech might already have stops, starts, and breaks that are dependent upon and also transform the breaths people need to take to say a phrase. The same may be inferred for musicians who play wind instruments or who sing. Thus it may be that dance rhythm, music rhythm, and poetic rhythm are connected to similar internal bodily or natural rhythms. Dance rhythm is also caused by rhythm in music or poetry in the sense that it can follow or represent these rhythms.

14 Email communication to the author. 15 Ellis, “Art of Dancing,” 9.

16 Coomaraswamy, The Dance of Siva; Mathur, Cultural Rhythms, 9.

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96   The Philosophy of Rhythm In the early twentieth century, Émile Jaques-​Dalcroze promulgated the ideas that music relies on internal bodily rhythms, and that movement, gymnastics, and dance could help musicians to learn their own rhythms, rather than rely on external rhythms set by a music teacher or score.17 His movement training method for musicians was called “eurhythmics,” and it was used to develop both rhythmic ability and expressivity. First, a music student needed to register the rhythms of the human body.18 For a musician to reach the highest level of artistry, however, her body had to transform these rhythms into an expressive art even while maintaining a natural effect in their expression.19 Thus Jaques-​Dalcroze believed that musicians should experience their own natural bodily rhythm in order to create intentional rhythm in performance. These intentional rhythms, this chapter holds, thereby become music rhythms through intentional variegation and enhancement under the rules of the genre of music in which it takes place.20 Even if music and dance are connected at their originating root level of the natural, or of an earlier point in history where they were synthesized, they can develop and change enough from there throughout time to be relations rather than clones. In 1913, for example, Mary Wigman performed Hexentanz without music. Merce Cunningham was also known to rehearse his dancers without any music and then add the music later (even as late as the initial performance). He did this so that dancers would not dance to the music in the sense of following it.21 We may also turn to works of dance that occur in silence, such as Emanual Gat’s Silent Ballet. Indeed, dancers often create dances without music. Establishing that dance rhythm can occur without music is, of course, not yet to establish that dance can eschew intentional rhythm altogether. The next question to be addressed is whether there can be such a thing as dance without dance rhythm.

4.  Dance without Dance Rhythm This section claims that dance can lack dance rhythm if it fails to have intentional regular, repeated pattern of beats and emphases in movement, even though there is some unavoidable natural rhythm in the dance due to internal bodily rhythms. In Balkan and in Greek dancing, for example, some dances start with a long piece of instrumental music that has no identifiable beat and that is both slow and uneven enough metrically that the dance movement to it might be classed as non-​dance rhythmic. There might also be dance that follows funeral wailing that does not have a repeated, intentional dance-​rhythmic structure; likewise dance movement that followed free-​style poetry. This chapter is reliant on an account of dance rhythm



17

Jaques-​Dalcroze, Rhythm, Music and Education; and Eurhythmics, Art and Education. Jaques-​Dalcroze, Eurhythmics, Art and Education, 7, 183. 19 Jaques-​Dalcroze, Eurhythmics, Art and Education, 86. 20 Louppe, Poetics of Contemporary Dance, esp. 50 and 83. 21 Kostelanetz, ed., Merce Cunningham, provides more on Cunningham’s methods. 18

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that might diverge from an account of music rhythm or poetic rhythm through differences in understanding what “rhythm” refers to in music, poetry, and dance. It is possible, for example, that there might be rhythm in dance that is not only not dance rhythm, as this chapter understands it, but that uses music rhythm or poetry rhythm, in the sense that these disciplines understand rhythm. Another example of dance without intentional dance rhythm might be Steve Paxton’s contact improvisation, a form of creative contemporary dance with the primary aim of transferring energy and movement dynamics between dancers and developing new movements in concert. Contact improvisation requires no explicit adherence to a pattern of beats and is free enough to allow any participant to move however they please, in contact with another person. It is not clear that dances created in this way must be intentionally rhythmic. A dancer can create a movement with a primary purpose that includes avoiding intentional repeated pattern of beats or emphases. There would still be rhythms of dancers’ breath and walking, but these would be unintentional and incidental. Thus Lauri Stallings, in And All Directions I Come to You, aimed to interrogate how we associate with one another in public space in “a constant flow of intuition and place . . . by letting time happen to offer emancipatory moments and a gathering among strangers.” Intentional repeated patterns of beats were not a primary concern. Thus one can find dances that lack the sort of dance rhythm proposed by this chapter, in which rhythm is either changed in some way from its natural state or the primary purpose of the dance is to highlight its rhythmic nature. It follows that dance rhythm is not a necessary condition for dance writ large, although there may be rhythm in dance that is unavoidable due to dancers’ identity as both persons and biological organisms. In conclusion, the primary theory of rhythm advocated by this chapter is the concept of dance rhythm, a sort of rhythm that is not simply the rudimentary kind found in the processes of the natural world, the truth of which has been shown through the use of danceworld examples. Dance is a minded activity of the human person that has social, political, entertainment, and artistic human purposes, and that can and does involve the use of rhythm. There is no dance at the level of biology only, and no dance rhythm at that level. Neither must dance, qua dance, involve dance rhythm, since dance is a kind of activity that can, but that need not, include intentional, repeated patterns of beats or emphases in movement. Finally, dance exists that has contingent and non-​essential elements that may have natural rhythm as defined earlier. When it does this is merely rhythm in dance.

Works Cited Bond, Karen E., “Recurrence and Renewal: Enduring Themes in Children’s Dance,” in Thomas K. Hagood and Luke C. Kahlich, eds, Perspectives on Contemporary Dance History: Revisiting Impulse, 1950–​1970 (Youngstown, 2013), 161–​92. Bresnahan, Aili, “How Artistic Creativity is Possible for Cultural Agents,” in Dirk-​Martin Grube and Robert Sinclair, eds, Pragmatism, Metaphysics and Culture: Reflections on the Philosophy of Joseph Margolis (Helsinki, 2015), 197–​216.

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98   The Philosophy of Rhythm Chasteen, John C., National Rhythms, African Roots: The Deep History of Latin American Popular Dance (Albuquerque, 2004). Coomaraswamy, Ananda, The Dance of Siva: Fourteen Indian Essays (New York, 1918). Danto, Arthur C., Transfiguration of the Commonplace (Cambridge, MA, 1981). Dewey, John, Art as Experience ([1934]; New York, 2005). Ellis, Havelock, “The Art of Dancing” [1923], Salmagundi, 33–​4 (1976), 5–​22. Gat, Emanuel (chor.), Silent Ballet, dance performance, Emanuel Gat Dance, 2008. Hamilton, Andy, Aesthetics and Music (London, 2007). Hamilton, Andy, “Rhythm and Stasis:  A Major and Almost Entirely Neglected Philosophical Problem,” Proceedings of the Aristotelian Society, 111.1 (2011), 25–​42. Jaques-​Dalcroze, Émile, Eurhythmics, Art and Education, tr. Frederick Rothwell, ed. Cynthia Cox ([1930]; New York, 1980). Jaques-​Dalcroze, Émile, Rhythm, Music and Education, tr. Harold F. Rubinstein ([1920]; New York, 1921). Jowitt, Deborah, “Modernism:  Modern Dance,” in Michael Kelly, ed., The Encyclopedia of Aesthetics, vol. 4 (Oxford, 2014), 374–​8. Kostelanetz, Richard, ed., Merce Cunningham: Dancing in Space and Time (Chicago, 1992). Langer, Susanne K., Feeling and Form: A Theory of Art Developed from Philosophy in a New Key (New York, 1953). Louppe, Laurence, Poetics of Contemporary Dance, tr. Sally Gardner ([1997]; Alton, 2010). Malone, Jacqui, Steppin’ on the Blues:  The Visual Rhythms of African American Dance (Chicago, 1996). Margolis, Joseph, Historied Thought, Constructed World: A Conceptual Primer for the Turn of the Millennium (Berkeley, 1995). Mathur, Nita, Cultural Rhythms in Emotions, Narratives and Dance (New Delhi, 2002). Sheets-​Johnstone, Maxine, “Man Has Always Danced: Forays into the Origins of an Art Largely Forgotten by Philosophers,” Contemporary Aesthetics, 3 (2005): https://​contempaesthetics.org/​ newvolume/​pages/​article.php?articleID=273. Stallings, Lauri (chor.), And All Directions I Come to You, dance performance/​roaming installation, with glo at Creative Time, Drifting in Daylight event (New York, 2015): http://​www. lauristallings.org/​world-​premiere-​2015/​.

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6 The Life of Rhythm Dewey, Relational Perception, and the “Cumulative Effect” Garry L. Hagberg

Why does rhythm speak to us so deeply? Patterns of accented or percussive sound that move us are meaningful. Yet we are hard-​pressed to say what associations or connotations create that meaning. What is required is something more elemental than personal or idiosyncratic associations; it is something that gives rhythm’s universal power articulate voice. This chapter argues that at this level, John Dewey’s Art as Experience has some deep insights.1 Here, I will focus on their implications for jazz improvisation.

1.  The Reflection and Re-​Creation of Life’s Rhythms: Dewey and John Coltrane’s Quartet Dewey uncovers a reciprocal relation between the organism and its environment that it is represented by rhythm:2 Life itself consists of phases in which the organism falls out of step with the march of surrounding things and then recovers unison with it—​either through effort or by some happy chance . . . the recovery . . . is enriched by the state of disparity and resistance through which it has successfully passed. If the gap between organism and environment is too wide, the creature dies. If its activity is not enhanced by the temporary alienation, it merely subsists. Life grows when a temporary falling out is a transition to a more extensive balance of the energies of the organism with those of the conditions under which it lives. These biological commonplaces . . . reach to the roots of the esthetic in experience.3

1 Dewey, Art as Experience, discussed in Hagberg, “Dewey’s Pragmatic Aesthetics.” 2 The importance of the organism-​in-​environment model is recognized by recent music theorists, though with little reference to Dewey. Clarke, Ways of Listening, Chs 1 and 3, importantly proceeds from and develops the work of psychologist James Gibson in environmental terms. 3 Dewey, Art as Experience, 14. Garry L. Hagberg, The Life of Rhythm In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0007

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102   The Philosophy of Rhythm In this passage we see the ideas of (a) falling out of step with one’s surroundings, (b) recovering rhythmical congruity with it, (c) the value of the experience of incongruent disparity for enriching subsequent experience, and (d)  the growth of life as a result of a “more extensive balance” with surrounding conditions. These conditions may be anthropological as much as biological, but in describing the tensions and resolutions of an organism (or person) within an environment, they simultaneously describe “the roots of the esthetic”—​Dewey’s most fundamental insight about rhythm. For Dewey, the aesthetic involves not only a mimesis of nature, but is already in nature; art is one with its environment: The first characteristic of the environing world that makes possible the existence of artistic form is rhythm. There is rhythm in nature before poetry, painting, architecture and music exist. Were it not so, rhythm as an essential property of form would be merely superimposed upon material, not an operation through which material effects its own culmination in experience.4

Detailed examples will explain the importance of Dewey’s insight on rhythm. The classic performances of John Coltrane’s Quartet, with drummer Elvin Jones and bassist Jimmy Garrison, exemplify Dewey’s insight. Close listening reveals the plausibility of Dewey’s mimetic relation between rhythm and the biological and anthropological experience of living, of life itself. Recorded live at The Village Vanguard in New  York on November 3, 1961, Coltrane’s “Impressions” uses an AABA 32-​bar song-​form structure, probably derived from Miles Davis’ earlier modal piece “So What,” which Coltrane had been playing with Davis. I will focus on Jones’ complex interconnection with Garrison, as a sort of hyper-​intelligent rhythmic propulsion machine. The sense of propulsion is established from the first beat, giving the sense of stepping into a rapid-​fire 4/​4 rhythm that has already been running—​like the space beyond the borders of a photograph that one knows is there but is not technically visible, or like picking up a telephone and suddenly listening in on a rapid-​fire conversation. In this sense it suggests something that predates our presence to it—​the “surrounding conditions” that are the given state of affairs and to which, in Dewey’s sense, we must adjust. Through the fifteen minutes of this piece, this propulsion is never lost, and its end also seems to suggest continuity beyond its audible limit. But much happens within this uninterrupted propulsion that Dewey’s words describe. In the initial statement of the melody (0:01–​0:29), Jones and Garrison are in lock-​step through the AA, establishing the rhythmic ground or “surrounding conditions.” The listener has an embodied sense that we are, in Dewey’s sense, together. With the beat that begins the B section (0:16–​0:22), Garrison departs into a syncopated walking bass-​line, in opposition to Jones’ non-​syncopated propulsion. 4 Dewey, Art as Experience, 153.

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The Life of Rhythm  103

While it lasts only five seconds, it places the listener where Garrison is: Dewey’s “falling out of step with one’s surroundings.” Then, in the beats (0:20–​0:22) closing the B section leading up to the last A, Garrison returns to a walking 4/​4; he and the listener are “recovering unison” with the surrounding environment. In Dewey’s terms, the experience of being back in step in the final A generates an enriched sense of rightness—​not “mere return to a prior state.” Garrison’s syncopated move within that context is a “state of disparity and resistance” through which we have passed. There is a foundational level of felt, embodied, rhythm in the re-​stabilized context of the final A (0:22–​0:28). Note also Dewey’s image of “too wide” a “gap,” with the resultant fate: “the creature dies.” This performance sounds, as we say, alive.5 The rich content of Dewey’s metaphor comes from his account of the root of aesthetic experience.6 Even in the brief moment that Garrison syncopates his bass line against the surrounding rhythmic conditions, one senses the direct musical analogue to an immediate environmental threat: one is not sure Garrison will make it back. That sense of risk is then felt often throughout the performance. Dewey makes another observation of central importance: Here in germ are balance and harmony attained through rhythm. Equilibrium comes about not mechanically and inertly but out of, and because of, tension. There is in nature, even below the level of life, something more than mere flux and change. Form is arrived at whenever a stable, even though moving, equilibrium is reached. Changes interlock and sustain one another. Wherever there is this coherence there is endurance. Order is not imposed from without but is made out of the relations of harmonious interactions that energies bear to one another.7

“[N]‌ot mechanically and inertly,” as with drum machines. One might say:  inert or mechanical rhythm is not rhythm. Mere measured duration provides only the blank canvas upon which rhythm can be created. Dewey’s equilibrium—​a sense of rhythmic balance and harmony—​arises from tension and is resolved within a dynamic, or “moving” complex of interaction. Thus, when Garrison’s sudden change in the bass rhythm (3:10–​3:16) establishes tension—​displacing the emphasis away from the first beat of each measure—​Jones layers intricate cymbal patterns on top, acknowledging the ambiguity and subtly contributing to it, particularly at 3:13–​ 3:15. Yet he keeps the underlying rhythm intact, creating the effect of two rhythm patterns bifurcating but still internally related, guaranteeing their reunion. 5 The sense of life awakens in listeners a corresponding interest in the history of the piece in question: understanding of a musical performance follows the structure of understanding a person, as I  discuss in Hagberg, “Jazz Improvisation.” 6 Dewey sees rhythm’s significance in anthropological more than biological terms: “Thus, sooner or later, the anticipation of man in nature’s rhythms, a partnership much more intimate than is any observation of them for purposes of knowledge, induced him to impose rhythm on changes where they did not appear. The apportioned reed, the stretched string and taut skin rendered the measures of action conscious through song and dance” (Art as Experience, 154). 7 Dewey, Art as Experience, 13.

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104   The Philosophy of Rhythm The effect is like that of two trapeze artists separating within a context of rapid movement, and then—​as if in slow motion—​reuniting where the one safely catches the other (at 3:16), or where, as Dewey puts it, equilibrium comes about. As he says, this is not mere flux and change; there is sense here. Parallel to Coltrane’s solo, whose melodic motifs generate their own variations with a sense of logical entailment, Jones and Garrison here follow out what their improvised patterns entail. What we hear in this performance would not be possible with a drum machine in place of Jones; nor by overdubbing in a studio. One could produce a fifteen-​minute recording, and it would have these players playing, but it would never sound like the original, nor achieve its animate-​creature sense—​it would never be, as we say, live music. Creating something like a living thing, the tensions, resolutions, and further developments arise from within that interactive entity: “Order is not imposed from without but is made out of the relations of harmonious interactions that energies bear to one another.”8 Again, the illuminating connection is between (a) the live organism interacting in a dynamic environment in a way that yields survival-​enhancing regularities that constitute forms or patterns of rhythm in nature, and (b)  the parallel emergent forms and patterns in aesthetic experience that constitute forms of art-​work “life”: For only when an organism shares in the ordered relations of its environment does it secure the stability essential to living. And when the participation comes after a phase of disruption and conflict, it bears within itself the germs of a consummation akin to the esthetic.9

Jazz improvisers create a sort of parallel world that both reflects and enacts the tension-​resolution relations, the rhythm-​finding stabilizations, the separations, the life-​enhancing negotiated reunifications, and the preservation and continuity of sense and coherence within a world of motion. Hence we hear life in music of this kind, and respond to it as a kind of animated presence.10 Accomplished players work hard to create a mimetic reenactment of the organism’s life of which Dewey speaks: Since the artist cares in a peculiar way for the phase of experience in which union is achieved, he does not shun moments of resistance and tension. He rather cultivates them . . .11

8 Dewey, Art as Experience, 14 9 Dewey, Art as Experience, 14. 10 It is telling that accomplished musicians and listeners with sufficiently trained ears will wince if a piece such as Coltrane’s “Impressions” is unexpectedly switched off by someone not in the listening group; if power suddenly goes out at an outstanding live performance; or (worse) a power plug is deliberately pulled. This reaction does not take place when muzak is unplugged. 11 Dewey, Art as Experience, 14.

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The Life of Rhythm  105

Fleetingly and powerfully, at 3:36–​3:43 Garrison lifts his line out of its temporal frame, which movement would be for Dewey a fleeting reminder of one cause of the “death” of the “organism,” the falling apart of the performance. Jones’ snare drum follows, and comments, as though he divides and reunifies.12 Just past three-​ quarters into this performance, Jones continues to play with so much overlayering of rhythmic commentary on the underlying pulse that one is not sure which is primary, yet the experience remains coherent. The effect is powerfully amplified by Garrison’s mix of bass pedals, syncopation, downbeat displacement, his moves into very high registers, and integrated returns with the walking bass. As Dewey writes, All interactions that effect stability and order in the whirling flux of change are rhythms. There is ebb and flow, systole and diastole; ordered change. The latter moves within bounds.13

Dewey rightly asserts the indissoluble union of (a)  human action within a bounded creative structure, where that action incorporates all the elements of tension, reunion, achieved enrichment, stabilization, destabilization, and restabilization, (b)  the embodied feeling of performing or comprehendingly experiencing such performances, and (c) the deep, engaging human meaning of such events: Contrast of lack and fullness, of struggle and achievement, of adjustment after consummated irregularity, form the drama in which action, feeling, and meaning are one.14

2.  Dewey, Rhythm, and Relational Perception Dewey sees rhythm in the world, in our interaction with and experience of the world, and as a foundational element in the arts, where worldly rhythms are depicted, or enacted.15 But his account requires amplification. It is a central tenet of American pragmatism, deriving from the work of William James and C. S. Peirce and developed by Dewey, that an empiricist-​based ontology gives relations between

12 Hagberg, “Dewey’s Pragmatic Aesthetics,” develops this point. 13 Dewey, Art as Experience, 15. 14 Dewey, Art as Experience, 15. 15 To comprehend Dewey’s vision of the pervasiveness of rhythmic patterns, one needs to recognize its scope from the astronomical to the microscopic: “The existence of a multitude of illustrations of rhythm in nature is a familiar fact. Oft cited are the ebb and flow of tides, the cycle of lunar changes, the pulses in the flow of blood, the anabolism and catabolism of all living processes. [But] every uniformity and regularity of change in nature is a rhythm . . . The very conceptions of molecule, atom, and electron arise out of the need of formulating lesser and subtler rhythms that are discovered” (Art as Experience, 155).

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106   The Philosophy of Rhythm things insufficient weight. Traditional empiricists hold that we perceive the stable solid object first, and only subsequently place it in a relational configuration. Pragmatists respond that this introduces a prismatic distortion in our perception and thought about the world. Relationally situated perception is central to Dewey’s understanding of rhythm, and of aesthetic experience: The Empire State Building may be recognized by itself. But when it is seen pictorially it is seen as a related part of a perceptually organized whole. Its values, its qualities as seen, are modified by the other parts of the whole scene, and in turn these modify the value, as perceived, of every other part of the whole. There is now form in the artistic sense.16

The fact of rhythm requires this mode of relationally situated perception. Its perception is “relationally constituted”—​a rhythmic pattern is not perceivable as single-​ slice sonic events added together.17 To understand Dewey’s fundamental insight more fully, it is necessary to grasp his conception of the live organism’s perception of form, as manifested in a visual composition, a streetscape, a painting, a set of sculptures within a curated exhibition, or the environmental setting within which we as responsive and interacting organisms act. For Dewey, this form is in essence a kind of rhythm. His “form in the artistic sense” is thus intrinsically rhythmic. Rhythmic form is (1) in the arrangement of the world; (2) in our perception or dynamic (each shifting and evolving combination modifying every other part through our interactive perception) interaction with that world; (3) in the arrangement and compositional organization of art; and (4) in our dynamic and interactive perception of that art.18 It moves toward its own internally generated fulfillment:19 form is not found exclusively in objects labeled works of art. Wherever perception has not been blunted and perverted, there is an inevitable tendency to arrange events and objects with reference to the demands of complete and unified perception.20

16 Dewey, Art as Experience, 141. 17 Simons, “The Ontology of Rhythm,” Ch. 3 in this book, discusses the need for recognizable repetition with a process (Section 3), and “the dependent nature of rhythm,” where he rightly says, “There is no such thing as a bare rhythm, on its own and subsisting independently of anything else. A rhythm is always the rhythm of some complex of sounds in a relationship” (Section 10). 18 Mondrian’s “Broadway Boogie-​Woogie” (1943) is a work of visual art that houses, in its content and in its titular significance, all four of these elements at once. 19 There are many examples of such internally generated fulfillment in jazz. Berliner, Thinking in Jazz, describes Dizzy Gillespie’s comment on an Art Blakey press roll as “likening its suspension in time to the effect of stretching a huge rubber band . . . the soloist feels the increasing tension of the mesmerizing press roll, until its eventual release rearticulates the piece’s rhythmic structure with so emphatic an accent” that—​now in Gillespie’s words—​“the world knows that that’s where the beat is” (329). 20 Dewey, Art as Experience, 137.

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The Life of Rhythm  107

3.  Dewey’s “Cumulative Effect” and Wayne Shorter’s Quartet Dewey refers to “a progressive massing of values, a cumulative effect,” emphasizing that this “cannot exist without conservation of the import of what has gone before.”21 This is evident in a live version of Wayne Shorter’s classic composition “Footprints” performed by his “Footprints Quartet.”22 It begins with a compression of the import of the piece. In 34 seconds at rapid tempo (faster and thus more compressed than any standard performance) we are given the entire head of the piece. Shorter’s compressed statement of the head is a restatement in fleeting microcosm of the import of what has gone before. The meaning of this rhythmic compression is a recapitulation, and for an experienced listener a re-​minding of Shorter’s own earlier performances, giving a sense of retrospection, reduced to maximal-​density essence. Dewey’s position aptly characterizes a further feature:  Shorter’s piece begins with a four-​measure solo soprano saxophone statement of the first section of the composed melody, with the rhythm section coming in at bar five, at which point Shorter improvises rapid melodic-​rhythmic motifs until he states the full head (from 0:16). So the whole piece is implied by its part without being entirely sounded (this is musical synecdoche), but now we have “movement toward a consummating close,” enabled by the “massing of values” that, as Dewey says, anticipates a resolution. Finishing the fragment-​statement of the head, the quartet as an organic entity seems to exhale fully (0:11–​0:14), with up-​tempo rhythmic definition suddenly dropping out. They resume propulsion by 0:15, to powerful effect, thus creating extreme suspense in Dewey’s sense, and an almost nervous anticipation of resolution. Listeners may well wonder how a coherent resolution is even possible. But then Dewey’s most fundamental point is that experience of rhythmic meaning is relational, and not the product of adding isolated fragments. Our aesthetic attention is a long form of mutually interacting sinews. With the improvised musical work as a metaphorical organism, accumulation is perceived also as preparation. At the early stage of this quartet’s performance, within the dense backward-​ looking recapitulation, we hear motifs that anticipate what is to come. This is the preserved coherence of which Dewey spoke: the ensemble maintains that delicate integration at the precipice of what he called a ruinous “arrest” and “break.” Just after the head, one hears what one assumes is the start of a piano solo, but the expectation is bent to the point of breaking.23 Shorter enters with brief fragments, 21 Dewey, Art as Experience. 22 Shorter, “Footprints.” Hagberg, “The Ensemble as Plural Subject,” discusses more fully the special kind of ensemble interaction taking place here. 23 Dewey observes that “breaking” in his sense can easily be falsely perceived in work that is new, highly original, or groundbreaking, and that it can take the proper preparation of the perceiver to make the coherence audible. This happened when jazz as high art emerged from what was primarily dance music, and drummers began using what they called “broken time”: “It takes time to discern whether the shock is caused by inherent breaks in the organization of the object, or by lack of preparation in the perceiver” (Dewey, Art as Experience, 175).

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108   The Philosophy of Rhythm drawn from the composed melody, and from the pianist’s improvisation. They propel forward—​accumulation and preparation on the edge, with moments of relative consummation. Toward the end of the most animated rhythmic motifs between saxophone and piano, a moment of repose (2:08–​2:15) seems to return to the relaxed tempo of the earlier recordings of the piece, and the bass instantly sounds the conventional vamp underlying these performances (2:12–​2:15). But bass and drums fragment the vamp into parts to sequence them as semi-​repeated rhythmic figures. Then, at 2:48–​2:53, drums establish a figure that inaugurates a new atmosphere, to which all players respond. There is an anticipation of how they will find their way out: a reminder of walking-​bass jazz inserted (3:35–​3:39)—​resumed strongly at 4:22–​4:27—​and a moment later (3:57) the bass and drum vamp resurfaces fully. A two-​chord vamp emerges (a ii-​V followed by a ii-​V a whole step down, from 4:49 to 6:38), which sounds almost too superficially pleasant.24 But complex intricacy and improvised challenges supervene, and an “internal tension” prevents “a fluid rush to a straightaway mark.” On listening closely, one appreciates Dewey’s claim: “The existence of resistance defines the place of intelligence in the production of a work of fine art.”25 Following a gradual ritardando and decrescendo, the piece closes with a poetic reverie. To “bring about the proper reciprocal adaptation of parts” here, a listener must realize that this final passage is a final evolution of the ensemble texture of the performance. The culminating two notes are in the bass—​the same notes as the conventional bass vamp introduction. Long preparation led to this culmination, which also suggests a new beginning. The perceiver, for Dewey, is indispensably making sense. And so, both player and listener are indeed very much like the live organism interacting within its environment. That sense is, for Dewey, fundamentally rhythmic. Here he summarizes what is indispensable in understanding rhythm’s power: Because rhythm is a universal scheme of existence, underlying all realization of order in change, it pervades all the arts, literary, musical, plastic and architectural, as well as the dance . . . Underneath the rhythm of every art and of every work of art there lies, as a substratum in the depths of the subconscious, the basic pattern of the relations of the live creature to the environment. It is not, therefore, just because of the systole and diastole in the coursing of the blood, or alternate inspiration and exhalation in breathing, the swing of the legs and arms in locomotion . . . that man delights in rhythmic portrayals and presentations  .  .  . ultimately the delight springs from the fact that such things are instances of the relationships that determine the course of life, natural and achieved. The supposition that the interest in rhythm which dominates the fine

24 Dewey writes: “The live creature demands order in his living but he also demands novelty. Confusion is displeasing but so is ennui” (Art as Experience, 167). 25 Dewey, Art as Experience, 138.

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The Life of Rhythm  109 arts can be explained simply on the basis of rhythmic processes in the living body is but another case of the separation of organism from environment.26

Works Cited Berliner, Paul F., Thinking in Jazz: The Infinite Art of Improvisation (Chicago, 1994). Clarke, Eric, Ways of Listening:  An Ecological Approach to the Perception of Musical Meaning (Oxford, 2005). Clarke, Eric, “Music Perception and Music Consciousness,” in David Clarke and Eric Clarke, eds, Music and Consciousness: Philosophical, Psychological, and Cultural Perspectives (Oxford, 2011), 193–​213. Coltrane, John, Impressions, audio recording (New York, 1963). Dewey, John, Art as Experience ([1934]; New York, 1980). Hagberg, Garry L., “Jazz Improvisation and Ethical Interaction: A Sketch of the Connections,” in Garry Hagberg, ed., Art and Ethical Criticism (Oxford, 2008), 259–​85. Hagberg, Garry L., “Dewey’s Pragmatic Aesthetics:  The Contours of Experience,” in Alan Malachowski, ed., The Cambridge Companion to Pragmatism (Cambridge, 2013), 272–​99. Hagberg, Garry L., “The Ensemble as Plural Subject: Jazz Improvisation, Collective Intention, and Group Agency,” in Eric F. Clarke and Mark Doffman, ed., Distributed Creativity: Collaboration and Improvisation in Contemporary Music (Oxford, 2016), Chapter 13. Mondrian, Piet, “Broadway Boogie-​ Woogie” (1943), oil painting, New  York, Museum of Modern Art. Shorter, Wayne, “Footprints,” Track 6, Footprints Live!, audio recording (Universal City, CA, 2002). Simons, Peter, “The Ontology of Rhythm,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C3.

26 Dewey, Art as Experience. Dewey’s opposition to the theoretical separation of the organism from its environment prefigures recent discussions of externalism in philosophy of mind. The embodied nature of rhythm as experienced in music, along with our Deweyan direct perception of rhythm in nature, presents a case in which the boundaries of selfhood as traditionally conceived are questioned: Clarke, “Music Perception.”

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7 Rhythm, Preceding Its Abstraction Deniz Peters

Discussions of musical rhythm often begin after an abstraction of its auditory, tactile, and temporal feel has taken place. This common process of abstraction turns rhythmic phenomena into a crystallized gestalt. Thus, thought on rhythm usually begins where the phenomenon of rhythm itself ends—​at the point where it turns into a representation, at the fringes of its experience. Rhythm as the product of analysis is carved out by intellect and fixated into sequences of long and short durations of material and their orderings and groupings. Likewise, notated durations as we know them in Western classical compositional and interpretational practice are already congealed into symbols, frozen into images, broken up into units. Temporal experience and its cohesion have at these stages become curiously attenuated, obscured, and fragmented—​at the periphery of where rhythm resides. Chris Hasty’s finely worked-​ out distinction, in this book, between two understandings of rhythm is driven, I think, by the same concern to avoid this hypostasis.1 What Hasty calls “an . . . order (of isochronous division or of fixed pattern)” is what I refer to as the end product of an abstraction and intellectual carving out. What, in turn, Hasty calls “flow . . . as . . . the active and characterful creation of things or events,” bringing the “subjective, idiosyncratic, and evanescent” sense of rhythm, is one way of describing rhythm at the level of experience. What’s more, Hasty’s call for a reversal of value to promote performance and to question the power of form as timeless agents of perpetual identity, with his distinction between fixed, abstract rhythm (R2), and its living origin, flow (R1), heads into the same direction as my call for a revaluation of our experiential knowledge about rhythm. In this chapter, I offer an alternative approach to the understanding of musical rhythm, not dissimilar from Hasty’s, by beginning non-​reductively where rhythm centrally resides: in doings and happenings, in our bodies and between each other. Andy Hamilton is one of the few authors to have done essential work in this regard, along with the other authors cited in this chapter.2 I claim that rhythm is an 1 See Chapter 15, “Complexity and Passage: Experimenting with Poetic Rhythm.” 2 Hamilton, “Rhythm and Stasis,” develops a projective account of rhythm, in which experiences of the rhythmicity of human behavior are, on the one hand, present in musical performance, and, on the other, imaginatively projected upon it. Hamilton qualifies his account as dynamic, with its essential recourse to human movement, and how the rhythm literally moves (37–​41), as an essentially embodied phenomenon; and as humanistic, in contrast to abstracting accounts that treat rhythm as “essentially a pattern of possibly unstressed sounds and silences” (36). Deniz Peters, Rhythm, Preceding Its Abstraction In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0008

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experiential phenomenon that is manifested when we attend to sound, movement, and action felt or seen, or to other perceptions and self-​perceptions, like feelings of pain, or pleasure. Lived rhythm, unlike conceptualized rhythm, exists where empathy unfolds as one makes or hears sounds made by someone else. Even silence can brim with our continued attention. In it, we may find ourselves living through the qualities of the sounds made in its vicinity. The current chapter is motivated by experiences of playing with various improvisers in duos and trios in recent years. Because the performances took place within the framework of a research project, I consciously took note of these experiences, which might otherwise have passed by as moments of superb correspondence, or simply as musical curiosities. We achieved a noteworthy series of improvisations in the sense of a shared, corporeal sense of time and temporal composition, epitomized during my work with Berlin-​based alto and baritone saxophonist Simon Rose.3 In one of these pieces, the first track on the recording (titled between, part 1), Rose and I approach a very slow shared pulse within the events progressing from the initial material—​a single, long-​held six-​note middle register piano cluster, played mf, with an emphasis on the Bb, followed by a sustained, internally varied multiphonic on Bb by Rose. The setting was exploratory and unpremeditated, although we analyzed our experience and observations after playing and before entering the next set of improvisations, which primed the subsequent playing. After initially playing the sounds separately (piano cluster, sax multiphonic, piano cluster), next came a combination of the two sounds, melting into a single sustained unit, twenty-​six seconds after the very first piano cluster. We returned to the combined single action about twenty-​three seconds onwards. There is much to say about how we composed a piece of nearly seven minutes out of these very sparse initial elements, adding only a handful of other elements in due course. For the current purpose, however, it is the timespan of twenty-​three seconds that is particularly noteworthy. That span reappears throughout the piece—​ immediately after the first instances, but also on various occasions throughout, even in the final two sonic instances with which the piece ends. Although the piece is one of unmetered, “floating” time—​no counting is involved, no sections establishing metric subdivisions—​what is striking is that we spontaneously found a shared sense of time at a level of very slow pulsation. The most likely explanation for this temporal orientation is breathing. A slow exhalation (literally present as causing and driving the sax multiphonic), followed by a correspondently quiet inhalation, plus a phase of holding the breath, might take this long. A very slow body rotation, or a combination of upper body retraction and extension could also take this duration. Here, any further rhythmic structure within the piece seems closely—​and organically—​related to the shared pulse that seems equivalent in length to a deeply relaxed breathing cycle. The piece, between, part 1, is a concrete example of how

3 Peters and Rose, Edith’s Problem.

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112   The Philosophy of Rhythm musicians enter rhythm from bodily durations, prior to any intellectual or symbolic abstraction from the psychological experience of those durations. The line of thought I develop stems from a number of related observations concerning how rhythm comes into being via interpersonal and self-​attention, which I summarize in the following seven propositions. (1) Duration can be something we live through, creating it through our embodied existence, and it is therefore expressive; (2) in listening, we sense or imagine a “doing,” the presence of which forms itself differently depending on the somatic or intellectual orientation and depth of our interpretation that is part of active perception; (3) rhythmicity forms in direct relation to interpersonal attention which shifts between self and other (embodied or imagined), an attention that drifts loosely and gradually between the extremes of utter concentration and complete detachment; (4) the qualitative experience of rhythm, and the process in which it establishes itself or vanishes, also depends on the kind of music making and listening engaged in (improvisation, composition, rehearsal, performance, first or repeated listening); (5) there seems to be a striking correlation between sonic togetherness—​when two players’ individual temporal senses fuse into one—​and somatic togetherness, a jointly felt long-​range pulsation; (6) rhythmicity spreads over various levels of detail, order, and scopes, as we indulge in feats of attention; (7) musical silence is not a void. I shall now analyze these seven observations.

1.  No body, no rhythm Rhythm is not simply duration, it is duration made. Durations and proportions can be abstracted into numerical values; but the result cuts out the sense of immediacy with which rhythm is shared between one person and another, or between a natural event and an observer, or between a musical event and a listener. With the sense of immediacy being lost, common reflections on rhythm face the challenge of deducing rhythmic immediacy from an intellectual response to rhythmic phenomena. Acknowledging that musical rhythm arises through our embodied existence in a space and on an instrument, it is instantly clear that durations are one with their bodily making—​including resonant bodies—​and that relations between durations are temporal and spatial relations between bodily acts and undergoings. Connected to this, and also an aspect of rhythm, is the expressivity of duration. A long-​held note at the top of a climactic vocal gesture in a performance of Fado,4 for example, is not merely a long note. It is upheld, sustained by the fervor of an emotional disclosure, of, for instance, despair, rebelliousness, or hope. Not only is the note’s tone one of despair, for example, but its extent is too; were it shorter, it would not be as despairing, rebellious, or hopeful (which is not to imply a direct 4 To give but one example: instances abound in a performance of “Alfama” by Carminho at Podium Mozaiek in Amsterdam, 2011. See https://​www.youtube.com/​watch?v=h8YfA7FL05M.

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relationship between length of tone and intensity of despair). Thus durational expressivity arises not only from one duration’s numeric difference to another, but from a note’s realization by the body for this length. As it is made bodily, duration can be adverbially expressive, to use Peter Goldie’s felicitous concept.5 It is the despair, the rebelliousness, or the hopefulness with which it is sung—​in Goldie’s sense, colored in by an emotion from a different context—​that give the note its tone and its length. Again, this is not to be understood in the sense of an isomorphic relation between duration and expressive content, but, when we do hear rebelliousness in a note, we hear it, in part, in its duration. Duration bears emotional expressivity despite the opacity of the intentional object of the singer’s emotion. By the music alone, without text or dramatic context, we do not know the despair, rebelliousness, or hope. Due to this opacity, and since duration encompasses bodily resonances that extend human instrumental actions, there is an additional aspect to the making of duration involving the imagination, to which I turn next.

2.  Perceptual enactment, attention, and hermeneutical models Just as duration is achieved through the body when making music, it is also enacted in imagination as part of perception when listening to music—​even when evoking it in one’s “inner ear.” There are two complementary aspects of this enactment; neither is necessarily conscious, but each can be focused on consciously and distinctly. One aspect is that of cognitive attending, the other that of bodily attending. On listening to a passage of minimalist music, for example, an accented note may come to my attention, and I may notice that I am briefly turning my attention to it, catching myself in the act of attending, sustained perhaps only for the duration of this very accented note. This would be conscious cognitive attending. Or, as I hear the accented sound, I may become aware of a short tensing around the stomach or a brief fluctuation in the solar plexus area, a trace of a movement in the larynx. This is conscious bodily attending. Such bodily attending can occur even with imagined music, as when imagining an intense beginning of an emphatic gesture. In attending I might also make a small or extended physical movement, involuntarily or intentionally, but this is yet another matter. Roland Barthes, in one of his inspired music-​related essays, reveals his bodily attending: In Schumann’s Kreisleriana (Opus 16; 1838), I actually hear no note, no theme, no contour, no grammar, no meaning . . . No, what I hear are blows: I hear what beats in the body, what beats the body, or better: I hear this body that beats.6 5 Goldie, The Emotions,  133–​4. 6 Barthes, “Rasch,” 299.

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114   The Philosophy of Rhythm In stark contrast to the intellectuality of grammar or meaning, the “blows” Barthes describes are somatically present to him as listener. With this, Barthes captures the interpersonal goings-​on in musical experience, since, clearly, someone is inflicting these blows. Who is this someone? Barthes refers to three beating bodies. One is Schumann’s: Here is how I hear Schumann’s body (indeed, he had a body, and what a body! His body was what he had most of all) . . .7

This is, of course, an imaginary body: Schumann’s body as imagined by Barthes through his musical experience of its creative agency, and expressivity, located most of all, for Barthes, at points of accent.8 Barthes points out that The beat—​corporal and musical—​must never be the sign of a sign: the accent is not expressive.9

This does not contradict the rhythmic expressivity I argued for in Section 1 (No Body, No Rhythm), as Barthes refers to linguistic expressivity. His word for the somatic expressivity I refer to is enunciation: What does the body do when it enunciates (musically)? And Schumann answers: my body strikes, my body collects itself, it explodes, it divides, it pricks, . . . it stretches out, it weaves . . .10

The second body Barthes considers is the performer’s: The beats are played too timidly; the body which takes possession of them is almost always a mediocre body, trained, streamlined by years of Conservatory or career, or more simply by the interpreter’s insignificance, his indifference.11

For Barthes, the interpretive tradition represses Schumann’s body as he envisages it. He carefully gauges his emphasis on physicality: “the body must pound—​not the pianist.”12 Yet Barthes also refers to a third body that is indeed literal—​the listener’s very real body:



7 Barthes, “Rasch,” 299. 8 Barthes, “Rasch,” 303. 9 Barthes, “Rasch,” 303.

10 Barthes, “Rasch,” 305–​6. 11 Barthes, “Rasch,” 303. 12 Barthes, “Rasch,” 303.

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Rhythm, Preceding Its Abstraction  115 It is not a matter of beating fists against the door, in the presumed manner of fate. What is required is that it beat inside the body, against the temple, in the sex, in the belly, against the skin from the inside, at the level of . . . “the heart.”13

Barthes coalesces these three bodies in the unified experience of the “Schumannian” body: There is a site of the musical text where every distinction between composer, interpreter, and auditor is abolished.14

That bodily site—​given through bodily attending—​is thus marked by an interpersonal dynamic. Barthes’ description of the somatic dimension of his listening experience shows that the rhythmicity of musical events can be literally felt by a listener. At its somatically most pronounced, then, rhythm can be felt as an event of the order of bodily contact and presence. For this to eventuate, the listener would have to be encultured to or else have acquired an openness to a bodily hermeneutic, as Barthes clearly has. Not all hermeneutic stances are like this of course. For instance, Martha Nussbaum’s exquisite, dreamlike evocation of musical experience is far removed from throbbing or voluptuous bodily experience.15 Likewise, Eduard Hanslick’s hermeneutic of the acousmatically moving forms of music, shifts, if taken to the extreme of many of his interpreters, into a visual, touchless frame.16 Rhythm, if listened to under Barthes’ bodily hermeneutic, is a felt encounter with the world’s vitality, an encounter which can be enjoyed or abhorred at this very level of bodily experience, and an encounter which may have the gripping immediacy of a physical interpersonal encounter.

3.  Mobility of attention In the process of listening to music our attention isn’t fixed; it travels. We are not fully in control of the way our attention moves, yet, since we may direct it, it is not entirely involuntary either.17 As our attention lingers, shifts, or is suspended, we do not simply follow or react to predetermined musical events that call for or compel our attention; we also half create the musical events we perceive by anticipating specific sonic qualities, or by finding them noteworthy. This partly bound, partly free, changing, retaining, and retreating of attention marks the perceptual process. As our attention zigzags across certain detail through the full spectral complexity

13 Barthes, “Rasch,” 302. 14 Barthes, “Rasch,” 303. 15 Nussbaum, Upheavals of Thought, 265–​71. 16 Hanslick, On the Musically Beautiful. 17 Our attention can either be drawn toward something, like a specifically articulated sound; or, in listening out for something, we can turn our attention toward it, like a particular detail within a texture.

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116   The Philosophy of Rhythm of the heard; as it narrows and widens, zooming in and out of textures; and as it oscillates between following distinct gestalt features and drifting, it moves, falls apart, reassembles. One must also distinguish between widened attention, e.g., of a polyphonic texture in its entirety, and peripheral attention, e.g., vaguely perceiving some sonic occurrence, a particular melodic line, say, or a particular sonority within a texture, though this is outside the main focus. The ability to distinguish individual strands of events from other sonic events, involving the very ability to discern subtle coherence, depends on skill and on the chosen, or simply habitual, mode of listening. Attention forms the entry to such discernment. I can attend to something unfathomable without discerning it, without relating it to its context and noticing its distinctness; but I cannot discern something without attending to it, since I cannot notice anything specific about something I fail to notice per se.18 As attention travels between the voluntary, self-​induced, and the involuntary, other-​induced, it travels toward and away from the other as manifest in the instrument, the performing actions, and the personalities (real and imagined) unifying those actions. The perceived “overall” rhythmicity which arises from these interpersonal attentional meanderings is co-​constituted. Performer and listener form a duo,19 in which durations are lived, and out of which the listener’s sense of time spontaneously ensues. A listener might at first not be aware of any regularity within attentional movements between a convolution of lived durations. Musical time at this point—​remote from analyzed durational patterns—​is fluid and flexible. The way in which a rubato stretches and condenses time sequentially or even between different textural parts evinces this primordial flexibility of temporal perception. During the course of listening, and as our awareness of timbral and gestural coherence grows, our sense of the agency and situatedness of durations as thing made grows too, combining composed, performed and (somatically) imagined agencies, substantially contributing to the rhythmicity we perceive. Time, in this view, is generated from social interaction, paralleling Norbert Elias’ striking conception of social time.20 A heard vitality in music thus bears witness to this dialogical enactment of time which clings to the emergent rhythmicity of interpersonally marked and created musical events. Some music can, however, counteract this vitality and enforce a rigid sense of time or remove it altogether. Such music may, at the extreme, be heard as “cold,” “dead,” or as transcending time, like Scriabin’s Prelude, Op. 74, No. 2. 18 I discuss a special case of remembering and backtracking what one has formerly failed to notice below, in Section 6. 19 Schütz, “Making Music Together,” 172. 20 Elias, Essay on Time, argues against a reified conceptualization of time (as found in naturalistic positions), understanding time instead as a symbol for a “socially learned synthesis” (24). His “synthesis” signifies the cognitive combination of various perceived processes, in which one (e.g. the ebb and swell of the tide or the coming and going of sun and moon) forms a reference to the other. Timing, as referencing between “socially standardised continua of changes” (39), is a socially acquired skill and actually orients and historically (and culturally) alters, Elias argues, human experience of time. In the view I unfold in this chapter, joint rhythm-​ making is an instance of the shared creation of timing in Elias’s sense.

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4.  Experiential variance One can encounter rhythm from different stances or as part of distinct activities, and rhythm appears differently from within these. As an improviser, my experience of generating rhythm is unlike that of a listener, in that I am free to vary durations as I live through them. It is also unlike that of a performer who is beginning to encounter an unknown score. It can, however, be compared to the experience of a performer who is performing an intimately familiar work, the interpretation of which she has raised to an artistic level by synthesizing the individually notated units back into a balanced and plastically shaped, refined, gripping and telling musical whole. In duo improvisation, rhythm has a different role, and experiential character, than solo playing. And in listening to a performance more than once, particularly when listening to a recording, rhythm reveals itself in various guises and stages, as discussed in Section 3, on the continuum between liminal and utterly distinct awareness.

5.  Pulsation, togetherness, and super-​individual fusion Alfred Schütz, in his classic essay “Making Music Together,” proposes that musicking is a paradigmatic case of social interaction, in which the “inner times” of composers, performers, and listeners synchronize in a “mutual tuning-​in.”21 Distinguishing the measurable clock time of the “outer world” from a non-​measurable, musically constituted temporal sense, Schütz calls music “a meaningful arrangement of tones in inner time.”22 This inner, musically given sense of time is, Schütz affirms, shared by all participants related to a specific work, who thus enter a state of being in the same temporal flow of events: Although separated by hundreds of years, the [listener] participates with quasi simultaneity in the [composer’s] stream of consciousness by performing with him step by step the ongoing articulation of his musical thought. The beholder, thus, is united with the composer by a time dimension common to both.23

Schütz further notes that performers, in playing together, achieve a pinnacle of shared consciousness and flow, which they actively establish by spontaneous negotiation and mutual anticipation, and hence share “in vivid present the Other’s stream of consciousness in immediacy.”24 21 Schütz, “Making Music Together,” 170, 173. Although he refers to Bergson’s concept of durée in defining his concept of inner time, he does not require this inner time be private, as the shared “stream of consciousness” that composers, performers, and listeners “live through in simultaneity” to him is identical, i.e., without the qualitative difference the idea of a truly private time would entail. 22 Schütz, “Making Music Together,” 170. 23 Schütz, “Making Music Together,” 171. 24 Schütz, “Making Music Together,” 171.

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118   The Philosophy of Rhythm Schütz’s understanding of a musically given sense of time is remarkably consequent: The coperformers may have recourse to these devices [viz. counting, metronome, the conductor’s baton] when for one reason or another the flux of inner time in which the musical content unfolds has been interrupted.25

This confirms that he takes “the flux of inner time” to be constitutive for the production of synchronized action, rather than a synchronization with an external timekeeper, a separate time-​keeping entity. This strikes me as a very attractive feature of his view. Yet, on the downside, Schütz does not seem to be aware of temporal variance in the case of listening. His idea of the listener being a co-​performer is that of a precise re-​creator of the composer’s temporal experience. But this is contrary to the phenomenology of listening, and discounts the roles attention and the perceptual making of duration play in the emergence of rhythmicity, for if one hears the same work a number of times, its temporal perception sometimes changes. For example, up-​tempo works can start to feel slower upon closer acquaintance. This is often the case with virtuosic literature, such as Rachmaninoff ’s Etudes-​Tableaux. There is not, therefore, a singular, fixed sense of time that necessarily emerges, even in a single listener’s multiple listening instances. Contra Schütz, it is thus unlikely that listeners are in the same stream of consciousness as the composer. Surely enough, were this the case, there could not be different interpretations of a single work. What is entirely possible, however, is an alignment of a listener’s temporal sense with that of a current performance. Yet again, the emergence of a shared temporal sense in the fullest, literally reciprocal sense, occurs between performers, if anywhere. What is arguably most interesting about Schütz’s notion of mutual tuning-​in from an aesthetic point of view, is that its mutual, bidirectional, symmetrical, dialogical form might indeed take place between performers. Here, two senses of time are genuinely being negotiated into a single shared sense of time; or, alternatively, a single, shared sense of time really emerges interpersonally as the activity of two beings, without two entirely separate senses of time being in place. Thought on this subject is elaborated and refined in recent work on entrainment, to which I turn next. Schütz’s argument raises a familiar question: How do performers entrain? Does entrainment presuppose an inner, biologically based and skilfully refined timekeeper of measured time, a sort of mental clock capable of temporally guiding movement so as to produce well-​kept time in performance? Or could, alternatively, the body be capable of producing precise regular movement on its own accord, without any distinct inner timekeeper as a guide? Would, further, an inter-​corporeal production of such movement be conceivable? Differently put: that two performers have to negotiate a shared sense of time, as Schütz elucidates, does not show that

25 Schütz, “Making Music Together,” 176.

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they have individual senses already in place; the sense of time might emerge between them, in the very interaction. The negotiation only shows that if individual senses are established and kept in place, they can also differ, which difference can be upheld, and is audible to all participants. Martin Clayton’s work shows that entrainment takes place despite differences in individual senses of time, and even despite their intentional upkeeping.26 To Clayton, every participant “knows that the process of sharing the temporal flow may be a rewarding one,”27 which is, ultimately, what he appeals to when claiming that “Musical rhythm is irreducibly social in nature . . . Musical rhythm originates in both endogenous physiological rhythms and the dynamics of interaction between individual human beings.”28 I shall complicate Clayton’s advanced understanding of togetherness by recounting an intriguing phenomenon I  encountered during duo and trio improvisations, namely, a particularly long bodily pulsation. The bodily rush, visceral widening, briefly increased subcutaneous flow, almost an inner combustion at times, can, when deliberately exaggerated, be externalized as a full body contraction and expansion, like a conductor’s full-​body gesture of phrasal emphasis. It is a feeling—​like a throb of pain, aggravation, or lust is a feeling—​and though sometimes accompanied by a conscious realization, it is not necessarily accompanied by a thought. I can produce this feeling at will outside a musical context. Multiple instances can be periodical, if I set my mind to it, with pauses (or bodily silences) between the individual pulses being of two or more seconds in length. Those pulsations can occur without metric subdivisions, yet they are rich with the feelings of suspense, anticipation, impact, and retention. They seem to me to be of the phrasal length observed by Nikki Moran,29 and by Clayton in his analysis of unintentional periodicity between tanpura players. Now, I can confirm these bodily pulsations can also occur unintentionally, when improvising with others. Remarkably, as I  experienced them arising in free improvisation, they are not cognitions that relate to an external timekeeper. None of the musicians openly established a common metric structure. Yet I experienced durationally extended pulsation; and the other players experienced them too, at exactly the same time as myself, as turned out in numerous post-​performance discussions and listening analyses. This, as far as I can see, would be an impossible thing in a free, non-​metric duo improvisation, i.e., without a reference timekeeper, unless we generated time together. While this observation accords with Clayton and even Schütz, it changes the interpretation of “inner time.” Given neither by external reference only, nor simply by biological disposition, inner time arises within a mutually empathic act between players. This shared, inner time allows even a small deviation from the temporal

26 Clayton, “Observing Entrainment.”

27 Clayton, “Entrainment and the Social,” this volume, 195. 28 Clayton, “Entrainment and the Social,” this volume, 196. 29 Cited in Clayton, “Observing Entrainment,” 29.

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120   The Philosophy of Rhythm fusion to become audible, as an ever-​so-​slight disjointedness, a disagreement. This is not a case of synchrony; there are not two clocks, but just one fused sense of time. That sense of time is fused by way of musicking: anyone who has ever performed unison passages30 will know that this cannot be achieved by counting, or by attention to meter alone. Such growing and flowing temporal fusions in an ensemble do not feel as if they can be intended. Instead, they feel like they arrive, or arise, and can be encouraged by preventing interference, i.e., by release rather than inhibition. Importantly, however, they are upheld by a sort of attention, as any distraction will risk their vanishing. Thus they are not inner in any “private” sense. Schütz speaks of a “We” as the emergent form of social interaction.31 I claim that this “We” exists, not as the sum of single individuals, but super-​individually, in temporally fused moments of musicking. Time, in these moments, is interpersonally found and founded. Despite the significant observation of the genuinely interpersonal genesis of such shared temporal experiences, it is not foundational for rhythm per se, but rather a point of epitomized rhythmic experience. Yet from the interpersonal side of the constitution, the affectivity of rhythmic intricacy might plausibly be seen to take root. This is recognized by Peter Nelson, who theorizes an “emotional and aesthetic binding” inherent in rhythm.32 This binding is social in going beyond a simple, perceptual binding into the realms of bodily interaction and interpersonal negotiation. To Nelson, to “grasp a rhythm” is “to abandon conscious control . . . to the physical engagement of the body with sound . . . which is always, inevitably engagement with another body.”33 Nelson also refers to how durational space is distributed between sound makers, e.g., between mother and infant, and in African polyrhythm.34 Nelson conceives out-​of-​timeness within a shared durational space as the medium for expressivity in “the actual flow of the rhythmic narrative,” in his example, mother–​infant interaction, where “minute alterations can have huge significance.”35 While Nelson’s line of thought helps elucidate the social ontology of rhythmic behavior, it only hints at potential causes of the affectivity of rhythm. He argues that Colwyn Trevarthen’s findings on mother–​ infant interaction, Gaston Bachelard’s thought on the significance of duration, and Pierre Bourdieu’s theory of gift exchange all support the idea that the “temporal spaces between sounds or actions . . . are pregnant with meaning”—​a meaning derived from the social juxtaposition of those involved in the exchange. Yet Nelson does explicitly analyze the concrete link between such rhythmic meaning and affect; perhaps because he adopts Trevarthen’s notion of pulse, whereby pulse is exteriorized, and expressed in 30 E.g. the first movement of Schubert’s Trio Op. 99 D 898; the second movement of his Trio Op. 100 D 929; or the fourth movement of his String Quartet No. 14 D 810, Der Tod und das Mädchen. 31 Schütz, “Making Music Together,” 17. 32 Nelson, “Social Theory of Rhythm,” 151. 33 Nelson, “Social Theory of Rhythm,” 151. 34 Nelson, “Social Theory of Rhythm,” 153. 35 Nelson, “Social Theory of Rhythm,” 153–​4. In taking temporal dissonance to be socially meaningful, Nelson thus develops a point that recalls Adorno’s idea of expressive melodic and harmonic dissonance.

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actions.36 Nelson treats pulse as “socially constructed ‘instants which stand out,’ ”37 and these instants remain, at least in his account, curiously disconnected from the body, such that listeners “think [rather than feel] one at the same time as another person.”38 When, however, one consistently understands rhythm as felt, such as in Andy Hamilton’s humanistic conception, sources of affectivity abound. One can then immediately spell out, for example, that the negotiation of temporal space and its occupation is charged with issues of power, dominance, submission, struggle, intimacy, and rejection not only in intellectual, symbolical terms, but in terms of felt experience. Towardness and union, or aversion and disjunction exist on a somatic plane, and become psychologically active through it. This reflection on jointly created pulsation shows how analyses of entrainment might be even further connected to analyses of social and psychological meaning; and, complementing Schütz’s and Clayton’s reasoning, and similar to Hamilton’s idea of projection, how bodily imagination must be accounted for in attempting to understand interpersonal rhythmicity.

6.  Rhythmic events, gestural levels, and attentional habits When rhythm enters one’s attention, it does so in constituting sonic events and chains, linear, and layered. The consistency and cohesion of these events develops and clarifies itself during the course of a piece, in listening as much as performing. Something that from a standard score analytical point of view clearly is a motive might not appear so at its incipient sounding; its motivic identity forms as it reappears, each time altering and enriching its durational expressivity, as relations to other sonic events begin to be heard, and as proportions articulate. Further, some events one initially or loosely hears as single may be made up of hundreds of tiny actions, such as the whizzing and flickering textures and the densely clustered but permanently transforming sonic fields in Friedrich Cerha’s Spiegel VI. Still, I go on to hear them as singular events, with the event character being gestural and flowing, from its appearance through to its disappearance. Whenever such gestural events are layered and arise from the lower threshold of audibility, I may attend to them only long after their inception. They can appear suddenly, when attention shifts to them; and retention may bring their prior presence into consciousness.39 Some gestures may consist of smoothly interwoven actions that are in themselves events at a smaller scale, so attending to the subtleties of a texture may reveal intricate 36 Nelson, “Social Theory of Rhythm,” 152–​3. 37 Nelson, “Social Theory of Rhythm,” 153, quoting Bachelard. 38 Nelson, “Social Theory of Rhythm,” 155. 39 To listen out for moments of gestural appearance and disappearance can make for an exquisite experience. A listener so inclined may choose to savor the borders of musical material, drifting away from other current sonic events if they are below a certain markedness. Here, the rhythmicity of the fuller sonic constellation can remain underarticulated.

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122   The Philosophy of Rhythm rhythmicity on various levels, intra-​gestural and inter-​gestural—​a rhythmicity that sometimes requires us to listen out for it. The striking motoric passages often found in Stravinsky or Prokofiev, or, radically, the gradually accumulating, massive orchestral “stomping” in Friedrich Cerha’s Spiegel VI, are protruding, sonic events of the “beating” sort, which might capture our focal attention initially, only to recede as we attend and bodily interpret the sonic and affective space between them. As listening progresses, especially during repeated listening, attentional habits might form, and existing ones might be challenged and altered. All of this plays into rhythmicity as it concretizes and recedes. On the aesthetic level, it might never reach the crystalline structure a score analysis suggests. In other words, the discreteness of abstracted rhythm is not thoroughly audible in the way pitch or timbre are. As with other psychological phenomena, rhythm has a dimension in which it is obscure, shrouded, submerged, only to emerge into consciousness at particular points of attending.

7.  The expressivity of silences I return briefly to the affective space between instances of orchestral “stomps” in Cerha’s Spiegel VI. Not only are these silences charged with the threatening character of an advancing large mass of marching bodies, congealing into a single, massive body, they also are convoluted around the edges, diffused by the imprecision of a forming horde. Thomas Clifton is one of the few authors to have written with subtlety about the experiential shades of the diverse ways in which silences are musically situated.40 Clifton distinguishes between temporal, spatial, and gestural silence.41 He also distinguishes between the time of a musical work and “our bodily time”; between silence “ridged by the perception of continuing pulses” and “pulseless silence”; and “gapping” silences and silences “in which melodic motion carries itself right through.”42 His examples show a delicate sensibility to how dedicated, attentive, active listening fills silences affectively. To this I add the experience of riveting silences in improvisation, in mid-​gesture, and particularly at the moment where for a certain duration the decision over whether the piece ends now—​or whether pulsation demands its being carried on and through—​hovers between two or more players. These examples remind that silences, like sounds, have a lived duration, are an equally important part of rhythmic experience, and that any sophisticated concept of rhythm should not be deaf to their phenomenological nuances. * * *



40 Losseff and Doctor (eds), Silence, Music, Silent Music, offers a few more examples of such rare work. 41 Clifton, “The Poetics of Musical Silence,” 164.

42 Clifton, “The Poetics of Musical Silence,” 165, 167, 174, 178.

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These thoughts are preliminary and invite extensive unpacking.43 Additional ground has been cleared in support of some specific revisionary approaches to the idea of rhythm as named in this chapter. Rhythm, in these revisionary views is clearly an interpersonal phenomenon. To this I add that rhythmicity comes to the fore and to itself as attention negotiates the presence of others with and within our own, in ways that can be both felt and cognized. While rhythmic durations as found in scores, formal analyses, and abstract conceptualizations are thin, thick durations are made durations and are experienced accordingly. Behind such made durations stand identities that are expressed in the coherence of the durations’ very making, i.e., the performer’s or composer’s identities, and the listener’s, plus—​via instrumental and stylistic practices and instruments as cultural artifacts—​collective identities, identities worldly and imagined. The expressive counterpoint of those rhythmically interwoven identities stands out at its most articulate in performances that manage to find a shared rhythmicity, where the sharing extends to and includes ensemble, and listener. Rhythmic resistances become intricately expressive where a fundamental rhythmic correlation exists; without such a correlation individual parts disengage (this disengagement may itself be generally expressive of aversion, alienation, or disinterest). Rhythm, preceding its abstraction, then, is the experience of a felt, dialogical hermeneutic at work between people, environment, and imagined agencies.44

Works Cited Barthes, Roland, “Rasch,” in The Responsibility of Forms, tr. Richard Howard (Berkeley, 1991), 299–​312. Carminho [Maria do Carmo Carvalho Rebelo de Andrade], “Alfama,” at Podium Mozaiek in Amsterdam, 2011: https://​www.youtube.com/​watch?v=h8YfA7FL05M. Clayton, Martin, “Observing Entrainment in Music Performance: Video-​Based Observational Analysis of Indian Musicians’ Tanpura Playing and Beat Making,” Musicae Scientiae, 11.1 (2007),  27–​59. Clayton, Martin, “Entrainment and the Social Origin of Musical Rhythm,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C12. Clifton, Thomas, “The Poetics of Musical Silence,” The Musical Quarterly, 62.2 (1976), 163–​81. Elias, Norbert, An Essay on Time ([1984]; Dublin, 2007). Goldie, Peter, The Emotions: A Philosophical Exploration (Oxford, 2000). Hamilton, Andy, “Rhythm and Stasis:  A Major and Almost Entirely Neglected Philosophical Problem,” Proceedings of the Aristotelian Society 111.1 (2011), 25–​41. Hanslick, Eduard, On the Musically Beautiful: A Contribution towards the Revision of the Aesthetics of Music, tr. Geoffrey Payzant ([1854]; Indianapolis, 1986).

43 Foreseeably, questions of the nature of meter, accent, beat, and other aspects of rhythm might reconfigure themselves from the newly gained view, rather than being elements out of which an understanding of rhythm needs to be uncomfortably construed. 44 Research for this chapter was funded by the Austrian Science Fund FWF: P25061-​G15.

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124   The Philosophy of Rhythm Hasty, Christopher, “Complexity and Passage:  Experimenting with Poetic Rhythm,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C15. Losseff, Nicky and Jenny Doctor, eds, Silence, Music, Silent Music (Aldershot, 2007). Nelson, Peter, “Towards a Social Theory of Rhythm,” in Jean-​Luc Leroy, ed., Topicality of Musical Universals/​Actualité des Universaux musicaux (Paris, 2013), 149–​56. Nussbaum, Martha, Upheavals of Thought: The Intelligence of Emotions (Cambridge, 2001). Peters, Deniz and Simon Rose, Edith’s Problem, CD LR 812, audio recording (Newton Abbot, 2017). Schütz, Alfred, “Making Music Together:  A Study in Social Relationship,” in Alfred Schütz, Collected Papers II: Studies in Social Theory, ed. Arvid Brodersen (The Hague, 1976), 159–​78.

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8 Mozart’s “Dissonance” and the Dialectic of Language and Thought in Classical Theories of Rhythm Michael Spitzer

1. Introduction The notion of “formalism” has exercised philosophers for many years, following Eduard Hanslick’s celebrated definition of music as “form moved in sounding [tönend bewegte Form].” When philosophers critique “formalism,” they assume that there is an alternative, perhaps more enlightened account of music. On the other side of the disciplinary fence, however, it is arguably the case that all musicologists are actually formalists. That is, scholars who engage professionally with music studies are generally committed to the idea that musical meaning is mediated through musical form; i.e., that there is no clear distinction between musical structure and musical meaning or expression (or content, Inhalt). Lydia Goehr, following Philip Alperson, calls this position “enhanced formalism.”1 An example of pure (“non-​enhanced”) formalism is to approach rhythm as an abstract theoretical category, divorced from musical meaning. I suspect that many authors in this book adopt that approach. This chapter takes the opposite line, arguing that rhythm is saturated with expression (meaning, content, Inhalt). To think of rhythm in this way leads me to challenge a conceptual opposition mounted by Jerrold Levinson between two kinds of musical understanding. On the one hand, he speaks of “musical expressiveness” as something “directly heard,” its immediacy distinguished, on the other hand, from a kind of knowledge inferred over time by the “properly backgrounded listener.”2 To my mind, an obvious objection to Levinson’s opposition between “directly heard” immediacy and “background” knowledge inferred over time is that hard-​earned inferences can become immediate habits of listening, that is, immediacy can be acquired. This is obvious when one thinks about the hundreds or thousands of practice hours it takes to learn to sight-​read a piano score with deceptive ease. Exactly the same point can 1 Goehr, Quest for Voice, 19. 2 Levinson, Contemplating Art, 101. Michael Spitzer, Mozart’s “Dissonance” and the Dialectic of Language and Thought in Classical Theories of Rhythm In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0009

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126   The Philosophy of Rhythm be leveled at the institutionalization of musical knowledge climbing up the developmental ladder, from childhood through higher education all the way up to advanced scholarship. An advanced listener has learnt to “directly hear” aspects of the music which might entirely elude a non-​expert listener. I shall illustrate this thesis with a piece by Mozart. Of all composers, Mozart enjoys an unearned reputation for immediacy and transparency. His music seems to have been effortlessly composed, and can afford a deceptively easy listening experience. This transparency is certainly intrinsic to Mozart’s musical style, and I will not seek to dispute it. My points, rather, are (a) that listening to Mozart can be enriched by music-​theoretical “background” knowledge; and (b) that this background can become, over time, just as immediate and transparent as the experience of the non-​expert listener. The fact that immediacy has been acquired (often laboriously over many years) does not prevent it from being immediacy. All this is by way of a grand apology for what comes next. The rump of this essay looks rather unpromising, and—​taken without apology or framing—​might well put off most non-​expert readers. My starting-​points are some dusty musicological treatises which nobody reads today, save perhaps two dozen historians of music theory scattered around the globe. One might well ask: Why would anybody trek through the highways and byways of eighteenth-​century compositional theory in order to understand rhythm and Mozart? The answer: because this furnishes an historical background which will enhance our appreciation of both the music, and of the theoretical category we call “rhythm.” To grasp what is at stake, let’s consider these two thought experiments. Figure 8.1 shows a Schlagfolge, an undifferentiated succession of drum beats, proposed by the Swiss Enlightenment philosopher Johann Georg Sulzer to help us imagine the origin of rhythm. He discusses it within his encyclopedia of the fine arts, Allgemeine Theorie der schönen Künste. Sulzer calls his Schlagfolge “a model of the simplest order of succession of things.”3 He wonders, “how can such a series of beats become pleasant, or receive an ethical or affective character?” According to Sulzer, the first step along the evolutionary path from the Schlagfolge to meter or rhythm proper is to differentiate the drum beats into strong and weak beats, a pattern Sulzer calls “simple [einfache]” rhythm. Differentiation creates a higher-​level kind of regularity that Sulzer terms “meter.” Metrical order enables a still superior pattern of regularity, as bars and phrases are grouped with each other by analogy to beats in a bar. The lesson to be drawn from Sulzer’s thought experiment is that late eighteenth-​ century theories of rhythm were stamped by epistemology. Sulzer was a post-​ Leibnizian philosopher, influenced by Wolff and respected by Kant. Whereas music theorists traditionally modeled rhythm in terms of the human pulse or a ticking clock, Sulzer deliberately creates an imaginary Schlagfolge because he believed that our rhythmic sense was an interpretative act of Einbildungskraft, imagination. Sulzer makes explicit analogies between the well-​formedness of a metrical group 3 Sulzer, Allgemeine Theorie, 527.

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Figure 8.1  Sulzer’s Schlagfolge

and the integrity of a philosophical concept, the unity of both having a spatial or geometric aspect. According to Sulzer, a series of beats (or indeed, of any objects) can, through a uniform pattern, be “united with a concept [mit einem Begriff zusammen gefasst].” Through uniformity, an infinite succession of events can be surveyed at a glance and held in the mind. Similarly, one need only grasp the rhythm of the first measure of a piece in order to fix onto the rhythm of the piece as a whole. This is to turn the time of music into space, so that it can be surveyed in the mind as a quasi-​ spatial form. In other words, musical form, by definition, is grasped metaphorically as “spatial,” and the importance of Sulzer’s philosophically inflected music theory is that he conceives musical form on the basis of a cognitive model of meter. That is, Sulzer’s model recognized the mind’s liking for symmetrical rhythmic patterns, in practice, in binary groupings of beats (two, four, eight, etc.); and—​building on that—​the mind’s predictive capacity:  for example, given two beats, the musical mind might expect the rhythmic group to be balanced by two more beats, making a larger group of four. The other side of this coin was that, by the late eighteenth-​ century, musical style (Haydn, Mozart, and their contemporaries) had evolved so as to fit the propensities of the musical mind. Or rather, music and listener expectations co-​evolved, and Sulzer’s theory reflected that. Before Sulzer, non-​cognitive models of rhythm saw rhythmic impulses as externally authoritative, by analogy to how the town clock, or the cycle of the seasons, marked time. Sulzer’s thought experiment suggests that our sense of rhythm is generative. Rhythm of the Schlagfolge isn’t inherent; it evolves gradually in our mind. What begins as hazy, or indeterminate, slowly becomes clear. In this way, Sulzer mirrors the generative aspect of Leibnizian epistemology, rising in stages from obscure sense impressions to conceptual clarity.4 In Sulzer’s terms, rhythm’s generative process rises from irregularity to regularity at ever-​increasing levels, climaxing with form and artistic expression. The generative nature of Sulzer’s theory leads me to the second example, taken from a composition treatise written slightly later than Sulzer, and much influenced by him. The Versuch einer Anleitung zur Composition (1782–​93), by the North German pedagogue Heinrich Christoph Koch, is the outstanding music-​theoretical text from this period and a key source for understanding classical style. Like Enlightenment theories of mind and language, Koch’s course is a story of origins; in formal terms, an “origin” is a small-​scale work such as a dance or a song, usually

4 My Metaphor and Musical Thought gives the Leibnizian background of Sulzer’s musical aesthetics, and a fuller account, with particular reference to Heinrich Koch, of eighteenth-​century theories of rhythm and language.

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128   The Philosophy of Rhythm

Figure 8.2  Koch’s Schlagreihe

no more than eight or sixteen bars in length. Hence the purpose of Koch’s regimen is to lead the beginning composer gradually from miniature exercises, such as dances and songs, to more accomplished, large-​scale forms such as sonatas and symphonies. Crucially, the kernel of Koch’s generative progression from small-​ to-​expanded form is a rhythmic idea. In other words, the evolution of rhythm establishes the template, at a later point in the treatise, for the evolution of form. The following model appears midway within his treatise, as an introduction to the section on form, and part of a chapter, “On the Nature of Measure in General.” Like Sulzer, Koch’s starting-​point is a thought experiment based on the perception of a series of similar objects, in this case a string of pearls or a row of billiard balls (Figure 8.2). Although these six dots are notated on a staff with crotchet tails, they may as well represent objects in the world, such as pearls or balls, as musical notes. Koch states that it is natural for the mind to separate them into groups, by instituting “resting points of perception [Ruhepuncte der Vorstellung].”5 Koch calls this series of beats a Schlagreihe rather than a Schlagfolge, but his derivation from Sulzer is obvious. Expressed like this in the abstract, the series lacks rhythm or meter. In performance, however, Koch states that we might attach the second note to the first, thereby instituting what he calls a “resting point [Ruhepunct]” on the third note. Koch’s notion of Ruhepunct,6 is extremely suggestive, because it points in two opposite directions. From one standpoint, it operates as a musical punctuation mark, an articulation of the stream of rhetoric. Analogies between the flow of rhetoric and the flow of a river are long-​standing, and they mapped easily onto conceptions of musical discourse as a flow of directed tonal motion, from start to final cadence. Johann Mattheson gives an influential diagram of a short musical dance annotated with degrees of punctuation, from commas through semicolons and colons to full stop, corresponding to gradations of tonal closure.7 Thus a comma represents a light boundary, or caesura (Latin for “cut,” Einschnitt in German) between two sub-​phrases, and a full stop is a terminal perfect cadence. The crucial point is that viewing musical articulation as punctuation is to survey music as goal-​orientated. Since streams of rhetoric push teleologically towards their close, punctuation marks, in language as in music, are interruptive and end-​directed. From an opposite standpoint, however, a Ruhepunct functions as a metrical accent, a Taktteil, which is to view music as head-​orientated (i.e., orientated to the beginning of groupings):

5 Koch, Anleitung zur Composition, 278. 6 Koch borrows the term from Batteux, Les beaux arts. 7 Mattheson, Der vollkommene Capellmeister, 224.

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Figure 8.3 Koch’s Schlagreihe with resting points (Ruhepuncten)

Figure 8.4  Model of the drift from rhythm to punctuation If the imagination of someone who wants to sing or play these six notes comprehends with the first of these notes only a second one so that a resting-​point of the imagination arises on the third note, they will perform the passage as the following figure metrically illustrates.8

Koch notates a bar-​line between the second and third notes, demonstrating that an accent occurs on the first beat of the second bar (Figure 8.3). A little later, he adds that “the resting-​point of perception, and also the weight or expression through which it is made understood through performance, falls on the first, third, and fifth note.”9 Koch’s concept of articulation is ambiguous, because it has the potential to be both head-​and end-​directed. If we hear a Ruhepunct as a punctuation mark, then it points toward the end of a phrase, as an interruption of a rhetorical stream whose sense is completed with the full stop. If we hear it as a metrical accent, then it is orientated toward the head of a phrase, the strong beat which is completed by a subordinate weak beat. Koch can unite these opposite functions because, in his terms, to mark a division simultaneously bestows a metrical emphasis on a note. And Koch sees articulation, grouping, and metrical differentiation as arising interdependently. The notes “become united under a single perspective, that is, the first of these notes must comprise the Ruhepunct der Vorstellung or point of division.”10 The second note (or, in triple meter, the second and third) is “grasped under the division point of the first note, that is, they are united with the first under a single perspective.”11 This metrically stressed note constitutes the first “essential part [wesentlichen Teil]” of the bar, the “gute Taktteile,” which is “intrinsically long [innerlich lang]”; the second “essential part” (the arsis) is called the “schlechte Taktteile,” and is “intrinsically short [innerlich kurz].” In Figure 8.4, I represent this flip in orientation from “rhythm” to “punctuation” in terms of notes alternately tensing away from a head

8 Koch, Anleitung zur Composition, 282. 9 Koch, Anleitung zur Composition, 282.

10 Koch, Anleitung zur Composition, 283. 11 Koch, Anleitung zur Composition, 283.

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130   The Philosophy of Rhythm and relaxing towards an end-​point.12 It is important to stress that this flip is not captured either in Koch’s or Sulzer’s own models, nor indeed in the compositional scores themselves. Rather, I argue that it is implicit within this ambiguous understanding of classical rhythm. The flip runs strikingly counter to canonic modern conceptions of tonal structure. Heinrich Schenker, the preeminent tonal theorist of the postwar era, saw direct tonal motion as moving in a single direction, ineluctably towards its telos. This teleological vector is preserved in James Hepokoski and Warren Darcy’s theory of classical form, the most influential recent model of classical music. I will draw out the further significance of this interpretation at the end of this chapter. For the present, there are multiple other lessons to be drawn from Koch’s thought experiment. A rhythmic impulse is not to be understood as an abstract theoretical construct, but in the context of musical form. As such, it is entangled within musical form’s dialectic with time. A composition pushes on towards its final cadence, just as, from an opposite standpoint, in a quasi-​geometrical spatial sense, the work’s hyper-​metrical groupings are gathered together from the perspective of its initial strong beat (hyper-​meter means considering a bar as a “beat” at a higher structural level, so that meter converges with form). Weak beats complete strong beats (head orientation) just as cadences complete phrases and pieces (end orientation). This space–​time dialectic is elaborated in Koch’s Anleitung zur Composition in its alternating emphasis on its two core principles of “punctuation” (phrase-​ending formulas) and “rhythm” proper, by which Koch means formal time-​span grouping orientated toward heads. A yet more radical lesson is implied by the title of this chapter, a dialectic between language and thought. “Punctuation” is no idle analogy, but a trace of music’s language character. Whilst the metaphor of “music as language” was prevalent in most ages, it was particularly acute in the late eighteenth century. Laying to one side the problematic issue of musical meaning, i.e., semantics, language’s syntactic side was certainly mirrored in the highly conventionalized character of the classical style—​ perhaps the most formulaic musical language ever to arise in the common-​practice era between Bach and twentieth-​century modernism. Most eighteenth-​century writers talked of music in terms of an “oration,” as in Mattheson’s famous annotation of a Marcello concerto using rhetorical figures.13 Koch calls the first half of a phrase a “subject,” and the second half a “predicate,” by analogy to the speculations about primitive grammar by contemporary linguists such as Karl Wilhelm Ramler.14 Thus, just as Ramler imagined that original word-​order placed the noun at the beginning of an utterance (akin to gesturing or pointing at an object in the world, such as a snake), Koch saw the opening sub-​phrase of a piece as akin to a grammatical subject. Musical “subject” = linguistic subject, pun intended. Similarly, the 12 I borrow the idea of tensing and relaxing branches from the Chomskian tree-​structures in Lerdahl and Jackendoff ’s generative model in Theory of Tonal Music. 13 Bonds, Wordless Rhetoric. 14 Spitzer, Metaphor and Musical Thought,  231–​2.

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musical sub-​phrase which completed the phrase as a whole—​typically, balancing a two-​bar start with a two-​bar conclusion—​was imagined as a linguistic predicate, such as a verb (e.g., “Snake, flee!,” or “Bread, give me!”). The crux of this metaphor, however, is not that classical music’s language character is a steady state, but that it interacts with its conceptual, formal, character in such a way that its element of linguistic expression is associated with endings. Punctuation is end-​directed, as we have seen; and this end-​orientation is to be understood, I will claim, by the same token that classical form becomes more lyrical, song-​like, or poetic, toward its ending—​typically in sonata-​form second groups. There is a received view that second subjects are more lyrical than first subjects, a truism borne out by many of Mozart’s sonata-​form first movements, such as his “Jupiter” Symphony. The first group is a fanfare for full orchestra; the second subject is a much more individuated melody for first violins. They “sing,” and one infers a metaphorical “voice,” with implicit “language.” The music, then, becomes progressively more language-​like toward the end of the form. By the opposite token, classical form is more properly “rhythmic,” geometric, or conceptual in its first half, just as Ruhepunct as metrical accent is head-​oriented. A third kind of rhythmic impulse will find its way into my account, one which is actually the most familiar of all, since it is the basis of the prototypical “just-​so” story of Enlightenment linguistics, whereby philosophers speculated on the origin of language in indexical gestures. A gesture is a rhythmic impulse, but—​unlike musical rhythm—​is also implicitly an act of semantic communication. Rhythmic gestures are different from the two sides of Ruhepunct also because they are unstructured singletons, free of metrical grouping. When they occur in classical music, it is as agents of wild or primitive expression. We will see that the first movement of Mozart’s “Dissonance” Quartet projects all three types of rhythmic impulse at different sections. This concluding analysis will illustrate my thesis that rhythm is best understood in rich compositional context rather than as an abstract theoretical category. Although this is true of how rhythm operates in all musical eras, it is particularly the case for late eighteenth-​century music. Before we get to Mozart, we need to dive into the detail of Koch’s Anleitung zur Composition, as its pedagogical, generative, progression from small-​scale to expanded form will mediate the leap from thought experiment to musical practice.

2.  Sonata Form as “Rhythm” Charles Rosen’s The Classical Style is the most influential study of the music of Haydn, Mozart, and Beethoven of the modern era. Discursive and panoramic in its scope, it nonetheless never loses sight of Rosen’s focal idea that the classical style is fundamentally one of dramatic balance. The quintessential expression of this sensibility for structural balance is the sonata. Every type and genre of classical music is revealed by Rosen to be infused with the principles of sonata form. These principles

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132   The Philosophy of Rhythm were quintessentially tonal rather than thematic. Against the received view that form was mostly a matter of motives and themes, Rosen contended that it was really projected by the tonal drama of tension and resolution. In a sonata form, tension was raised through the exposition’s modulation from the tonic to the dominant, and resolved by the return of the tonic in the recapitulation. The same drama was unfolded within a short musical phrase. Typically, an opening sub-​phrase would end on a dominant half-​close, and would be answered by a sub-​phrase cadencing on the tonic. The phrase thus encapsulates the tonal shape of the whole, suggesting that the sonata evolved generatively from a small-​scale model. I want to suggest that this tonal drama of tension and resolution is a kind of rhythm. It follows on from the rhythmic models theorized by Sulzer and Koch as the kernel of late eighteenth-​century musical language. Admittedly, tension and resolution are features of all tonal music, including styles which don’t sound “rhythmic” at all, such as Wagner’s Tristan und Isolde. Nevertheless, classical works do sound rhythmic because they project rhythm’s qualities of symmetry and articulation through the symmetry and articulation of their architecture at all levels.15 The periodicity of classical phrase structure expresses the regularity of the Schlagfolge. The sharp articulation of the classical style through phrase-​endings and cadences shares the Schlagfolge’s phenomenal quality as a series of points. That is, classical form concentrates its syntax in finely articulated points of tonal closure. But how do we get from the literal rhythm of a Schlagfolge (or Schlagreihe) to the “metaphorical” rhythm of a musical phrase, or indeed the expanded form of a full sonata? This takes us back to the pedagogical journey of Koch’s treatise, whose purpose is to lead us step-​by-​step from small-​scale (literal) to large-​scale (metaphorical) rhythm. Figure 8.5 arrives toward the end of Koch’s pedagogical journey, after he has taught the novice composer how to handle many varieties of small-​scale forms such as minuets and songs. Though only eight bars long, it is actually a miniature outline of a hypothetical sonata-​form exposition. The first thing to note about this model is that it comprises four two-​bar segments, and that it thus notionally outlines a recursive expansion of the Schlagfolge: four beats become four bars become four two-​bar segments. The four phrases project different tonal functions, encapsulated within the varying tonal orientations of their endings: a tonic-​phrase (ending on B); a dominant-​phrase (ending on A); a phrase on the dominant of the dominant (ending on A); and a dominant cadence (ending on D). Koch’s quadratic structure could be regarded, then, as a form of tonal rhythm—​the four beats of a bar expanded into four differentiated phrase endings. Such an interpretation predicates a kind of non-​continuous listening, since the four phrase endings fall at two-​bar intervals.

15 Talk of form as “rhythmic” was especially fashionable in the 1980s, in association with Schenkerian reduction of structural levels. See, e.g., Schachter, “Durational Reduction”; Rothstein, Phrase Rhythm in Tonal Music.

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Figure 8.5  Koch’s schema of a sonata-​form exposition

The second point to note is that the sub-​phrases are defined as much by their symmetrical proportion as by their endings. In Koch’s words, phrases and segments are distinguished from one another as parts of the whole chiefly by two characteristics: first, the type of their endings . . . second, the length of these parts along with a certain symmetry or proportion.16

He terms the former principle “punctuation,” and the latter—​somewhat confusingly for modern readers—​“rhythm” proper (confusing because we might call this “meter”). Regarding punctuation, Koch uses a white square to indicate the end of an inconclusive phrase and a white triangle to show the end of a segment. Cadences, the most conclusive punctuation of all, do not require a symbol. Where I have departed from Koch’s original is in bracketing and characterizing bars 2–​4 as “rhythm,” and bars 5–​8 “punctuation.” We hear the phrase endings at bars 2 and 4 as weak beats with respect to the strong beats at bars 1 and 3. The first half of the piece is orientated towards the opening tonic; it is head-​orientated. A switch occurs midway through the period (the quaver rest at bar 4) from head-​orientation toward an end-​directed hearing, as the phrase-​endings now drive toward the final cadence. Put simply, this miniature exposition divides into a first half, which extends the opening tonic; and a second half, which is directed to the dominant close. Another way of looking at this is that the tonic key is most firmly established at bar 1, and the dominant key at bar 8. Now, the term “half ” here is highly moot, cuts to the core of the metaphorical nature of classical “rhythm,” and is illustrated by what happens when Koch demonstrates how his eight-​bar model can be expanded into a thirty-​two bar sonata-​form exposition. That his exposition is thirty-​two bars long might suggest that its form is mechanically periodic, perhaps comprising four eight-​bar

16 Quoted in Baker, Heinrich Koch,  2–​3.

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134   The Philosophy of Rhythm phrases: four beats of a bar expanded, successively, to four bars, eights bars, sixteen bars, and thirty-​two bars. In fact, Koch introduces his thematic interpolations and subsidiary material in a highly differentiated fashion, so that the first “half ” (corresponding to bars 1–​4 of the model) is expanded to ten bars; and the second “half ” (bars 5–​8 in the model) is blown up much more massively into twenty-​two bars. Nevertheless, the disproportion between the first and second groups of the exposition notwithstanding, its two “halves” are experienced as quasi-​rhythmically symmetrical—​the tonic half answered and balanced by the dominant half, a symmetry which is the basis for the subsequent tonal drama in the development and recapitulation. That classical sonata form is experienced as being symmetrical is a mystery which has never been properly treated in the history of music theory. Koch’s achievement in his Anleitung was to refine Sulzer’s notion of symmetry, and apply it systematically to late eighteenth-​century musical style. Koch’s profoundest insight was that symmetry was not determined by mechanical phrase length alone. Instead, it depended also on the content of the phrase, by which he meant the rhythmic, thematic, and tonal detail. Thus, in the right contexts, it was perfectly possible, for example, for a four-​bar antecedent phrase to be balanced by a five-​bar consequent, with no feeling of irregularity: witness the many five-​, seven-​, and nine-​bar phrases in Mozart. To explain this, Koch institutes a “material–​formal” distinction: a five-​ bar consequent can be heard as deviant “formally” (against the eight-​bar grid), but as regular “materially” (with respect to its content). Koch’s other major insight was that new principles of symmetry and grouping emerge at higher levels. Hence, on the intermediate level of the phrase, “rhythm” is constituted not by the beats of a bar but by a grid of cadences, signs of closure. At this level, the issue of symmetry fades, since the exact number of bars or the exact length of phrase becomes non-​pertinent to even the most self-​conscious listener, and is replaced by a sensibility for complementary harmonic functions. The 10/​22 imbalance clarifies the sonata form’s dialectic between time and space, language and thought. The relative brevity of the tonic group enables the listener to grasp the half-​close at bar 10 with respect to the tonic opening; namely, as a head-​orientated formal group—​what Koch terms “rhythm.” Conversely, the phrase extensions in bars 11–​32 comprise a series of end-​directed tonal punctuation marks, a chain of cadential evasions pushing towards the close. How, then, does Koch’s heuristic match actual compositional practice? Quite well, as it happens, especially regarding the sonata forms of Mozart. Mozart’s sonata form expositions are typically articulated by what current sonata theory calls a “Medial Caesura,”17 a dramatic “cut” between the end of the tonic group and the start of the secondary group. Haydn’s expositions tend to be more fluid, but Koch’s model certainly applies well to Mozart’s greater penchant for architectonic symmetry. Secondly, Mozart’s second groups are generally much longer than his primary groups, and also feature

17 Hepokoski and Darcy, Elements of Sonata Theory.

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chains of interrupted cadences. Thirdly, his second groups are almost always more lyrical than his primary groups, evincing an onset of a language character within the expositions. This vocal quality was evident in the punctuation of Koch’s musical material, but not in its content, which doesn’t seem particularly song-​like. Let’s now see rhythm and punctuation in action in a particular work by Mozart.

3.  Mozart’s “Dissonance” Mozart’s String Quartet in C major, K. 465, earned its soubriquet from its dissonant Adagio, whose chromaticism was avant-​garde for its time. It holds the key for the narrative I shall tell about the sonata-​form exposition it introduces. This exposition moves through the two kinds of metaphorical rhythm Koch theorizes, and I shall consider it first. The exposition, the first four bars of which are shown in Figure 8.6, comprise a 22-​bars tonic group (including the “first subject”), followed by a transition, a dominant second group, and a coda—​an order of events stereotypical of a sonata form. The group demonstrates the recursively geometric periodicity of what Koch terms “rhythm” proper. The 2 + 2 sub-​phrases in Figure 8.6 answer each other, by analogy to the four beats in a 4/​4 metrical group. It does not take much imagination to hear bars 23–​6 as “metrical” (or hypermetrical) in this respect. These four bars are balanced at a higher level at bars 27–​30, which together constitute an eight-​bar antecedent phrase to a putative period. The expected eight-​bar consequent phrase

Figure 8.6  Mozart, String Quartet in C major, K. 465, “Dissonance,” bars 23–​6

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136   The Philosophy of Rhythm to this antecedent is expanded to fourteen bars (bars 31–​44), but this extension does not disturb the perception of overriding symmetry. The cadence at bar 44 completes a large-​scale rhythmic group established by the first beat of bar 1; the group is head-​orientated. At twenty-​and-​a-​half bars (including the half-​bar upbeat at bar 71), the G-​major second group (bars 71–​91) is more or less the same length as the tonic group, but its phrase-​structure is strikingly dissimilar (Figure 8.7). After a compressed eight-​ bar period (bars 71–​9), clearly articulated as 4 + 4, there follow three four-​bar sub-​ phrases, each punctuated with a perfect cadence. In short, the group comprises four perfect cadences of escalating power, driving ever more forcefully toward the end. The group is highly end-​directed. Where the tonic group is symmetrically “rhythmic,” the second group is divided up in chain form, as a series of tonal “punctuation” marks of ever-​increasing closure. Mozart’s practice, then, conforms nicely

Figure 8.7  Mozart, bars 67–​97

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Figure 8.8  Introduction, bars 1–​4

to Koch’s theory of a shift from “rhythm” to “punctuation” across the two “halves” of a sonata-​form exposition. But that is not the whole story, because the quartet begins with a twenty-​two-​ bar slow introduction (Figure 8.8). It’s typical of Mozart’s ear for balance to make all three panels nearly the same length:  introduction (22 bars), tonic group (22 bars) and dominant group (22 ½ bars). Its harmonic language could hardly have afforded greater contrast to that of the diatonic clarity of the exposition. The phrases unfold a sequence of interlocking interrupted cadences through outlandish modulations: from C major through B♭ minor, F minor, E♭ major. Each harmonic surprise creates a tonal shock whose gestural impact constitutes “rhythm” in a different, third, sense, to that presented in the exposition. Not rhythm as hypermetrical periodicity; nor as rhetorical punctuation; but rhythm as seemingly disconnected impulses. The “Dissonance” Quartet’s harmonic language sounds wild. The sudden clarification of tonality and phrase-​rhythm at bar 23 effects a kind of “sunrise” of Enlightenment reason against the backdrop of this wildness. That is how contemporary listeners would have understood this tonal narrative, one rehearsed in countless other works, most famously in Haydn’s Creation.18 Mozart’s wildness also reflects current accounts of “primitive” rhythm, most famously in Johann Forkel’s Allgemeine Geschichte der Musik (1788). Like so many of his contemporaries, Forkel was fascinated by evolutionary theories of language—​ indeed, musical language. He hypothesized that the language of music originated with a primitive phase of disconnected gestures, because, in his view, “primitive nations are only capable of rhythmic music,” and seem to be drawn to percussive or noisy instruments.19 Forkel believed that individual musical tones were unmediated cries of passion, hence “primitive man” communicated through “interjections and simple words, with which he described external objects in his immediate surroundings.”20 Forkel was not alone in his time in comparing such disconnected



18 The dramatic shift from “The Representation of Chaos” to the creation of light. 19 Forkel, Geschichte der Musik, 5. 20 Forkel, Geschichte der Musik, 6.

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138   The Philosophy of Rhythm gestures with “sentences that are formed merely from nouns.”21 Whereas many of these ideas can be traced to Condillac and Rousseau, their best-​known exponent in the German-​speaking lands was J. G. Herder. Echoing Herder, Forkel views historical progress as an evolution from a “language of feeling [Empfindungsprach]” to a “language of ideas [Ideensprache].” Crucially for our discussion, Forkel sees this progression as pivoting on repetition, i.e., meter: Man, in his earliest state, quickly realized that all simple things can be maintained through a certain kind of regular repetition. This regular repetition of simple things, which in itself is capable of hardly any variety, we call in music ‘meter’, or, to give it its original term, ‘rhythm.’22

If a single tone is a mere gesture, then Forkel compares a series of undifferentiated beats to a phrase “which describes not only an object, but also its quality, and binds the two together, as when I say not just ‘tree’ but ‘tall tree’, or ‘the tree is tall’, etc.”23 Just as primitive races are slow to achieve this level of linguistic sophistication, it takes them a long time to “arrange a series of tones in such a way . . . that a melody, akin to a spoken sentence, can arise.”24 A style capable of connecting notes into a melody is thus, for Forkel, analogous to a “language of ideas.” Mozart’s quartet exposition thus unfolds three kinds of “rhythm”: gestural, periodic, and punctuational. The order by which these three types unfold is significant in itself. Indeed, the evolution of Mozart’s language across the three junctures of his exposition—​introduction, first and second groups—​parallels Herder’s ternary historical model: When language evolved from the primitive wild stage to a state befitting the newly found orderliness of social and political organization, it became a poetic and sensual medium, rich in the features that distinguish poetry from prose, these features including fresh inversions and simplicity in the use of connecting particles.25

The periodic phrasing and clear articulation of the first subject evinces a “newly found orderliness.” On the basis of this civilized syntax, the second subject at bar 71 can relax into “a poetic and sensual medium.” Mozart’s theme is a pastoral musette, imitating the bagpipe’s base drone and augmented-​4th skirl. A musical representation of Nature, the theme is a musical version of the natural word-​order which Herder and others identified with poetic expression as those “fresh inversions” that “distinguish poetry from prose.” The boldest inversion is the C# on the down-​beat of measure 72, a signal instance of the gestural head-​positions of primitive syntax.

21 Forkel, Geschichte der Musik, 5. 22 Forkel, Geschichte der Musik, 4. 23 Forkel, Geschichte der Musik, 5. 24 Forkel, Geschichte der Musik.

25 Quoted in Scaglione, German Word Order, 74.

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The appoggiatura has been displaced (“inverted”) from its normative position as a syntactic phrase-​ending, i.e., a tonal cue. Placing the appoggiatura in front liberates the expressive, material dimension which civilized syntax brackets out. Nevertheless, the musette is by no means as irregular as the “wild” opening of the quartet, since its sonorities are disciplined by metrical phrasing. As a hybrid between form and formlessness, Mozart’s second subject corresponds to the median position of modern German in Herder’s eyes, a language that can “still combine the advantages of the poetic stage with those of the philosophical, a high degree of order as well as freedom.”26 Mozart’s is also a language both of the head and the heart, of civilization and nature. One is reminded of Mozart’s description to his father of his concertos K. 413–​15 as “a happy medium between what is too easy and too difficult”: they are “pleasing to the ear, and natural, without being vapid.”27 In conclusion, I hope that my foray into the thickets of historical music theory has supported my claim that rhythm has an intrinsically expressive dimension, in line with the “enhanced formalism” of the musical experience. “Rhythm” has always been as much an ideational category in intellectual history as a specifically musical parameter—​just as “harmony” shaded into “Universal Harmony,” and “melody” has its own metaphorical penumbra. I have elsewhere sketched the genealogy of these three metaphors: rhythm, melody, and harmony.28 Rhythm, which became the dominant structural metaphor during the Classical era, is particularly fascinating because it intersects with notions of gesture and language. Twentieth-​ and early twenty-​first-​century approaches to rhythm (and meter) have shorn away its ideational, metaphorical dimensions and, in the process, impoverished its capacity to represent aspects of musical meaning not captured by traditional analytic techniques. Otherwise put, they have perpetuated a false dichotomy between musical structure and musical expression, or “form” and “content.” By contrast, I have sought in this chapter to show how rhythm is inextricably bound up with music’s rational and linguistic qualities; and to suggest that a trajectory from reason to language is wired into the normative course of musical processes. Although my entry-​point into this sphere has been through recherché historical manuscripts, I maintain that the truths they illuminate are immanent to the music and available to listeners today.

Works Cited Baker, Nancy, Heinrich Koch: Introductory Essay on Composition (New Haven, 1983). Batteux, Charles, Les beaux arts réduits à un même principe (Paris, 1746). Bonds, Mark Evan, Wordless Rhetoric: Musical Form and the Metaphor of the Oration (Cambridge, MA, 1991).

26 Scaglione, German Word Order, 75. 27 Mozart, Letters, 2: 833.

28 Spitzer, Metaphor and Musical Thought.

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140   The Philosophy of Rhythm Forkel, Johann Nicolaus, Allgemeine Geschichte der Musik, vol. 1 (Leipzig, 1788). Goehr, Lydia, The Quest for Voice: On Music, Politics, and the Limits of Philosophy (Oxford, 2002). Hepokoski, James and Warren Darcy, Elements of Sonata Theory: Norms, Types, and Deformations in the Late-​Eighteenth-​Century Sonata (Oxford, 2006). Koch, Heinrich, Versuch einer Anleitung zur Composition, 3 vols (Rudolstadt, 1782–​93). Lerdahl, Fred and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, MA, 1983). Levinson, Jerrold, Contemplating Art: Essays in Aesthetics (Oxford, 2006). Mattheson, Johann, Der vollkommene Capellmeister [The Perfect Chapelmaster] (Hamburg, 1739). Mozart, Wolfgang Amadeus, The Letters of Mozart and his Family, 2 vols, ed. Emily Anderson (London, 1966). Rosen, Charles, The Classical Style: Haydn, Mozart, Beethoven (London, 1971). Rothstein, William, Phrase Rhythm in Tonal Music (New York, 1989). Scaglione, Aldo, The Theory of German Word Order from the Renaissance to the Presence (Minneapolis, 1981). Schachter, Carl, “Rhythm and Linear Analysis: Durational Reduction,” Music Forum, 5 (1980), 197–​232. Spitzer, Michael, Metaphor and Musical Thought (Chicago, 2004). Sulzer, Johann Georg, Allgemeine Theorie der schönen Künste, Part 2, vol. 2 (Biel, 1777).

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9 Rhythm and Popular Music Alison Stone

1.  Popular Music and a Question about Rhythm and Value In this chapter I explore some ways that rhythm affects us in popular music. This raises straightaway the question of how “popular music” is to be understood: the concept is notoriously problematic and while many attempts have been made to define it, all are contentious. Different authors use the term differently, and overall the term covers “a wide range of fundamentally different musics,” as Max Paddison points out.1 Some authors take “popular music” to encompass traditional folk music; for others, “popular” and “folk” oppose both one another and a third term, “art music.” Within this tripartite popular–​folk–​art division, “folk” is supposedly the traditional music of the people rather than the elite, stemming from rural and pre-​modern contexts, while “popular” music is also non-​elite but this time aimed at the urban masses in industrial, modern, commercial contexts. Since the nineteenth century, the musical styles and practices of cabaret, music hall, minstrelsy, cabaret, and “light” classical music popularized for dancing have all at times been counted as “popular.”2 So have jazz, blues, country, Tin Pan Alley, and big band music; rhythm-​and-​blues and rock ’n’ roll in the 1950s; and more recently the array of genres that descend from rhythm-​and-​blues and rock ’n’ roll—​including rock, pop, soul, funk, electronic dance music (EDM), and rap. Clearly, then, “popular music” encompasses a range of musical forms and styles. They are diverse not only in their specifically musical features, but also in their social meanings and their levels of compliance with or antagonism to the context of capitalist commodity production. My focus in this chapter is on the field of popular music genres since rock ’n’ roll, which I call either “post-​rock ’n’ roll music” or just “popular music” for short (thus, unless otherwise indicated, from here on I use the term “popular music” in

1 Paddison, “Critical Reflections,” 197. Birrer, “Definitions and Research”; Jones and Rahn, “Definitions of Popular Music”; Middleton, Studying Popular Music, esp. Ch. 1; Gracyk, Rhythm and Noise, esp. Ch. 1, and “The Aesthetics of Popular Music”; Leach, “Popular Music”; and Tagg, “Analysing Popular Music,” address the problems of defining popular music. 2 Scott, Sounds of the Metropolis, discusses the evolution of the category of “popular” music. Alison Stone, Rhythm and Popular Music In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0010

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142   The Philosophy of Rhythm this restricted sense). These post-​rock ’n’ roll genres still differ enormously, but they share the following cluster of features: (1) extensive recording and technological mediation, prioritizing recording over performance. (2) four layers of texture: (i) melody (vocal or not), (ii) harmony, (iii) functional bass, and (iv) “explicit beat,” i.e., indefinitely pitched percussion (“unpitched” for short). Allan Moore explains: The vast field that is popular music . . . exhibits a strong tendency to display four functional layers. Not all will be present in every example, not all will remain unchanging throughout . . . However, while one layer may be absent, or changes in these layers may occur in the course of a track, they do so against the background assumption of their presence. It is the principal norm of popular music.3

Although the musicians who provide the bass and explicit beat layers are often said to work as a unit to form a band’s “rhythm section,” these are two theoretically distinct layers of texture with distinct roles. The role of bass, in particular, is to mediate between the pitched elements (melody and harmony) and the unpitched percussion, playing notes that define the chords and underlie the melody, but stating a definite, usually repeated rhythm that locks in with the percussion. (3) Particular instruments realize these layers according to a historical pattern—​ respectively:  (i) vocals, electric guitar, or synthesizer; (ii) electric guitar or synthesizer, again, for the chords; (iii) bass guitar or synthesized bass; and (iv) drums, drum-​machines and other percussion media. But instruments can swap roles: for instance, in rap the vocals are sometimes entirely unpitched, and so function rhythmically and not melodically. (4) A common approach treats chords “vertically” rather than “horizontally.”4 (5) Songs tend to be constructed repetitively, with small units of musical material presented at each layer of sound, and these units repeated in temporal alignment with one another, e.g., with phrases of melody repeated in time with repeated chord sequences. These combined blocks of repeated materials are then repeated, with variations, to yield whole songs organized in verse/​chorus or similar formal patterns.5

3 Moore, Song Means,  20–​1. 4 Moore, Song Means, 71. 5 Covach, “Form in Rock Music,” discusses verse/​chorus, AABA, and other forms in popular music. On feature (1), see Gracyk, Rhythm and Noise; on (2) and (3), Moore, Song Means, 20–​1; on (4), Moore, Song Means, 71; and on (5), Middleton, Studying Popular Music. A cluster-​based account places a song in the popular (post-​rock-​’n’-​roll) field if it exemplifies, to a sufficient degree, enough standard features of this field.

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In this chapter I  focus on another feature commonly found in post-​rock ’n’ roll music: a strong rhythmic dimension.6 It is because of this emphasis on rhythm that music in many popular genres solicits us to dance and move; songs can energize, elate, enrage, depress our spirits, or wind us down. These affective reactions have somatic roots, bound up with changes in bodily energy. Art music has somatic effects too, but popular music genres such as rock ’n’ roll, disco and EDM are most notable in this regard. Leading into my exploration of this rhythmic dimension, I want to begin with a question about value. Theorists such as Robert Grossberg recognize rock ’n’ roll’s (and related genres’) rhythmic dimension and bodily appeal, and for Grossberg these features are sources of positive value, as the power of the music lies not in what it says but in what it does, in how it makes one move and feel. . . . Rock and roll is corporeal and ‘invasive’ . . . [and] without the mediation of meaning, [its] volume and repetitive rhythms produce a real material pleasure . . .7

Rock’s effects, Grossberg continues, “do not necessarily involve the transmission, production, structuration, or even deconstruction of meaning.” Likewise for Jeremy Gilbert and Ewan Pearson, some popular music—​EDM—​acts directly on our bodies by prompting us to dance.8 However, while Adorno agrees that some music compels physical movement and certain affective and energetic reactions, he views this negatively. His criticisms of 1930s commercial dance-​band music also apply to rock ’n’ roll and successive pop genres, to find that compulsion a negative rather than positive value. He claims that the rhythmic and corporeal force of dance-​band music is problematic because its unvarying “basic beat” dominates listeners. For him, this form of music compels while short-​circuiting our intellects, preventing critical reflection on these processes.9 Adorno alerts us to an area of concern in rock ’n’ roll and its successors because, to reiterate, music in these genres typically includes a layer of “explicit beat” provided by percussion instruments and repeated throughout, though with variation. Apart from jazz hybrid genres (jazz-​funk, jazz-​rock, etc.), it is rare for improvisations to complicate matters. Normally each song maintains a constant percussion pattern throughout. An illustrative example of constant percussion maintained throughout a pop song is the drum layer in Michael Jackson’s “Billie Jean” (the 1983 single version as subsequently included on Jackson, Number Ones). The drum pattern here is standard in popular music (Figure 9.1). The snare drum

6 Shuker, Understanding Popular Music, 7, comments of popular music that its “only common element” is “a strong rhythmical component, and generally, but not exclusively, . . . electronic amplification.” That said, the rhythmic component is stronger in some genres, such as disco, than others. 7 Grossberg, We Gotta Get Out, 113. 8 Gilbert and Pearson, Discographies. 9 E.g. Adorno, Introduction to the Sociology of Music, 29.

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144   The Philosophy of Rhythm

Figure 9.1  Michael Jackson, “Billie Jean,” cabasa, drums, bass guitar, and synthesizer, timing c.00:20–​00:24

sounds on the even divisions of the 4/​4 beat (i.e., beats two and four), the bass drum on the odd divisions (beats one and three). The drums thus spell out the 4/​4 metre to which “Billie Jean,” like the majority of popular songs, is set. By counting to the recurring drum pattern listeners can identify how the music is organized. Drums are present from the start, and bass guitar, bass synthesizer, and cabasa appear on measure three. Staccato chords, played on another synthesizer, enter on the eleventh measure. Thus, the drums establish the metric framework into which the other instruments fall. If explicit beat spells out meter, meter also regulates the repetitions of musical elements. Metric constraints govern the length of each element (e.g., the bass line in “Billie Jean”) and the points in time when each element begins and ends, thereby coordinating the elements presented at each layer of sound. Higher-​level groupings determine the length of each song section and the points at which instrumental patterns change between sections. For example, the chorus section of a typical popular song might be constructed out of (a) four repetitions of a four-​chord sequence, within which each chord is presented for one measure; these align with (b) four phrases of melody, each four measures long; (c) eight repetitions of a two-​measure bass line; and (d) sixteen repetitions of a one-​measure percussion pattern. These repetitions can be coordinated due to the presupposed uniform metrical grid, against which the durations of all iterated units are measured. The worry suggested by Adorno, then, is that repetitive organization in popular music dominates individual musical materials with a quasi-​mathematical grid. Explicit beat spells out the regulating role of this grid. Further, in its structured repetition, popular music is organized by “measured time.”10 This is abstract, mathematized time, an artifact of modern science, abstracted from the irregular, qualitatively varying, lived time of human experience, and from the uneven temporal processes of nature. To control natural processes, time is reduced to successive units of identical duration, a series of infinitely divisible “nows” that we can reckon

10 Abel, Groove.

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and calculate with to intervene into nature. The musical result is meter, where a measure is the basic temporal unit, each of these units can be divided (e.g., into four quarter-​notes), and those divisions can be subdivided again ad infinitum. In the other direction, measures can be added endlessly to build up compositions of any length; this time is divided into identical units. Further, from Adorno’s perspective, clock-​time is an integral factor in industrial society and the factory system, enabling productive tasks to be broken down into their components and those components to be timed, apportioned to different individuals, and coordinated. Thus popular music’s repetitive organization renders it potentially complicit with capitalism and its domination over the material world—​both the materiality of human bodies and of natural things. I’ll argue, though, that in its typical approach to meter and rhythm, popular music challenges rather than reinforces the domination of clock time over the lived, bodily world. Crucially, popular music typically has a layer of explicit percussive rhythm (see Section 2). The rhythms of the other sound layers either reinforce or pull against the percussion rhythm, and so come to form a dynamic of partly conflicting, partly intertwining energies (Section 3). In virtue of these complex rhythmic pulls-​and-​pushes, popular songs solicit us to move our bodies in time with them (Section 4). But songs do not exert compulsive force on our bodies as Adorno feared. Rather, we make sense of songs’ conflicting energies at a bodily level. In moving to music we are effectively thinking through its rhythms with the tacit, practical intelligence of our bodies, modeling movements of our body parts on shifts of emphasis and timing in the music. In turn, we apprehend the music as energetic just because it invites bodily participation. The measured time that enables this rhythmic dimension to crystallize within popular music is a formal construct that elicits the intelligent activity of our bodies. Precisely these formal and conceptual qualities enable the music to take on an energetic character and enable our bodies to exercise intelligent agency in response. So, against Adorno, our bodies are empowered. Contrary to Grossberg, however, they are empowered as intelligent agencies and not as brute material objects.

2.  Explicit Beat and the Backbeat Explicit beat or explicit rhythm is one of the four typical layers of sonic texture in popular music.11 It is “explicit” in several respects: (1) Whether they are real or synthetic, the standardly used drums of popular music (snare drum, bass drum, toms, hi-​hat, and cymbals) are unpitched, with most of the other percussion commonly used in pop songs—​hand-​claps, floor-​stomps, tambourines, maracas, etc. Being unpitched, these instruments

11 Moore, Song Means, 20–​1; Gracyk, Rhythm and Noise.

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146   The Philosophy of Rhythm or media provide only rhythm without also contributing to melody and harmony. Because not all these percussive media are drums, I talk throughout of “percussion” rather than “drums” regarding this layer of the texture, except in specific reference to drums. (2) Typically the percussion layer is present throughout a song. Some percussion patterns are episodic: cymbal splashes or drum fills marking transitions between sections, or drum solos. But generally those episodes are part of the percussion layer present throughout a song. Popular songs without unpitched percussion do exist—​such as the Beatles’ “Eleanor Rigby”—​but are rare. (3) The percussion layer normally presents a short rhythmic pattern or cell that is repeated either for the whole song or a whole section. As in “Billie Jean,” it is common for a percussion pattern to last for one measure and so be repeated once per measure. Multiple repetitions of these patterns are then assembled to make up the entire percussion layer of a track. Usually these patterns are repeated with variations, or with additional episodes such as drum fills. (4) Popular music tends to emphasize the backbeat, i.e., beats two and four in each measure in 4/​4 time. This is usually done by sounding the snare drum on beats two and four, and the bass drum on one and three. Because the snare drum is smaller than the bass drum its sounds have higher frequencies (although no precise pitch) and therefore stand out more, so that the snare’s whip-​crack sound cuts through the texture more audibly than the duller thud of the bass drum. The prominence of the snare drum can be increased further by other means, such as its being struck more forcibly, mixed louder, treated electronically, recorded with echo, or a combination of these. For example, Bruce Springsteen’s “Born in the USA” emphasizes the snare-​drum beats so heavily that they sound like explosions. This bass-​and-​snare-​drum combination is pervasive in popular music. Measures of 4/​4 time can be subdivided into eight parts, with additional drum sounds placed on some of these—​generating, for example, a double back-​beat (Figure 9.2). By subdividing the 4/​4 beat further, additional possibilities for variation can be produced. Each quarter-​note beat can be divided into three parts (so that the meter is effectively 12/​8), or the beat can be subdivided into sixteen parts, generating the very busy and complicated rhythms heard in funk. Changing which percussion instruments or parts of the drum set are used, for instance using only tom-​toms, yields further variations, as does use of time signatures other than 4/​4—​most often 3/​4 and 6/​8—​although 4/​4 remains overwhelmingly common. And, albeit rarely,

Figure 9.2  The double backbeat

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songs can include changes in meter, or measures or parts of measures can be unexpectedly dropped or added. We can identify further sources of variation from Charles Keil’s picture of “groove,”12 i.e., variations over time on a repeated rhythmic pattern. For Keil, groove arises when some instruments sound out a steady beat—​say, four beats to the measure on the bass drum—​while other instruments sound slightly ahead of or behind that same beat—​say, the snare drum sounds slightly before or behind beat two in each measure—​thus “leaning” forwards or backwards, however infinitesimally.13 The “timing discrepancies” that interest Keil are minute—​as when a forward-​leaning snare drum regularly sounds on, say, what is effectively point 1.9 in the measure or even 1.85. Timing nuances arise, then, when one instrument presupposes a finer-​grained subdivision of the measure to the one that the track explicitly spells out. By introducing such nuances, the standard popular music beat (i.e., the bass-​and-​snare, odd-​and-​even, combination) can be greatly varied. Dick Bradley’s account shows why these variations matter. He rightly treats rock ’n’ roll as derived from rhythm-​and-​blues, where The setting up of a regular, more or less homogeneous rhythmic ‘background’ and a partly or wholly improvised foreground of one or more instruments and/​or voices, set against the background, offers . . . an image . . . of ‘individual’ actions in the context of the shared experience of externalized, alienating time. By ‘externalized time’ I refer to . . . the mediation of the clock . . . [as] a precondition for the economic system of capitalism . . .14

Thus, for Bradley, constant rhythmic patterns upheld by the rhythm section of a rhythm-​and-​blues band enact measured time, a concomitant of capitalism. Yet, Against a stretched-​out, unyielding temporal background—​the beat—​the singer, guitarist, horn-​player or whoever, uses  .  .  . anticipations of the beat, delays, accelerations . . . , melodic improvisation . . . and . . . freely varied timbre/​sound production, to detach his or her . . . sound from the beat, cutting across or against the beat . . .15

That strategy continues in rock ’n’ roll, for Bradley, so that what he calls “the beat”—​ the constant, explicit rhythm in the background—​ceases to be alienating and is made into a resource against which individuals can realize themselves freely and creatively.16 The contributions of vocalists, lead guitarists, etc., musically and symbolically enact the freedom of the individual from oppressive clock-​time.17

12 Keil and Feld, Music Grooves.

13 Keil and Feld, Music Grooves, 61–​2; see also Roholt, Groove. 14 Bradley, Understanding Rock ’n’ Roll, 48.

15 Bradley, Understanding Rock ’n’ Roll, 49. 16 Bradley, Understanding Rock ’n’ Roll, 50. 17 Bradley, Understanding Rock ’n’ Roll, 51.

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148   The Philosophy of Rhythm For Bradley, that freedom is symbolized by the rhythmic, melodic, and other variations that vocalists or “lead” instrumentalists effect against the explicit beat. But we can also apply Bradley’s argument to the explicit beat layer itself. Yes, we might say, the snare and bass drums (or other percussion instruments) present a standard beat that encapsulates clock time, but that beat is subjected to countless variations. These variations on what each percussion instrument is doing, and how and when it does it, embody the freedom of individuals to modify and inflect the standard bass-​and-​snare  beat. Moreover, there is a stronger sense in which popular music’s standard bass-​ and-​snare beat establishes an alternative to clock time and its attendant power relations—​not only in the endless variations under which it appears, but in its standard 4/​4 bass-​and-​snare shape. We turn here to Ted Gracyk’s account of explicit rhythm, which follows jazz historian Gunther Schuller in describing the backbeat, descending from early jazz, as a “democratized beat.”18 To explain this, I need to clarify how I understand rhythm, meter, and beat. The definition of musical rhythm is contested, but we may take it that a rhythm arises when within a series of connected sounds some stand out over others as “stronger” than others. Several factors, not just relative volume, make for strength or weakness.19 A  rhythm, then, is a pattern of stressed and unstressed sounds. Meter is “bonded rhythm”:20 a system for organizing and imposing regularity on rhythmic patterns so that the strong and weak points regularly fall in certain places relative to one another. Not all music is metric (many songs that follow the varying emphases of speech are non-​metric, save for the cadence of speech) and different metric systems exist in different cultures. My concern, however, is with meter in its Western form as it has crystallized from 1600 onwards, since this kind of meter is what popular music generally presupposes. In this system, pulses in the flow of time are evenly placed and used to demarcate the music into measures, each containing a given number of pulses. The first pulse—​or beat—​in each measure is strongest.21 This is because it marks the boundary between measures, and is thus the point to begin counting out the time. While the first beat in each measure is thus accented, musicians may or may not physically stress it (subtly or conspicuously). Beats, then, are points or pulses in time that mark out the divisions of the measure to which a song is set, and in this sense need not be sounded. On the other hand, in popular music, because there is normally an “explicit beat” layer, it is normal that at least some pulses are sounded. Standardly, when the metre is 4/​4, the bass and snare 18 Schuller, Early Jazz; Gracyk, Rhythm and Noise. 19 “Rhythm may be defined as the way in which one or more unaccented beats are grouped in relation to an accented one” and “such factors as duration, intensity, melodic contour, regularity . . . play a part in creating an impression of accent” (Cooper and Meyer, Rhythmic Structure of Music,  6–​7). 20 Sachs, quoted in Hamilton, Aesthetics and Music, 136. 21 “Meter is the measurement of the number of pulses between more or less regularly recurring accents. Therefore, in order for meter to exist, some of the pulses in a series must be accented—​marked for consciousness—​relative to others. When pulses are thus counted within a metric context, they are referred to as beats. Beats which are accented are called ‘strong’; those which are unaccented are called ‘weak’ ” (Cooper and Meyer, Rhythmic Structure of Music, 4).

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drums distribute between them the task of sounding out the four pulses that divide each measure. Thus implicit pulse becomes explicit beat. Meter establishes a hierarchy between the beats in each 4/​4 measure, with beat one on top, beat three behind it, then two, then four.22 Because it stresses the backbeat, popular music’s basic beat rejects that metric hierarchy, re-​emphasizing the beats that are marked metrically as weak. Implicitly, then, popular music’s typical stress on the backbeat subverts the hierarchy bound up with meter and, by extension, can be said to reject the broader set of power relations bound up with measured time. However, the word “democratization” is potentially confusing, as the formerly weak beats seem simply to be raised to dominant position.23 Popular music, it may be argued, stresses the backbeat but still presupposes an accent on beat one. In that case beats one (and three) would be privileged metrically while beats two (and four) are privileged in actual practice—​resulting in rough overall equality. But does popular music presuppose that the downbeat is accented? Joel Rudinow argues otherwise, stressing African influences: Western musicology has been given to theorizing the back beat as a ‘displacement’ of accent from presumed normal expectations . . . and thus as an instance of ‘syncopation’, which is in turn understood to be basically a matter of upsetting rhythmic expectations . . . however, the presumption as to which expectations are ‘normal’ is objectionable from the point of view of ethnomusicology . . . unlike European and European-​derived musical traditions, African-​derived rhythmic organization does not always accent the reference beat (the one) . . . [which] need not even be enunciated. . . . it would be a misleading . . . to theorize the back beat as . . . a ‘departure from normal rhythmic expectations.’24

Perhaps post-​rock ’n’ roll music simply operates with a norm on which beats two (and four) rather than one (and three) are accented. But this view is incorrect. Contrary to Rudinow, popular music works with inherited Western meter as well as African-​rhythmic practices, and continues to accent the downbeat, while instituting a new norm of stressing the backbeat. The two forces—​metric and rhythmic, structural and practical—​are pitted against one another to generate conflicting energies.

22 “Fundamental to the idea of meter is the notion of periodic alternation of strong and weak beats . . . For beats to be strong or weak there must exist a metrical hierarchy—​two or more levels of beats” (Lerdahl and Jackendoff, Theory of Tonal Music, 19). For them, if we ascend a level—​in 4/​4, from quarter-​notes to minims—​ the “strong” beats at 4/​4 level (one and three) are the ones that remain present at the minim level; hence their strength. 23 Abel, Groove,  49–​50. 24 Rudinow, Soul Music,  121–​2.

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3.  Sources of Rhythmic Tension To see how metric accent is presupposed in popular music, we must look beyond explicit beat to other layers of sound. In popular music, each layer of sound is typically made up of repetitions of small elements, each with a rhythm that is reiterated—​ unchanged or varied—​when the element recurs. These rhythmic qualities tend to be pronounced in popular music, partly because instruments are often played quite percussively, and also because of the role of repetition, so that rhythmic patterns recur and build up momentum. Most importantly, the rhythmic qualities of these elements are enhanced by their relations with the songs’ explicit beat layer, through which they acquire rhythmic functions either as pulling against or with emphases presented by the percussion. Given the norm that drums stress the beats sounded by the snare drum, reciprocally it is normal for at least some other layers to pull against the snare drum and with the bass drum. Because the bass drum typically sounds on beat one of each measure, the instruments that reinforce the bass drum pull the emphasis towards beats that are metrically accented. In measures 11–​12 of “Billie Jean,” the snare drum stresses the backbeat. But all other instruments pull, to some degree, with the bass drum. First, the bass guitar: a slightly greater stress occurs on the notes occurring on beats one and five, in time with the bass-​drum beats. The first bass note in each measure, on beat one, stands out further, being on the tonic pitch F♯ and reinforced by the first stabbing synthesizer chord in each measure. The backbeat remains most emphasized, but bass guitar and synthesizer chords effect a significant pull of energy back towards beat one. Moreover, bass guitar and synthesizer parts indicate that metric accent is presupposed, for each cycle through their repeated elements begins on beat one. The synthesizer signals this with quaver-​length tonic chords on the first beat of each measure, cementing the tonic and confirming the metric accent. Likewise, each iteration of the bass line begins on beat one: the bass line starts from the tonic at this point. In popular music more broadly, chord cycles generally begin on beat one of a measure and chord changes generally occur at that point too; placement of vocal phrases also reflects metric accent, with vocal lines generally starting around beat one of a given measure. Thus meter is central to the cyclical and repetitive mode of organization of popular songs. “Billie Jean” illustrates something else. Synthesizer and bass guitar lines reinforce the bass drum, but also stress the second “half ” of each second beat, a point in time not enunciated by either the bass or snare drums. The bass line puts a slight emphasis at this point by returning to the tonic pitch here, while the second synthesizer chord likewise sounds here, whereas we might have expected it to sound on beat three. Thus bass line and synthesizer chords “lean” slightly ahead of the bass drum, creating a sense of tension and adding to the song’s qualities of

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anxiety, nervousness, and agitation. The track has a “forward-​leaning” groove with reversed connotations to “backward-​leaning” grooves, which are typically relaxed and laid-​back. This is not the sort of minute timing nuance considered earlier with regard to Keil, yet something interesting is going on. In binary terms: (a) Bass/​snare-​drums: (b) Keyboard: (c) Bass guitar:

1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0

Returning to the idea that the popular music beat is “democratized,” the unexpected placements of sounds in (b) and (c) introduce a further type of democratization. Any 4/​4 measure can be subdivided indefinitely, but initially into eight equal parts. Thus 1 2 3 4 becomes 1 and 2 and 3 and 4 and Each eighth-​note pair (1-​and) adds up to a quarter-​note beat (1) at the higher level, where each quarter-​note beat begins on the first of each eighth-​note pair, giving it priority. This norm filters down from the higher-​level prioritization of beat one as marking the start of each measure. Here is another hierarchy implied in meter, which can be subverted by beginning a sound on the second half of any quarter-​ note beat (whether or not the sound runs on into the next beat). The same kind of subversion or syncopation (a “timing displacement”) can be accomplished at any subdivision of the beat: the finer-​grained the subdivision, the more possibilities for subversion. This kind of syncopation presupposes measured time and metric hierarchy just as the stressed backbeat does: the norm must be presupposed to be subverted. Thus, popular music presupposes metric hierarchy by using that hierarchy, playing it off against the stress on the backbeat and against timing displacements to create a dynamic pull of energies between different beats—​those that are metrically accented and those that are rhythmically stressed or sound in unexpected places. Metric accent is mobilized into a resource for producing dynamic pulls and counter-​pulls of energy within a song. Central to this process is the presence of an explicit beat layer to which every layer of sound becomes related. Songs become fields of energy, containing forces pulling and pushing with and against one another. We apprehend the music in this way insofar as we come to enact its tensions with our bodies and so experience the music’s rhythmic tensions as being energetic in turn—​as sharing in the character of the bodily energies and impulses that they invite. Or so I now argue.

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4.  Rhythm and Bodily Agency Critics and proponents of popular music agree that it acts on our bodies through its explicit rhythmic dimension. But what is the nature of this action? One might assume that it is causal, affecting our bodies much as one billiard ball knocks another into motion. However, this cannot be correct; our bodies are not mere causal mechanisms. We are bodily agents. As de Beauvoir writes, the body is “our grasp on the world and the outline of our projects.”25 She does not mean that I use my body as an external vehicle for executing my plans, as I use a car or bicycle for traveling to work, picking up and putting it down as required. Rather I, as body, decide what projects to pursue just in deciding how to do something physically by forming an initial bodily sketch or outline of the action, which I then execute. But if my body is thus the primary location of my agency and not a mere mechanism, efficient causation cannot be the route along which musical rhythms affect us somatically. To consider how these effects occur, we look at the nature of our bodily agency as explored by de Beauvoir and other phenomenologists such as Merleau-​Ponty. Their view is that my projects are inherently bodily, involving I-​as-​body navigation. I-​as-​body make sense of surrounding space from the perspective of my possibilities of movement. This is a tacit process; I act actions, adjusting my movements, and forming habits, such as the postures by which I  keep a bicycle balanced. For Beauvoir and Merleau-​Ponty, this is primarily how I experience my body—​as identical with me to the extent that I am an everyday, practical agent going about my daily activities. I exercise intelligence tacitly, identical with the practical operations of my body. There is a secondary perspective that we each take on our bodies: I regard my body from the outside, as an object. For Merleau-​Ponty, I adopt this perspective when breakdowns occur in my habitual, practical, routines: if something malfunctions, say if I become ill, I turn and look at the body with which, from the primary first-​ person perspective, I was simply identical.26 In this perspective I “have,” rather than “am,” my body. The secondary perspective makes possible a tertiary, scientific one—​ in which, having adopted the standpoint of viewing our bodies and their processes as objects, we scrutinize and analyze them in abstract, scientific terms. We use explicit intelligence to make calculations regarding the body, and experience this kind of intelligence as set over against the body. My bodily agency can be interpreted in several ways. For early Sartre, I freely envisage possible actions, and in the light of them, confer meaning on the world.27 If I choose to take an uphill walk, the hill becomes an opportunity or challenge, not an obstacle or indifferent natural feature, as when I want to travel quickly to the



25 De Beauvoir, The Second Sex, 66, translation emended.

26

Merleau-​Ponty, Phenomenology of Perception, 157.

27 Sartre, Being and Nothingness, 628.

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hill’s other side. Plausibly, though, the relation between environment and activities is more reciprocal than Sartre has it. Environments, situations, and objects are not formless until we frame possibilities; rather, any environment presents us with determinate possibilities. A steep hill does not offer a casual, effortless stroll. Objects and situations afford us definite possibilities of action. What these possibilities are depends on objects’ physical properties, although the possibilities do not reduce to this physical base, but arise in the relation between objects and agents.28 From this perspective, music affords us various possibilities of action. In the case of popular music these include singing or singing-​along; imitating performers’ gestures and behaviors; playing along, if one has the skills; moving in time; dancing; exercising; and regulating one’s emotions by listening to certain songs to cultivate a given mood. Bodily movement is central to all these activities. Playing, performing, and singing-​along involve repeated bodily movements, and uses of popular music in exercise depend on its propensity to energize us. Emotional regulation, too, has a bodily component, with music raising or decreasing our levels of energy. The movements that popular music encourages do not reduce to dancing. There is an immense variety of ways of moving to popular music, with dance practices themselves ranging from the anarchic to highly structured, rule-​governed dance routines (such as the Macarena); from individual to collective behaviors; and from the restrained and decorous to the ecstatic and euphoric. Ways of moving can fall short of dancing proper: bobbing one’s head, tapping one’s fingers or feet, jiggling slightly while performing tasks around the house, or making gestures such as punching the air or leaping. Focusing on bodily movement, rather than dance more narrowly, how does popular music afford possibilities for movement? Bill Haley remarked that I felt that if I could take, say, a Dixieland tune and drop the first and third beats, and accentuate the second and fourth, and add a beat the listeners could clap to as well as dance, this would be what they were after.29

Haley’s remark pertains to the norms for different layers of sound both to emphasize different beats and also to put sounds and silences in unexpected places relative to the beat that other layers of sound spell out. These differences invite listeners to align movements and gestures of their different body parts with these different points of emphasis or timing in the music, for example by clapping hands on beats two and four (with the snare drum) while separating the hands on beats one and three (with the bass drum). Someone might do this while, say, first centering their pelvis on beats one and two then thrusting out their hip on beat three and four. Schematically, we align different body movements with different divisions of the

28 My understanding of the concept of affordance comes from Beauvoir and Merleau-​Ponty. See also DeNora, Music in Everyday Life, 45. 29 Gillett, Sound of the City, 24.

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154   The Philosophy of Rhythm beat and make each movement when the emphasis falls in a given place. As we move, we exert energy. We feel the energy in our bodies shift from one place to another, as different body parts are tensed and relaxed in moving them. Mostly we do not consciously plan these gestures, although someone can practice a particular routine in the mirror. Generally, moving to music is carried out at a directly bodily level without reflective control. Moreover, there is no set way in which particular rhythmic patterns must become mapped by bodily movements. Here the intelligent body devises endless ways to map rhythmic shifts corporeally (usually incorporating social and cultural mediations, so that dance styles carry social connotations). Thus, when the music offers us possibilities of movement, we gain a possibility of bodily self-​realization instead of passively accepting the effects of compulsive force. Our bodies exercise practical agency by generating meaningful patterns of movement. In addition, they exercise latent intelligence, making sense of music’s rhythms by generating these patterns. We do not make explicit calculations regarding the music and how to move to it—​e.g., “this song has a bpm (beats-​per-​minute) of 130 so I should move my legs at this speed.” Rather, there is a trial-​and-​error process by which we attempt certain movements to a given track and adjust them until they “fit” the music. DJs and studio practitioners may calculate that songs with a certain bpm arouse people to dance. But here they assume an already existing practice in which we respond to music at a tacit, bodily level. By virtue of its pronounced rhythmic qualities, then, popular music appeals to our bodies as perceptive agencies. Our response is intelligent and creative in finding individual and endlessly variable patterns of movement that map those rhythms. This is a positive value of popular music; it invites us to participate in its rhythms, exercising our latent bodily intelligence. To return to our problem of value, the rhythms of popular songs do presuppose measured time: popular music is constructed repetitively with homogeneous time serving to measure out and coordinate its repetitions. But the repeated elements have their own rhythms in relation to the explicit beat—​supporting it, pulling against it, or oscillating. Thus, measured time enables the rhythms of each layer of sound to stand in a dynamic relation. The pull of stressed backbeat against metric accent presupposes meter; the tensions produced by unexpected placements of sounds or silences rely on the metric subdivision of the beat. Thus, measured time is used in popular music to intensify its rhythmic quality and its consequent invitation to movement. Measured time is used to further the realization of the intelligence and creativity of our bodies. This way of employing measured time subverts the power relations embedded in the clock time that organizes scientific inquiry and industrial social life. Whereas ordinarily clock-​time is an instrument by which nature and materiality are analyzed, controlled, and dominated, in popular music measured time becomes a resource for creating fields of energy that empower embodied human agents.

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Works Cited Abel, Mark, Groove: An Aesthetic of Measured Time (Leiden, 2014). Adorno, Theodor W., Introduction to the Sociology of Music, tr. E. B. Ashton ([1962]; New York, 1976). Birrer, Frans, “Definitions and Research Orientation:  Do We Need a Definition of Popular Music?,” in David Horn, ed., Popular Music Perspectives, vol. 2 (Exeter, 1985), 99–​106. Bradley, Dick, Understanding Rock ’n’ Roll:  Popular Music in Britain 1955–​ 1964 (Milton Keynes, 1992). Cooper, Grosvenor W. and Leonard B. Meyer, The Rhythmic Structure of Music (Chicago, 1960). Covach, John, “Form in Rock Music: A Primer,” in Deborah Stein, ed., Engaging Music: Essays in Musical Analysis (Oxford, 2005), 65–​76. De Beauvoir, Simone, The Second Sex, tr. H. M. Parshley ([1949]; London, 1988). DeNora, Tia, Music in Everyday Life (Cambridge, 2000). Gilbert, Jeremy and Ewan Pearson, Discographies: Dance Music, Culture and the Politics of Sound (London, 1999). Gillett, Charlie, The Sound of the City ([1970]; revd edn, London, 1983). Gracyk, Theodore, Rhythm and Noise: An Aesthetics of Rock (Durham, NC, 1996). Gracyk, Theodore, “The Aesthetics of Popular Music,” Internet Encyclopaedia of Philosophy (2008): https://​www.iep.utm.edu/​music-​po/​. Grossberg, Lawrence, We Gotta Get Out of this Place:  Popular Conservatism and Postmodern Culture (London, 1992). Hamilton, Andy, Aesthetics and Music (London, 2007). Jackson, Michael, Number Ones, audio recording (Los Angeles, 2003). Jones, Gaynor and Jay Rahn, “Definitions of Popular Music:  Recycled,” Journal of Aesthetic Education, 11.4 (1977), 79–​92. Keil, Charles and Steven Feld, Music Grooves (Chicago, 1994). Leach, Elizabeth Eva, “Popular Music,” in J. P.  E. Harper-​Scott and Jim Samson, eds, An Introduction to Music Studies (Cambridge, 2009), 188–​200. Lerdahl, Fred and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, MA, 1983). Merleau-​Ponty, Maurice, The Phenomenology of Perception, tr. Colin Smith ([1945]; London, 2002). Middleton, Richard, Studying Popular Music (Milton Keynes, 1990). Moore, Allan F., Song Means: Analysing and Interpreting Recorded Popular Song (Farnham, 2012). Paddison, Max, “Critical Reflections on the Concept of Popular Music,” Rivista di Analisi e Teoria Musicale, 21.1–​2 (2016/​17), 197–​214. Roholt, Tiger C., Groove: A Phenomenology of Rhythmic Nuance (London, 2014). Rudinow, Joel, Soul Music:  Tracking the Spiritual Roots of Pop From Plato to Motown (Ann Arbor, 2010). Sartre, Jean-​Paul, Being and Nothingness, tr. Hazel E. Barnes ([1943]; London, 1993). Schuller, Gunther, Early Jazz: Its Roots and Development (Oxford, 1968). Scott, Derek B., Sounds of the Metropolis: The 19th-​Century Popular Music Revolution in London, New York, Paris, and Vienna (Oxford, 2008). Shuker, Roy, Understanding Popular Music (2nd edn, London, 2001). Tagg, Philip, “Analysing Popular Music:  Theory, Method and Practice,” Popular Music, 2 (1982),  37–​65.

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10 Rhythms, Resemblance, and Musical Expressiveness Ted Gracyk

For no melody has the power to awaken a true sensation or a real feeling in us if the rhythmic does not order all movement of the tone-​feet in a way that produces some pleasing relationship together and against each other. Johann Mattheson, The Perfect Chapelmaster (1739)

Contemporary philosophers have had much to say about the expressive power of music. However, the current volume excepted, they seldom discuss musical rhythm.1 Given the empirical evidence that almost everyone who listens to music is aware of its rhythms,2 philosophy of music betrays a surprising neglect of rhythm’s potential relevance to our perception of musical expressiveness. I  argue rhythm plays an indispensable role in establishing a relevant resemblance between musical expressiveness and human expression of emotion. Standard objections to resemblance accounts of musical expressiveness disappear when we recognize that entrainable rhythms play a role in music’s expressiveness. Finally, while arousalism does not supply a general account of musical expression, entrainment’s role in expressiveness bridges the divide between “resemblance” and “contagion” accounts of music’s expressiveness.3

I Objects and events that lack mental states cannot express emotions. Yet there is a standard use of “express” that recognizes that non-​sentient objects can be used as vehicles to express emotions. Why is music among these things? The underlying 1 Notable exceptions include Hamilton, Aesthetics and Music, 119–​52, and Scruton “Thoughts on Rhythm.” 2 Drake et al., “Tapping in Time,” 1–​23. 3 Davies, “Infectious Music,” defends a complementary explanation of contagion. Features of my argument are suggested by Davies, “Artistic Expression”, and Cochrane, “Theory of Musical Expressivity”; neither assigns a central role to entrainment. Ted Gracyk, Rhythms, Resemblance, and Musical Expressiveness In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0011

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problem is how and why we successfully map the language of emotional expression onto music.4 I employ the neutral phrase “expressive qualities” as a generic label for any features of a public display that indicate which emotion is being expressed. A display of expressive qualities expresses an emotion when it reveals an occurrent emotion.5 Such qualities may also be displayed when no such emotion is present, as when there is either insincerity or there is mere expressiveness. Thus one feigns surprise for the surprise birthday party that was not actually a surprise. Composers and musicians frequently build expressive qualities into their music without thereby expressing their own emotions. It is thus possible that very few musical compositions express the emotions of their composers. A composer wracked with grief is unlikely to have composed Mahler’s Kindertotenlieder. The same point holds for Janet Baker’s performances of Mahler’s Kindertotenlieder. Baker’s expressiveness is like Natalie Wood’s tears in the film West Side Story (1961)—​it is likely that she performed sadness.6 However, while it is obvious that the ability to shed tears on cue is a good way to feign sadness, why does singing a specific melody, orchestrated in a certain way, convey the depths of grief? The expressive quality of “Wenn dein Mütterlein” is independent of the libretto, for the music conveys grief even if one does not understand German. The core problem is that knowledgeable listeners display considerable agreement about which expressive qualities are present in instrumental music—​for example, that the ending of Vaughan Williams’ Symphony No. 6 is perceived as resignation. Some contend that these recognitions of grief and resignation are cases of metaphorical thinking.7 However, there is no reason why we must consciously apply the concept of sadness to the music in order to perceive its sadness. Yet that would have to be the case if we were to hold that we employ a metaphor when we say that music has a particular expressive quality. At the same time, our intersubjective agreement does not require literal usage. Thus Todd contends that any talk of musical tempo involves reference to “a fictitious variable since it cannot be measured directly.”8 He might be right, but reference to a fictitious variable does not disrupt the meaningfulness of conversations about tempo, such as the suitability of Beethoven’s very precise tempo indications for his symphonies. Finally, music’s expressiveness is not explained by regarding music as a universal language of the emotions. For example, Raga Yaman is a flowing, soothing melodic framework, generally performed as a flute piece. Knowledgeable Hindustani listeners regard it as expressing romantic yearning (sringâra). In its cultural 4 I set aside any position that says that the correlations between musical properties and emotive predicates are arbitrary and conventional. 5 This distinction derives from Tormey, The Concept of Expression. 6 Appeal to an expressive persona is promoted by Levinson, “Musical Expressiveness” (1996), and Robinson, Deeper than Reason; criticisms are found in Davies, “Contra the Hypothetical Persona”, and Kivy, Antithetical Arts. 7 Trivedi, “Music and Imagination,” 116–​17. Vermazen, “Expression as Expression,” 206, criticizes the metaphor account. 8 Todd, “Kinematics of Musical Expression,” 1941.

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158   The Philosophy of Rhythm tradition, its performance can be understood to express longing, most often the romantic longing of separated lovers.9 It can also express religious longing. However, listeners unfamiliar with the Hindustani tradition do not perceive its intended expressivity. Playing it for American students, I have asked them to select its rasa or “taste” from the standard rasa list—​the majority identify the mood as sorrowful (nearer to karuna, compassion). These results correspond with those of a more systematic study, where American students perceive expressive qualities, but do not strongly agree on their identification.10 At the same time, the majority of my students identify the Adagietto from Mahler’s Fifth Symphony as sringâra (longing) rather than karuna (compassion, or sorrow). Despite their ignorance of Mahler’s music generally and the Adagietto specifically, their familiarity with the basic structures of Western classical music guides and justifies a fine-​grained response. Such experiments confirm that many musical indicators of expression are culturally specific and learned, and therefore the test of expression must be the consensus of culturally immersed or knowledgeable listeners.11 As Meyer writes, “the languages and dialects of music are many.”12 This point extends to rhythm, too, and so also to the latter’s expressive contribution.

II A piece of music has a particular expressive quality if that quality is a perceptible feature. I endorse a variation of the resemblance account of musical expression. Some musical properties sufficiently resemble human expressive qualities to allow us to perceive the music as possessing expressive qualities. This is appearance emotionalism, the position that the crucial resemblance “is that between music’s temporally unfolding dynamic structure and configurations of human behavior associated with the expression of emotion.”13 As Stephen Davies writes, “music is expressive in recalling the gait, attitude, carriage, posture, and comportment of the human body.”14 However, I am interested only in pursuing the limited idea that our perception of rhythm is essential to perceiving some of the requisite resemblance. On the account that I defend, connections between rhythms and the gait and comportment of the human body are often sufficient to establish the resemblances.15 Appearance emotionalism faces serious criticisms. First, the resemblance involves cross-​categorical perception. However, it is unclear how sound patterns resemble non-​audible aspects of human bodies. Second, to the degree that there is a resemblance between auditory motion and movements of human bodies,

9 Sharma, Music Aesthetics, 120.

10 Chordia and Rae, “Understanding Emotion in Raag.” 11 Levinson, “Musical Expressiveness,” 107.

12 Meyer, Emotion and Meaning in Music, 62. 13 Davies, “Artistic Expression,” 181. 14 Davies, “Artistic Expression,” 182. 15

Lidov, “Emotive Gesture in Music,” proposes a resemblance theory in which posture is equally important.

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there are equally strong resemblances between sound patterns and other things we encounter. It is not sufficient to argue—​as in Jenny Judge’s contribution to this volume—​that there is movement-​related content present in our perception of rhythm.16 Appearance emotionalism owes us an account of why we perceive musical patterns as human in appearance. Why doesn’t the slowness of a Mahler adagio make us think of a turtle’s motion, instead of a human motion?17 Third, there is no independent way to specify what counts as a “sad musical appearance,” independent of the judgment that the music appears sad. Apart from such specification, we cannot even say which degree of resemblance will be sufficient to count as musical expressiveness. However, if we cannot offer a “translation rule” that ties the human appearances to the musical appearances, then reference to resemblance is an explanation without substance.18 The first two of these three objections are disarmed by my proposal about entrainable rhythms, and the third is answered by the fact that my proposal recognizes that empirical inquiry should offer us greater clarity about our “translation” rules.

III Concerning rhythm, the account I propose applies to all music with a recognizable meter—​a discernible, entrainable beat. According to a standard textbook, rhythm refers to the entire time aspect of music and, more specifically, . . . a rhythm refers to the particular arrangements of long and short notes in a musical passage. . . . Meter is background; rhythm is foreground.19

Any given meter can support an infinite variety of rhythmic manifestations; for example, contrast variation thirteen of Beethoven’s Diabelli Variations (Op. 120) with Anton Diabelli’s original waltz. Beethoven’s thirteenth variation preserves Diabelli’s waltz meter, the Vivace tempo, and the key of C major. However, Beethoven employs spaced chords and dramatic stretches of silence to transform Diabelli’s straightforwardly sunny oom-​pah-​pah into an exercise in vacillation. As William Kinderman emphasizes, Here the sheer strength of Beethoven’s rhythmic conception makes a mockery of Diabelli’s theme . . . The humor of the variation consists in its expressive use of silence: our expectations are alternately strained by the forceful gesture of the chords and then dissipated into nothing.20

16 See Chapter 4, “ ‘Feeling the Beat’: Multimodal Perception and the Experience of Musical Movement.” 17 Trivedi, “Resemblance Theories,” 227. 18

Levinson, “Hearability-​as-​Expression,” 192–​204,  196–​8.

19 Kerman and Tomlinson, Listen, 9. 20 Kinderman, Beethoven, 215.

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160   The Philosophy of Rhythm The two Presto variations preserve the original key and meter. Where variation ten frolics gleefully, the nineteenth charges forward with determination. The expressive differences among these waltzes are largely due to differences in tempo and, where there is a shared tempo, to rhythmic differentiation. As Justin London writes, “Meter is a perceptually emergent property [of music]”; we frequently impose rhythmic organization even when no perceptible accents are present.21 More importantly, the experience of meter requires entrainment—​ attentional and bodily anticipation of a periodically regular accent, of invariance within variance. An extended rhythmic sequence can typically be heard in any number of metric frameworks, a point of some importance to my subsequent argument. Because rhythm and meter are intertwined, any attempt to treat one as logically prior to the other is ultimately specious. Crucially, there cannot be a perception of metric regularity within rhythmic diversity unless there is entrainment: “Musical meter is the anticipatory schema that is the result of our inherent abilities to entrain to periodic stimuli in our environment.”22 However, this anticipation involves something more than mere attentive expectation. A listener’s anticipatory schema is a mental representation of sensory-​guided action involving their own musculoskeletal system.23 Perception of a beat and a tempo requires motor planning of bodily action. Foot tapping is the paradigm demonstration of entrainment. A  basic referent tempo is established by the length of time between these strong accents, with longer lengths providing slower music. Thirty beats per minute is the slowest that we respond to as an entrainable beat; it is experienced as crawling, barely moving. Metric perception also involves awareness of subdivisions heard within the baseline beat. Listeners who foreground twelve tonal events within the “space” of two downbeats hear that musical line as moving more rapidly than do listeners who focus on four tonal events within the hierarchy of events in that same stretch of music. Metric entrainment is more than just a means of counting notes and gauging musical tempo. It also involves an awareness of our bodily deportment and movement that synchronizes us with the occurrent music. To have a sense of tempo is, in part, to have a sense of our own velocity, either of the whole body or of a limb.24 Even if we do not move to music, we do not feel its beat unless we engage in “beat induction” by constructing a “motor representation of the musculoskeletal system,” that is, we do not locate the beat unless we perceive how we ourselves would move—​and what at what speed—​in synchronizing our movements to the regular strong accent.25 This correspondence between bodily motion and musical understanding is routinely exploited so that music can be used to lock a group into a measured pace, or

21 London, Hearing in Time, 4. 22 London, Hearing in Time, 12. 23 Todd, “Kinematics of Musical Expression.” 24 Todd, “Kinematics of Musical Expression.” 25 Todd, “Sensory-​Motor Theory of Rhythm,” 26; see also Todd, “The Kinematics of Musical Expression,” and London, “Musical Rhythm.”

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so that work songs can be used to synchronize workers. Synchronized dancing is another adaptation of entrainment. However, beats per minute do not tell the whole story. Rhythms coincide and are hierarchically ordered. Music with a steady tempo becomes phenomenally faster and slower as musical events are crowded within, or dispersed among, the anticipated downbeats. Again, the point is illustrated by comparing Diabelli’s original waltz with Beethoven’s thirteenth variation; or Bruce Springsteen’s standard arrangement of his own song, “The River.” It opens with a harmonica and an indeterminate meter, settles into a plodding tempo, and then suddenly bursts into a rapid rush of giddiness at the line: “But I remember us driving in my brother’s car.” Yet the downbeats are as evenly spaced as before. The rapidity and the accompanying emotional change are largely due to the way that the melodic line suddenly becomes dense with notes. Because we regard the vocal melody as central to the musical action, the music seems to speed up, even if, metronomically, it does not. Entraining to the melodic motion, we recognize that keeping pace with it involves a sudden increase in our own effort and velocity. Yet we have the same “beats” per minute as before in the supporting instrumentation, where we find that tactus or primary beat level. In contrast, when trills and similar musical figures are understood as ornamentation, their rapidity is not interpreted as speeding up the music.

IV We now see how entrainment supplements appearance emotionalism. Peter Kivy’s formulation of the resemblance theory of musical expressiveness identifies a similarity between the tempo of music and the tempo of the movement of people experiencing particular emotions: The most obvious analogue to bodily movement is . . . rhythm . . . in all sorts of ways, the rhythmic movement of the human body in all kinds of emotive expressions is mirrored by and recognized in music. [Thus] funeral marches are slow and measured, as sadness slows and measures our expression of it.26

Kivy notes that a “jagged and halting rhythm” will also have a direct analogue in human expressive behavior, but otherwise ignores the expressive potentiality of rhythm. This neglect is not surprising. Outlining a contour model of expressiveness in which the experience of auditory contours permits recognition of analogous human expressive behavior, Kivy emphasizes the music’s melodic line as expressively more pertinent than its rhythms. The rising and falling of the melody is what really matters. Tempo is relevant, for it must not be inappropriate to the expressive contour.

26 Kivy, Sound Sentiment, 55.

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162   The Philosophy of Rhythm However, tempo is not the whole story. Mari Riess Jones has shown that we “rely heavily on rhythmic properties to differentiate melodies.” A melodic contour generally becomes unrecognizable “if its original rhythm changes, even when temporal segmentations and statistical pitch properties are unchanged.”27 In short, the perception of rhythmic detail is essential to the perception of melody, and therefore rhythm is an important variable in the expressive differences presented by rhythmic and thus melodic variations of a melodic contour. Davies is more explicit about the resemblance between rhythm and the appearances of expressive human gestures; though like Kivy, he focuses on movement from low to high, with little explicit discussion of rhythm and tempo.28 His account is consistent with mine, for he says that the “resemblance that counts most for musical expressiveness . . . is that between music’s temporally unfolding dynamic structure and configurations of human behavior associated with the expression of emotion.”29 These dynamic structures include “subtle nuances of timing.” Thus “music is expressive in recalling the gait . . . and comportment of the human body.”30 And of course gait and comportment are influences on carriage and posture. Our first challenge to the expressive centrality of resemblance was the issue of cross-​modal resemblance. How does the listener know which gait and comportment of the human body is associated with a particular piece of music? Considerable guidance arises from entrainment with the music’s primary beat level. Normally, the primary beat establishes a tempo of beats per minute within a range that crawls (at thirty beats per minute) to one that shudders in rapid spasms (at 240 beats per minute, the upper range of our discrimination for downbeats).31 If I can entrain to the music’s primary beat, which I must do if I am to grasp its tempo, then I know how I will comport myself in time to it. I know if my gait is fast or slow, sluggish, comfortable or frenetic.32 If the music establishes one tempo in its primary beat level and another tempo at another level of the rhythmic hierarchy, I may entrain to both, by sensing or simulating how different parts of the same body will move at different speeds. Some tempos are conducive to whole-​body resonance, as in a swaying motion, while others encourage limb movement.33 (Contrast the bodily motion of waltzing with the rigid body and arm stance that accompanies elaborate footwork, as in some Irish dancing.) In order to perceive rhythm, the listener must know how a human body—​his or her own—​will move in relation to that music. For most people, the key resemblance between the movement of music and the gait and comportment of the human body is not located in an imagined visual appearance. We grasp the music’s gait in a preconceptual recognition process. Knowledgeable



27 Jones, “Music Perception,” 10.

28 Davies, Musical Meaning and Expression, 229–​39.

29 Davies, “Artistic Expression,” 181. 30 Davies, “Artistic Expression,” 182. 31 London, Hearing in Time, 127. 32 London, Hearing in Time.

33 Todd, “The Kinematics of Musical Expression,” 1948.

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listeners feel the beat. Even the listener who has internalized the rule of sitting perfectly still in the concert hall will entrain to the music. The centrality of entrainment explains our near-​universal propensity to interpret music as human gait and comportment. A listener might deny engaging in any conscious comparison of musical movement and human movement. But entrainment explains why people perceive expressive movement without having to recognize the resemblance. The second objection is now defused. We interpret an adagio as a slow human movement because we judge the tempo in terms of the template it provides for our own movement. Not knowing how a turtle controls its musculoskeletal system, I do not hear an adagio as a turtle’s motion, for I do not feel it that way. Perhaps I could do so, if I consciously thought about a turtle while listening to the first movement of Mahler’s Symphony No. 10, but this would be a capricious response to Mahler. Perception of rhythm is, by default, a representation of a pattern of human movement. Once this is established, we can go on to interpret many movements musically. My strategy parallels Wollheim’s account of representational seeing, grounding responses to two major objections—​ the cross-​ modality and multiple resemblance problems—​to animation-​resemblance accounts of musical expression. Just as Wollheim posits the capacity for seeing-​in as logically prior to seeing pictures in painted surfaces, an entrainment account of musical expression holds that the ability to hear expressiveness in rhythmic sounds is logically prior to hearing some musical patterns as expressive gestures. Another advantage of the appeal to entrainment is that it implies that our awareness of temporal patterns in music “is a musically peculiar instance of a more general perceptual and cognitive ability.”34 Because these abilities are biologically rooted and biologically constrained, we are limited in the range of basic meters that we can perceive. With visual representation, Wollheim holds that viewers can distinguish between the painted surface and whatever they see “in” that surface. Nonetheless, the perception of the painted surface is inseparable from the picture: there is one experience with two distinct aspects.35 Similarly, listeners can distinguish between the sounds and their musical properties.36 Furthermore, perception of the relevant motion is not an inference from the rhythmic structure, and neither the perception of rhythm nor its resemblance to expressive human behavior requires thinking about it under any particular description. Absent description and inference, expressiveness does not require the deployment of metaphor or analogy. This account owes no further explanation of why, from among all the things that music resembles, listeners “choose” to compare the sad music to sad human gestures and movements rather than, say, to the droop of the willow tree or the movement of turtles. We do not choose the comparison.37 34 London, Hearing in Time, 5. 35 Wollheim, Painting as an Art, 46. 36 E.g. Scruton, Aesthetics of Music, 16–​20, distinguishes sounds and tones. 37 My account is consistent with Nussbaum, The Musical Representation, 33, which explains musical representation in terms of Gibsonian “affordances”—​environmental invariants that perceiving organisms interpret as affording possibilities of action.

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164   The Philosophy of Rhythm This account is bolstered by the emerging consensus that, normally, we recognize the emotional states of others by feeling them ourselves—​by physically mimicking or imaginatively simulating their bodily actions. This imaginative simulation prompts simulated emotional response. To a large extent, an individual’s capacity to recognize a particular emotion in another person depends on her capacity to mimic that emotion.38 This mimicry is not necessarily conscious. As Giacomo Rizzolatti puts it, the brain’s natural mirroring function “allow[s]‌us to grasp the minds of others not through conceptual reasoning but through direct simulation. By feeling, not by thinking.”39 Rhythmic entrainment is a special application of this general human capacity. We are naturally disposed to entrain with other people. Without conscious effort, we feel (and frequently synchronize with) any rhythmic motion of people we observe. In turn, entraining the body normally simulates emotion. By extension, if a tempo and rhythmic structure corresponds to movement patterns associated with a particular emotion, then competent listeners will tend to agree on the expressive character of the music, for they will become aware of its particular expressive qualities by consulting the same mental process that is employed to determine the expressive behavior of an actual person expressing occurrent emotion. And, again, there need not be conscious recognition of the way that both musical movement and human movement move us, spatially and thus emotionally (even if only as a simulation). The process of identifying music’s rhythms allows listeners to identify the sadness of a Mahler adagio by feeling, not thinking. This account of entrainment, movement, and expression has the additional benefit of explaining why musical expressiveness arouses emotions. It does so, in part, by engaging the same recognition-​contagion combination that ordinarily accompanies awareness of people in our immediate environment. Consequently, the entrainment theory of rhythm deflates the charge that appearance emotionalism lacks translation rules that correlate human appearances to specifiable musical structures. Thus London explains how specific ranges of beats per minute align with distinctive gaits as established by the number of steps taken in locomotion.40 The difference between perceived andante and allegro correlates with walking strides and running strides, respectively. Since these strides impose numerous gait differences beyond mere steps per minute, the musculoskeletal system aligns to a musical andante differently than to an allegro. Entraining to these tempos, we are aware of these musculoskeletal differences. If we move beyond tempo to consider basic rhythmic variations within andante and allegro tempos, we are likely to find that there is considerable intersubjective agreement in human comportment when entraining to these variations. Thus, rhythms show promise in



38 Damasio, The Feeling of What Happens, 65–​77, provides examples. 39 Rizzolatti, quoted in Blakeslee, “Cells That Read Minds.”

40 London, “Musical Rhythm,” and “Problem(s) of Rhythm Perception.”

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providing some basic translation rules, though few listeners will be conscious that they “know” them. Finally, entrainment as a catalyst for emotional contagion addresses an issue about musical expressiveness. It answers an objection to resemblance accounts by Levinson, namely, that appeal to perceptual processes does not elucidate the concept of musical expressiveness.41 True: it treats musical expressiveness as a special case of a more general experiential phenomenon. The elucidation lies in appeal to the mechanism by which we establish a central resemblance between perception of music’s rhythms and perception of human movement. Beyond that, the analysis rests on the concept of expressiveness as it applies to expressive behavior. These behavioral patterns do not infallibly express emotion, either in persons or in other situations. Yet the expressive character of grief, joy, and so on can be perceived in any behavior or process that resembles behaviors that normally indicate grief. Entrainment explains why we so readily perceive expressive qualities in familiar kinds of music with entrainable rhythms: it is of a piece with our relatively effortless ability to perceive the emotions in the people around us.

V A new problem arises from the claim that entrainment and emotional contagion—​ our “mirroring” of music’s perceptible expressive qualities—​is non-​inferential, natural, and typically unconscious. If true, why doesn’t everyone perceive the same expressiveness in all music with entrainable rhythms? Why aren’t we moved emotionally by any such rhythm? Earlier, I denied that music is a universal language, noting that consensus about the expressive character of a particular piece of music tends to be restricted to listeners familiar with its musical tradition. Against this, it might appear that rhythms are universally accessible, and therefore entrainment should ensure cross-​cultural access to the basic expressive quality of entrainable music. Thus, everyone should be moved in the same way by most music. Yet few listeners are equally moved by all music. So the theory seems to make the wrong predictions. Three points defuse this problem. First, there are significant differences in how rhythm is handled in different musical cultures and subcultures; being adept in one does not make someone equally competent in all others. Entrainment should not be considered a “passive” response: enculturation informs recognition of complex rhythms. Second, rhythm is merely one of several factors responsible for musical expressiveness. At the same time, different emotions can share similar movement profiles (e.g., serenity and grief). But if melody and harmonization play anything like the role assigned to them in standard accounts, it is no surprise that entrainment is frequently countermanded or clarified by other musical cues. Neophytes

41 Levinson, “Musical Expressiveness,” 106.

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166   The Philosophy of Rhythm and knowledgeable listeners respond differently. Third, it becomes more difficult to simulate the emotion of another person when he or she is the object of one’s own emotion; it is difficult to mirror the regret of someone with whom one is angry, or to empathize with a friend’s joy while one envies them. Likewise, music is an occasion and object of full-​blown emotion, as when an unfamiliar style elicits boredom, puzzlement, or irritation. Acquired associations and prejudices about a particular style can generate strong negative emotions, overriding the rhythm’s contagion effect. Someone who disdains religious music might be less likely to entrain to a Bach cantata. My account emphasizes the importance of kinematic anticipation of rhythm, not mere awareness of the tempo of the baseline beat. The former requires far more engagement than the latter and so the requisite kinematic anticipation is less likely to be grasped by anyone whose situation or musical tastes interfere with engagement. My account of the connection between an unconscious kinematic response and musical expressiveness is necessarily sketchy. However, it suggests how we can identify music’s expressive qualities in the absence of overt representation of content. It posits that our capacity for recognition of music’s resemblance to human behavior is inherent in the perception of rhythm. Consequently, expressive qualities are grasped in a natural sympathetic response. This account reconciles details of the resemblance theory and the contagion theory, which are typically treated as opposing strategies for explaining music’s expressive power.42

Works Cited Blakeslee, Sandra, “Cells That Read Minds,” New  York Times (January 10, 2006):  http://​www. nytimes.com/​2006/​01/​10/​science/​10mirr.html. Chordia, Parag and Alex Rae, “Understanding Emotion in Raag: An Empirical Study of Listener Responses,” in Richard Kronland-​Martinet, Sølvi Ystad, and Kristoffer Jensen, eds, Computer Music Modeling and Retrieval: Sense of Sounds (Berlin, 2007), 137–​44. Cochrane, Tom, “A Simulation Theory of Musical Expressivity,” Australasian Journal of Philosophy, 88.2 (2009), 191–​207. Damasio, Antonio, The Feeling of What Happens: Body and Emotion in the Making of Consciousness (New York, 1999). Davies, Stephen, Musical Meaning and Expression (Ithaca, 1994). Davies, Stephen, “Contra the Hypothetical Persona in Music,” in Themes in the Philosophy of Music (Oxford, 2003), 152–​68. Davies, Stephen, “Artistic Expression and the Hard Case of Pure Music,” in Matthew Kieran, ed., Contemporary Debates in Aesthetics and the Philosophy of Art (Oxford, 2006), 179–​91. Davies, Stephen, “Infectious Music:  Music Listener Emotional Contagion,” in Amy Coplan and Peter Goldie, eds, Empathy: Philosophical and Psychological Perspectives (Oxford, 2011), 134–​48. Drake, Carolyn, Amandine Penel, and Emmanuel Bigand, “Tapping in Time with Mechanically and Expressively Performed Music,” Music Perception, 18.1 (2000), 1–​23. Hamilton, Andy, Aesthetics and Music (London, 2007).



42 This essay profited enormously from comments by Justin London and Joseph G. Moore.

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Rhythms, Resemblance, and Musical Expressiveness  167 Jones, Mari Riess, “Music Perception: Current Research and Future Directions,” in Mari Riess Jones, Richard R. Fay, and Arthur N. Popper, eds, Springer Handbook of Auditory Research (Vol. 36): Music Perception (New York, 2010), 1–​12. Judge, Jenny, “‘Feeling the Beat’:  Multimodal Perception and the Experience of Musical Movement,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C4. Kerman, Joseph and Gary Tomlinson, Listen (7th edn, Boston, 2012). Kinderman, William, Beethoven (Berkeley, 1995). Kivy, Peter, Sound Sentiment: An Essay on Musical Emotions (Philadelphia, 1989). Kivy, Peter, Antithetical Arts: On the Ancient Quarrel Between Literature and Music (Oxford, 2009). Levinson, Jerrold, “Musical Expressiveness,” in The Pleasures of Aesthetics (Ithaca, 1996), 90–​125. Levinson, Jerrold, “Musical Expressiveness as Hearability-​as-​Expression,” in Matthew Kieran, ed., Contemporary Debates in Aesthetics and the Philosophy of Art (Oxford, 2006), 192–​204. Lidov, David, “Emotive Gesture in Music and Its Contraries,” in Anthony Gritten and Elaine King, eds, Music and Gesture: New Perspectives on Theory and Contemporary Practice (Aldershot, 2006),  24–​44. London, Justin, Hearing in Time: Psychological Aspects of Musical Meter (Oxford, 2004). London, Justin, “Musical Rhythm: Motion, Pace and Gesture,” in Anthony Gritten and Elaine King, eds, Music and Gesture:  New Perspectives on Theory and Contemporary Practice (Aldershot, 2006), 126–​41. London, Justin, “Entrainment and the Problem(s) of Rhythm Perception,” in Peter Cheyne, Andy Hamilton, and Max Paddison The Philosophy of Rhythm: Aesthetics, Music, Poetics, eds (Oxford, 2019), C11. Mattheson, Johann, Der vollkommene Capellmeister [The Perfect Chapelmaster] (Hamburg, 1739). Meyer, Leonard B., Emotion and Meaning in Music (Chicago, 1956). Nussbaum, Charles O., The Musical Representation: Meaning, Ontology and Emotion (Cambridge, MA, 2007). Robinson, Jenefer, Deeper than Reason:  Emotion and Its Role in Literature, Music, and Art (Oxford, 2005). Scruton, Roger, The Aesthetics of Music (Oxford, 1999). Scruton, Roger, “Thoughts on Rhythm,” in Kathleen Stock, ed., Philosophers on Music: Experience, Meaning, and Work (Oxford, 2007), 226–​55. Sharma, Manorama, Music Aesthetics (New Delhi, 2007). Todd, Neil P. McAngus, “The Kinematics of Musical Expression,” The Journal of the Acoustical Society of America, 97.3 (1995), 1940–​9. Todd, Neil P.  McAngus, “Sensory-​ Motor Theory of Rhythm, Time Perception and Beat Induction,” Journal of New Music Research, 28.1 (1999), 5–​28. Tormey, Alan, The Concept of Expression (Princeton, 1971). Trivedi, Saam, “Music and Imagination,” in Theodore Gracyk and Andrew Kania, eds, The Routledge Companion to Philosophy and Music (London, 2011), 113–​22. Trivedi, Saam, “Resemblance Theories,” in Theodore Gracyk and Andrew Kania, eds, The Routledge Companion to Philosophy and Music (London, 2011), 223–​32. Vermazen, Bruce, “Expression as Expression,” Pacific Philosophical Quarterly, 67.3 (1986), 196–​224. Wollheim, Richard, Painting as an Art (Princeton, 1987).

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11 Metric Entrainment and the Problem(s) of Perception Justin London

1. Introduction As Tim Crane writes in the Stanford Encyclopedia of Philosophy, the “problem of perception” is that we may or may not be able “to reconcile some apparently obvious truths about our experience of the world with the possibility of certain kinds of perceptual error.”1 Current psychological research in rhythm perception shows the existence of different kinds of error to those most discussed in the philosophical literature, which has tended to focus on vision. Before discussing the ramifications of this research for the problem of perception, however, we shall first rehearse the problem in its more familiar, visual setting. Two much-​discussed problems of perception, which have broad epistemic ramifications, are the problem of illusion and the problem of hallucination. In illusion, what we often perceive is not what is actually there, but rather a distorted version of the world; yet we are somehow able to accommodate this fact in our perceptual judgments. In hallucination, we perceive (or believe we perceive) things that are not actually present at all. This chapter will not consider the problem for perception created by hallucinations, other than to say that the difficulties created by illusions and other sensory distortions may well persist in the case of hallucinations, insofar as the latter are grounded upon or otherwise primed by our perception and sensation of real objects and events in the world. The problem of illusion is, as those who work in psychophysics know quite well, simply the problem of perception itself. A classic example of an “illusory” percept is that of a rectangular white table. When we observe the table, we may see a rectangular top with certain proportions, but if we view it from different perspectives, its height-​to-​width ratio may change, and it may no longer appear as a rectangle at all (i.e., it may appear trapezoidal). Similarly, depending upon lighting conditions, the table may not appear white, but red, or brown, or blue. Since the object cannot be both rectangular and trapezoidal, or both red and white, our perceptions seem 1 Crane, “Problem of Perception,” section 1.1. Justin London, Metric Entrainment and the Problem(s) of Perception In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.001.0012

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172   The Philosophy of Rhythm (a)

(b)

Figure 11.1  Kanizsa triangle, organized array (left panel); disorganized array (right panel)

incoherent—​we see a red table which is really white, a trapezoidal table which is really rectangular, and so on. These observations are advanced as a critique against “direct” or “naive” realism—​the claim that we have direct access to objects and events in the world through our senses. The alternative proposal is that if we have a coherent percept of a white table under these conditions, we can only do so via some mental representation which mediates our incompatible sensory data.2 While an “ecological” approach to perception, most famously that of James J. Gibson, is able to account for some aspects of the problem of illusion by shifting the problem from that of illusory versus real objects to the pickup of invariant information in a dynamic perceptual array,3 research both old and new in perception and psychophysics has shown that our perceptual systems themselves may generate illusory or otherwise false perceptions. Consider Gaetano Kanizsa’s well-​known visual contour illusion.4 When the various shapes (visual “cues”) are arranged as in the left-​hand panel of Figure 11.1, we see an equilateral triangle with edges defined by an illusory brightness and grayscale contrast. In the right-​hand panel, with some of the cues 2 Here, “sensory data” is used in its psychological sense, that is, the output of our sensory organs, and not to invoke “sense-​datum” theories of perception. 3 Gibson, The Senses. 4 Kanizsa, “Subjective Contours.”

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repositioned, the triangle vanishes. Kanizsa’s illusion illustrates how our perceptual systems fill in missing information, as in the case of occluded visual objects, or intermittently masked sound sources, and can thus generate complete percepts from partial cues. The larger lesson is that our perceptual systems are not passive filters or transmitters of information, but are actively engaged with the stimuli that is presented to them. Similarly, treating our senses as perceptual systems (to paraphrase Gibson) breaks down the distinctions between sensation, perception, and cognition, as these systems are characterized by a dynamic flow between the perceptual periphery, higher levels of the central nervous system, and everything in between. The function of perception is not to register sensation, but to pick up information, and so rather than picking out individual features of a stimulus (its apparent size, shape, color, etc.)—​that is, all of John Locke’s individuated primary and secondary qualities—​the task of our perceptual systems is to make the most coherent sense of the changing stimulus array. The perception of rhythm adds another set of problems to this task of reconciliation. In the remainder of this chapter, I shall discuss some of the limits and mechanisms of our perceptual faculties for auditory rhythm, along with their epistemic ramifications. Specifically, we only have a direct perception of rhythms within a limited temporal range. Our perception of rhythm seems to be inherently cross-​modal, and that rhythmic perception is often non-​veridical, as we may add subjective accents and grouping structure to otherwise undifferentiated stimuli. I shall then conclude with some broader considerations of musical ontology as they relate to this perceptual problem.

2.  Problems in Rhythmic Perception 2.1  The Speed Limits of Rhythm Consider a simple rhythm—​a long note followed by two shorter notes in a 2:1:1 proportion. This L-​S-​S rhythm is a particular temporal “shape,” and we can readily grasp it as the same even if it is sped up or slowed down; think of a repeated rhythm or melodic motive that is subject to a ritardando or an accelerando. Thus rhythms would seem to be relational structures, not dependent upon any particular, absolute value for each element. Indeed, within most performances there is a considerable amount of expressive variation to the exact timing of rhythmic sequences, and yet we do not hear these as categorically different rhythms.5 If the L-​S-​S rhythm is played too quickly, however, we will lose our sense of three distinct notes, as Karlheinz Stockhausen demonstrated,6 when continuously sped-​ up rhythm becomes a pitch with a particular timbre. Likewise, if it is played too 5 Clarke, “Categorical Rhythmic Perception.” 6 Stockhausen, “Unity in Electronic Music.”

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174   The Philosophy of Rhythm slowly, our sense of the three articulations forming a coherent temporal group is lost. Thus while rhythmic shapes are relational in nature, their component elements are subject to absolute limits: the shortest interval between event onsets cannot be less than 100 milliseconds, and the longest cannot be more than about 2 seconds. It is within this temporal range that we have a direct apprehension of temporal patterns “as rhythms.” While the 100ms limit is both fairly crisp and uniform across most listeners and listening contexts, the 2 second limit is somewhat “squishier,” as it is more dependent upon both context and the individual listener. Nonetheless, within this range we are able to (a) individuate the elements that make up a pattern or sequence; (b) determine their number; and (c) determine their duration. So, for example, in this range we are able to distinguish quadruplets from quintuplets, and make categorical distinctions between long versus short notes.7 I take it as self-​ evident that if one cannot make these sorts of discriminations and determinations, one cannot tell one rhythm from another, and hence one cannot be aware of the particular rhythm one is perceiving/​has perceived. Of course, all of our sensory modalities have their limits, such as the spectral limits of vision, but rhythm differs in that we may have some awareness of the structural attributes of both faster and slower temporal patterns and events. We can, for example, count a series of four very slow notes, and thus “hear” a very slow quadruplet, or we may recognize that the pitch and durational contour of a musical motive which originally occurred within the 100ms–​2 second range has been translated beyond it through a process of rhythmic augmentation or diminution, and have some sense of its proportional invariance. Thus we are often tempted to describe our experience of smaller and (especially) larger patterns and events in the same way we describe our experience of temporal sequences within the 100ms–​2 second range.8 What is perhaps the great enabler of such parlance is the presence of musical and analytic notations, which allows composers and musicians to grasp via the visual modality temporal relationships which lie beyond what one may aurally grasp, in some cases leading musicians to believe that they have direct aural grasp of extremely large-​scale structures.9 Aside from these “metaphorical” extensions of rhythmic and metric terms beyond the 100ms and 2 second speed limits, there is a more significant epistemic problem for rhythm, as what is and is not a rhythm is mind-​dependent. That is, due to the limits in our sensory systems, much of which are pre-​conscious, temporal sequences “become rhythms” only when they occur within a particular temporal range, and thus their ontological status as “rhythms” seems dependent upon contingent aspects of human perceptual systems. That is, while we are able to grasp faster versus slower versions of a melody within the 100ms–​2 second range, if it should cross one of those boundaries, it may cease to be a coherent rhythm or melody. 7 I survey relevant psychological research in “Rhythm,” and Hearing in Time. 8 e.g. Cooper and Meyer’s analyses, in Rhythmic Structure, of formal structures as rhythms writ large, or a twenty-​measure passage as an extended “upbeat” or anacrusis. 9 Salzer, Structural Hearing.

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2.2  Rhythm Perception is Inherently Cross Modal Given that we are creatures of a certain size and with certain capacities for movement, our perceptual systems have evolved so that we attend to events and perform actions at timescales that are relevant to the ways in which we can (and cannot) act in our environment. The 100ms–​2 second range is key for most human perception and action, and so it is within this range that we are able to achieve sensorimotor coordination with external temporal processes (both musical and non-​musical), most notably in terms of entrainment, but also for our coordination with other serial patterns. Indeed, rhythmic perception and action is one of the best examples of “embodied cognition,” as hearing rhythms involves covert or overt motor behavior and the concomitant activation of motor areas of the brain.10 When we encounter a regular series of temporal events within the 100ms–​2 second range, our sensorimotor system spontaneously entrains to it. Entrainment may be defined as the phase-​locking of a “driven” rhythm to a periodic “driving” rhythm, such that for every n cycles of input there are m cycles of the driven rhythm.11 Our rhythmic entrainment is a dynamic form of “resonance” between our sensorimotor systems and rhythms in our environment.12 For when we listen to music, we don’t merely register the pattern of durations or event onsets, but we literally move with them. The hallmarks of entrainment are (a)  that the listener can adapt in period (tempo) and phase (coordination), should the driving rhythm change; (b) that the listener can correct for errors of phase and period in his or her own behavior to maintain coordination; and (c) that the listener’s rhythmic behavior is self-​sustaining, should the input be intermittently absent. As many studies have shown, our rhythmic behaviors, ranging from tapping along to a metronome to the performance of string quartets, display patterns of self-​sustenance and adaptation that are characteristic of an entrained system.13 Entrainment models can very ably account for particular characteristics of human rhythmic behavior and perception, in that: • We tend to entrain within a certain range, and prefer particular rates of activity with that range (viz., the optimal resonances of our sensorimotor system). • We require some minimal inputs from the “driving rhythm”—​the music we are listening to—​before we can begin to feel a sense of beat or pulse (the driven rhythm that is our response to it). • We can extract a beat or pulse even if the rhythmic input is only quasi-​periodic.14 10 On embodied rhythmic cognition, see Eitan and Granot, “How Music Moves,” and Toiviainen et al., “Embodied Metre.” For the neurobiology of rhythm perception, see Chen et al., “Musical Rhythms”; Grahn, “Neuroscientific Investigations”; and Grube and Griffiths, “Temporal Encoding.” 11 Glass and Mackey, Clocks to Chaos. 12 Chen et al., “Musical Rhythms.” 13 Repp, “Tapping Literature”; Repp and Su, “Recent Research”; Himberg, “Interaction”; and Wing et al., “String Quartet Synchronization.” 14 Rankin et al., “Fractal Structure.”

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176   The Philosophy of Rhythm • Once established, our sense of beat can persist through rests, long notes, or even against contrary stimuli, as in the case of syncopated passages. • Our sense of accent need not derive from phenomenal aspects of music—​i.e., it is not simply read from the longest or loudest notes—​but arises from the interaction between our perceptual systems and the phenomenal rhythmic “inputs” which may or may not have a range of accentual cues. More details (and examples) of these phenomena are given in Section 2.3. The more immediate point to be made, however, is that if entrainment arises in our sensory-​motor system, and there is a large and growing body of evidence from neuroscience that it does, then that system plays a pivotal role in our perception of periodic auditory rhythms, which temporal sequences we would reflexively describe as “rhythmic.” This in turn means that the perception of these rhythms is inherently cross-​modal. It is not simply that we extract information about the temporal structure of an auditory signal, and thus can distinguish rhythm A from rhythm B. Rather, our perception of temporal regularity in music—​grounded in our perception of a beat of pulse—​is part of a broader, embodied response to that auditory array, what is referred to as a perception-​action loop. This embodied response is active, not passive, as it causes the listener to interact with his or her auditory environment in a certain way. In the course of that interaction, however, our perception of the auditory signal often changes.

2.3  Entrainment Adds Rhythmic Differentiation and Rhythmic Structure Our capacity for entrainment in a broad range of contexts, both musical and non-​ musical, is the basis of beat perception in music. First, however, it should be noted that beat perception occurs within a sub-​range of the 100ms–​2 second range for rhythmic perception. The fastest rate at which we can perceive a beat is an order of magnitude slower than the rate to which we can synchronize, count, and reliably make durational discriminations. Our fastest beat perceptions occur in the range of 200–​300ms (again, depending on context), and there a strong tendency to hear a beat around 100–​120 bpm (500–​600ms) for most adult listeners, as that is the rate at which we are most likely to spontaneously tap a regular beat.15 Note that most metronomes, even electronic ones, do not go beyond 300 bpm (200ms inter-​beat interval), and typically are closer to 200 bpm (200ms inter-​beat interval). Having a faster metronome is of little use, as we cannot maintain 1:1 synchrony at more rapid rates. We can, however, maintain 2:1 (and 3:1 and 4:1) synchrony up to a subdivision rate of about 100ms.16

15 McAuley et al., “Time of Our Lives,” gives a survey. 16 Repp, “Rate Limits.”

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Figure 11.2  Beat interpolation in the opening theme of Brahms’ Symphony No. 4 in E-​minor,  Op. 98

As a result of the limits and preferences of beat perception, our perceptual system makes distinctions amongst different rhythmic rates. Fast periodicities with inter-​onset intervals in the 100–​300ms range are heard as subdivisions of a slower beat, and when confronted with a pattern of multiple, nested periodicities, we tend to hear a beat at whatever periodicity is closest to the range of 100–​120 bpm (500–​600ms). If there are regular cues, but at a much slower rate, we are likely to interpolate the missing beats, and thus hear these “loud rests.”17 Consider the opening melody from Brahms’ Fourth symphony, shown in Figure 11.2. The crotchet/​quarter-​notes are too quick in most performances to be heard as beats, while the semibreve/​whole-​ notes are too slow. Yet even when we hear this without orchestra accompaniment, we readily interpolate beats at the minim/​half-​note level (as per the cut time signature). This is again due to entrainment—​for our entrainment to musical rhythms can and usually does involve a nested set of periodicities. In Brahms’ melody these periodicities are in 4:1, 2:1, and 1:1 relations, with the “1” (the crotchet/​quarter note) being only intermittently present in the melody. As our rhythmic entrainment habitually involves more than just 1:1 periodic relationships, this leads our sensorimotor systems to add layers of rhythmic structure even when there are no cues for those layers in the musical/​rhythmic stimulus. Thus when we listen to a metronome, we hear groups of 2, 3, or 4 ticks—​the so-​ called “tick-​tock” phenomenon. Such “subjective rhythmization” has been known to psychology since the nineteenth century,18 and its neurological correlates have recently been shown.19 Figure 11.3 shows two interpretations of the “same” melody (composed by the author). When played at a fairly rapid rate (8th notes faster than 140 beats per minute), and without any other cues (such as dynamics or articulation) this sequence of isochronous pitches can be construed by listeners as in quadruplets (outlining the G-​major triad, as indicated by the circled notes), or in triplets (emphasizing the notes of the G-​major scale). The brackets indicate the recurrence of grouping patterns in each instance. There are manifold effects of this subjective grouping: we not only hear quadruplets versus triplets, but also (a)  different tempos, as the



17 London, “Loud Rests”; Snyder and Large, “Gamma-​Band Activity.” 18 James, Principles of Psychology.

19 Brochard et al., “ ‘Ticktock’ of our Internal Clock”; Large, “Resonating to Musical Rhythm.”

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178   The Philosophy of Rhythm

Figure 11.3  A “metrically malleable” melody notated in (a) 4/​4, and (b) 9/​8, showing alternate listening construals

Figure 11.4  The “Standard Pattern” (or “Bell Pattern”) timeline found in many styles and genres of African music. Upper system: construed as a three-​(or six-​) beat pattern. Bottom system: construed as a four-​beat pattern

subjective beats are at different periodicities, and (b), concomitant with the subjective grouping, different accentuation of the various notes in the melody. Subjective rhythmization thus differentiates as well as organizes otherwise undifferentiated or ambiguous rhythmic stimuli. While some aspects of subjective rhythmization are probably innate (e.g., a bias for hearing things in twos rather than threes, based on the way we most often engage our sensorimotor system as bipedal creatures), our subjective rhythmization is also influenced by our musical enculturation. Consider the “standard pattern” or timeline20 that is heard in many varieties of North African music, as shown in Figure 11.4. The top system illustrates the way most non-​African listeners tend to hear the pattern (as well as the way in which many beat-​tracking algorithms will parse it): the first note is heard on the downbeat, the third note on the second beat, and the third beat is interpolated into a series of syncopated notes (see arrows). This is the simplest construal, with two of three beats articulated by the pattern and the syncopation “contained” within the second and third beats of the measure. The bottom staff, however, is the characteristic way it is heard by enculturated listeners. It contains a greater and more complex amount of syncopation, and the third beat (which is relatively accented according to the metrical framework) is not articulated by the pattern at all. Indeed, as someone who has learned to hear the pattern in both 3 and 4 (and who can switch his perception

20 Agawu, “West African Rhythm.”

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of it at will, much like other figure–​ground reversals), I note that what is striking is that the “same” series of bell strikes seems to become a different rhythm altogether when its subjective organization and accentuation changes. Thus while our rhythmic perception is often wholly stimulus driven, in other contexts our perception of beats, beat patterns, and rhythmic groups depends upon the way our perceptual system structures the auditory stimulus. Like the filling in of illusory contours in the Kanizsa triangle, our auditory system fills in missing beats in an otherwise regular pattern of stimuli, adds grouping and accent to an undifferentiated or ambiguous series of tones, and maintains an established pattern of grouping and accent when subsequent events are undifferentiated, ambiguous, or even contradictory, as in the case of syncopation. It is worth noting that this phenomenon is not unique to rhythm perception, as our auditory system also fills in information in non-​musical contexts, such as hearing speech in noisy environments, where we nonetheless believe we actually hear the masked or absent sounds. This makes sense from an evolutionary perspective, as our perception often occurs in suboptimal conditions, with objects poorly lit, partially obscured, masked by other stimuli, and so forth. What is most interesting for discussions of epistemology of rhythm (and epistemology more generally) is that these “illusory” percepts are fundamentally unlike the classic examples of perceptual illusions (e.g., the apparent rectangular versus trapezoidal shapes of a table top viewed from different positions). While from a Gibsonian perspective there is no problem of finding the “true shape” of an object—​as there is no “true shape,” but rather a set of invariant relationships based on the structure of the perceptual array—​in the case of entrainment, and subjective accents and grouping, it is the perceptual system itself that generates the illusory beats and groups. Moreover, it seems that we can learn to perceive such groups (as in the case of the African standard pattern), and these perceptions may be subject to some volitional control—​as I can shift my sense of the organization of a rhythmic pattern, and effectively change its rhythmic qualia. This would seem to raise more fundamental problems of perception than those arising from simply ignoring the effect of position and perspective when viewing a static visual array.

3.  Erroneous Rhythms: Epistemic and Ontological Upshots While subjective rhythmization was identified by psychologists in the nineteenth century and neuroscientists in the twenty-​first, our rhythmic proclivities have long been known to composers and musicians. Subjective rhythmization was known in the seventeenth century under the rubric of quantitas intrinseca, the intrinsic or “inner value” of the notes in a measure. Here is Wolfgang Caspar Printz, writing in 1676:

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180   The Philosophy of Rhythm Further, the position in the measure has a peculiar power and virtue which causes notes that are equal to one another, according to their time signature, to seem longer or shorter.21

In many discussions of quantitas intrinseca it is often clear that this sense of accent is not due to dynamic intensity or articulation or other acoustic cues. Rather, the “peculiar power and virtue” of a note’s metric position is just the way our subjective rhythmization conveys different degrees of accent to the different positions in a subjective (metric) group. If musicians are aware, however intuitively, of the ways in which our perceptual systems work, then this raises some interesting problems for rhythmic epistemology and musical ontology. It is one thing to note that if we hear an undifferentiated series of sounds—​a ticking clock, say—​and subjectively group them into twos or threes, then we have an illusory percept. The auditory object (the series of ticks) is unstructured, yet we perceive structure that is not there. But music isn’t just a periodic series of sounds to which we can entrain. It is a cultural artifact produced for our specific interaction with it—​hence those “illusory” accents, groups, etc., may be intended to be heard by the composer. A painter who wished someone to see a triangular shape could make use of the Kanizsa illusion; a Chicago blues player can use the “stop-​time” figure to create a strong sense of meter even when two of four beats in a measure go unarticulated, as our entrainment will fill in the missing beats. Are those missing beats “part of the music?” They are obviously not part of the acoustical signal, but if a piece of music is not just a series of sounds, but a series of sounds designed to be heard by human listeners in certain ways, then perhaps one is warranted in saying that those subjective beats are part of the music. For we would not want to say that the stop-​time figure, or Brahms’ melody given above, are only intermittently in a duple meter—​our sense of meter is continuous, as is our sense of rhythmic continuity. Likewise, if syncopation is “part of the music,” then it too requires the supplementation of our perceptual systems for it to emerge, as its characteristic rhythmic quality depends upon a tension between an endogenous pulse and phenomenal articulations which do not coincide with it. In short, if we admit that music exists not in the acoustical signal, but in the mind of the listener who hears that signal, then those features of the music which are present in the listener’s mind as a result of the apprehension of that signal are in fact part of the music. In other musical styles, creating rhythms which afford multiple modes of perceptual engagement may be a vital part of their musical aesthetic. In much West African drumming the percussion ensemble collectively creates a rhythmic fabric which can be heard in different meters (3 versus 4, as in the standard pattern given above) and with the rhythm aligned to the beat and downbeat in different ways. This metric malleability allows the listener to reconstrue the rhythmic pattern as it



21 Quoted in Houle, Meter in Music, 80.

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is repeated multiple times—​what David Locke has termed a “gestalt flip.”22 This essential ambiguity depends upon our perceptual systems being able to add rhythmic organization, that is, to selectively focus on some rhythmic cues while ignoring others. There is no single “veridical” way to hear such a pattern—​only multiple modes of engagement. To conclude, I hope to have shown that an examination of what is known about our perception of rhythm raises some interesting issues for questions of perception and epistemology more generally. While considering our senses as perceptual systems solves some problems of perception, it creates other, perhaps deeper ones. In the case of musical rhythm, our rhythmic percepts are often non-​veridical, as we hear subjective groups, accents, and beats. Perhaps more than vision, a consideration of auditory perception, and our auditory perception of rhythm in particular, reminds us that the perceptual process is not a linear chain of information from the external world to the mind, but an active interplay between mind and world.

Works Cited Agawu, Kofi, “Structural Analysis or Cultural Analysis? Competing Perspectives on the ‘Standard Pattern’ of West African Rhythm,” Journal of the American Musicological Society, 59.1 (2006),  1–​46. Brochard, Renaid, Donna Abecasis, Doug Potter, Richard Ragot, and Carolyn Drake, “The ‘Ticktock’ of our Internal Clock: Direct Brain Evidence of Subjective Accents in Isochronous Sequences,” Psychological Science, 14.4 (2003), 362–​6. Chen, Joyce L., Virginia B. Penhune, and Robert J. Zatorre, “Listening to Musical Rhythms Recruits Motor Regions of the Brain,” Cerebral Cortex, 18.12 (2008), 2844–​54. Clarke, Eric F., “Categorical Rhythmic Perception: An Ecological Perspective,” in Alf Gabrielsson, ed., Action and Perception in Rhythm and Music (Stockholm: Royal Swedish Academy of Music 55, 1987), 19–​33. Cooper, Grosvenor and Leonard B. Meyer, The Rhythmic Structure of Music (Chicago, 1960). Crane, Tim, “The Problem of Perception,” in E. N. Zalta, ed., The Stanford Encyclopedia of Philosophy (2014): https://​plato.stanford.edu/​archives/​win2014/​entries/​perception-​problem/​. Eitan, Zohar and Roni Y. Granot, “How Music Moves: Musical Parameters and Listener’s Images of Motion,” Music Perception, 23.3 (2006), 221–​47. Gibson, James J., The Senses Considered as Perceptual Systems (Boston, 1966). Glass, Leon and Michael C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton, 1988). Grahn, Jessica A., “Neuroscientific Investigations of Musical Rhythm:  Recent Advances and Future Challenges,” Contemporary Music Review, 28.3 (2009), 251–​77. Grube, Manon and Timothy D. Griffiths, “Metricality-​Enhanced Temporal Encoding and the Subjective Perception of Rhythmic Sequences,” Cortex, 45.1 (2009), 72–​9. Himberg, Tommi, “Interaction in Musical Time,” PhD thesis (University of Cambridge, 2014). Houle, George, Meter in Music, 1600–​1800 (Bloomington, 1987). James, William, The Principles of Psychology ([1890]; Cambridge, MA, 1983). Kanizsa, Gaetano, “Subjective Contours,” Scientific American, 234.4 (April 1976), 48–​52. Large, Edward W., “Resonating to Musical Rhythm: Theory and Experiment,” in Simon Grondin, ed., The Psychology of Time (Bingley, 2008), 189–​232. Locke, David, Drum Gahu: An Introduction to African Rhythm (Tempe, 1998).



22 Locke, Drum Gahu, 24.

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182   The Philosophy of Rhythm London, Justin, “Loud Rests and Other Strange Metric Phenomena (or, Meter as Heard),” Music Theory Online, 0.2 (1993): www.mtosmt.org/​issues/​mto.93.0.2/​mto.93.0.2.london.html. London, Justin, “Rhythm,” in J. Tyrrell and S. Sadie, eds, The New Grove Dictionary of Music and Musicians, vol. 21 (Oxford, 2001), 277–​309. London, Justin, Hearing in Time:  Psychological Aspects of Musical Meter ([2004]; 2nd edn, Oxford, 2012). McAuley, J. Devin, Mari Riess Jones, Shayla Holub, Heather M. Johnston, and Nathaniel S. Miller, “The Time of Our Lives: Life Span Development of Timing and Event Tracking,” Journal of Experimental Psychology: General, 135.3 (2006), 348–​67. Rankin, Summer K., Philip W. Fink, and Edward W. Large, “Fractal Structure Enables Temporal Prediction in Music,” Journal of the Acoustical Society of America, 136.4 (2014): doi: 10.1121/​ 1.4890198. Repp, Bruno H., “Rate Limits in Sensorimotor Synchronization with Auditory and Visual Sequences: The Synchronization Threshold and the Benefits and Costs of Interval Subdivision,” Journal of Motor Behavior, 35.4 (2003), 355–​70. Repp, Bruno H., “Sensorimotor Synchronization:  A Review of the Tapping Literature,” Psychonomic Bulletin & Review, 12.6 (2005), 969–​92. Repp, Bruno H. and Yi-​Huang Su, “Sensorimotor Synchronization: A Review of Recent Research (2006–​2012),” Psychonomic Bulletin & Review, 20.3 (2013), 403–​52. Salzer, Felix, Structural Hearing: Tonal Coherence in Music (New York, 1962). Snyder, Joel S. and Edward W. Large, “Gamma-​Band Activity Reflects the Metric Structure of Rhythmic Tone Sequences,” Cognitive Brain Research, 24.1 (2005), 117–​26. Stockhausen, Karlheinz, “The Concept of Unity in Electronic Music,” tr. Elaine Barkin, Perspectives of New Music, 1.1 (1962), 39–​48. Toiviainen, Petri, Geoff Luck, and Marc Thompson, “Embodied Metre: Hierarchical Eigenmodes in Spontaneous Movement to Music,” Cognitive Processing, 10.2 (2009), 325–​7. Wing, Alan M., Satoshi Endo, Adrian Bradbury, and Dirk Vorberg, “Optimal Feedback Correction in String Quartet Synchronization,” Interface, 11 (2014): doi: 10.1098/​rsif.2013.1125.

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12 Entrainment and the Social Origin of Musical Rhythm Martin Clayton

But the sounds of nature alone do not follow any rhythmic pattern. Rhythm is the product of social life. The individual by himself could not invent it. Work songs, for example, arise from regular repetition of like motions among cooperating workers. Were these motions rhythmic in themselves, the songs would not provide the service expected of them. The song offers a model to the cooperating workers; the rhythm flows from the song into their movements. Hence it assumes a prior collective agreement . . . At a very young age, we are familiarized with musical ‘beat’. But society, not nature, has done this for us. Maurice Halbwachs, “The Collective Memory of Musicians” (1939),  171–​2

1.  On the social origin of musical rhythm As Maurice Halbwachs’s essay confirms, the social origin of musical rhythm is not a novel topic. For Halbwachs, work songs are a paradigm case: their rhythm may be intimately linked to the bodily movements necessary for the job at hand, but it is the song that bestows rhythmic organization on the “motions” (gestes) of work. The song’s function is collectively to organize the movements of the group, and its existence “assumes a prior collective agreement.” In this chapter I take inspiration from this fragment of Halbwachs’ argument to outline a new approach to this issue, and in doing so, argue for a return to his concern with social interaction in theorizing rhythm. The problem Halbwachs leaves unanswered is, if musical rhythm is social in origin, how does it come into being—​how is his “prior collective agreement” reached? Alfred Schütz, although casting Halbwachs as the straw man, did not explicitly contest the latter’s point about the social origin of rhythm.1 Schütz’s argument that all communication is made possible by what he called the “mutual 1 Schütz, “Making Music Together.” Martin Clayton, Entrainment and the Social Origin of Musical Rhythm In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.001.0013

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184   The Philosophy of Rhythm tuning-​in relationship,” in which individuals come to share their experience of inner time, does however contradict Halbwachs. For Schütz, rhythmic coordination is prior to any collective (social) agreement. In this chapter I argue that rhythm in fact emerges spontaneously both in individuals and, crucially, in interactions between them, and that it is therefore both natural (physiological) and social in origin. Since Fred Lerdahl and Ray Jackendoff ’s seminal Generative Theory of Tonal Music (1983), music theory has seen a decisive shift to explanations of rhythm in terms of the cognitive capacities of the human individuals who perceive it. Rhythm, for late twentieth-​and early twenty-​first-​century theorists, is not an immanent quality of a musical work or performance. Rather, it emerges in the individual’s engagement with an auditory stimulus. Thus, for example, only rhythmic structures perceptible by the human cognitive apparatus can be successfully deployed in music. Most current theorists would accept Justin London’s premise, building on psychologist Mari Riess Jones’ theory of attentional periodicity, that the perception of musical meter depends on the entrainment of an individual’s attentional rhythms to regularities in an auditory stimulus.2 This understanding of metrical perception—​in Ed Large’s gloss, the entrainment of neurological oscillators3—​does not preclude looking at a range of issues concerning the ways in which musical rhythm is actualized through interactions between individuals engaged in music. Moreover, I will argue that although meter can be explained through a perceptual and cognitive theory, further development of such a theory must take into account recent perspectives on the inseparability of perception and action—​including the role of bodily movement in rhythm production—​and thus requires understanding human interaction as inherently embodied and socially situated.4 Understanding rhythm as generated in such situations offers a route to understanding the links between social situation, cultural context, and rhythmic structure, an area which has suffered from being limited to simplistic homology theories.5 The position I will argue in this paper can be summarized as follows. First, musical rhythm is possible only thanks to inherently rhythmical, endogenous biological processes taking place in each individual human’s body. These processes are oscillatory, and tend to produce quasi-​periodic patterns in action and perception. Such rhythmical processes are, however, characteristic not of Homo sapiens per se, but of life in general. Since most species do not make music, these processes are a necessary but insufficient condition for the emergence of music. What distinguishes Homo sapiens is, rather, a flexible capacity to coordinate individual internal rhythms between members of a group. It is due to this capacity that rhythmical structures emerge in the course of entrainment between the endogenous rhythms of individuals. (By “entrainment” is meant the mutual influence of, and

2 Jones, “Attentional Rhythmicity”; London, Hearing in Time. 3 Large, “Neurodynamics of Music.”

4 Knoblich and Sebanz, “Social Nature of Perception,” “Evolving Intentions.” 5 Clayton, “Time of Music.”

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potentially synchronization of, independent rhythms.6) In this sense, Halbwachs was right to argue that musical rhythm is irreducibly social. My claim here is that musical rhythm originates in, and is sustained by, interaction between individuals, and thus cannot be reduced to individual psychological functions. Of course, it remains possible to produce or to listen to music individually. There also exist forms of music that superficially seem to exist independently of any social interaction, e.g., music created through aleatoric (chance-​dependent) or algorithmic processes. While such cases are not my main focus, I  nonetheless include them in my argument, since music made alone, enjoyed alone, or created through random or simple rule-​based systems nonetheless manipulates musical concepts, structures, processes and/​or materials whose origin remains social. Music and its rhythms may (in evolutionary time) have emerged spontaneously in social interaction. However, such emergent structure is only a small part of the music-​making of modern societies around the world. In practice, such emergent structures are sedimented into specific patterns which are transmitted between members of a given society. In some cases, but certainly not all, such structures are reflected on and represented, and thus theorized, as rhythmical structure. In the rest of this chapter I will expand on this argument, and reflect on Hindustani classical music as a case study in interpreting rhythmic structure as an index of historically sedimented human interactions.

2.  The rhythmic individual: Endogenous rhythms The living human body is replete with rhythmical processes:  respiration, heartbeat, locomotion (e.g., walking and running), circadian and menstrual cycles are some of the more obvious examples. Various theories have linked musical rhythm to those endogenous rhythms with periods in the range of a few seconds: respiration, heart rate, and human locomotion. The tempo of music has often been linked to the heartbeat, for instance, though Curt Sachs argued that the relationship to a normal walking gait was a more pertinent comparator.7 A musical beat is not normally synchronized with walking, although most people can walk in time with music if requested,8 and of course related movements are frequently synchronized to music in dance. Hamish MacDougall and Steven Moore demonstrated a strong preference for locomotive movement at around 2 Hz/​120 bpm across a range of subjects carrying out various everyday tasks, noting the apparent relationship to spontaneous tempo (expressed in finger tapping) and to preferred musical tempi.9 It seems that Sachs’ intuition has been confirmed.10 Spontaneous motor tempo has

6 Clayton et al., “In Time.”

7 Sachs, Rhythm and Tempo, 32–​3; discussed in Clayton, Time in Indian Music, 82. 8 Styns et al., “Walking on Music.”

9 MacDougall and Moore, “Marching to the Beat.”

10 Moelants, “Preferred Tempo Reconsidered.”

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186   The Philosophy of Rhythm been well studied by psychologists. Devin McAuley et al., who took into account the age of subjects, demonstrate that while spontaneous motor tempo tends to slow down significantly over the life course, for most adults the preferred value nonetheless tends to be a period of about 500–​600ms (1.67–​2 Hz; 100–​120 bpm).11 Plentiful and consistent evidence, therefore, shows the existence of endogenous rhythms in the human brain and body that tend to be expressed most commonly in this range. What is less often remarked on, but is particularly evident in musical contexts, is that individuals also tend to be able to switch between tempi, for instance between 150 bpm and 75 bpm (half as fast). Frederik Stynes et al. show that when asked to walk in time with music, subjects who are able to do so (the majority) nonetheless do so at different rates related to the nominal musical tempo. Given a piece of music at 60 bpm, for example, the majority walk at this pace, but some walk at 120 bpm and a few at 30 bpm.12 Will et al. hypothesize that the complex responses of listeners asked to tap along to music without a clear beat can be explained partly through such switches in mode.13 Accordingly, someone who can produce a spontaneous tapping rate of 120 bpm can easily switch to half or double this rate, especially if the faster or slower rhythm more closely matches a stimulus in their environment. If Large’s model of rhythm perception as effected by banks of interconnected neuronal oscillators is a reasonable approximation of the physiological structures underlying rhythmic behavior, then this switching ability is exactly what one would expect, since such oscillator networks tend to spontaneously generate hierarchical patterns of beats (i.e., a network that produces a 2 Hz oscillation is likely to also produce activity at 1 Hz and 4 Hz). Furthermore, in line with an overarching perspective in cognitive science that sees action and perception as mutually implicated, brain structures capable of generating rhythmic behavior at these time scales are also capable of entraining to rhythmic stimuli at the same time scales. Thus, an individual capable of producing a spontaneous 2 Hz tapping rhythm will normally be able to synchronize this underlying rhythm to a 2 Hz auditory signal; or to a 4 Hz signal; or to adjust this rhythm to match an auditory signal at 1.9 or 2.1 Hz. Jones argued that such internal rhythms control the deployment of attentional resources, and thus attentional energy is periodic and can be entrained to environmental stimuli. This idea underlies London’s model of metrical perception, where internal rhythms entrain to features of the musical stimulus.14 The rhythmic structure of music is rarely as simple as a 2 Hz pulse, of course. In practice, metrical patterns and their percepts are usually hierarchical in nature. What London’s theory suggests is that hierarchical temporal patterns in the brain can entrain to hierarchical patterns of an auditory stimulus. Most of what I have presented in this section currently has the status of a dominant view in music cognition and music theory. Individuals have internal rhythms

11 McAuley et al., “Time of our Lives.” 12 Styns et al., “Walking on Music.”

13 Will et al., “Pulse and Entrainment.” 14 London, Hearing in Time.

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which can be studied through movement, or at the level of brainwaves; they are hierarchical and cover a particular range of frequencies; and they can be tuned to regularities in the environment, including the sounds of a musical performance. This picture is convincing, as far as it goes. But it is not the whole story in determining the origin of musical rhythm. It is also important to consider what happens when two or more individuals interact, and their individual rhythms influence and entrain each other.

3.  The rhythm of interaction: Entrainment, attention, and emergence As noted above, what appears to be unique to humans is the flexibility and precision with which one individual can adapt to the rhythmic structures of another’s actions. Numerous examples of inter-​individual entrainment occur in other animal species: synchronous flashing in fireflies, synchronous courtship in fiddler crabs, and so on.15 Mostly, however, these seem to be automatic and invariable processes. Thus fireflies, to be capable of flashing in synchrony, require simply the ability to both generate a periodic flashing behavior and to perceive the light signals of others. If the information about another individual’s activity can influence its own, the laws of dynamical systems will see to it that a large group of animals synchronizes. In fireflies, frogs, crabs, and crickets, interpersonal entrainment is not a flexible process which can be deployed consciously in order to meet a specific goal. In Homo sapiens it certainly is; most obviously in making music, and in some kinds of sporting activity (e.g., the synchrony of a rowing team), but there seem to be no parallels to this in the behavior of other primates. Aniruddh Patel hypothesized that the ability to entrain to auditory signals is related to the development of a capacity for vocal learning, and is thus more likely to be demonstrated not in other primates but in birds (and some other animals).16 Patel et al.’s famous study of a sulphur-​ crested cockatoo apparently entraining its movements (albeit intermittently) to recorded music supports such a theory,17 as does Adena Schachner et al.’s paper in the same journal volume, which includes analysis of a large corpus of YouTube animal videos. However, as Schachner et al. point out, “avian species do not entrain to auditory beats in their natural behavioral repertoire.”18 In this respect, then, we can continue to claim with some confidence that music is a uniquely human achievement, dependent crucially on the capacity for flexible interpersonal entrainment of endogenous rhythms. This capacity is worth considering in more detail, then, before considering its expression in music-​making.



15 Buck and Buck, “Flashing of Fireflies”; Backwell et al., “Courtship in Fiddler Crabs”; Strogatz, Sync. 16 Patel, “Musical Rhythm.”

17 Patel et al., “Musical Beat in a Nonhuman Animal.”

18 Schachner et al., “Spontaneous Motor Entrainment,” 835.

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188   The Philosophy of Rhythm The ubiquity of evidence in musical performance notwithstanding, interpersonal synchrony was first analyzed by William Condon in the 1960s.19 Studying sound films of normal conversational interactions, annotating both phonetic production in speech and the movement of body parts frame by frame, he claimed to have identified both intrapersonal and interpersonal entrainment throughout his corpus. Where such synchrony was lacking, he suggested, was in cases of pathology: stroke, autism, and so on.20 Condon’s method was difficult to replicate, and his results were treated with skepticism for some time, but more recent studies have demonstrated that interpersonal synchrony in conversational interaction is, if perhaps less pervasive than Condon claimed, nonetheless real. While the majority of studies of the structure of conversation focus on its sequential structure—​turn taking, repair mechanisms, and so forth—​the mutual entrainment of endogenous rhythms seems to be a feature of conversation at least some of the time. While it may still be a matter of disagreement whether such entrainment is a necessary condition for communication, as Schütz argued,21 that it can and does happen is no longer seriously disputed. The conclusions of Adam Kendon—​one of the most distinguished scholars to have followed Condon in this endeavor—​are still pertinent today: interactional synchrony is best regarded as an achievement of the interactants that is attained when the participants come to govern their behavior in relation to one another in respect to a commonly shared frame or joint plan of action.22

Kendon’s position foreshadows more recent developments in psychology and related fields that are relevant to the argument of this chapter, including the ideas of joint action and distributed cognition. These and related terms mark out a distinct research field. This field is concerned with processes of interaction through which two or more individuals come to share a commitment to carry out a task together, as a result of which thinking takes place between a group of individuals in the context of a particular environment and set of tools.23 While this chapter is not the place for a thorough review of these literatures, it is becoming increasingly clear that occasions of joint commitment and action lend themselves to interpersonal entrainment (as Kendon suggested), and that they cannot be fully explained by describing the actions of individuals. These actions are not summative: they need to be studied in terms of the interactions themselves, and consideration needs to be given to emergent patterns of action. Interpersonal entrainment in contexts of joint action—​including even a casual conversation—​is often entirely spontaneous and unconscious. It is an emergent property of the interaction, bound by the general properties of dynamical

19 Condon and Ogston, “Segmentation of Behavior.” 20 Condon, “Behavioral Organization.” 21 Schütz, “Making Music Together.”

22 Kendon, Conducting Interaction, 115.

23 Gilbert, Living Together, provides a relevant philosophical theory of “joint commitment.”

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systems, and its emergence is closely linked to mutual attention, especially visual attention. Given similar verbal content, two people are more likely to mutually synchronize their movements if they look at each other. Exactly the same findings are replicated in studies of music-​making: entrainment happens spontaneously, even when individuals try to avoid it, and it happens more readily given mutual visual attention.24 Interpersonal entrainment, I argue here, is where we should look for the genesis and cultural evolution of musical rhythm, and for its relationship to rhythm in other human behaviors. Individuals spontaneously generate rhythmic (periodic) actions, and are able to entrain to periodicities in their environment, and to periodicities in the actions of others. This interpersonal entrainment happens spontaneously, but can also happen deliberately. That is, interactions that might at some point have occurred spontaneously are deliberately re-​enacted, and in their recreation may be consciously moderated. Crucially, the patterns of interpersonal entrainment that emerge in music-​making are far more complex, flexible, and amenable to conscious manipulation than the simple patterns of synchrony in fireflies or crabs. Amongst other animal species, humans have a remarkably flexible capacity for interpersonal entrainment. Within human behaviors, music-​making tends often to foreground the precision or flexibility with which we are able to coordinate our actions. The patterns of coordination that emerge, and which can be reliably and stably produced by groups of people, are far more varied than many accounts of dynamical systems would seem to imply. The famous Haken–​Kelso–​Bunz (HKB) equation, for instance, models in simple mathematical form the interaction between two oscillators. The equation tells us that such a system has two stable modes, with the rhythms in phase or in an antiphase relationship, the former more stable than the latter.25 Psychologists’ finger-​tapping experiments confirm that such simple behaviors conform with the predictions of HKB: people spontaneously and stably tap in phase or anti-​phase with each other. Even a cursory consideration of musical performance, however—​regardless of which musical culture is under consideration—​tells us not only that most musical actions are far more complex than simple finger taps, but that they are coordinated in ways far more varied than HKB’s two modes. Periodic rhythms of different speeds are coordinated, for instance, in various hierarchical and/​or polyrhythmic configurations, while many more subtle phase relationships than 0º and 180º are widely exploited. Musical rhythm, then, depends on both endogenous rhythms and their expression in periodic actions, but also on a uniquely flexible capacity humans share for the mutual entrainment of such actions in joint action contexts. In other words, rhythm is both natural and social in origin. If this argument is accepted, though, what are the implications for our understanding and interpretation of musical rhythm?

24 Clayton, “Observing Entrainment”; Lucas et al., “Inter-​Group Entrainment.” 25 Kelso, Self-​Organization of Brain.

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4.  Reading social interaction in musical rhythm If musical rhythm is irreducibly social in origin, it is equally true that it varies culturally. This is true on whichever scale we conceive “culture,” whether we use the term to distinguish Europeans from Indians, or opera-​goers from clubbers. Existing accounts of that diversity leave a lot to be desired, as do theories of the relationship between social factors and cultural variability. Early comparative musicology developed seemingly logical, if completely unfounded, theories explaining the evolutionary progression from one-​or two-​note melodies to heptatonic modes, and from unison to harmony. In talking about rhythm a greater confusion abounds, as is evident in the summit of this phase of musical scholarship, Curt Sachs’ Rhythm and Tempo.26 Sachs’ discussion of topics such as the role of bodily movement and the relationship to language and poetry remains of interest, and he offers his own version of the social-​origin-​of-​rhythm thesis when he states that an “impulse in man’s evolution towards a stricter rhythm appears to have come from choral adaptation.”27 His account of the differences between primitive and advanced civilizations, however, becomes confused and self-​contradictory. Rhythm in “primitive” culture is distinguished by its imprecision, he argues, drifting from one meter to another to no meter at all. Nonetheless, the same author suggests that the sophistication of African and Indian drumming is striking, demonstrating that we should not confuse primitiveness with simplicity. Sachs’ own apparent confusion on this point betrays the fact that the term “primitive” was itself becoming anachronistic, as ethnomusicology abandoned the search for evolutionary narratives. In the case of rhythm, no coherent story was ever proposed in the first place. Since Sachs, the challenge for some writers has been to describe the complexity and subtlety of various rhythmic systems. Arguments have raged over appropriate modes of representation, whether or not a particular kind of music (especially African traditions) had meter in the Western sense or not, whether it should or should not be rendered in standard notation, and so forth.28 While African music scholarship has tended to stress the importance of bodily movement from an early stage, some studies of Indian and Indonesian music scholarship have attempted to map rhythmical structures onto cosmological concepts. I have argued elsewhere that these homology theories—​e.g., that cyclic Indian musical metrical structures reflect a Hindu worldview based on very long recurring world-​cycles (yuga)—​are fundamentally flawed, and will not recapitulate that argument here.29 Rhythm was one of the parameters addressed by Alan Lomax’s Cantometrics project.30 Although this did not include metrical theory or analysis per se, Lomax was interested in the

26 Sachs, Rhythm and Tempo.

27 Sachs, Rhythm and Tempo, 39.

28 Agawu, Representing African Music. 29 Clayton, “Time of Music.” 30 Lomax, Folk Song Style.

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cultural variability of what he called “rhythmic style.”31There has been relatively little engagement with general or universal theories of rhythm and meter, despite the richness of material in studies such as Simha Arom’s monumental African Polyphony and Polyrhythm; or my own model of North Indian tala, which attempts to locate this form of rhythmic organization in the context of a generalizable theory of meter.32 Recent signs of a reversal of academic fashions include Michael Tenzer’s “Cross-​Cultural Topology of Musical Time,” which frames a collection of analytical case studies in terms of a common set of descriptive terms.33 Western-​focused theories of rhythm and meter since Lerdahl and Jackendoff have at least gestured toward the idea of universal theories. The adoption of a Chomskian “generative grammar” approach suggests that their model should in principle be expandable to cover any form of metrical organization, as Chomsky’s is for different languages, although in practice little attempt has been made to implement this. Similarly with London’s theory: since it is based on supposedly universal human capacities, it ought to be possible to expand it, with modifications, to cover any form of meter. Although London’s monograph itself does not stray far from the Western tonal idiom, this possibility is beginning to be explored.34 It seems clear that just as evolutionary theory offered little, and homology theory led us up a cul-​de-​sac, ongoing conversation between music theorists, music psychologists, and ethnomusicologists is leading to a florescence of cross-​cultural theorization of rhythm and meter. For all the positive aspects of these developments, however, the death of homology as a model, and Cantometrics as a method, leave us with a vacuum where we might be looking for connections between cultural specificity of rhythmic structures and ethnographic accounts of the meanings and functions of particular musical styles. There is no reason to believe that such an endeavor will be easy, that ways of organizing rhythm musically can be easily and transparently related to some aspect of social relations, or to ideologies expressed in other cultural spheres. One reason for this is that musical styles and repertories are historically constructed and sedimented, so that as social relations and institutions change, modes of musical performance are not created anew but adapted and recreated from what was previously practiced. If the rhythmic organization of a particular musical style reflects anything, it is not the current form of the social institutions to which its performers belong, but a long and incremental historical process of emergence, transformation, and adjustment in the face of social conditions that change either subtly or dramatically. Nonetheless, the work of unpicking some of these processes is potentially very valuable when it comes to understanding the ways in which music reflects and constructs social realities, and is implicated in layers of shared and differentiated

31 Lomax, “Variation of Rhythmic Style.”

32 Arom, African Polyphony; Clayton, Time in Indian Music.

33 Tenzer, “Cross-​cultural Topology.” 34 Clayton, “Theory and practice.”

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192   The Philosophy of Rhythm behaviors and intentions across humanity. Making no claim to finality, then, the last part of this paper offers some thoughts on the rhythmic organization of Hindustani classical music in the light of the proposals above.

5.  Hindustani classical music and its rhythm Before looking at some examples from actual performances, a brief summary of Hindustani rhythmical concepts and terms may be useful (readers familiar with the topic may safely skip the next two paragraphs). The various genres and styles of Hindustani (North Indian) classical music are classified into metered and unmetered sections. Performances usually begin with unmetered sections (alap, ranging in duration from a few seconds to an hour or more), which in their extended form gradually develop from very slow and loosely structured, to faster music more clearly structured around a simple pulse or beat. The metered forms that follow are organized according to one of a small number of tala patterns. Talas are conceived as metrical units or cycles comprising a fixed number of equal time intervals (matras); these matras are organized into two or more vibhags (sections/​divisions). Thus a tala is a repeating hierarchical pattern comprising a sequence of nominally equal time units. Melodic and rhythmic compositions and extemporization are performed within the tala framework. The simplest way of demonstrating the relationship to the tala is to conclude improvised episodes by returning to the mukhra, a part of a composition used as a refrain, or with a cadential figure ending on the first beat (sam). A common form of cadential figure is the tihai, which comprises a motif (simple or complex) repeated three times. The approach to the sam, especially at the end of an improvised section, is termed aamad (arrival), and achieving this process in an aesthetically pleasing manner is an important aim of the performers. The normal mode for a performance (other than a drum solo) is for the singer or instrumentalist to be designated as “main artist” and make all decisions about repertoire, tempo, and so on, with a drummer designated as “accompanist”; in many performances, nonetheless, drummers take opportunities to display their own ability to take the musical lead. If the most obvious question to ask about rhythm in Hindustani classical music is “How does tala work?,” the less obvious question, on which I want to focus here, is “What does tala do?” That is, “What does the rhythmic organization of Hindustani classical music achieve for those performing and listening to it?” First, it is clear that the general structuring principle outlined above—​the transition from unmetered to metered—​helps to organize the attention of everyone who engages with it in specific ways. In particular, a solo instrument or voice performing slow, unmetered music (alap) affords listeners a specific kind of attention, which Jones and colleagues refer to as “analytic attending.”35 Since there is no regular beat

35 Drake et al., “Rhythmic Attending.”

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structure, the music does not easily afford a motoric response or a forward-​looking, predictive (protensive) mode of listening. Although the performer may be planning ahead, the listener is forced to pay attention to the sound in the present. In terms of social relations, such a musical performance is likely to develop in a context in which contemplation, introversion, and perhaps meditation, are valued, and within which an ethos can be created that encourages such attention. In other words, it is likely to develop in quite particular social settings, in which highly skilled specialist musicians are afforded the patronage required to develop their art. Historically, alap in the modern sense is not described in the earliest historical sources on Indian music such as the Natyashastra (Science of Drama), where music is described as an adjunct to dramatic presentation, but first appears in a ninth-​century treatise called Brihaddesi.36 It appears to have developed long after various metrical song forms had been established. The transition from unmetered to metered music is a significant one, which many musicians conceive in terms of a shift from an inward to outward-​facing attitude. Nayan Ghosh, uniquely placed as a highly regarded performer on both sitar and tabla, explained the difference as follows: Alap is a journey inward and the gat [metered] portion is a journey outward, that’s where there’s a dialogue. The two people are musically conversing with each other . . . A step further would be where the audience also becomes so much a part of that whole conversation that you forget that there are three entities: the main artist, the accompanist, and the audience.37

As Ghosh makes clear, the transition from alap to tala-​bound sections marks a move from an individual engagement with the musical materials to a social, dialogic engagement.38 The livelier, more rhythmic music is played together with an accompanist, and makes most sense when listeners actively engage with the tala structure (which they may show by means of specific hand gestures). In performance, rhythm emerges from melody, and social engagement from contemplation—​which, intriguingly, likely reverses the direction in which these forms emerged historically. Metered music affords what Jones calls “future-​oriented attending,”39 in which the listener is attuned to a regular temporal structure and unpacks the music in real time with reference to a protention of the temporal structure. The listener knows roughly what the soloist is trying to achieve in aamad (the return to sam, the “one”), and roughly when it must occur, hearing the music in relation to possibilities she herself can imagine. This knowledge is possible due to a combination of two

36 Widdess, “Emergence of Dhrupad.” 37 Nayan Ghosh, Interview, Mumbai, May 23, 2005. 38 Alap can involve dialogue, for instance when two singers or instrumentalists alternate in its performance, or when a singer is accompanied by a melodic instrument. The paradigm case is, however, strictly that of solo performance. 39 Drake et al., “Rhythmic Attending.”

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194   The Philosophy of Rhythm things: the regular beat which affords entrainment, and familiarity with the particular tala pattern, which provides a conscious knowledge of the number of beats in a tala cycle. In other words, an enculturated, expert listener is not only entrained to the musical beat, which is open even to a complete novice listener, but also actively deploys culturally specific, shared knowledge. In the metered sections, these learned metrical structures organize interactions which in turn indicate social formations and relationships. As demonstrated by Clayton,40 tala structures the interactions between soloist and accompanists, and also between musicians and listeners, with the latter often being drawn into visibly demonstrating the fact that they share the flow of the tala and therefore appreciate the musicians’ achievement in creating transitions that are both consonant with this framework and aesthetically pleasing (which may include “unexpected”). This process can be understood as something like Schütz’s “mutual tuning-​in relationship,” in which participants share the temporal flux of inner time.41 Clearly, in this case, it is shared, culturally specific knowledge that affords this mutual tuning-​in. Shared temporal flow is usually experienced as felicitous. Psychological studies of much simpler experiences in which individuals share temporal structure in analogous ways empirically demonstrate the link between interpersonal entrainment and social effects, such as increased prosocial behavior, affinity, and feelings of belonging to a group (entitativity).42 How much stronger might such effects be in real-​life situations, which may also be highly affective and meaningful in terms of real social identities and relationships? No wonder that ethnomusicologists such as John Blacking have argued for many years that musical performance leads to heightened “fellow-​feeling” and hence social bonding.43 The story is not so simple, however, since this sharing of inner time—​to use Schütz’s language—​takes place within a hierarchical setting. It is socially shared, but the individuals doing the sharing are placed in hierarchical relationships: main artist to accompanist, expert to lay listener. Such hierarchies are both expressed and understood, but may also be contested. What happens when an accompanist doesn’t wish to be led? In practice such situations are familiar to musicians in this tradition, and many moments of conflict can occur, though they are usually concealed from audiences. Singer Ranjani Ramachandran spoke about her experience as a young soloist having to manage more senior accompanists: in one [concert a] senior tabla player was very mad at me. I was not getting the laya [tempo] I wanted. I gave one laya, and he actually didn’t give the right laya; then I changed it. So he got very mad! He just stopped and looked at me: I didn’t know

40 Clayton, “Khyāl Performance.” 41 Schütz, “Making Music Together.” 42 Marsh et al., “Social Connection.” 43 Blacking, “Anthropology of the Body.” Emile Durkheim’s influence was strong on both Halbwachs and Blacking.

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Entrainment and the Social Origin of Musical Rhythm  195 how to react! I didn’t do anything; he then started. He was just trying to say: ‘You cannot do this to me, you cannot tell me what laya I should play.’44

The shared knowledge of tala structures, then, affords a high degree of coordination and common ground, in a felicitous sense of cooperative interaction and mutual tuning-​in. It also organizes specific relationships that are potentially or actually antagonistic.45 Tala organizes a musical interaction in such a way that an individual invites others present to share a temporal structure that he has chosen. Everyone present knows that the process of sharing this temporal flow may be a rewarding one. They also know that it may require them to adopt a submissive attitude toward a leader. Is embodying such a position also felicitous? If not—​if, for example, it seems to imply subservience to a younger musician—​then can this leadership be contested without compromising the positive outcomes hoped for? In many years’ involvement in this musical culture as listener, I have observed some—​but in truth very few—​occasions where such tensions resulted in a breakdown of communication between musicians, and a consequent failure to achieve even the most basic of performance aims. Rather more often, performance operates in a less clearly defined mode in which individuals may or may not be engaged in contest of some form. Is the tabla player deliberately playing slightly slower than the main artist wants? Or is he struggling to understand what is required? Or is he doing what was requested, but nonetheless being implicitly scolded by a main artist who simply wants to make a statement of his own leadership? Are the musicians really competing to see who can play fastest and most brilliantly? Or are they complicit in presenting a staged performance of faked antagonism that does not in fact reflect their real investment in the event? Such issues are often unclear, because musicians tend to be complicit with each other at least in as much as any true antagonism should be concealed from the audience. In any case—​whether teamwork, antagonism, or some state between—​these interactions are framed by the shared knowledge structure that is tala. If the view outlined is to be productive, it requires more detailed ethnographic and interpretive work on a range of musical genres. In the case of Hindustani classical music, if the basic social function of tala is as described above, we might ask if specific talas, and specific tempi, have particular, nuanced social functions, or simply supply variety, and the option to fit given texts or melodic patterns in different rhythmic configurations. Given that the organization of performing ensembles varies, including in the extent to which they are strictly hierarchical or tend to egalitarianism, how does this variety interact with the social affordances of the tala system? Can both hierarchical and egalitarian groups be organized by the same system, or does change in the former correlate in some way with change in the latter? Does the rhythmical structure of music exert an influence on social

44 Ranjani Ramachandran, singer, Interview, Pune, February 19, 2010. 45 Clayton and Leante, “North Indian Classical Music.”

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196   The Philosophy of Rhythm institutions, or vice versa? Possible questions are legion, and the more abstract they become, the likelier they are to apply to other societies and other musical forms.

6. Conclusions Musical rhythm is irreducibly social in nature. The social origin and functions of rhythm have been proposed many times in the past—​Halbwachs and Sachs are not the only scholars to have made such a proposition—​but recent work in music psychology and ethnomusicology allows us to reframe the argument in a new way. In this view, musical rhythm originates in both endogenous physiological rhythms and the dynamics of interaction between individual human beings. These dynamics lead to often complex forms of emergent structure, and thus musical rhythms are not simply the sum of rhythms produced by individuals. If this point is conceded then the social origin of rhythm is uncontestable, and we may turn our attention to the ways in which cultural variety relates to interaction dynamics that are common to all humans. Nonetheless, in this view the social and the cultural are not set against the “natural,” since the endogenous rhythms of which musical rhythm is built are biological processes, and the dynamics of their interactions follow the same rules as interactions between mechanical systems such as pendulum clocks. The “social,” to put it another way, emerges from the “natural.” Human musical rhythm is remarkably flexible, complex, and diverse. Its diversity suggests that local factors have an important role to play in shaping rhythmic systems. It is less clear how systematically these local factors can be linked to aspects of social organization. Is it simply the case that given the nature of physiological rhythmic systems, and the dynamics of interactions between dyads and larger groups, a huge number of possibilities are inevitably generated, and distributed more or less randomly around the globe? Or is there some identifiable process by which the emergence, selection, and refinement of different approaches is driven by (or drives) the development of social institutions and cultural norms? The paucity of plausible theory in this area demonstrates that there are no easy answers. Aside from the difficult issue of how different rhythmic structures and systems develop, a renewed focus on the social also points us to reconsider the social functions and efficacy of musical rhythm. Regardless of where rhythm comes from, let alone what it may be taken to symbolize, what does it do? In what ways do different kinds of meter, or non-​metrical organization, afford particular kinds of interaction and attentional focus between individuals? Why might these kinds of interaction be found interesting, rewarding, or emotionally satisfying? What can we do with musical rhythm to guide our interactions; what cannot be done without it? The argument presented in these pages is intended, above all, to call for more attention to be given to such questions.

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Works Cited Agawu, Kofi, Representing African Music: Postcolonial Notes, Queries, Positions (London, 2003). Arom, Simha, African Polyphony and Polyrhythm (Cambridge, 1991). Backwell, Patricia, Michael Jennions, Neville Passmore, and John Christy, “Synchronized Courtship in Fiddler Crabs,” Nature, 391 (January 1, 1998), 31–​2. Blacking, John, “Towards an Anthropology of the Body,” in John Blacking, ed., The Anthropology of the Body (London, 1977), 1–​28. Buck, John and Elisabeth Buck, “Mechanism of Rhythmic Synchronous Flashing of Fireflies,” Science, 159 (March 22, 1968), 1319–​27. Clayton, Martin, Time in Indian Music: Rhythm, Metre and Form in North Indian Rāg Performance (Oxford, 2000). Clayton, Martin, “Observing Entrainment in Music Performance: Video-​Based Observational Analysis of Indian Musicians’ Tanpura Playing and Beat Marking,” Musicae Scientiae, 11.1 (2007),  27–​60. Clayton, Martin, “Time, Gesture and Attention in a Khyāl Performance,” Asian Music, 38.2 (2007),  71–​96. Clayton, Martin, “The Time of Music and the Time of History,” in Philip V. Bohlman, ed., The Cambridge History of World Music (Cambridge, 2013), 767–​85. Clayton, Martin, “Theory and practice of long-​form non-​isochronous metres. The case of the North Indian rupak tal,” submitted article. Clayton, Martin and Laura Leante, “Role, Status and Hierarchy in the Performance of North Indian Classical Music,” Ethnomusicology Forum, 24.3 (2015), 414–​22. Clayton, Martin, Rebecca Sager, and Udo Will, “In Time with the Music:  The Concept of Entrainment and Its Significance for Ethnomusicology,” European Meetings in Ethnomusicology, 11 (2005), 1–​82. Condon, William S., “An Analysis of Behavioral Organization,” Sign Language Studies, 13 (1976), 285–​318. Condon, William S. and W. D. Ogston, “A Segmentation of Behavior,” Journal of Psychiatric Research, 5.3 (1967), 221–​35. Drake, Carolyn, Mari Riess Jones, and Clarisse Baruch, “The Development of Rhythmic Attending in Auditory Sequences: Attunement, Referent Period, Focal Attending,” Cognition, 77.3 (2000), 251–​88. Gilbert, Margaret, Living Together: Rationality, Sociality, and Obligation (Lanham, 1996). Halbwachs, Maurice, “The Collective Memory of Musicians,” in Maurice Halbwachs, The Collective Memory, tr. and ed. Lewis A. Coser ([1939]; New York, 1980), 54–​83. Jones, Mari Riess, “Attentional Rhythmicity in Human Perception,” in James R. Evans and Manfred Clynes, eds, Rhythm in Psychological, Linguistic, and Musical Processes (Springfield, 1986),  13–​40. Kelso, J. A. Scott, Dynamic Patterns: The Self-​Organization of Brain and Behavior (Cambridge, MA), 1995. Kendon, Adam, Conducting Interaction:  Patterns of Behavior in Focused Encounters (Cambridge, 1992). Knoblich, Günther and Natalie Sebanz, “The Social Nature of Perception and Action,” Current Directions in Psychological Science, 15.3 (2006), 99–​104. Knoblich, Günther and Natalie Sebanz, “Evolving Intentions for Social Interaction:  From Entrainment to Joint Action,” Philosophical Transactions of the Royal Society B:  Biological Sciences, 363 (2008), 2021–​31. Large, Edward W., “Neurodynamics of Music,” in Mari Riess Jones, Richard R. Fay, and Arthur N. Popper, eds, Springer Handbook of Auditory Research, 36: Music Perception (New York, 2010), 201–​31. Lerdahl, Fred and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, MA, 1983). Lomax, Alan, Folk Song Style and Culture (New Brunswick, 1968).

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198   The Philosophy of Rhythm Lomax, Alan, “The Cross-​Cultural Variation of Rhythmic Style,” in Martha Davis, ed., Interaction Rhythms: Periodicity in Communicative Behavior (New York, 1982), 149–​74. London, Justin, Hearing in Time:  Psychological Aspects of Musical Meter ([2004]; 2nd edn, Oxford, 2012). Lucas, Glaura, Martin Clayton, and Laura Leante, “Inter-​Group Entrainment in Afro-​Brazilian Congado Ritual,” Empirical Musicology Review, 6.2 (2011), 75–​102. McAuley, Devin, Mari Riess Jones, Shayla Holub, Heather M. Johnston, and Nathaniel S. Miller, “The Time of Our Lives: Life Span Development of Timing and Event Tracking,” Journal of Experimental Psychology: General, 135.3 (2006), 348–​67. MacDougall, Hamish G. and Steven T. Moore, “Marching to the Beat of the Same Drummer: The Spontaneous Tempo of Human Locomotion,” Journal of Applied Physiology, 99.3 (2005), 1164–​73. Marsh, Kerry L., Michael J. Richardson, and Richard C. Schmidt, “Social Connection through Joint Action and Interpersonal Coordination,” Topics in Cognitive Science, 1.2 (2009), 320–​39. Moelants, Dirk, “Preferred Tempo Reconsidered,” in C. Stevens, D. Burnham, G. McPherson, E. Schubert, and J. Renwick, eds, Proceedings of the 7th International Conference on Music Perception and Cognition (Sydney, 2002), 580–​3. Patel, Aniruddh D., “Musical Rhythm, Linguistic Rhythm, and Human Evolution,” Music Perception, 24.1 (2006), 99–​104. Patel, Aniruddh D., John R. Iversen, Micah R. Bregman, and Irena Schulz, “Experimental Evidence for Synchronization to a Musical Beat in a Nonhuman Animal,” Current Biology, 19.10 (2009), 827–​30. Sachs, Curt, Rhythm and Tempo: A Study in Music History (London, 1953). Schachner, Adena, Timothy F. Brady, Irene M. Pepperberg, and Marc D. Hauser, “Spontaneous Motor Entrainment to Music in Multiple Vocal Mimicking Species,” Current Biology, 19.10 (2009), 831–​36. Schütz, Alfred, “Making Music Together:  A Study in Social Relationship,” Social Research, 18 (1951),  76–​97. Strogatz, Steven, Sync: The Emerging Science of Spontaneous Order (New York, 2003). Styns, Frederik, Leon van Noorden, Dirk Moelants, and Marc Leman, “Walking on Music,” Human Movement Science, 26 (2007), 769–​85. Tenzer, Michael, “A Cross-​Cultural Topology of Musical Time,” in Michael Tenzer and John Roeder, eds, Analytical and Cross-​Cultural Studies in World Music (Oxford, 2011), 415–​39. Widdess, Richard, “The Emergence of Dhrupad,” in Joep Bor, Françoise ‘Nalini’ Delvoye, Jane Harvey, and Emmie te Nijenhuis, eds, Hindustani Music:  Thirteenth to Twentieth Centuries (New Delhi, 2012). Will, Udo, Martin Clayton, Ira Wertheim, Laura Leante, and Eric Berg, “Pulse and Entrainment to Non-​Isochronous Auditory Stimuli:  The Case of North Indian Alap,” PLoS ONE, 10.4 (2015): doi:10.1371/​journal.pone.0123247.

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13 How Many Kinds of Rhythm Are There? Michael Tenzer

The question “how many kinds of rhythm are there?” seems preposterous but the response is still obvious: there are infinite kinds. Rhythm is movement or flow; it is time’s doppelganger. It is a percept of the mind, and equally a product of it. If a definition is intractable, we can at least attempt to inventory and sort. Langston Hughes addressed the topic in an enchanting children’s book, by ruminating on naïve categories: the rhythms of nature, music, words, athletics, machines, daily life, furniture, unseen rhythms, and more.1 Musicologist Curt Sachs launched his classic inquiry by asking, “What is rhythm? The answer, I am afraid, is, so far, just—​ a word: a word without a generally accepted meaning.”2 But he went on to assert his own, self-​consciously provisional, categories. Christopher Hasty says that “Everything the word ‘rhythm’ implies can be found in music.”3 I would emend this as follows: everything the word “rhythm” implies can be made musical, for the reach of the sign “music” in our time—​owing equally to the work of composers and the discoveries of ethnomusicology—​has far exceeded its earlier semantic capacities. The relationship between music and rhythm is paradoxical: rhythm’s provenance in nature makes it bigger than music, yet music’s provenance is imagination, so it can replicate and enlarge nature’s reach. Grasping the scope of musical rhythm now requires accounting for its encoding into bacterial DNA, as in the composer-​protagonist of Richard Powers’s 2014 novel Orfeo; or the idea of a rhythmic event spanning dozens of human generations, such as John Cage’s “Organ2/​ASLSP (As Slow as Possible),” launched on the chapel organ of the Burchardikirche in Halberstadt in 2001 with the final cadence scheduled for 2639;4 or sound events so tiny and “granular” that they are to entrainable periodicities as nanocomputers are to PCs.5 Discrete meter is undermined by Arapaho Wolf Dance singers, seemingly uncoordinated with their drum,6 or the incrementally accelerating and unstable micropulses of Tunisian sṭambēlī.7 Human



1 Hughes, The Book of Rhythms.

2 Sachs, Rhythm and Tempo, 12. 3 Hasty, Meter as Rhythm, 3.

4 See http://​news.bbc.co.uk/​2/​hi/​7880793.stm and related internet videos. 5 Roads, Microsound.

6 Nettl and Levine, “Four American Indian Songs.” 7 Jankowsky, “Tunisian Sṭambēlī.”

Michael Tenzer, How Many Kinds of Rhythm Are There? In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.001.0014

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200   The Philosophy of Rhythm sound production that those outside the culture would regard as music, might be culturally defined as a shaman’s incantation, the muezzin’s call to prayer, or cattle auctioneering.8 Conversely, humpback whales produce what we suspect must be like music, if we could only decode it. Though each may be seen as an outlier to the preponderance of human music, we marginalize such cases at our peril. For while we do so, others are inventing or discovering more extreme cases at the accelerating rate typical of our era. Whether we speak of the rhythm of music or the music of rhythm, their extent is far richer than the putative opposition between the regularities of metrical ground and the liberty of rhythmic figure that until recently framed discussion. Music is a layered social construction shaped by biological and historical factors, but it is still possible to characterize it. This chapter considers several kinds of frameworks for rhythm that offer complementary vantages. My perspective is shaped through investigation of world music genres9 and developments in music in the modern and digital eras. It takes features such as regular meter and periodicity, predominant in Western scholarship, as one among many possibilities. Five perspectives are presented: music and language, the anthropology of music, rhythm as percept, rhythm as object, and the advancing technologies of music and time.

1.  Are Language Rhythms Distinct from Musical Rhythms? Jean-​Jacques Rousseau regards music as historically prior to language.10 J.  G. Herder makes speech prior,11 while for some recent writers they have a common genesis.12 What differentiates their rhythms? Even now language and music are not entirely separate systems. They partner in song, but more important are the many language–​music hybrids: tonal languages, heightened speech used for poetry, storytelling, and oratory, music-​mnemonic systems (like do-​re-​mi solfège and its Indian equivalent, sargam), and speech surrogates like the myriad African talking drums capable of reciting histories and proverbs. Mesoamerican Chinantec supports so many tonal and accentual distinctions—​twenty-​one: seven tonal levels (or contours) with three accent types—​that adepts can utter grammatically impeccable sentences in the form of whistling.13 To the outsider, a whistled Chinantec sentence is a melodic sound stream poised between music and speech. Musical rhythm is more varied than language rhythm. It has periodic and nonperiodic variants, without constraints of lexicality, and with weaker forces of 8 https://​www.youtube.com/​watch?v=Ea7gn8hhEFA portrays cattle auctioneering. 9 Tenzer, ed., Analytical Studies in World Music; Tenzer and Roeder, eds, Cross-​Cultural Studies in World Music. 10 Rousseau, “Origin of Languages.” 11 Herder, Origin of Language. 12 Brown, “ ‘Musilanguage’ Model of Evolution”; Mithen, The Singing Neanderthals. 13 See https://​www.youtube.com/​watch?v=QPuE0UMEMEs.

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grammar and syntax. It thus ranges from the highly pulsed and repetitive to the extraordinarily loose and smooth. Language, in contrast, is constrained by its high standards of precision in communication. It features stress-​or syllable-​based rhythms, meticulous grammar and syntax, and lexical meaning; it cannot tolerate much periodicity, music’s signature formation. Periodicity and repetition in language tends to “musicalize it” for the perceiver’s ear, as Diana Deutsch has shown14—​a phenomenon that orators and preachers know and exploit. In his comparative survey of rhythm in language and music, Aniruddh Patel concludes that language rhythm should be viewed as an aperiodic “system of organized timbral contrasts.”15 Render music aperiodic, however, and it remains music.16 Conversely, though music may strive for meanings like language’s, it can capture only its rhythm; when a jazz performer “talks” through their instrument, we catch no precise linguistic sense. Music’s imprecision grants it an ability to layer rhythms polyphonically. Polyphony in language makes a din, which is why the notion instead connotes temporal succession, or an atemporal colloquy—​e.g., a “polyphony of voices” in debate. Thus music’s realm of rhythm can penetrate farther into language’s than vice versa. When language adopts the rhythms of music, we feel that it has become musicalized. But when musical rhythm swallows language rhythm its identity as music is enriched.

2.  Rhythm Dispersed in Anthropological Categories Twentieth-​century ethnomusicology identified rhythmic structures previously unimaginable. Awareness of many kinds of music has gradually revealed the Western concept of autonomous art to be parochial. Relinquishing this ethnocentric attitude, dissolving the artist–​artisan divide, allows music-​makers everywhere to be seen as producing rhythm appropriate to social needs. In contemporary globalized life much of this production is classified as art or entertainment, but for much of human history it was more likely to maintain the cohesion necessary for group survival. Cross-​cultural comparison is problematic, though. The more deeply one knows the particulars of a cultural formation the more difficult it is to place in relation to others. An anthropology of rhythm considers human rhythmic production in interaction with the social order, the environment, and natural order, and the capacities of the body and consciousness to synchronize and unite people in rhythm. In terms of the social order, we might consider how music differs among hunter-​gatherer, pastoral/​agricultural, monarchic/​high culture, and modern state-​based polities—​ the four commonly posited broad stages of its evolution.17 We could ask, what is 14 Deutsch, Musical Illusions. 15 Patel, Music, Language, and the Brain, 51, 150. 16 Lerdahl and Jackendoff, Theory of Tonal Music, however, posits a more intricate and closer relationship between music and language rhythm. 17 Wiora, The Four Ages of Music.

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202   The Philosophy of Rhythm hunter-​gatherer music like? And what are the rhythms of pastoralists? Our focus is not, in this case, on what they sound like, but what they are used for. Alan Merriam described music’s practical use as how it is “employed in human society”—​to put a baby to sleep, induce trance, cause troops to march in time, accompany a ritual, dance, or others.18 He distinguished practical use from symbolic function, such as “emotional expression,” and establishing “a sense of security vis-​à-​vis the universe.”19 Rhythms might be understood as types correlated by usage, with evidence based on accumulating cultural case studies. For some hunter-​gatherer societies this is a productive line of research. Musical uses in such cultures are often parsimoniously meted out among songs and repertoires with little overlap; members of the society can easily correlate a piece with a specific activity. Thus the Aka Pygmies of Central Africa have a large repertoire of songs, of which only seven are sung without instruments, although handclaps can be used. These are respectively used for the birth of twins, the trapping of an antelope, the telling of tales, the comforting of a child whose mother is pregnant, a lullaby, children’s games, and calling back men from a hunt. Only one song, that for singing over a corpse, may not be sung with either instruments or handclaps. Other Aka repertoires featuring instruments in different combinations all signify entirely different circumstances and activities.20 Related classifications by activity, though only partly susceptible to correlation with the Aka, could be gleaned from research on the Jul’hoansi in Namibia.21 In such isolated groups, one surmises that the inventory of musical items is proportionately small and efficiently distributed among different uses. We could apply this line of thinking in other similar societies, if we had data acquired by asking the same questions and with similar research methods. And as we apply the rubric of usage in latter-​day, larger and more complex cultures, we find many other kinds of music: music of worship, harvest songs, work songs, military music, anthems, fanfares, and so on. The natural environment generates another rubric for sorting rhythms. Certain kinds of rhythm work in certain places, from thick forests to concert halls. Both symbolic function and practical use evolve from ancient practices that are cultural responses to environmental conditions, beliefs about them, and propensity for mimesis. The floating unmeasured rhythms and extended song forms of many Central Asian pastoralists reflect long periods of solitude in open spaces intrinsic to their nomadic lives. It might make little sense to entrain a steady beat in such an expanse and with little opportunity to coordinate with others. Tuvans value vocal imitation of wind and water to engage in conversation with their spirit presences in nature,22 while Chukchi shamans in eastern Siberia placate animal spirits by imitating bear

18 Merriam, Anthropology of Music, 210, 209–​28. 19 Merriam, Anthropology of Music, 219, 210. 20 Fürniss, “Aka Polyphony,” 166.

21 England, Music Among the Jul’hoansi.

22 Levin and Suzukei, Rivers and Mountains Sing.

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and other animal sounds;23 neither of these suggest a role for equally spaced beats. Aka Pygmies, hyperaware of the dangers of forest life, have an elaborate repertory of rhythmically unpulsed and uncoordinated mimetic “sound signatures” including whoops, yodels, and calls, evoking such things as animal cries, water, and tree and brush noises.24 Combining them with gesture and movement, these are enacted at the forest camp for their general community value and to educate apprentice hunters, their multi-​modality suggesting an original continuum between speech and song. In collectivist cultures of many sizes and kinds, the steady musical beat and strict periodicities are powerful agents for social cohesion. The Aka have their repertoire of pulsating, cyclically structured songs. The modern Balinese gamelan stress an aggressive rhythm virtuosity in which twenty-​five or more players switch instantaneously between radically different speeds, meters, and textures—​the result of many generations of agricultural and ritual communality, and an ingrained competitive striving among the small island’s internal groups. In neighboring Java, the similarly periodic but very different gamelan music enacts pulsating rhythm in a much smoother, insinuating, and restrained way. The contrasts are partly explained by the refining influence exerted by powerful Javanese courts into the late twentieth century, as opposed to the recent more populist turn in Bali. In Japan, another large ensemble, gagaku, is more spacious in its rhythm, in which control of the ever-​ fluctuating pulsation is continually passed back and forth between players.25 Even more than Javanese gamelan, gagaku reflects values of the emperor’s court, where it has been in insular residence for more than a millennium. Hasty direct correlations risk over-​simplifying cultures. Javanese and Balinese music comprise more than gamelan, and Japanese music is more than gagaku. Balinese duck farmers and water buffalo herders amuse themselves with free-​ rhythm bamboo flute melodies that a central Asian shepherd might relate to. Individual gamelan and gagaku compositions may contain free-​rhythm sections, the result of long assimilation of indigenous and foreign socio-​musical influences. Tuvans have highly pulsed songs, and shepherds sometimes strum lutes. Cultures, with genres, repertoires, and compositions, are multi-​level constructions and accretions reflecting complex pasts, reflected in rhythms. Explanations in terms of society, geography, culture, environment, or climate only partly make sense of the diversity, though at a general level, subdivision of the world of rhythm along geographical or cultural lines makes practical sense. Broad features of hunter-​gatherer, pastoral, African, European, or Indian rhythms are easily distinguishable. But high-​level similarities obscure teeming diversity at ground level.



23 Nattiez, “Throat Singing.”

24 Lewis, “As Well as Words,” 238.

25 Terauchi, “Japanese Court Music (Gagaku).”

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204   The Philosophy of Rhythm

3.  Perception of Rhythm We now turn to the distinction between rhythm in real time, and frozen as if out of time, corresponding to J. M. E. McTaggart’s temporal A-​series and B-​series.26 The A-​series comprises past, present, and future. The perceiver experiences temporality as durations unfolding with respect to the present, moving through time with the advancing “now.” In the B-​series time is rendered spatially as if on a canvas. With respect to any given point there is only before and after, no transient experience of passage. As an A-​series percept rhythm events are susceptible to a phenomenological description of active rhythmic experience. As B-​series objects, a set of rhythms is categorized by structural type, as we shall see in Section 4. Can we compare different kinds of rhythm experience? We take into account biological predispositions, such as limits on what the memory can retain in real time, how fast or slow a pulsation can be latched onto, and how complex or scant a rhythm structure can get before it becomes too difficult to parse. Insider cultural perspectives often conflict with outsider ones around these issues too. For example, outsiders often misperceive the orientation of pulsation in unfamiliar music, or are unable to aurally disentangle the separate constituents of unfamiliar polyrhythmic textures. An A-​series portrayal of rhythm in time should be an account of changing perception of events, and how their accumulation alters rhythmic experience—​how the rhythm “feels” rather than what its properties and proportions are. In such an account there are not kinds of rhythm, but kinds of rhythm sensation—​though to be communicated it must be recollected and objectified afterwards, softening the distinction from the B-​series. In recent music theory, influenced by process-​oriented philosophers William James, Henri Bergson, A. N. Whitehead, and Gilles Deleuze, phenomenological approaches are prominent, especially in Hasty.27 Rhythm is conceived as a dynamic interaction between events and awareness. Hasty’s motivation includes rejection of the tyranny of the score in Western art music, which can be seen as overly regimenting what ought to be the fluid experience of listening and performing. Hasty’s elegant apparatus has only a choice few components, notably the notion of a “projection” stemming from a beginning, in which we become aware of an event with duration and imagine its outcome. A second event onset creates expectation of a third one with an equal duration thereafter, due to our propensity to entrain isochrony. When the third onset occurs it could anticipate, delay, deny, or confirm this expectation. Events are “continuations” if felt to follow from a previous projection, or “anacruses” if retroactively felt to have anticipated a subsequent, more



26 McTaggart, “The Unreality of Time”; Gell, The Anthropology of Time, 151.

27 Hasty, Meter as Rhythm.

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important onset. Rhythmic experiences comprise far more complexity than a mere three onsets, and become extremely rich affairs. In ethnomusicology, A-​series ideas have often appeared, but usually to render a cultural, not an individual, sensibility. It is difficult to depict how people in other societies experience their rhythms. To focus too much on difference is to essentialize; to focus overly on sameness is to undermine a culture’s genuine identity. This permanent tension is complicated further by rapid twenty-​first-​century cultural change and mixture. To date, ethnomusicology’s fealty has been to the notion of culture, hence to difference, downplaying biology. As fieldworkers learn to perform others’ music and aspire to ever-​more faithful inside viewpoints, they have sometimes tried to explain how it feels to experience the music in performance, or have given a platform to indigenous voices. Africa, and black music generally, has been a major focus. John Chernoff describes the exhilarating sensations of being unexpectedly thrust into a leadership role, drumming with his teachers at a village festival in Ghana.28 Chernoff, having experienced ecstatic communion with Ghanaian drummers, argues for distinctively African aesthetic modes of attending and “being” in music, corroborated by his teachers’ own reports. Anne Danielsen, a Norwegian who performed in funk bands, learned the grooves of ‘blackness’ in Oslo: Being in a groove, feeling the right feeling, letting presence happen, from the inside, from a position within time, within the experiential now, this is probably what funk is all about, and we should perhaps leave it at that, in all its meaningful non-​sense.29

More driving repetition in African musical rhythms may explain the contrast with European rhythmic experience from an A-​series view. Chernoff and Danielsen argue that repetition in a highly pulsating and rhythmically layered groove engenders participation, entrainment, embodiment, and pleasure. Western art music of the past few centuries can groove, but is mostly more interested in change than repetition. That people don’t dance to it much may be due more to cultural proscription. European rhythms still offer a highly embodied experience that suffuses listeners with pleasure. For Danielsen and Chernoff to grant blackness an exclusive purchase on these qualities, may just be to other it, reiterating the historical Afro–​Euro–​American entanglement between whiteness and blackness. But could we not broaden the perspective? Don’t cultural actors in Asia and beyond have such experiences? We need A-​series reports of many other kinds of rhythmic experience before we can talk about how many kinds there are.



28 Chernoff, African Rhythm and African Sensibility, 139. 29 Danielsen, Presence and Pleasure, 204.

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4.  The Rhythm Object A-​series rhythm is continuous; B-​series rhythm has discrete parts, and can be replicated from memory or fixed in notated and recorded representation. The B-​ series rhythm object can be measured for density, grouping structures, rates of change, variety of durations, attack and decay contours, frequency (pitch) range, harmony, and form. Most consideration of musical rhythm is done under this rubric, and we must consider its limitations. In the history of musical rhythm, B-​series thought postdated A-​series thought, and was required for the invention of music notation. Conscious awareness of rhythm accelerated human rhythmic invention, resulting in the emergence of complex, multi-​part, or extended musical forms. Musicological and music-​theoretical awareness has mainly been the fruit of B-​series concepts. In contrast with the mimesis of nature that may have led to earlier rhythmic expressions noted above, the division of time and rhythm into concatenated sections of a musical form probably developed in conjunction with the tropes and narratives of storytelling conventions, prescribed stages of ritual, or poetry. Consciousness of rhythm beyond direct experience led to the autonomous practice of musical composition. In this “composer’s account,” B-​series conceptions are hierarchic entities both synchronically and diachronically, especially where (as in most music) there exist musical forms of various kinds, and polyrhythm, understood in its simplest sense as co-​articulation of two or more rhythms. Moving through time, rhythms can be small bits concatenating into a larger whole, or wholes divisible into many parts, while at any given snapshot of a local span they may be embedded in streams or layers. Layers have interrelated durational values involving either the division of longer durations into shorter units, or the inverse; these relationships may be mathematically proportional or not. Thus in the gamelan music of Java and Bali, diachronic rhythms often comprise cyclic groups of rhythmic events of various sizes that repeat, for a few or many times, before possibly being supplanted by others of similar or different dimensions. The rhythms are also synchronically stratified, that is, moving on different instruments at different densities and durations. Spatial analogies of “wholes,” “streams,” “spans,” and “strata” suit the B-​series stance; musical structures are envisioned as existing in space, viewable from various angles, shrunken or enlarged. Gamelan music often avails itself of this possibility, presenting cycles in diminution, augmentation, and at different speeds. For composer Witold Lutoslawski, Form owes its existence to the ability of the listener to remember the music he has heard and to integrate its individual sections while he listens so that . . . he is [capable] of perceiving it as an idea that, like a painting or a sculpture, exists outside the limits of time . . . The composition . . . begins an independent existence of its own

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How Many Kinds of Rhythm Are There?  207 in the consciousness of the listener due to the facilities of memory . . . Unrestricted by time, the composition can be conceived in its entirety in one brief moment.30

With these features, the B-​series provides opportunities for cross-​cultural categorization, using simple criteria of sound and structure. We may generate a typology of rhythmic structures by considering: (1) which kinds of changes in sound parameters are creating rhythm, individually or in combination—​there are essentially three kinds: change of duration; change of pitch or tone color; and change of envelope.31 (2) whether rhythms are distributed proportionally (measured by pulsation, explicit or implied), or if they are unmeasured or “free.” (3) presence or absence of layers. (4) use or absence of repetition and periodicity at different structural levels.32 Yet these structural concepts—​pulsation, layers, repetition—​present ontological ambiguity in a musical context. Repetition is problematic because of its temporality, and music’s multidimensionality. “Temporality” refers to the fact that repetition always involves “change of context.” By virtue of its new position in a succession of (precisely repeated) events, the repeated object acquires an altered identity.33 However, we can still recognize its original identity once abstracted from its temporal flow—​which is B-​series objectification’s strong point. A trickier puzzle is that of multidimensionality and layers. Rhythm has fused, co-​existing components—​pitch, intensity, duration, timbre. Repetition in actual music typically involves variation, where components are fixed while others shift, presenting a combinatorial explosion of possibilities. One difficulty in B-​series analysis is that of identifying equivalence classes among a set of rhythm objects, each of which may be different from another but assigned the same identity in some cultural rubric. John Blacking coined the useful term “non-​change” to describe the many variations that do not acquire a cultural status of true difference, such that they can be interchanged within a performance, or among performances, or evolve over historical time, without shifting identity.34 Nonetheless, by any outside standard, there usually is difference between two items said to be equivalent to one another. The converse is often true as well: rhythms exactly the same are sometimes assigned culturally different identities. Certain identical patterns played in the Shona mbira dzavadzimu tradition may belong to any of several repertoire items classified as “pieces,” and outsiders cannot intuit the criteria used to sort patterns 30 Lutoslawski, in Stucky, Lutoslawski and His Music, 127. 31 For changes in pitch or tone color, even when durations repeat without change, there is still a strong sense of movement. “Pitch and tone color” is meant to encompass harmony as well. The envelope of a sound comprises its physical intensity, attack and decay contour, articulation, etc. 32 Tenzer, “Generalized Representations.” 33 Rahn, “Repetition,” 50. 34 Blacking, “Musical Change,” 17.

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208   The Philosophy of Rhythm to pieces. In this music the ontological distinction between “variation,” “piece,” and “repertoire” is fluid; there is a pool of pattern resources with overlapping distribution into different kinds of use. Last, many vivid cases of ambiguity relate to perception of pulsation and meter. An obvious typology divides rhythm into two broad realms, measured and unmeasured. But the distinction is not simple: consider the rhythmically complex notated music of composers like Elliott Carter or Brian Ferneyhough, both necessitating intense control and synchronization by performers. Due to the great variety of durations and complexity of their proportional interrelationships, this music often sounds as though unregulated by pulsation. An objective B-​series pulse for the performer can be obscure to the perceiver. Timing of pulsation in clearly metered situations may also be ambiguous. Many Western musical scores designate straightforward rhythms and meters selected by the composer. These are often, but not inevitably, what the music transmits to the experienced perceiver, a fact that Haydn often exploited to delightful effect. It is twenty or thirty seconds into the first movement of his Symphony 80 before experienced listeners can determine, without seeing a conductor, how to beat a pulse. Haydn’s rhythms are childlike, but do not sync as the acculturated ear expects. Without consulting a score, one would never know that the opening rhythms of Stravinsky’s Agon are notated to fall after the beat rather than on it. Most listeners hear this fanfare-​like passage as launching from a strong beat, but Stravinsky did not want performers to hear it that way. For the joke to succeed, Haydn could rely on an enculturation that Stravinsky could not expect, so one may ask: What effect or sensation was he trying to produce? Nicholas Slonimsky wryly recounts how he re-​notated perplexing changing-​meter passages in Stravinsky’s Rite of Spring in 4/​ 4 time, to make it more comprehensible for conductor Serge Koussevitzky—​to the latter’s gratitude, apparently troubling neither composer nor audience.35 Related problems are apparent with orally transmitted musics, whose pulsation can be misunderstood without cultural expertise. “Preference rules”36 putatively accounting for how listeners parse sound streams to determine metric structure do not obtain for some African music, where a participant’s internally referenced pulsation stream is not manifest in musical sound. To its makers, this is no problem: the music is not just in the sound, but also in their collective mind. Despite ethnomusicological discoveries, it is still important to transcribe world music, but notation must be supplemented by explanation and ethnographic corroboration. Interpreting notation requires cultural expertise. The discrete spatial increments of any notational technology are imperfectly suited to the task of representing music measured by a pulsation inherent in the music, or music in free rhythm whose values can be measured only against a pulsating external source such as a clock. Representations of rhythm cannot achieve objective accuracy.

35 Slonimsky, Perfect Pitch, 69.

36 E.g. Lerdahl and Jackendoff, Theory of Tonal Music.

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Yet the belief that notation—​a B series representation—​”is” the music remains an instructive myth. Rhythm is not an object:  it involves collaboration between acculturated perceiving mind and encountered sounds. A-​series rhythm must be communicated after the fact and can never fully portray subjective experience, while B-​series rhythm must be grounded in perception, which has psychological and cultural dimensions. Every rhythm representation and analysis—​even controlled responses in laboratory stimulus experiments measuring rhythm cognition—​ devolves to a set of judgments and approximations. Such approximations verge on a limit of accuracy that may suffice depending on one’s purpose, but especially in light of cross-​cultural encounter, can never be assumed to do so. Representations of rhythm, in whatever signifying form they take, are at best opportunities for intersubjective communication. The aim of the representation is to approach objectivity through discourse.

5.  Rhythm and Technology Development of music, like that of language, probably spanned different eras in which biologically and culturally selected features, including specialized adaptations and spandrels, converged into what we at some point identified as music. But musical capacities have never stopped evolving. Rhythm viewed in co-​ evolution with technology can be seen to have been in a process of expansion since humankind’s musical beginnings, along continua of increasing precision, complexity, and range. The vocabulary of rhythms has tracked the growth of technology, in tandem with their signification. At music’s beginnings, vocalizations likely underwent a transformation from loud calls that defined territory and expressed alarm, to intricate patterns reinforcing social connections and increasing environmental mastery.37 In a similar way, while in the very recent past electronically produced rhythms were perceived as “alarmingly” bizarre, antisocial, dehumanizing, even dangerous, the ubiquity of digital music synthesis has humanized their sound, as attested by popular electronic dance music cultures. For both early and modern humans, signs of danger morphed into signs of control. Consider again the exclusively corporeal technology of the first music, its limits set by the body. Recent thinking on the question of universals in music characterizes the prototype of all music as (1) vocal, (2) constructed on the degrees of a scale, and (3) possessing a system of rhythmic organization.38 But the human voice has rhythmic limits set by throat diameter, lung and breath capacity, and other physiological factors. We can usually manage about two octaves in pitch range, while the musculature of the jaw and tongue constrain the rapidity and precision with

37 Krause, Great Animal Orchestra, 115.

38 Molino and Nattiez, “Typologies et Universaux,” 357.

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210   The Philosophy of Rhythm which sounds can be articulated. Add to this whoops, shrieks, grunts, whispers, multiphonics (such as those produced by Tuvan throat singers), percussive clicks and clucks, percussion played with the hands on the body, and rich possibilities for timbral modulations—​the body alone still has unsurpassed expressive power. But as far as rhythmic production, there was much more to come. The 103 recordings on Voices of the World, a three-​CD set compiled by researchers at the Musée de l’Homme, represent the global diversity of vocal capacity in traditional musics.39 Sixty countries or territories are represented, from all inhabited continents, and fifty-​six peoples/​traditions. The focus on vocal traditions reflects the centrality of voice and song to music everywhere. The collection’s producers ordered the tracks according to kinds of vocal sounds and combinations, including cries, breathing techniques, recitations and declamations, harmonies, and several species of polyphony. There are rhythmic extremes, such as a tone sustained at high amplitude for more than twenty seconds by a singer at a death rite in Paraguay, or the cacophonous group vocalizations of Shuar women in Ecuador, which exhibit maximal density of vocally produced rhythm. Vocal music’s palette can be enhanced by using the mouth as a resonating chamber, such as in the recording of a boy in New Guinea who has tied a beetle to a stick and blown through its buzzing wings to amplify their sound (a rough prototype of the harmonica, perhaps). Similarly resonated are the extended family of mouth (Jew’s) harps, present worldwide, which are played either by pulling a string attached to the instrument’s reed “tongue,” or by striking it with a small beater.40 The last two cases are rhythms unattainable by the body alone. No sound made by a human body can oscillate as quickly or with quite the same timbre as a beetle’s wing. Nor can body percussion produce a report as sharp as that of a hard baton struck against a hard wooden or stone surface. Instrumental music has been defined as “the use of the limbs or other body parts to produce structured, communicative sound, possibly using additional objects.”41 Rhythms with a non-​corporeal vibrating medium extend the lexicon. Although the B-​series view of musical time depicts pulsations as discrete instants, organology and choreology show that different media give rise to different materialities of these instants. The rhythms of dance form a distinctive part of this range of experiences. Lower limbs and torso cannot articulate time as quickly as the mouth, throat, or hands, so dancers perform musical meter in terms of those broader gestures. For Tellef Kvifte, “specific characteristics of body movement [in dance] correspond to characteristics of meter in the associated music,” and meter

39 Zemp et al., eds, Voices of the World. The CDs are out of print but the entire collection can be streamed at https://​archives.crem-​cnrs.fr/​archives/​collections/​CNRSMH_​E_​1996_​013_​001/​, with an excellent, downloadable booklet. 40 Zemp et al., eds, Voices of the World: CD 1, track 1; CD 3, track 2; CD 2, track 33; and CD 2, track 34, respectively. 41 Fitch, “Biology and Evolution of Music,” 183.

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may be regulated in part by a “common slow pulse” articulated by dance, as well as grounded in an isochronous fast pulse.42 Percussion has great precision; drum skins, or the vibrating surfaces of idiophones like clappers and bells, respond quickly. Early idiophones and membranophones afforded the music-​maker a range of production techniques the body could not aspire to. This accelerated the invention of rhythm pattern types, their aggregation into polyrhythms, and the development of musical ensembles that combined timbres and generated a clear regulative pulsation. Aerophones mirror and amplify gestural patterns of breath flow and embouchure. Bowed chordophones, powered by the motion of the arms, introduced the possibility of virtually unlimited sustain, transcending the durational contours afforded by instruments with natural decay curves, like the breath or the resonance of gongs or bells. Plucked chordophones such as lutes enabled cultivation of finger dexterity, later developed by the invention of ergonomic keyboard instruments. Each instrument generates characteristic profiles of attack, sustain, and decay that contribute to rhythmic tactility. Instrument construction and materials affect rhythm at all levels. Now that we have tools to measure it, recent research has been devoted to microrhythm—​the subcutaneous world of rhythm faster than that of the main pulsation (tactus). Microrhythmic formation is responsible for what is known variously as musical groove, swing, or feel. Contrary to longstanding assumption that pulsations are isochronous and (essentially) cross-​culturally equivalent, we have learned that it is distributed in a splendid variety of ways around the planet. There is plentiful tolerance for rhythmic irregularity in ostensibly regular contexts, and many systems for combining or dividing regular durations into irregular ones. Drummers in Mali divide their beats unevenly in at least three ways,43 and jazz improvisers develop microrhythmic idiolects based on the genre’s style, their personal concept, and rhythmic capacities of their instruments.44 In the early twentieth century, Western composers dreamed of total rhythmic control through mechanical or electronic means:  Varèse’s “liberation of sound.” Conlon Nancarrow was meticulously punching his compositions on to player piano rolls in Mexico City by the mid-​1940s, creating an unprecedented oeuvre of rhythm relationships that no human at the time could produce manually, including polyrhythms in ratios of 14/​15/​16, or 2/​√2. He invented the rhythms creative minds dared to imagine thereafter. Emphasizing the power of the imagination to stimulate the body to new capacities, by the 1990s several contemporary music ensembles were confidently performing Nancarrow works that would have turned any past musician who contemplated the idea a shade of pale white.



42 Kvifte, “Categories and Timing,” 77.

43 Polak and London, “Mande Drumming.” 44 Benadon, “Slicing the Beat.”

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212   The Philosophy of Rhythm In the realm of electronic music, rhythms can be fine-​tuned at the particle level accessible through software interface systems like Pro Tools, using techniques such as cut-​and-​paste and microsampling. The ability to manipulate rhythms digitally, beyond the threshold of perceptible difference, is one of our era’s rhythmic signatures and frontiers. These thresholds are of two kinds:  that of merely discerning “at the same time” from “not at the same time,” and that of entrainment. According to some experiments, only 2 milliseconds separation is required to discern the presence of two separate events—​i.e., their non-​simultaneity—​whereas a 100-​milliseconds separation is needed to entrain the two events in a metrical context.45 The intentional shifting of a rhythmic event by some small amount ahead or behind its expected arrival in relation to a regular pulsation may not be perceived as change in beat or tempo; rather, it could fall within a region of tolerance. But the combination of simultaneous rhythmic layers, juxtaposed and misaligned by different tiny margins, can create perceptual effects that human musicians could not make—​such as making a rapid-​fire “stutter,” or making a beat feel “fat” or extended in “presence” beyond an instantaneous duration. This effect, and others like it, are an aesthetic goal in digital production of popular music. Brøvig-​Hanssen describes some of these effects in relation to electronica artist Danger Mouse’s Grey Album and other works.46 The popularity of such music is evidence of how the body and technology nourish one another, generating new appetites and kinds of rhythm. If musical instrument technology has thus shaped rhythm, now consider rhythm’s development through the lens of the technology of time. Rhythm evolves in tandem with our awareness of time, its measurement, and changing concepts of what it is. Our bodies are chronometers, a capacity we inherited from our forebears all the way up the evolutionary line. John D. Palmer locates time awareness in the very DNA of fruit flies, and periodic behaviors in some of the most primitive single-​ celled creatures. The photosynthesizing protozoa Euglena obtusa, for example, a species of algae, rise and fall with tidal movement even when kidnapped from their riverbed abodes and cooped up in the dark in laboratory jars.47 Palmer suggests that time measurement, hence rhythm, is inseparable from the replicating structure of subcellular life. It is present in all life, manifest in Euglena and Drosophila, cockroach activity patterns, bear hibernations, bird migrations, and a million other remarkable instances.48 Early humans measured time by environmental cues: day and night; tides; menstruation and the moon’s phases; the seasons; patterns of food availability; the aging body. These instinctive cues formed a crucible for the emergence of theories of mind, in which people came to conceive time as an entity beyond the self, vaster than what direct experience teaches. Cultural time is marked by group and individual memories, generations, lineages, patrimonies, dynasties, myths, and history.

45 London, Hearing in Time,  27–​8.

46 Brøvig-​Hanssen, “Opaque Mediation.” 47 Palmer, The Living Clock, 4.

48 Palmer, The Living Clock,  38–​44.

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If the earliest vocal music, as suggested above, was a way of enhancing group cohesion, cultural time measurement advanced cultural continuity and identity through the recording of oral and written histories and the prescribing of calendrical and life-​cycle rituals. The Dagbamba of northern Ghana measure historical time through the beating of specific drum rhythms, archived and preserved by a guild of specialist musicians, to narrate the lives of ancestors. Javanese and Balinese traditional calendars structure time in varying-​length, nested and coordinated cycles of weeks that regulate both practical realities (e.g., the frequency of market days) and propitiations to unseen forces, thus integrating quotidian and supernatural conceptions of time. Religious representations posited temporalities beyond human awareness, such as the Hindu yuga (epochs), calibrated in cosmic spans by the speed of the beats of the hourglass drum shown in the dancing Lord Shiva’s raised right hand. Chronometry refined our idea of time flow independent of experience, based on increasingly precise calculations. Though musicians have always needed a while to figure out what to do with them, chronometric tools aid the development of musical rhythm. Mechanical clocks led to metronomes, which naturalized certain parameters of rhythm and tempo, while the fine, latter-​day resolution of digital clocks brought us microsampling. If time for us today is fully quantifiable and imaginable at orders of magnitude from the Cesium-​decay second to the parsec of 3.3 light-​years, from the most infinitesimal Big Bang “singularity” to the outer reaches of the multiverse, it is because we have the technology to measure and conceive it. The parsec and the Cesium second may not have insinuated themselves into musical rhythms yet, but they probably will. They could appear at first in the imagination of some intrepid composerly intelligence, leading subsequently to a creative construction that, were we able to experience it—​overcoming parochial conceptions of rhythms—​might be very different from anything we consider to be music now.

6.  Conclusion: Metarhythm We began by paying homage to the vast realm of rhythm. From the start we ruled out the likelihood of defining it. But persisting with the title question, we visited the five sub-​domains of language, anthropology, perception (the A-​series), structural analysis (the B-​series), and technology, in each case seeking a way to characterize rhythm. We found that rhythms of language and music are not so distinct as one may think at first; that there are limits to how much one can associate particular rhythms with cultural formations; that the perception and the objectification of rhythms are highly imperfect enterprises; and that rhythmic variety is constantly expanding as a function of technology. The results were not terribly promising for anyone hoping to get a handle on how to slot rhythm into types and categories, and to enumerate the extent of its manifestations. Others, with less need to find

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214   The Philosophy of Rhythm rigorous order in nature or in human affairs, may celebrate rhythmic diversity for its own sake. We might consider that, cumulatively, the five topics discussed yield an emergent phenomenon—​call it metarhythm. What is metarhythm? It is the rhythm of rhythm:  the encompassing movement by which human conceptions of rhythm evolve and interact. It is the eons-​long process paralleling the expansion of human consciousness, during which the rhythms of the natural world gradually entered into explicit human awareness. There, in imagination, both individual and cultural, they replicated, developed, are tinkered with and added to. The canvas on which metarhythm unfolds is the same natural and temporal one as that of rhythm itself. But metarhythm organizes rhythm into shifting planes of concept and signification as the mind confers many dimensions of meaning upon it. And at a certain moment the rhythms created by human imagination acquired a potential even bigger than those of the natural world. Each metarhythmic configuration is a description of human rhythmic understanding and capacity for some cross-​section of the evolving composite process, and these understandings and capacities are always on the move. This is not, in the end, anything like a definition or a categorization of rhythm, but an assertion that its definitions and categories are contingent and changing. The signifiers of rhythm and music remain what they are, but what they signify does not.

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How Many Kinds of Rhythm Are There?  215 Hughes, Langston, The Book of Rhythms ([1954]; New York, 1995). Jankowsky, Richard C., “Rhythmic Elasticity and Metric Transformation in Tunisian Sṭambēlī,” Analytical Approaches to World Music, 3.1 (2013), 34–​61. Krause, Bernie, The Great Animal Orchestra:  Finding the Origins of Music in the World’s Wild Places (New York, 2012). Kvifte, Tellef, “Categories and Timing:  On the Perception of Meter,” Ethnomusicology, 51.1 (2007),  64–​84. Lerdahl, Fred and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge, 1983). Levin, Theodore and Valentina Suzukei, Where the Rivers and Mountains Sing (Bloomington, 2010). Lewis, Jerome, “As Well as Words: Congo Pygmy Hunting, Mimicry, and Play,” in Rudie Botha and Chris Knight, eds, The Cradle of Language, Vol 2: African Perspectives (Oxford, 2009), 236–​56. London, Justin, Hearing in Time:  Psychological Aspects of Musical Meter ([2004]; 2nd edn, Oxford, 2012). McTaggart, J. M. E., “The Unreality of Time,” Mind, 17 (1908), 457–​73. Merriam, Alan P., The Anthropology of Music (Evanston, 1964). Mithen, Steven, The Singing Neanderthals:  The Origins of Music, Language, Mind and Body (Cambridge, MA, 2006). Molino, Jean and Jean-​Jacques Nattiez, “Typologies et Universaux,” in Jean-​Jacques Nattiez, ed., Musiques: Une encyclopédie pour XXIe siècle, vol. 5: L’unité de la musique (Paris, 2007), 337–​96. Nattiez, Jean-​ Jacques, “Inuit Throat Games and Siberian Throat Singing:  A Comparative, Historical, and Semiological Approach,” Ethnomusicology, 43.3 (1999), 399–​418. Nettl, Bruno and Victoria Lindsay Levine, “Strophic Form and Asymmetrical Repetition on Four American Indian Songs,” in Michael Tenzer and John Roeder, eds, Analytical and Cross-​ Cultural Studies in World Music (Oxford, 2011), 288–​315. Palmer, John D., The Living Clock: The Orchestrator of Biological Rhythms (Oxford, 2002). Patel, Annirudh D., Music, Language, and the Brain (Oxford, 2008). Polak, Rainer and Justin London, “Timing and Meter in Mande Drumming from Mali,” Music Theory Online, 20.1 (2014). Powers, Richard, Orfeo (New York, 2014). Rahn, John, “Repetition,” Contemporary Music Review, 7.2 (1993), 49–​57. Roads, Curtis, Microsound (Cambridge, 2004). Rousseau, Jean-​Jacques, “Essay on the Origin of Languages,” Essay on the Origin of Languages and Writings Related to Music, tr. and ed. John T. Scott ([1781]; Hanover, NH, 1998), 289–​332. Sachs, Curt, Rhythm and Tempo: A Study in Music History (New York, 1953). Slonimsky, Nicholas, Perfect Pitch: A Life Story (Oxford, 1988). Stucky, Steven, Lutoslawski and His Music (Cambridge, 1981). Tenzer, Michael, ed., Analytical Studies in World Music (Oxford, 2006). Tenzer, Michael, “Generalized Representations of Musical Time and Periodic Structures,” Ethnomusicology, 55.3 (2011), 369–​86. Tenzer, Michael and John Roeder, eds, Analytical and Cross-​Cultural Studies in World Music (Oxford, 2011). Terauchi, Naoko, “Surface and Deep Structure in the Tōgaku Ensemble of Japanese Court Music (Gagaku),” in Michael Tenzer and John Roeder, eds, Analytical and Cross-​Cultural Studies in World Music (Oxford, 2011), 19–​55. Wiora, Walter, The Four Ages of Music (New York, 1965). Zemp, Hugo, Bernard Lortat-​Jacob, and Gilles Léothaud, eds, Voices of the World: An Anthology of Vocal Expression, audio recording, CMX-​37410/​12 (Paris, 1996).

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14 Temporal Processing and the Experience of Rhythm A Neuro-​Psychological Approach Udo Will

1. Introduction Temporal experience is a central aspect of the life of humans and other species because of ever-​present changes in their world. These changes, at least at the macroscopic level of actions and experiences, are not unstructured. There are regularities, and detecting them enables organisms to adapt to a changing environment. As constructs, time and rhythm are shaped by physiological and psychological processes, and socio-​cultural concepts.1 This chapter focuses on our direct experience of time and rhythms, covering a range from sub-​seconds to a few minutes, as distinct from remembrance of time. The latter concerns temporal phenomena beyond the minute range, and different cognitive processes. The chapter focuses on auditory temporal and rhythmic processing. The term “rhythm” is used to refer to qualities attributed to ordered successions of events and their temporal relationships, without implying particular kinds of regularity or pattern repetition—​which are taken to characterize specific types of rhythm. Experience of time and rhythm involves basic building-​blocks:  detection of events, identification of duration, and temporal order—​ relational properties of event sequences. I  examine “timing” mechanisms as ways of relating aspects of events to body-​ internal periodic processes, discussing movement-​ related periodicities. I show that temporal and rhythmic processing are not unitary phenomena and that rhythm cannot be understood as abstractly cognitive. Next it is argued that recent reports about processing differences for vocal and instrumental rhythms suggest that different temporal mechanisms are available for intra-​modal processing. An important part of these differences is explained by involvement of different sensorimotor networks in processing rhythms. Finally, a discussion of features of Australian Aboriginal music shows that different temporal features of 1 Will, “Cultural Factors.” Udo Will, Temporal Processing and the Experience of Rhythm In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.001.0015

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vocal and instrumental rhythms are detectable. The chapter concludes by showing implications for relations between speech, vocal, and instrumental rhythms and their evolution.

2.  Basic components of temporal experience Basic constituents of our temporal experience include detection of simultaneity; temporal order; perception and estimation of duration; temporal integration; perception and production of intervals and interval sequences; and temporal alignment or synchronization of event sequences. These processes rely on our ability to detect events, determine their relationships (durations and sequential order) and “time” them with reference to some internal measure.

2.1  Event Detection Perception is not a passive act; “you live through an event by coupling with it.”2 Three types of changes can be distinguished: brief and rapid changes are experienced as “point events”; changes over a prolonged period are perceived as continuous; change that occurs at rates too slow to be perceived but can be reconstructed through memory—​however long one stares at a clock’s hour hand, it never seems to move, though at some point one infers that it must have. Detection of events is generally based on a multi-​feature analysis. Simultaneous changes in several sound parameters have been shown to facilitate identification and to render it more reliable.3

2.2 Duration State-​ changes are temporally extended phenomena, and the term “duration” designates the length of a state change, demarcated by onset and offset. It also designates the time between two successive (point) events. These two interval types are also known as filled and empty intervals. Filled auditory intervals are perceived more accurately, and as longer than, empty intervals.4 However, this effect does not seem to generalize to interval sequences; accuracy for empty rhythms is consistently better than for filled rhythms.5 Identification of temporal order (Section 2.3) seems to improve if events are separated by silent intervals.6

2 Noë, “World in Time.” 3 Cheong and Will, “Empty and Filled Rhythms”; Klyn et al., “Differential Short-​Term Memorization.” 4 Wearden et al., “Internal Clock Processes”; Nakajima, “Empty Duration Perception”; Rammsayer and Skrandies, “Temporal Information Processing.” 5 Klyn et al., “Differential Short-​Term Memorization.” 6 Warren and Obussek, “Temporal Order”; Thomas and Brown, “Time Perception.”

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218   The Philosophy of Rhythm Studies indicate that perception of intervals shorter than 2–​3 seconds are perceived as qualitatively different from longer intervals, with shorter intervals eliciting synchronization of body movements, while longer intervals are perceived as having no effect on them.7 Temporal processing in the two time ranges also involves different physiological processes.8 Our perception of duration is also influenced by our movements. Events are perceived as longer when observed, and self-​generated actions are congruent, indicating an intimate link between temporal perception and our actions.9 Duration perception is an active, guiding component in an organism’s interaction with its environment.

2.3  Temporal Order The minimum interval needed to perceive auditory events as separate is c.2–​3ms. While this threshold is largely a peripheral phenomenon, perception of simultaneity rests on the fact that onset perception of events with extended duration is influenced by their duration. The perceived onset of a stimulus is increasingly delayed relative to the physical onset when the stimulus duration increases.10 The perceived onset can be regarded as a function of the duration and the temporal envelope of the sound.11 Longer stimuli must start earlier than shorter ones, to achieve perceptual synchrony. The sequence of events can be determined only if they are separated by 30–​50ms (temporal-​order threshold), the same for all sensory modalities—​increasing to 100–​300ms for sequences with more than three events, its size markedly affected by the relatedness of the events. The existence of temporal-​order thresholds indicates discrete temporal processing units.12 Events within intervals not exceeding such thresholds, though non-​simultaneous, are not perceived as having a temporal order. The temporal integration within these units provides functional moments of experienced co-​temporality.13 Such integrative units seem to be central constituents of temporal processing in both perception and action, and they have been identified within the various modalities. In cross-​modal tasks like the McGurk effect,14 and in sensorimotor synchronization tasks, synchronized tapping to regular auditory stimuli becomes impossible with intervals less than c.250ms.15 Temporal-​order thresholds thus demarcate fundamental units of temporal perception. Temporal processing appears to be discontinuous, performed in discrete

7 Nakajima et al., “Successive Sound Bursts.”

8 Lewis and Miall, “Brain Activation Patterns.” 9 Press et al., “Moving Time.”

10 Schimmel and Kohlrausch, “Interaural Differences.” 11 Schütte, “Subjektiv gleichmäßiger Rhythmus.”

12 Pöppel, “Temporal Perception,” “Lost in Time.” 13 Wittmann, “Moments in Time.”

14 “Try the McGurk Effect,” Horizon (online video).

15 See this volume, Chapter 11, London, “Metric Entrainment and the Problem(s) of Perception.”

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units, and characterized by intra-​and inter-​modal binding and co-​temporality. Experience of temporal phenomena is then created through an experience of succession of such units. The contrasting view that our experience of time is limited to perception of a “timeless” present cannot explain how we perceive motion, change, and succession.16 Conversely, the notion of functional moments suggests that our experience has inherent temporal properties. We experience not timeless slices but temporally extended chunks, which are in turn integrated into larger units that permit experience of change, motion, and rhythm.

2.4  Specious Present These larger units fall into a time range that also marks the above transition between short and long durations. This specious present is organized in ways in part suggested by the stimuli themselves, but also by integrative processes that incorporate context as well as implicit knowledge about the events.17 Paul Fraisse distinguishes perception, and estimation of duration or remembrance of temporal phenomena.18 Within the specious present we can directly perceive durations, rhythms, and repeating patterns. Beyond that range they are not experienced as temporal gestalts. Penelope Lewis and Chris Miall argue similarly that shorter range timing is “automatic,” reflecting the engagement of processes associated with the production of skilled movements, while longer range timing is “cognitive,” dependent on neural systems associated with attention and memory.19 Integration limits of the subjective present can be overcome through the use of additional cognitive means and strategies. While sensory memory plays a role in the psychological present, it is working memory, supplemented by phonologic storage and rehearsal systems, that extends our temporal horizon into the minute range, with long-​term memory estimating durations beyond that range. Additionally we can employ strategies like counting and subdivision as important means to keep track of periodicities in the multi-​seconds range that extends beyond the psychological present, as done for rhythm and form cycles in Classical Indian music and jazz, for example.

3.  Movements and timing Growing evidence suggests that action-​and movement-​related periodicities play a role in some timing references. A  dynamic, enactive perspective distinguishes discrete actions like pointing or reaching, from continuous actions like walking,

16 Le Poidevin, The Images of Time. 17 Michon, Making of the Present.

18 Fraisse, “Rhythm and Tempo.”

19 Lewis and Miall, “Brain Activation Patterns.”

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220   The Philosophy of Rhythm dancing, or music-​ making. Computational simulations suggest that periodic movements are not just a concatenation of discrete movements, but that distinct control mechanisms underwrite the two. Discrete movements are governed by fixed-​point dynamics. Their timing cannot originate from their own dynamics and requires external timing control arising from neural structures not involved in the realization of their dynamics. In contrast, continuous movements, if they are not too slow, are governed by limit cycle dynamics. They are autonomous and their timing emerges from the movement dynamics.20 Experimental support for distinct mechanisms comes from an fMRI study that found partly overlapping but distinct activation patterns for discrete and periodic wrist movements.21 It is likely that at least part of the specific activations in the discrete condition reflect the necessary “external” timing control, and that this control is realized not in a single neural structure, but in a distributed network. If timing of continuous, periodic movements autonomously emerges from their movement dynamics they can in turn serve as timing references. For human locomotion, MacDougall and Moore have shown that power spectra of periodic activity in everyday contexts (walking, running, cycling) exhibit a dominant peak at 2Hz.22 The peak frequency was not found to correlate with gender, age, height, weight, or body mass index and can therefore be considered as a central, movement-​related resonant “frequency” or internal periodicity. It can function as a reference in temporal judgments of event sequences mentioned earlier, and other perceptual and motor tasks: various studies have shown corresponding peak frequencies in spontaneous tempi of finger tapping tasks, preferred metronome tempo, resonance in perception of musical pulse and related brainwave synchronization.23 However, not all periodic processes of our body have the same resonance frequencies—​the brainstem-​controlled breathing cycle, related to voice production, has a period of c.0.25Hz. An important aspect of periodic movements is that, although their timing is an autonomously emerging property, the controlling oscillatory circuits are nevertheless influenced by sensory inputs or volition, assuring that movements performed are activity-​appropriate. For example, periodic limb movements that are performed spontaneously and in the absence of any external stimuli are executed with frequencies corresponding to the internal periodicity. However, if external stimuli are present, the internal periodicity and the ensuing “personal tempo” get modified and, in the case of regularly timed external stimuli, become entrained to the external stimuli.24 The resulting periodicity is perceived as pulse because, whether irregular or quasi-​periodic, the sensory input affects both internal periodicity and

20 Huys et al., “Distinct Timing Mechanisms.” 21 Schaal et al., “Rhythmic Arm Movement.” 22 MacDougall and Moore, “Marching to the Beat.” 23 Fraisse, “Rhythm and Tempo”; Van Noorden and Moelants, “Perception of Musical Pulse”; Will and Berg, “Brain Wave Synchronization.” 24 Will et al., “Pulse and Entrainment.”

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motor sequence, even if spinal pattern generators are not released and movements are not performed, e.g., in passive listening to music. The idea that motor adjustments to, and temporal judgments of, event sequences, especially those of music, are made on the basis of a comparison of external and internal periodicities has been developed in entrainment theory. The idea is based on the notion of attentional cycles that are synchronized with the internal periodicity, and thus permit determining the degree of synchronization between external event sequences and internal periodicity.25 While we are now obtaining a detailed picture about pulse (or beat) in temporal processing, the role of meter is less clear. The concept of meter applied by most researchers is that developed in Western music since the seventeenth century, which is very different from the concept of meter in poetry and in non-​Western music (see Section 6).26 The modern Western concept is based on the idea of isochronous time units, and refers to a cyclical pattern of strong and weak units or beats. It is considered to act as a framework for the actual (melodic) rhythms that may or may not be congruent with the underlying meter. The implicit ambiguities of this concept are largely ignored in experimental research, for example by only selecting rhythmic stimuli congruent with the meter. Depending on the experimental task, processing of meter seems to involve temporal as well as non-​temporal components. While temporal components, e.g., detection of repeating patterns, are similar to those involved in rhythm processing, non-​temporal components like training experience, memory, and attention seem to be required.

4.  Sensory timing mechanisms, vocal and instrumental rhythms To reiterate, a framework of intrinsic timing models suggests that the different sensory modalities use specific temporal processing mechanisms.27 The identification of modality-​ specific components poses a challenge for approaches that regard rhythms as abstract, disembodied cognitive representations of temporal relationships and assume that rhythm processing is an amodal process.28 Furthermore, even within one modality rhythm processing may differ with stimuli and tasks. Tsun-​Hui Hung showed that, for decision tasks on auditory rhythms, there are significant behavioral (reaction time, accuracy) and brain activation (fMRI) differences for vocal and instrumental rhythms.29 Differences between these two rhythm types were also found in short-​term memory tasks.30 In rhythm 25 Jones, “Time, Our Lost Dimension”; Large and Jones, “Dynamics of Attending”; Jones and McAuley, “Time Judgments.” 26 Will, “Cultural Factors.” 27 Merchant et al., “Common Mechanism”; Shuler and Bear, “Reward Timing”; Bueti et al., “Sensory and Association Cortex.” 28 Deutsch “Recognition of Durations”; Povel and Essens, “Perception of Temporal Patterns.” 29 Hung, “One Music? Two Musics?” 30 Klyn et al, “Differential Short-​Term Memorization.”

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222   The Philosophy of Rhythm reproduction tasks, memorization of vocal rhythms seems to recruit the participation of the articulatory loop, but memorization of instrumental rhythms does not.31 This may explain why in many musical traditions instrumental rhythms are learned in “speakable,” verbalized form. Verbal labels are better memorized than the original instrumental sounds because they can be better maintained in working memory.32 Klyn et al. discuss factors that contribute to differential processing of vocal and instrumental rhythms.33 The first relates to extraction of temporal features for rhythm detection. For instrumental sounds used in their study (clapsticks) the task can be reduced to intensity peak or sound onset detection. Extraction of vocal rhythm, conversely, requires simultaneous consideration of multiple features: identification of changes in dynamics, pitch, and spectra. Furthermore, the human voice has a typical spectral energy distribution, and relative independence of fundamental frequency and resonance characteristics of the vocal tract, not present in instrumental sounds.34 Another factor is that the human brain seems to possess specializations for processing of human vocal sounds and vocal rhythms.35 These are understood as neuronal and cognitive adaptations to the acoustic complexity and vital biological role of vocal sounds in intra-​species communication.36 For humans, quickly identifying sounds as vocal, and processing them as speech sounds, can be crucial socially, and it is something humans perform effortlessly and automatically. Specialization and preference for vocal sounds may help explain faster reaction times for vocal rhythms than instrumental ones. Finally, research on sensory motor integration in the auditory system suggests another contributing factor.37 Vocal and instrumental rhythms are produced via different motor-​effectors in the body: larynx, tongue, lips and jaws (mouth cavity) for vocal, and upper (and sometimes lower) limbs for instrumental rhythms. The larynx is innervated by the laryngeal branch of the vagus nerve; the tongue mainly by the hypoglossus nerve plus a smaller projection from the vagus nerve; lips by the facial nerve; while jaw movements and the shape of the mouth cavity are controlled by the trigeminal nerve—​all under supranuclear control from the ventral part of the primary motor cortex. Limb movements, on the other hand, are performed through activity of spinal motor neurons that in turn are controlled by the medial and dorsal part of the primary motor cortex. Vocal and instrumental rhythms clearly involve different neural networks. In addition, differences in response to 31 The articulatory loop is a working-​memory mechanism that prevents pronounceable memory content from decaying through repeated articulation. 32 Cheong and Will, “Empty and Filled Rhythms.” 33 Klyn et al., “Differential Short-​Term Memorization.” 34 Fant, Acoustic Theory of Speech. 35 Belin et al., “Voice-​Selective Areas”; Bent et al., “Cognitive Processing of Pitch”; Zatorre et al., “Auditory Cortex”; Hung, “One Music? Two Musics?” 36 Wang, “Communication Sounds in Primates.” 37 Pa and Hickok, “Parietal-​Temporal Sensory-​Motor Integration”; Wang, “Communication Sounds in Primates.”

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decision and reproduction tasks provide a first hint at how encoding differences for these rhythms may be linked to different sensory-​motor activations.38

5.  Contrasting vocal and instrumentAL rhythms The existence of different sensory-​motor networks for vocal and instrumental rhythms explains why most instrumental rhythms, but not speech rhythms, are organized along regular periodic intervals, even where melodies are irregular.39 Although syllable sequences in prose may show certain regularities, attempts at explaining speech rhythms in terms of an underlying regular time interval grid or pulse sequence have not been successful.40 In contrast, instrumental rhythms are produced through periodic limb movements, characterized by a sharp resonance frequency, modifiable intentionally or through sensory input. Constraining periodicities for speech (breathing cycles or breath groups) are much more flexible, and less directly determined by other bodily activities.41 However, the regularity of speech rhythms can be increased. First, temporal regularities increase when there are phonological similarities, grammatically matched constructions, or repetitions of syllable groups.42 Second, regularities also increase when speech is aligned with periodic motor movements as in gesturing and music-​making, in chant, song, or rap. Speech is frequently aligned with body movements, such as in gesturing and musicking, which aids communication. Temporally regular utterances of a speaker permit a listener’s attentional periodicity to become aligned to them.43 Temporal restructuring of heightened speech and poetry, resulting from use of language-​related factors like rhymes, formulaic expressions, and repetitions, also facilitates memorization in both performers and listeners.44 A  special form of restructuring of heightened speech, which developed as an oral tradition and enhances both temporal regularization and memorization, is organization of syllable sequences on the basis of contrastive prosodic features. This “poetic meter” arranges syllables in patterned sequences “measured” by distinct number of syllables and the patterns created through length or, in tone languages, tone contrasts. Thus in Vedic and some Australian Aboriginal poetry, where syllable length is a contrastive language feature, syllables are organized in patterns of short–​long contrasts, but without assignment of fixed durational proportions. Early Chinese poetry used the contrasts of level and deflected tones, which also implied length contrast, and 38 Klyn et  al., “Differential Short-​Term Memorization” (experiments 2 and 3); Wang, “Communication Sounds in Primates.” 39 Will et al., “Pulse and Entrainment.” 40 Cummins, “Rhythm in Speech.” 41 Moore, “Rhythm in Speech: A Response,” argues from system dynamics for the relative independence of spoken language from other bodily functions. 42 Cummins and Port, “Stress Timing.” 43 Dooling, “Sentence Perception.” 44 Rubin, Memory in Oral Traditions.

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224   The Philosophy of Rhythm later developed forms with fixed arrangements of tonal patterns.45 In all three cases length contrasts are relative and flexible, not based on absolute, isochronic length units (see Aboriginal examples, Section 6). Poetry in China and Australia, but also in Africa, uses additional dynamic accents—​not linked to fixed positions within a meter—​freely and creatively. Thus the temporal structure of heightened speech and song poetry is distinct from that of accompanying instrumental music which is based on internal periodicity of periodic movements (pulse-​based) and whose rhythms are created from quasi-​isochronous unit intervals and/​or subdivisions and multiples thereof. In contrast to Western musical meter, there is no indication that processing of poetic meter requires distinct timing processes, whereas employment of memory-​related processes seems indispensible. With the foregoing characterization of differences between vocal and instrumental rhythms, we now examine how these differences are manifested in human musical behavior outside the laboratory.

6.  Australian aboriginal music The following reviews analytical data from music performances of two Australian Aboriginal groups, the Pitjantjatjara from Central Australia, and the Dyirbal from Queensland, and temporal features of vocal and instrumental components. Their traditional music consists of vocal melodies, sung solo or in unison, and rhythmic accompaniment.

6.1 Vocal rhythms Phonemes and phonotactics of everyday language seem to be generally preserved in Aboriginal song language, but syllable durations are not. In Pitjantjatjara, a Central Australian language with contrastive word-​initial syllable length, long syllables are approximately twice as long as short ones.46 In songs, however, long syllables are up to four times longer than short ones, and there appear to be at least two length-​ categories of short syllables.47 Variances of syllable duration indicates consistency of song duration and word rhythm across performers and performances, and mean syllable durations show phonetic-​articulatory influences on the fine structure of the word rhythms.48 For example, approximants seem to have a lengthening effect. Song words are organized in groups of fixed number of syllables (“text lines”), which are often immediately repeated. “Small songs” may consist of different text lines, each containing identical number of syllables with the same short–​long

45 Level tones have a longer duration than deflected tones. 46 Tunstill, “Pitjantjatjara Song.”

47 Will, “Oral Memory in Australian Song.”

48 Ellis, Aboriginal Music; Will, “Oral Memory in Australian Song.”

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pattern. As different text lines are made up of different words, the syllable timing in performance, i.e., the actual rhythm may differ from line to line, though lines share the same long–​short syllable pattern. Different text lines within a small song can have different numbers of syllables, e.g., the first having eight and the second seven syllables, or vice versa. For the Dyirbal of Queensland, song language also follows phonology and grammar of everyday language, which, however, has no contrastive length; words are, apart from some injections, two or multi-​syllabic, with stress on the first syllable of every root and the first of suffixes.49 The dominant form of text lines from Dyirbal Gama songs (a type of corroboree song) has eleven syllables, grouped by a fixed primary stress pattern into five, two, and four syllables.50 This description is based on analyses of the spoken song texts, but a slightly different picture emerges if we analyze song performances. The timing of syllables in Gama songs shows subdivision of the eleven-​syllable text lines into two groups of five and six syllables, with a long syllable at the end of each group and a range of different subdivisions of the second group. Although syllable length contrast is not used in everyday language, it helps to organize timing of song language. Furthermore, stress patterns of spoken text lines do not determine timing patterns of syllables in Gama songs. Though primary stress syllables tend to be slightly shorter than secondary or non-​stressed syllables, the difference was not significant. The first and second, but not third, primary stress coincides with the main subgrouping of the text line. Due to the considerable syllable duration variance (much larger than for Pitjantjatjara songs) there is considerable variation in the actual text line rhythms, despite a common short/​long pattern.51 Compared to everyday language, Pitjantjatjara and Dyirbal song language is constrained by factors that support memorization and performance, e.g., number of syllables per text line and relative syllable length (short–​long) pattern. These memory aides are not necessarily based on features of everyday language, as indicated by the length contrast in Dyirbal song language. Text lines that share the same metrical pattern may not show the same vocal rhythms in performance; i.e., metrical organization of a text line does not determine durational structure or rhythm.

6.2 Instrumental rhythms Many Aboriginal songs have percussive accompaniments consisting of slapping thighs, hand claps, or beating sticks, boomerangs, bottles, tin cans, etc. Two types of beating accompaniment can be discerned. One consists of clap intervals of approximate equal length that correspond to an underlying motor pulse, with mean beat



49 Dixon, The Dyirbal Language.

50 Dixon and Koch, Dyirbal Song Poetry.

51 Will, “Oral Memory in Australian Song.”

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226   The Philosophy of Rhythm intervals ranging from 0.25 to 2.2 seconds. The other consists of clap pairs of unequal length; chronometric analysis suggests that it is formed by a subdivision of the underlying basic motor pulse. Variance of the intervals is considerably larger than for the first type and durations of the clap pairs cover a sub-​range of the first type.52 Frequently songs show only one type of accompaniment. If both types occur within one song they are often used in different sections. Beating accompaniments are performed with remarkable regularity and stability across performances and performers. Accompaniment is an independent time marker that does not vary with changes in other layers of a performance (vocal rhythm and melody).53 The independence of the accompanying rhythms from the vocal rhythms is evident from chronometric analyses.54 For instance, Dyirbal songs generally show weak synchronization between vocal and instrumental rhythms. Also, there was no indication that the primary stress pattern of Dyirbal Gama songs leads to a temporal or dynamic 4-​2-​4 sub-​grouping of the accompanying rhythm, as suggested by Dixon and Koch. It can therefore be argued that the clap accompaniment shows no organization in terms of a Western musical meter as there are no hierarchically related beat levels. However, accompaniment patterns clearly structure the performance and therefore serve as additional performance memory aids. The “lines” of Dyirbal gamma songs, for example, are generally accompanied by five (unequal) pairs of stick beats (i.e., ten stick beats), but the vocal “text line” rhythms may not span the whole length of the accompanying pattern. Nevertheless, whatever the performance duration of the eleven-​syllable text line, the repeat of a vocal line or the start of a next line does not commence before the completion of the ten stick beats—​even where some syllables are missing in the middle of text lines. These are indications that text lines are performed and organized along clapstick patterns or subgroups thereof. The number of clapstick beats seems to serve as an orientation or reference frame during performance, and performers appear to be aware of this function of the accompaniment as they sometimes explicitly acknowledge it. In Pitjantjatjara and some other regional Aboriginal songs, instrumental accompaniment also has a synchronizing and entrainment effect on the vocal rhythm layer. For Pitjantjatjara songs it was possible to demonstrate the synchronizing effect directly because some small songs are often performed twice in a performance, once without and once with beating accompaniment. In the latter case durations of syllables or syllable groups are adjusted so that some syllables become synchronized with stick beats or claps, and variance of syllable duration is significantly reduced.55 Synchronization of vocal and accompanying rhythms has a facilitating effect on repetition and recall, an effect Havelock describes as a principle governing poetic performances in oral cultures.56 However, entrainment between vocal and

52 Will, “Oral Memory in Australian Song”; Will, “Kognitiven Musikethnologie.” 53 Ellis, Aboriginal Music.

54 Will, “Oral Memory in Australian Song.” 55 Will, “Oral Memory in Australian Song.” 56 Havelock, Preface to Plato.

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instrumental rhythms does not seem to be automatic. In Dyirbal songs synchronization between the two rhythms was much weaker than in Pitjantjatjara songs. Dyirbal social life is in transition, and the role of communal performances is in decline. Changes in social life of this group may have eliminated factors favoring entrained performances.57

7. Conclusions For over thirty years, time research was dominated by the idea that temporal processing is accomplished by a unitary, amodal process across various task domains. Recently, alternative models have arisen that reject dedicated neural structures because temporal processing is inherent in neural dynamics. In these models, timing functions are executed by multiple, overlapping neural systems, which may be flexibly engaged depending on context; temporal processing is modality, task, and context specific. The reported processing differences for vocal and instrumental rhythms is compatible with such models, and poses a challenge for the idea of rhythm as an abstract feature of event sequences. In the auditory domain rhythm processing has discernable sensory components. The differences in temporal processing can be explained by the ways sensory input changes as agents interact with the environment. From an enactive perspective, the distinction between vocal and instrumental rhythm appears to reflect their different origins in relation to the human body—​one produced actively inside the body, the other created through limb action on external objects—​as well as their different significance in human interaction and communication. This interpretation resonates with the analysis offered by W. Tecumseh Fitch’s comparative research into the origins of music, which combines cross-​cultural, intra-​specific and inter-​specific perspectives.58 He emphasizes that “the music faculty” consists of various components with different evolutionary histories, which talking about “music” as a unitary phenomenon obscures. In support of a multi-​ component view of music that treats vocal and instrumental music as distinct, he discusses lines of evidence from design features of music and language to the evolution of analogous and homologous behavioral traits. In addition, to reiterate, vocal and instrumental rhythms differ also in temporal processing. These different lines of research offer new perspectives on the relationship between speech and music. Thus it would be difficult to maintain that the rhythm of speech is at the origin of vocal music, which in turn gives rise to instrumental music.59 Although they all exhibit different temporal properties, speech and vocal 57 Clayton et al., “In Time with the Music”; see also this volume, Chapter 12, Clayton, “Entrainment and the Social Origin of Musical Rhythm.” 58 Fitch, Biology and Evolution of Music. 59 Arom, African Polyphony; Agawu, African Rhythm.

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228   The Philosophy of Rhythm music are both based on the voice, produced inside our body through engagement of vocal folds, lungs, mouth cavity, etc. Instrumental sounds are produced through interactions of our limbs with external objects, or with resonating parts of our own body. Hence, vocal rhythms—​in speech and vocal music—​and instrumental rhythms derive from different ways of interacting with our environment and are controlled by different temporal mechanisms. Thus instrumental music should be considered in parallel to vocal music, not as derived from it.

Works Cited Agawu, Kofi, African Rhythm: A Northern Ewe Perspective, tr. Martin Thom, Barbara Tuckett, and Raymond Boyd (Cambridge, 1995). Arom, Simha, African Polyphony and Polyrhythm:  Musical Structure and Methodology (Cambridge, 1991). Belin, Pascal, Robert Zatorre, Phillipe Lafaille, Pierre Ahad, and Bruce Pike, “Voice-​Selective Areas in Human Auditory Cortex,” Nature, 403.6767 (2000), 309–​12. Bent, Tessa, Anne R. Bradlow, and Beverly A. Wright, “The Influence of Linguistic Experience on the Cognitive Processing of Pitch in Speech and Non-​Speech Sounds,” Journal of Experimental Psychology: Human Perception and Performance, 32.1 (2006), 97–​103. Bueti, Domenica, Bahador Bahrami, and Vincent Walsh, “Sensory and Association Cortex in Time Perception,” Journal of Cognitive Neuroscience, 20 (2008), 1054–​62. Cheong, Yong Jeon and Udo Will, “Empty and Filled Rhythms: An Inquiry into the Different Cognitive Processing of Vocal and Instrumental Rhythms,” conference presentation, Society for Music Perception and Cognition (2015). Clayton, Martin, “Entrainment and the Social Origin of Musical Rhythm,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C12. Clayton, Martin, Rebecca Sager, and Udo Will, “In Time with the Music:  The Concept of Entrainment and Its Significance for Ethnomusicology,” European Meetings in Ethnomusicology, 11 (2005), 1–​82. Cummins, Fred, “Looking for Rhythm in Speech,” Empirical Musicology Review, 7.1–​2 (2012),  28–​35. Cummins, Fred and Robert F. Port, “Rhythmic Constraints on Stress Timing in English,” Journal of Phonetics, 26.2 (1998), 145–​71. Deutsch, Diana, “Recognition of Durations Embedded in Temporal Patterns,” Perception & Psychophysics, 39.3 (1986), 179–​86. Dixon, Robert M. W., The Dyirbal Language of North Queensland (Cambridge, 1972). Dixon, Robert M. W. and Grace Koch, Dyirbal Song Poetry: The Oral Literature of an Australian Rainforest People (Brisbane, 1996). Dooling, D. James, “Rhythm and Syntax in Sentence Perception,” Journal of Verbal Learning and Verbal Behavior, 13.3 (1974), 255–​64. Ellis, Catherine J., Aboriginal Music, Education for Living: Cross-​Cultural Experiences from South Australia (Brisbane, 1985). Fant, Gunnar, Acoustic Theory of Speech Production, With Calculations based on X-​ray Studies of Russian Articulations (The Hague, 1970). Fitch, W. Tecumseh, “The Biology and Evolution of Music:  A Comparative Perspective,” Cognition, 100.1 (2006), 173–​215. Fraisse, Paul, “Rhythm and Tempo,” in Diana Deutsch, ed., The Psychology of Music (New York, 1982), 149–​80. Havelock, Eric A., Preface to Plato (Cambridge, MA, 1963).

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Temporal Processing and the Experience of Rhythm  229 Hung, Tsun-​Hui, “One Music? Two Musics? How Many Musics? Cognitive Ethnomusicological, Behavioral, and fMRI Study on Vocal and Instrumental Rhythm Processing,” PhD thesis (Ohio State University, 2011). Huys, Raoul, Breanna E. Studenka, Nicole L. Rheaume, Howard N. Zelaznik, and Viktor K. Jirsa, “Distinct Timing Mechanisms Produce Discrete and Continuous Movements,” PLoS Computational Biology, 4.4 (2008): https://​doi.org/​10.1371/​journal.pcbi.1000061. Jones, Mari Riess, “Time, our Lost Dimension: Toward a New Theory of Perception, Attention, and Memory,” Psychological Review, 83.5 (1976), 323–​55. Jones, Mari Riess and J. Devin McAuley, “Time Judgments in Global Temporal Contexts,” Perception & Psychophysics, 67.3 (2005), 298–​317. Klyn, Niall A.  M, Yong-​Jeon Cheong, Erin T. Allen, and Udo Will, “Differential Short-​Term Memorization for Vocal and Instrumental Rhythms,” Memory, 24.6 (2015), 755–​91. Large, E. W. and Jones, M. R., “The Dynamics of Attending: How People Track Time-​Varying Events,” Psychological Review, 106.1 (1999), 119–​59. Le Poidevin, Robin, The Images of Time: An Essay on Temporal Representation (Oxford, 2007). Lewis, Penelope A. and R. Christopher Miall, “Brain Activation Patterns during Measurement of Sub-​and Supra-​Second Intervals,” Neuropsychologia, 41.12 (2003), 1583–​92. London, Justin, “Metric Entrainment and the Problem(s) of Perception,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C11. MacDougall, Hamish G. and Stephen T. Moore, “Marching to the Beat of the Same Drummer: The Spontaneous Tempo of Human Locomotion,” Journal of Applied Physiology, 99.3 (2005), 1164–​73. Merchant, Hugo, Wilbert Zarco, and Luis Prado, “Do we have a Common Mechanism for Measuring Time in the Hundreds of Milliseconds Range? Evidence from Multiple-​Interval Timing Tasks,” Journal of Neurophysiology, 99.2 (2008), 939–​49. Michon, John A., “The Making of the Present: A Tutorial Review,” in Jean Requin, ed., Attention and Performance, vol. 7 (Hillsdale, NJ, 1978), 89–​111. Moore, Roger K., “Finding Rhythm in Speech: A Response to Cummins,” Empirical Musicology Review, 7.1–​2 (2012), 36–​44. Nakajima, Yoshitaka, “A Model of Empty Duration Perception,” Perception, 16.4 (1987), 485–​520. Nakajima, Yoshitaka, Shinsuke Shimojo, and Yoichi Sugita, “On the Perception of Two Successive Sound Bursts,” Psychological Research, 41.4 (1980), 335–​44. Noë, Alva, “Experience of the World in Time,” Analysis, 66.289 (2006), 26–​32. Pa, Judy and Gregory Hickok, “A Parietal-​Temporal Sensory-​Motor Integration Area for the Human Vocal Tract: Evidence from an fMRI Study of Skilled Musicians,” Neuropsychologia, 46.1 (2008), 362–​8. Pöppel, Ernst, “A Hierarchical Model of Temporal Perception,” Trends in Cognitive Science, 1 (1997),  56–​61. Pöppel, Ernst, “Lost in Time: A Historical Frame, Elementary Processing Units and the 3-​Second Window,” Acta Neurobiolohiae Experimentalis, 64.3 (2004), 295–​301. Povel, Dirk-​Jan and Peter Essens, “Perception of Temporal Patterns,” Music Perception, 2.4 (1985), 411–​40. Press, Clare, Eva Berlot, Geoffrey Bird, Richard Ivry, and Richard Cook, “Moving Time:  The Influence of Action on Duration Perception,” Journal of Experimental Psychology:  General, 143.5 (2014), 1787–​93. Rammsayer, Thomas H. and Wolfgang Skrandies, “Stimulus Characteristics and Temporal Information Processing:  Psychophysical and Electrophysiological Data,” Journal of Psychophysiology, 12 (1998), 1–​12. Rubin, David C., Memory in Oral Traditions:  The Cognitive Psychology of Epic, Ballads, and Counting-​Out Rhymes (Oxford, 1995). Schaal Stefan, Dagmar Sternad, Rieko Osu, and Mitsuo Kawato, “Rhythmic Arm Movement is Not Discrete,” Nature Neuroscience, 7.10 (2004), 1137–​44.

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230   The Philosophy of Rhythm Schimmel, Othmar and Armin Kohlrausch, “On the Influence of Interaural Differences on Temporal Perception of Noise Bursts of Different Durations,” Journal of the Acoustical Society of America, 123.2 (2008), 986–​97. Schütte, H., “Subjektiv gleichmäßiger Rhythmus: Ein Beitrag zur zeitlichen Wahrnehmung von Schallereignissen,” Acustica, 41.3 (1978), 197–​206. Shuler, Marshall G. and Mark F. Bear, “Reward Timing in the Primary Visual Cortex,” Science, 311 (2006), 1606–​9. Thomas, Ewart A.  C. and Irvin Brown, “Time Perception and the Filled-​Duration Illusion,” Perception & Psychophysics, 16.3 (1974), 449–​58. “Try the McGurk Effect: Is Seeing Believing?,” Horizon (online video), BBC Two (2010), episode 4 of 15: https://​www.youtube.com/​watch?v=G-​lN8vWm3m0. Tunstill, Guy, “Music and Language, and Other Aspects of Pitjantjatjara Song,” unpublished paper, University of New England (Armindale, 1985). Van Noorden, Leon and Dirk Moelants, “Resonance in the Perception of Musical Pulse,” Journal of New Music Research, 28.1 (1999), 43–​66. Warren, Richard M. and Charles J. Obusek, “Identification of Temporal Order within Auditory Sequences,” Perception & Psychophysics, 12.1 (1972), 86–​90. Wang, Xiaoqing, “On Cortical Coding of Vocal Communication Sounds in Primates,” Proceedings of the National Academy of Sciences, 97.22 (2000), 11843–​9. Wearden, John H., Roger Norton, Simon Martin, and Oliver Montford-​Bebb, “Internal Clock Processes and the Filled-​Duration Illusion,” Journal of Experimental Psychology:  Human Perception and Performance, 33.3 (2007), 716–​29. Will, Udo, “Oral Memory in Australian Song Performance and the Parry-​Kirk Debate:  A Cognitive Ethnomusicological Perspective,” in Ellen Hickmann and Ricardo Eichmann, eds, Studien zur Musikarchäologie, vol. 4 (Rahden, 2004), 161–​80. Will, Udo, “Perspektiven einer Neuorientierung in der kognitiven Musikethnologie,” in Wolfram Steinbeck and Rüdiger Schumacher, eds, Selbstreflexion in der Musikwissenschaft (Kassel, 2011), 193–​211. Will, Udo, “Cultural Factors in Response to Rhythmic Stimuli,” in James R. Evans and Robert Turner, eds, Rhythmic Stimulation Procedures in Neuromodulation (London, 2016), 279–​306. Will, Udo and Eric Berg, “Brain Wave Synchronization and Entrainment to Periodic Acoustic Stimuli,” Neuroscience Letters, 424.1 (2007), 55–​60. Will, Udo, Martin Clayton, Ira Wertheim, Laura Leante, and Eric Berg, “Pulse and Entrainment to Non-​Isochronous Auditory Stimuli:  The Case of North Indian Alap,” PLoS ONE, 10.4 (2015): https://​doi.org/​10.1371/​journal.pone.0123247. Wittmann, Marc, “Moments in Time,” Frontiers in Integrative Neuroscience, 5.66 (2011): https://​ doi.org/​10.3389/​fnint.2011.00066. Zatorre, Robert J., Pascal Belin, and Virginia B. Penhune, “Structure and Function of Auditory Cortex: Music and Speech,” Trends in Cognitive Science, 6.1 (2002), 37–​45.

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15 Complexity and Passage Experimenting with Poetic Rhythm Christopher Hasty

I The following exploration of poetic rhythm understands rhythm not as an already-​ formed order (of isochronous division, or of fixed pattern), but as the ongoing shaping of events and their succession. Succession is an order, of one-​after-​another; but it need not be regarded as a fixed order of separate, externally related terms. If we can admit internal relations into the terms of succession and say that no event is without actual and potential involvement in others, then succession can be understood also as continuous. That is to say, if “one after another” can mean “one informed by (or forming itself out of) another,” then there is no ultimate separation of the terms “one” and “another,” and the continuous (“ongoing” and “shaping”) succession of rhythm can be admitted. Questions of separate and together, discontinuity and continuity, multiplicity and unity can find a favorable environment in the venerable idea of rhythm. Although the word “rhythm” has come to imply the regularity of a repeated and separable unit or pattern of units, it can also evoke the dynamic or temporal connotations of flow—​not as movement through a homogeneous substance (“time”), but as a continuous and at the same time articulated process, the active and characterful creation of things or events. This creation can be felt. The word “rhythm” is especially valuable because it continues to speak of feeling/​valuing/​attending—​as when we speak of “the rhythmic” or characterize “rhythm” as, for example, sexy, engaging, subtle, exact, erratic, confusing, primitive. As a shaping, rhythm is always a valuing that involves emotional investment and choice (agency), the choice to attend or not, and of how much to invest in attending. Such valuing operates in the realm of the aesthetic, as feeling or sensing, and thus points to the aesthetic as a fully temporal category. Poetry is a rhythmic verbal art to the extent that it can intensify attending and feeling. Taking poetry here as something actually made—​ read, said—​ means resisting reduction to the structure of a fixed and timeless text. But to give text its due as process, let’s understand poetry as an artifact (written or not) made to be Christopher Hasty, Complexity and Passage In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0016

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234   The Philosophy of Rhythm performed, said/​heard again and again. Even if performance (in the case of a written artifact) involves reading and a silent saying/​hearing, it is a reading event that, like saying/​hearing aloud, takes time. Rhythm implies performance, at least if we understand that there cannot be rhythm (as there cannot be sound) at an instant. Rhythm takes time. To take performance seriously, think of the Late Latin performare, to fully, completely form. What is not performed is not fully formed. (Think of performing a service or a task.) And yet, “performance” has narrowed to mean making public to entertain others (thus, even a “private performance” has an audience). Without at all denying the importance of others, I would ask the reader to think of performance more generally as the action of actually making—​making poetry, making music, making sense. Shifting perspective toward performance moves us toward a temporal perspective, from which performance always results in something new. “Experimenting” is understood as nearly synonymous with “performing”—​ repeating, and thereby learning something new. Experimenting is more specialized—​a performance aimed at questioning, asking about, seeking. We perform experiments to test and to reflect, aiming to comprehend more. Practicing a skill like singing music or reading poetry can have this character of experimentation.

II Although “rhythm” and “poetry” are not focal concepts of process thought, “experience” is. The process-​thought perspective I take affirms process as activity, ongoingness, emergence, movement, growth, learning.1 Such thinking feels itself in opposition to the thought of substance, stasis, mechanism, timeless transcendence, and knowledge as a secure possession. There can be virtue in sharpening the opposition, and in finding a balance, especially if both terms change in order to balance. With this latter virtue in mind, rather than dwell on the opposition of process thought to, say, substance thought, I will attempt to exemplify and instantiate process by experimenting with poetic rhythm, reading/​hearing/​saying a single stanza from Keats’ Endymion, namely, the beginning of the “Hymn to Pan.” This excerpt will serve as a laboratory for experimenting with problems of poetic rhythm. Written poetry is an excellent vehicle for rhythmic experimentation, largely because it can be returned to repeatedly, and because all readers have access. Experimenting with written music is more difficult and restrictive. To experiment in detail with hearing or playing from score can take much time and energy, and few have the skills to work with a score. To take full advantage of the example in Figure 15.1, I ask that the reader join in the experiment by repeatedly trying out saying. With repetition a reader will, I hope, make discoveries—​some in line with my suggestions, and some not.

1 Rescher, Process Metaphysics, gives a general and ecumenical definition. My narrower perspective is informed especially by James, and Whitehead, Bergson, and Deleuze. Pred, Onflow, connects James and Whitehead with John Searle and Gerald Edelman.

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These experiments aim at feeling events of different sorts or levels and focus especially on duration or timing. They involve action (saying) and reflection (thinking-​ about) in alternation. Indeed, there is a rhythm of experimenting: if thinking about creates events, thinking about takes time. My position is that there is no ultimate escape from time and passage. But, at the same time, I truly value the practice and also the instruments of thinking-​about—​abstractions, diagrams, categories, schemata that appear to resist passage. In fact, I will preface the following analysis with some such abstraction—​a distinction between rhythm performed (said, heard, felt) and described or talked about. I call the rhythmic-​performative “R1,” and the description of rhythm (about rhythm) “R2.” R1 is the actually felt or sensed course of events, or their emergence; a process of event-​formation in which repetition is transformed into novelty and felt as such, felt as fully “now.” R2 is an intellectual construction of rhythm involving naming, description, analysis—​any thinking about. A dominant variety of R2 overvalues itself to the point of denigrating or denying R1, the temporal or performative. R1 is denigrated when it is dismissed as mere performance, merely subjective. To the extent the temporal, dynamic, ongoing is a threat to stability—​to fixed objects, eternal laws; to the extent there is the threat of evanescence and disappearing, ineffability and loss of control, R2 moves to eliminate R1 as an illusion—​the illusion of time’s arrow, or of time as anything more than a mere formality. But since R2 here means any construction, it can also refer to event-​or process-​based constructions such as I will explore with poetry. I specify the difference when I speak of the old R2 or ask for a new R2. Again, any R2 will, in fact, be its own R1 as it is actually done. Thus, there is no real escape from time or passage. It is crucial to understand that R2 must be performed—​in speaking, reading, writing, thinking about (all present progressive tense). Moreover, music-​ poetic rhythmic performances and practices are never isolated from discourses. Positing R1 as primary does not denigrate or demote such discursive (R2) activities, but acknowledges the primacy of temporality and process. It also suggests a perhaps inescapable (more or less Diltheyian) hermeneutic circle connecting R1 and R2; suggesting also that such regenerative, rhythmic work can be more or less creative, more or less sterile. Positing R2 as secondary is to recognize that no R2 description can capture an intricacy that is always on the move. But we can make room for intricacy if we make room for movement, and perhaps fashion an R2 practice that might remember and honor its R1 involvements.

III The “Hymn to Pan” stands out in Endymion as a fictively pre-​composed piece, a poem within the poem, sung by a chorus.2 An imaginary-​archaic ritual invocatio, 2 Two weeks after the publication of Endymion, these five stanzas were excerpted and published as “Hymn to Pan,” in Yellow Dwarf (May 9, 1818).

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236   The Philosophy of Rhythm O thou, whose mighty palace roof doth hang

(1)

From jagged trunks, and overshadoweth Eternal whispers, glooms, the birth, life, death Of unseen flowers in heavy peacefulness; Who lov’st to see the hamadryads dress

(5)

Their ruffled locks where meeting hazels darken; And through whole solemn hours dost sit, and hearken The dreary melody of bedded reeds— In desolate places, where dank moisture breeds The pipy hemlock to strange overgrowth; Bethinking thee, how melancholy loth

(11)

Thou wast to lose fair Syrinx—do thou now, By thy love’s milky brow! By all the trembling mazes that she ran, Hear us, great Pan!

(15)

Figure 15.1  Keats, “Hymn to Pan,” first stanza (from Endymion, Book 1, lines 232–​46), annotated.

the first stanza (one long sentence!) proceeds by naming the attributes of the god whose name is withheld until he is at last ready to be brought into full presence. This withholding is at the same time a holding on to the initial sonorous address O thou!, which evolves as the stanza goes on, holding and developing of the god’s attention. Pan here is approached as a latent power to be coaxed from his eternal realm, awakened, pulled into the mundane, and reminded of his experience of suffering—​ his loss of Syrinx—​that can make him open to human need. There is in this invocation a progression from naming and describing his immemorial habitat (ll. 1–​4); to his seeing (5–​6) and then hearing (7–​10); to his remembering (Bethinking) a

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crucial incident (11–​14) that brings remorse or pity; and finally, to his naming—​ recognizing and being called forth by his name: O thou! . . . Hear us, great Pan! Reading this stanza, we can live through a discourse or course of thought—​a dense, moving journey, vividly present. I have chosen this passage in part because it is so clearly designed to hold on to its opening gesture of address.3 The word-​ sounds that carry the address vanish right away but are carried on by others, and so continue working through the passage. Thus, O thou! is sustained in the following phrase, beginning with whose, and again in Who lov’st to see (5) . . . dost sit, and hearken (7) . . . Bethinking thee (11) . . . Thou wast to lose fair Syrinx—​do thou now (12), By thy love’s milky brow (13), and finally in his audacious naming, Hear us, great Pan! (15). The words of the initial address need not be remembered, because they are never dismembered from the course that follows. They are there in the intensification of bringing forth the god, the acceleration of lines 11–​15, and in the closing of the stanza. They are held in this way only by moving, carrying the rhythm forward. That is, they are sustained by continuing to inform senses that are made only by virtue of their power to inform—​a power sustained/​made possible only by what is made of them, by their successors—​followers that hold the fate of their success. In the extrinsic mode of R2, we step outside the flow to identify and hold on to separate parts (like O thou! and Who lov’st), and so make a different discourse with its own (much less compelling) rhythm. Perhaps we can negotiate this difference by experimenting with the text as an opportunity for spoken performance and so oscillate between R1 (saying) and R2 (thinking about saying). Rather than account for the structure of the text or talk about it as something given, we can experiment with it, by saying it. Let’s say the goal of saying is to stay with the evolving rhythmic course of thought. Although each saying will be different, constraints will be general—​habits, rules, laws of speech (postulated by theories of prosody, syntax, semantics). Variation in saying around these constraints will help us better understand them. Let’s begin by saying the first line, syllable-​by-​syllable. As M.  H. Abrams demonstrates, syllables are “mouth events,” gestures that begin and end either in silence, or in beginning a new gesture, an immediately following syllable.4 The rhythm of syllables is, I propose, the way they flow from one into another. The motion is continuous from one part to another, each becoming what it is by virtue of an informing past and future. These syllable-​parts are thus events or becomings that become determinate entities whose achieved definiteness is both their pastness (as determined) and their future-​directedness (as potentially determining). As they pass, the syllables prepare one another. We can feel/​hear the vowel rebound in O thou!, thou setting up whose (feel the pursing of the lips in O, thou, and

3 Hasty, “Rhythmusexperimente—​Halt und Bewegung.” 4 M. H. Abrams, Fourth Dimension of a Poem, 1–​29, 30–​52, eloquently describes poetry as involving “the lungs, throat, mouth, tongue, and lips,” especially in “the material, articulative aspect of Keats’ language” (32).

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238   The Philosophy of Rhythm whose). Feel/​hear the sudden darkening (the movement to the back of the mouth) from mighty palace-​to -​roof, and farther, through doth to hang. Notice also the fricative, labiodental-​to-​linguadental movement from lips–​–r​oof–​–​to tongue–​–d ​ oth. Hear the “timings” of such movements; they are part of the how of our saying, influencing and influenced by all the countless factors that contribute to the poetic discourse. This how is what I call, adjectivally, “the rhythmic.” Feeling the flow of syllables also involves specifically metrical differences, quantitative-​qualitative distinctions variously called “strong-​weak,” “long-​short,” “accented-​unaccented,” “beat-​offbeat.” Traditionally, the alternation of such differences has been framed as the production of poetic feet, separate units arranged in a line—​here five iambic feet structuring the ten syllables. This traditional R2 description, even if it could be satisfactorily applied to all lines of iambic pentameter (which it has not been), cannot capture the intricacy of a rhythmic performance. Indeed, no R2 description can capture an intricacy that is always on the move. But we could make more room for intricacy were we to make more room for movement. The approach I advocate here has the analytic virtues of R2 while being open to the novelty/​particularity of R1—​a sort of R2 that can experiment with and learn from R1 by explicitly taking passage into account. To find a place for passage, prosodic objects would have to be conceived as events that can emerge in our actual saying. Phonological prosodists have been far more ready than poetic prosodists to focus on such events.5 “Can emerge” here indicates a bridge from labeled object (R2) to performance (R1), and perhaps (ideally) back again, returning with more questions about the object and its labeling. This bridging is made by experiment. Thus my invitations to feel/​hear the vowel repetition O thou!, itself preparing whose, and the darkening movement to the back of the mouth with -​roof all ask for testing. These things/​ actions present opportunities for our saying, with the implication that such attending can valuably extend or enhance our attention. As a written or remembered artifact, poetry, like music, is an opportunity for experimentation, saying/​hearing/​reading, again and again. Thus poetry is unlike the “spontaneous,” unwritten speech of phonological prosody. And yet, as recorded or transcribed by the phonologist, the latter too is an artifact that invites experimentation. Testing is common also in poetic analysis, where scansions are tried out and revised. Traditional scansion practices are pedagogically useful in drawing attention to duration and patterning in the saying of poetry. If successful, traditional pedagogy serves as scaffolding for increasingly complex sayings. As a vehicle for learning, traditional prosody leads to a complexity beyond its own limited categories. Indeed, if we take temporality seriously our aim cannot be to discover the way poetry should be said—​it will always be said anew. Certainly, there are more or less satisfying, more or less sensitive readings that take more or less of the poem’s intricate potentiality into account. But more potential remains than any performance can deliver, including incompatible potentials. This inescapable 5 E.g. Attridge, Poetic Rhythm on “beats” and emphasizing performance.

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multiplicity is the cumulative, historical (temporal) work of poetry in human society. For those literary scholars who value univocity, such multiplicity can seem a danger; for an actor, reader, or poet, it is a blessing. Similarly, performing musicians are keenly attuned to the inexhaustibility of the artifact, though musicologists posit underlying, fully determined and fixed structures. Where research focuses on process (open, experimental, novel, negotiable), rather than on product as “artwork” (fixed, closed, same), there will be less need to determine what will or should be said—​an impossible goal in any case. Speaking the first line of the “Hymn to Pan,” we can feel/​hear five beats, marked | in Figure 15.1.6 Offbeats are marked \ or /​depending, as we shall see later, on their movement relative to a preceding or following beat:  \ designates arsic function (falling, moving away from) and /​anacrustic function (rising, moving toward). My proposal opposes the traditional construal of beats and offbeats as ultimately separate (externally related) entities, each occupying its own temporal slot; rather, the relation is a temporal dependency in the creation of duration. Beats, I argue, last through the whole duration that leads from one beat to the next. Offbeats in various ways continue this becoming-​duration. Rather than “offbeat” I prefer to say “continuation.” Continuation (\ or /​) names that part-​event that does not end the present event (|). Thus, in the situations labeled | \ and | /​, the slanted line does not end the duration promised by the vertical. Continuation is the beat’s duration, its enduring. The marks /​and \ designate articulated continuations, themselves events that begin and end and have their own durations. We could conceive of them as separate “units” only by disregarding their function of continuing the creation of an event already underway. Traditional R2 construes separate units. The difference between R2 units and R1 events is that the former, unlike the latter, are independent of process/​passage. To construct an R2 that respects the temporality of R1, we must turn from unit-​object to event. An event begun (|) is present as long as it is going on, growing in duration, in the process of determining what it will eventually be when it becomes past. Moreover, its becoming is not only its present process of determining “itself ” but also its becoming determined—​some (definite, ended) thing—​ for others yet to come. The new beat beginning with migh-​ doesn’t come out of nowhere (as does O), but out of the preceding beat thou! whose (| /​), inheriting that beat’s duration as a potential for its own. Again, no event is without actual and potential involvement in others. We later consider the emergence of successive beats as measured and measuring, but for now let’s take beats as given, and inquire farther into their internal structuring. The distinction between two sorts of continuation, \ and /​, is a functional one, between “closing” (“moving away from”) and “opening” (“moving toward”). In saying the first line, O can be felt leading to thou (much as whose moves on to mighty), whereas -​ty can be felt following or receding from migh-​ (as -​lace trails after pa-​). For the function labeled \ we can use the terms “afterbeat,” “offbeat,” 6 Attridge, Poetic Rhythm, discusses “beats,” emphasizing performance.

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240   The Philosophy of Rhythm or “thetic,” and for /​“upbeat” or “anacrustic.” We might say that \ depends on a prior |, for we are still attached to the present duration. Our interest is in being-​ in this duration, feeling how much time is left to complete the present event. The backslash \ does not imply a retrospective looking-​back—​the time that’s left is definitely moving ahead. Anacrusis (/​)  looks forward, feeling how much time we have to prepare for the upcoming event. The functions \ and /​are quantitative and qualitative categories. Anacrusis is in a sense untethered from dependence on the event already begun, but not from continuing the duration already begun. This untethering tends to happen relatively late in the beat duration, close to the following beat. Afterbeats usually occur closer to their beat’s beginning. Being untethered allows anacrusis to precede a first beat, as in O. In such cases, anacrustic function emerges only when its follower (thou!) comes to have a sufficiently long duration to become a first beat, always a duration longer than that of the anacrusis. The feeling of afterbeat (arsis) and upbeat (anacrusis) is a matter of both timing and aim. Timing here is a decision of when to move based on how much time we have left in the present duration, and on our aim in moving; timing always involves aim. “Timing” is used here as an R1 term, an activity—​as, for example, when we speak of an athlete’s, actor’s or comedian’s timing. Such timing is fully contextual, a choice for when to say involving complications of intonation, situation, and aim. In this broad sense, “timing” might be another word for rhythm focused on the production of new events. For \, the aim is of completing and thus holding onto the beat duration, before moving to the next beat, and it considers how long the present beat might last; for /​, the aim is of completing and thus holding onto the duration now begun, \ “measures” how long the present event might yet last. For /​, the aim is moving to the next beat as a new beginning—​how much time we yet have before the upcoming new event. We might think of the difference as that of a focus on the closing (\) and opening (/​ ) of a present event. Often the distinction is syntactically-​semantically motivated. The continuation whose (/​) opens to and asks for something (whose what?), a noun that eventually emerges in palace-​roof. The intensive auxiliary doth (/​)  asks for a verb (leaving behind the palace-​roof that does the hanging). And since the verb hang here is intransitive it can hang briefly at the end of the line. The syllable -​ ty (\) completes migh-​; thus migh-​ asks for -​ty. These askings-​for are potentials actualized in the line’s rhythmic flow:  \ a potential for actualization within the present beat, and /​a potential for actualization in a successor. To perform this stanza is to experiment with rhythms of actualizing potentials. This experimentation will lead to a variety of timings far more subtle than indicated by the symbols |, \, and /​and perhaps call into question some of the labelings I have suggested (for example, in line 8 the -​dy of melody might be suppressed as a beat, as might that in line 14 if we accelerate to ran; in line 13, thy might begin a beat continued by love’s). Notice especially the variety of patterns among

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Experimenting with Poetic Rhythm  241

the lines—​only lines 2 and 4 are given the same sequence of labels, but even here there are differences in timing. The continuation in jagged can come more quickly than that in unseen, and heavy peacefulness asks for a longer fourth beat than does overshadoweth. None of the movements labeled |, \, or /​is actually the same in performance. We know there are beats because we can feel them. The feeling is not just one of succeeding events but of successive events that are in some sense “equal” or commensurate. The question then is how beats come to be felt. Again, this is a question of process (how) rather than product (what). From a processive-​temporal perspective, to be is to be a potential for further becomings. Beats, as events/​durations, must have the power to affect a successor, to shape its becoming. To turn from products to process and thus acknowledge temporal difference I suggest the term “projection” as a “throwing forth” of one (past) event’s relevance for a (present) successor. It is a throwing and catching, two continuous moments, not one relation of equality (“isochrony”) detached from relata. “Projection” may be held as a general term. The projection of beats in particular will be one of durational quantity—​how much time, how long. Quantity or “length” is one among many sorts of relevance. Later we will consider other sorts of projection. For now, “projection” will be an abbreviation for the quantitative-​durational projection of beats, and thus synonymous with meter. Thus, meter is understood not deterministically or mechanistically, but as fully creative. To focus first on feelings of quantitative–​durational projection, try saying O thou, whose mighty

stopping and listening for how long the second beat lasts. Several tries will be useful in developing a feeling for duration here. The first beat can be lengthened or shortened. The syllable -​ty might come more urgently (quickly) or more leisurely (slowly). We can listen for a more or less clear ending of the second beat. Or we can take this duration for the precise timing of a following beat, saying palace. If we do choose to say palace, we can experiment with earlier or later sayings, and with sayings too early or too late, where “too early” could be felt as an interruption of the second beat and “too late” a hiatus or break in which the second beat no longer works to give us a third. Although this experiment asks for an unusual attentiveness to durational quantity in finely observed distinctions, it points to the context-​sensitivity of timing and the special relevance of immediate succession in our decisions of when to say, and how we value this when. More importantly, such experimentation can also serve quickly to get us more deeply involved in the poetry. Introducing more context and time will help hold onto such distinctions. Try the following two (re-​composed) lines: O thou, whose mighty palace roof

Doth hang from jagged trunks

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242   The Philosophy of Rhythm Here four longer beats are marked. Those heard in mighty, -​roof, and jagged are now heard as continuations: still beats in themselves, they function also to continue larger beats already begun. In this case, try stopping with trunks and listening for how long this beat lasts. A longer duration can be felt, and it should be easier to hear the silence after trunks filled with a continuation of the beat’s duration, a duration inherited from its predecessor. (A similar opening of duration might be heard in stopping with hang.) We might even feel traces of a \, a silent smaller beat inherited from the preceding beat’s \ (in jagged). To sharpen the difference projective context makes, say trunks (or hang) by itself. In this case, duration will be relatively indeterminate—​if trunks by itself begins a beat, how long does it last? Here the silence is not filled with a palpable duration (no more or less definite silent continuation). Projection is a single process that involves two moments: the creation of an event which itself passes into a new creating. I will call these two projective and projected respectively. Neither is an actual duration. Rather, they are both potentials—​ projective potential, potential for a successor, and projected potential, potential used in the self-​creation of a new (present) event, for example, the potential we attended to in saying/​hearing mighty and trunks. Figure 15.2 will facilitate our discussion: Two events A and B are represented here, each a beat. We can use hand claps to make the two, again hearing a more or less determinate duration in the silence that follows the second clap. The first event attains its duration only with the beginning of a second. Its duration is now determined and past—​we cannot now do anything to change this duration. The second event, now present, will attain its duration when it becomes past. The dotted line, labeled P’, symbolizes the relevance of the past duration in the new event. P’ does not symbolize B’s duration—​B will have its duration when it becomes past, but this duration is not represented here. The solid line with an arrowhead, labeled P, shows the relevance of a past, determined duration for a successor. Both P and P’ are potentials or virtuals—​creative powers. P is a potential for future actualization (thus the arrow), and it is a determinate potential (thus the solid line), a fact that can’t be changed. P’ is a potential actualizing in the present and thus indeterminate or on its way to determinacy (thus the dotted line). Note that P is not actualized in P’—​P’ is still potential, projected into the event B, inhering as an inheritance from A. P’ is an actualizing potential—​“present

A

B

P

P’

Projective potential

Projected potential

Figure 15.2  The two sides of “projection”

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Experimenting with Poetic Rhythm  243

potential.” Actual here means present, going on, and so potential can be actual or actualizing if it is working in a present event. Two limitations of Figure 15.2 should be pointed out, each detracting from complexity and passage. The diagram shows only one potential working in B, but in any event there must always be many potentials at work. A and B must involve many more factors than durational quantity (even with hand claps). And there must be a context that involves past events preceding A that B must take into account, and future events that can shape B’s course and how or what it takes from A (say, preparing for a third beat). Both these limitations point to the impossibility of an actual same as one or identity, such as we might represent in a diagram by “A” or a line segment as a unit. Yet metrics as the science of unit measurement accepts both these limitations in positing isochrony or a “same time.” Before returning to a reading the “Hymn”, I shall consider the question of isochrony from the perspective of projection. The projection of beats is achieved beat-​by-​beat, each different in what it achieves and offers. Even in a line where beats are felt as precisely equal, the isochrony must be achieved beat-​by-​beat—​not given in advance as an already determined, atemporal grid. “Isochrony” is problematic if it means “the same length of time” apart from context, and if it implies a train of equal durations apart from the novel contexts that arise beat-​by-​beat. The “same” (or “similar”) implies a comparison of products, entities as faits accomplis, and thus returns us to an R2 unit-​based perspective in which time is a formality. (Again, from a perspective of process, beats are faits accomplissant.) Released from these reductions, isochrony can be thought in processive terms as repetitions of durational quantity arising from the actualization of potentials offered by past durations. Since this actualization is part of the self-​creation of the new event which involves many factors that together form the context of this becoming, actualization cannot be separated from contextual complexity. If the context of interwoven factors supports the actualization of projected potential, and our focus is on duration—​ how much time we have for the present event and how much time we have to prepare for the next—​we can attune to isochrony as repetition of durational quantity. Conversely, context may be reduced to favor isochrony. Rather than many factors working to support this actualization, factors that challenge the actualization may be suppressed. Whether by a process of enhancing projective potentials, or one of eliminating conflicting potentials, the actualization of a definite durational potential can become keenly felt, as in the feeling of the new beat. This actualization can be felt only as difference, the difference of now—​the present emergence of a new. This difference is real. Without this distinction P’ (actualizing) would reproduce P (actualized) as exactly the same. This would result in a “pure isochrony” in which the difference of events would be that of position on a timeline. In such a determined world there would be no novelty, no passage. This would be the world of classical deterministic physics in which temporal passage, “the arrow of time,” is seen as illusory, in which time can be understood as the difference of times conceived as a numerical order.

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244   The Philosophy of Rhythm There is another problem with isochrony, more empirical and so more difficult to deal with—​the question of what counts as the same. Repetition of quantity can be highly variable. Successive beats can be the same but shorter or longer, faster, or slower. Successive beats can also be “just right,” “dead-​on.” A keen feeling of “the” beat is not simply a matter of objective clock-​time duration, but also also of focus or prominence. With much accentual verse, a keen feeling of what we might call strict isochrony is a dominant factor in our saying. In the nursery rhyme, “Humpty-​ Dumpty” (Figure 15.3), a “sing-​song” isochrony determines the precise timing of syllables leading to an “equal division” of beats in triplets, even where there is only one continuation, as in Hump-​ty: one-​(two)-​three. In Figure 15.3 I  have reluctantly distinguished arsic (\)  and anacrustic (/​ ) continuations—​the dominance of triplets can overshadow the phonological dependencies to make the distinction otiose. The contrasting (compounded) third line can invite a variation in the triplets, lengthening the first syllable and making the second shorter in a “dotted rhythm” (to use the musical term). Thus inflected, the second continuation of the second beat in line 4, to-​, can be similarly shortened (such “dotted rhythms” are still within the triplet). To further illustrate the pressure of these beats, try substituting for the last line the following: Couldn’t put Humpty-​ Dumpty together again. I believe that there will be only one way to do this (finer points of timing aside) and that it will come easily. The power of these beats derives from a projective depth indicated by labeling alternating beats as continuations of larger beats. As evidence of these greater projections, notice the duration opened by the last syllable of the substitution—​(a)gain. To test the projection, try beginning the poem again from here. When is the right time to say Humpty-​? What would

Humpty

Dumpty

sat on a

wall,

Humpty

Dumpty

had a great

fall,

And all the king’s horses,

Couldn’t put Humpty

and all the king’s men,

together

again.

Figure 15.3  One version, among many, of the nursery rhyme “Humpty Dumpty” as an illustration of the determinacy of tetrameter (and also as an example of the pattern long-​long-​short-​short-​long)

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Experimenting with Poetic Rhythm  245 O thou, whose might·

y pal·

S

S L

L

S

L

ace roof S

L

doth hang S

L

Figure 15.4  The first line said as strict iambic pentameter (five isochronous beats each of the form “weak-​strong”) in obvious violation of the line’s complexity

seem too soon? What is the effect of waiting “too long” or the difference “too late” makes?7 Rather than limit isochrony to such situations, I speak of degrees of isochrony, but loosely, given the variety of applications. I distinguish relatively strict isochrony from loose, flexible isochrony, and treat -​chrony not as clock-​measured time but as event-​measured duration. Duration in the intended sense is not a purely quantitative timespan, but a spanning of time in the old sense of stretching or reaching across. Thus we might think of duration substantively as an action, a process of enduring (from durus, hardening, solidifying) or becoming an event. Duration in this sense blurs the quantity–​quality distinction. The continuations labeled \ and /​shape duration, as do the syntactic/​semantic values of the words we say, the physical movements of our bodies (vocal apparatus), and the larger socio-​cultural environments of our saying—​all working together. If isochrony can never be an exact repetition, and if what constitutes similarity in duration is quantitative–​qualitative, we can allow for degrees of isochrony and perhaps allow that there may be situations in which the isochronous–​non-​isochronous distinction is not clear-​cut. To experiment with projection in the first line, let’s try three performances in order of increasing attunement to the complications of context, taking more into account in our timing of beats/​syllables. First (Figure 15.4), a strict-​isochronous sing-​ song reading of five iambic feet, where iambic means /​|. To make the continuations anacrustic—​against the grain of syntactic-​semantic dependencies—​we must make the continuations short, moving them close to the following beats. This reading demonstrates (purported) iambic feet. Although the decision to reproduce iambs is made prior to the performance as part of the context of performance (in this case a context that works to limit the context of other factors), the performance is still made beat-​by-​beat—​not predetermined by an atemporal grid. In Figure 15.5 the performance is more open to difference and variation in timing with the distinction of /​and \ (“iambs” and “trochees”). The more or less equal spacing of beats shown here represents, like Figure 15.4, a relatively strict 7 Concerning question of scale, one might feel some trace of even larger projective potentials in which the second half of the line functions as continuation (by focusing in two rather than four beats per line). Such a possibility would clearly show that projection is dependent on many factors (for example, beginning again Humpty-​, emerging parallelisms, rhyme). In this connection, a large pattern emerges in this poem, one found in other poems (all limericks, for example), and in many musical phrases comprised of four “measures” (not necessarily bars). As here, the third line or measure is “compounded” or “divided” relative to the others, leading us hear a sort of acceleration or compression in the third part as, say: long | long | short-​short | long or | | | \ |. See my Meter as Rhythm, 113–​15, 225–​36 for discussion of this pattern in music.

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246   The Philosophy of Rhythm isochrony. Note that in Figures 15.4 and 15.5, unlike Figure 15.3, there is no robust larger projective environment to support a strict isochrony, just a decision to deliver the line “in time”—​the time of a purported five-​beat regularity (and in Figure 15.4, a five-​foot regularity). But here, unlike Figure 15.4, we might relax the regularity, or give less keen awareness to it as we attend to other things, such as the timings of continuations (and perhaps feel the change from “iambs” to “trochees” and back again). Figure 15.6 shows further differences in timing, taking more into account than the distinctions of /​and \, and allowing a freer, more variable isochrony. Should we call such a performance non-​isochronous? The performance represented here (where line-​segment length loosely corresponds to durational quantity) shows an acceleration to –​roof. This performance begins with longish O thou! taking into account the focus on this address, which is to be held throughout the stanza, the punctuation, and the emerging syntactic/​semantic in which the anacrustic whose promises a new clause. Experimenting with a relatively slow tempo may be helpful, at least initially, in giving more time for feeling variation and for sensing potentials for rhythmic complexity. After experimenting with this slow tempo, the line can be said faster (much like practicing a piece of music). If migh-​ty is said quickly we will be left with a long stretch if we attempt to reproduce the first beat’s duration—​we must either endure a long silence or begin to intone the second syllable. One solution is to move more quickly to a third beat. The projective potential of the first beat is still relevant in the second if we feel an acceleration—​indeed, this potential is precisely what allows a feeling of acceleration. If we were to shorten further the second beat, making it too short—​too short to realize the projected potential—​the result would

O thou, S

whose might·y

L

S

S

L

pal·ace

roof

S L

L

doth hang S

L

Figure 15.5  The first line said as five more or less isochronous beats, but now allowing for complexities of “weak” and “strong”

O thou, S

L

whose might·y S

S

L

pal·ace roof S

S

L

doth hang S

L

Figure 15.6  The first line said as five “flexibly isochronous” beats whose flexibility or variability is determined (or “controlled”) by higher levels of complexity

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Experimenting with Poetic Rhythm  247

be felt as an interruption, palace-​coming too soon. But note that this feeling too is the product of projection, a projection interrupted. The power (potential, virtue) of projection is weakened only by withdrawing attention, feeling less, taking less into account. Now that we have begun an acceleration, we will be inclined to continue it, for acceleration is now part of the second beat’s projective potential. The third beat inherits from the second not an “absolute” length but acceleration (projection is thoroughly relative and contextual). Nothing here contravenes this inheritance; much supports it. Palace-​is emerging as a second adjective, like mighty, still under the sway of whose and not yet (fully) discharged in the promised noun. Palace-​, like mighty, has a short first syllable. Indeed, in the mouth pa-​ can move to -​lace more easily and hence more quickly than migh-​to -​ty. There is also a syntactic-​semantic intensification at work that can serve acceleration: [mighty [palace-​[roof]]]. Acceleration is broken in the fourth beat with -​roof. Here is our long-​awaited noun and the opening for a verb. (Notice that acceleration might be continued by further compounding: for example, whose mighty palace-​by-​the-​sea.) It is from -​roof that the relative clause closes in doth hang (whose . . . roof doth hang). The deceleration makes -​roof momentarily focal and sets up the verb (doth) hang, which will be crucial for comprehending the larger clause (lines 1–​4)—​doth hang will be revived or sustained in overshadoweth, which in turn must be held for its adverbial phrase in heavy peacefulness at the end of the clause. Notice too that a feeling/​hearing of the sudden darkening in -​roof (from mighty and especially palace-​) enhances/​is enhanced by the deceleration. As a measure of the force of a possible multidimensional focus on -​roof, notice that it is here possible to break the “Compound Rule,” requiring a stress for the first element of a compound word, and here to stress -​roof relative to palace-​. These rhythmic possibilities are motivated (in part) by syntactic possibilities, and serve the syntax in an ongoing process of making sense. The qualifier whose implies (creates syntactic projective potential for) some as yet unspecified noun. We await the appearance of “the” noun, even if we “know” it in advance; and it is in this particular waiting that we are in time and rhythm. The qualifier whose also implies a verb that would follow the noun (a “what” for the noun to be or to do—​ here, finally, to hang) and thus opens the prospect for a longer clause, helping us hold onto the movement from whose to the end of the clause. Whose is our link to thou! (sustaining thou!) and remains throughout the first four lines. Its renewal in who, line 5, initiates a second phrase-​event and thus an end to the first. And again, O thou! lasts well beyond its qualifiers, whose and who (thee and thou). Implying, awaiting, opening the prospect for, remaining, renewing, reviving, sustaining, holding, these point to a sort of projection, a working-​in—​present into future, or past into present. But in contrast to the quantitative-​durational projection of beats, lexical-​semantic and syntactic projection does not require immediate succession—​ whose can be effective long after the word has ceased to sound. As we move to larger contexts we will return to the question of other sorts of projection and to contexts that expand beyond beats.

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248   The Philosophy of Rhythm

IV Having come to the end of our first line we are already on the threshold of a larger context, that of the line-​event. Lines ask to be performed/​heard as events, things that begin and end. The following line is a new beginning. What then of the projective potential of the fifth beat? Does the first beat of a line take its measure from the last beat of the preceding line? It is difficult to generalize. Indeed, even within a line, projective relevance may be attenuated through hiatus (as in line 12 following Syrinx), and there can be great variety in the distinctness with which beats are felt (for example, in lines 8 and 11).8 Such situations are neither defective nor departures from the norm; beat suppression is a part of projective complexity (in how many iambic pentameter lines can we feel clearly only four beats?). The emergence of line-​events carries its own complexity—​the sixth beat (jagged) is now also a first beat with its own anacrusis from (like O, thou!). There is now a continuity of lines as well as beats. However it is accomplished in terms of timing, stress, and pitch contour, the articulation of lines involves a feeling of beginning again and, in the case of this stanza, beginning a new line of iambic pentameter. Does the articulation of lines create the poetic meter or does the poetic meter make the lines? Without the need to continue making pentameter lines there would be no reason to hear hang as an ending (it is not an ending in my recomposed version on page 241). Iambic pentameter is a form, a complex potential made of countless lines internalized (learned, memorized, embodied) by poets and readers. I suggest that such a form does not work as an out-​of-​time abstraction (except in pedagogical contexts) but instead as a repertory of many past experiences constrained by a rule that might be most simply put: (1) ten syllables (or nine if “headless,” or eleven if a final continuation) most often beginning with anacrusis, (2) predominately one continuation per beat, (3) five beats (or four where there are more continuations).9 Thus, a play between the constraint of syllable “count” and the constraint of beat “count”—​where “count” is internalized, becomes a bodily feel. Having these two dimensions in play in this way is part of the charm of this form or habit. Think of form as our habits of playing, and not just the rules of the game. Such a form (like “the” sonnet, sonata, chaconne) has power or potential because it has so often been repeated that it has become a rich reservoir of past experiences for readers and writers of poetry.10 But the form would not have been so often repeated (to become 8 In line 8 the -​dy of melody could enter early as a syncopation. In syncopation the syllable enters just before the beat it bears (which must be felt as such for there to be an early or “just before”), as if an anacrusis were to become a following beat, perhaps to detach from the crucial (for Pan) mention of bedded reeds. Line 11 is the turning point—​Bethinking thee. (Note the ending of line 10 with the triple, | \ \.) Here it is easy to say the two beats of melancholy quickly, twice as fast as the two preceding beats, thus making -​choly a continuation of the larger beat, and perhaps give momentum for moving straight into the next line Thou hou wast to lose. (As we shall see, from here it may be tempting to depart from the pentameter norm.) 9 These three constraints clearly work together—​any two taken together will produce the third. 10 Of course, the question arises: which version of “the” sonnet, sonata, chaconne? Indeed, each of these terms has its own taxonomical structure or history. That is to say, form need not be understood as a fixed and separate entity, nor need structure be thought fixed if it is possible to think of structure in terms of history.

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P

b

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d

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Figure 15.7  Beat-​to-​beat projections in which each new event is focally aware simply of its immediate predecessor

a form) if it did not offer something of value. In its long history, iambic pentameter has been developed on the basis of changing cultural values. Many writers have pointed to the values of complexity and spontaneity as opportunities afforded by the iambic pentameter line.11 Derrick Attridge has specifically pointed to the resistance of the line to the strong inclination toward “doubling” found in tetrameter (creating “2-​beat” potentials such as we saw on pages 241 and Figure 15.3).12 One value that emerges from the choice of five beats is a flexibility with regard to continuations and timing, allowing departures from strict isochrony. Flexible timing is made possible by an openness to contextual complexity generally suppressed in tetrameter. Comparatively strict or flexible here does not imply more or less metrical verse (meter is not a rigid grid). From a temporal or projective perspective, pentameter is no less metrical than tetrameter (nor “free rhythm” necessarily less metrical than strict). Flexibility in timing is a mark of intense potentials working together, and thus an intensely metrical phenomenon. As we saw on page 241, four beats can give rise to a larger beat where beats 2 and 4 become continuations. Since the diagram in Figure 15.2 showed only two beats, we should explore this possibility with more complex diagrams, that provide an opportunity to consider projection further. Figure 15.7 represents four consecutive projections. I have omitted event labels and added brackets to represent the actual achieved durations (a–​e) of the five events. Again, the dotted lines are potentials, not actuals. For each event is shown an actualized duration (a–​e); a potential for its actualization (dotted line); and a potential for actualization in another event (line with arrowhead). In Figure 15.8 things are more complicated. Discussing Figure 15.2, I  said that one limitation of the diagram was in not showing anything before A (or after B). Figure 15.8 shows more context. The third beat enters a world of relevance larger than that of beat 2, and thus can assume a larger potential. Here, I show the emergence of a projective potential R given to the new beginning with beat 3 as a potential for reproduction (R’), and I show this 11 E.g., Easthope, Poetry as Discourse. 12 Attridge, Poetic Rhythm, 153–​8, finds the power of doubling so strong that he classifies pentameter as one of many non-​quadratic, non-​2 × 2 meters.

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250   The Philosophy of Rhythm I 1

II 2

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6(1) T

denial of projective potential

7(2)

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S’ interruption (denial of projected potential)

Figure 15.8  A representation of projective complexity showing the resistance of a five-​beat line to the determinacies of four, or rather two, beats (Attridge’s “doubling”). NB: this diagram is not meant to represent the complexity of most “pentameter” lines where a reduction to two is not an issue. (Indeed, in some “pentameter” nine-​or ten-​ syllable lines there are four beats, but these situations are hardly “square.”)

potential actualized in the duration of a second, larger beat labeled II.13 What then of the relevance of beat 2? Here I suggest a denial of Q’ (crossed out) in a second beat-​event that takes its measure from a now first beat (I). In this way beat 2 becomes a continuation. Beat 2 is still relevant for beat II, as is beat 1. The first event (I) would not be this event with this potential (R) apart from all that constitutes it. To show beat 2’s potential in this new context we might, instead of crossing Q out, move Q’ over a space to fall under beat 4, showing a delay of Q’ rather than a denial of Q. This might account for our timing of a corresponding continuation in beat II (and of the vivid feeling of silent beats). Perhaps both denial and delay can be involved and more one or another depending on context. For example, since beat II is from the start actualizing an R’ potential, beat 4 will emerge already as continuation and not as “denied beginning,” as if it knew nothing of its fate. Or we might imagine a situation when we feel a sudden expansion into larger measure and thus denial of the smaller. Such possibilities point to the openness of potentials in their emergence (and, more specifically, to the projective relevance of continuations which did not appear in Figure 15.2). Things can change quickly in complex situations. Figure 15.8 shows a projection S–​S’ interrupted by the beginning of a new beat IV (if large) or 6 (if small, and thus a sudden reduction of beat length). The interruption (\→ |) actively denies projected potential S’ (rather than a denial of projective potential as in Q) and might be felt as a too-​early new beat. There must be reasons for feeling beats. For present purposes, let’s say that beat 6 (or IV) begins a new line. So if we have large projective potentials—​“2-​beat” projective potentials (i.e., two small beats)—​we now have two choices: to wait before beginning the new

13 For illustration try trimeter, saying, “O thou! whose mighty roof /​Doth hang from jagged trunks” hearing a long measured duration with roof before beginning the second line; or Blake’s “I love the jocund dance, /​The softly breathing song.”

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line, allowing S’ to play itself out (as in trimeter, the earlier odd number), by default making six beats, or to begin the new line as an interruption.14 Neither choice is what iambic pentameter aims for. The solution is to avoid 2-​beat measures or reduce their strength, as in Figure 15.6 where acceleration and deceleration cut across possible 2-​beat measures following the 1 + 3 + 1 syntactic division: O thou! | whose mighty palace-​roof | doth hang. This sort of reduction reflects an opening of the line to an intricacy of context not afforded by larger measures. Complexity of many potentials (factors) working together can complicate beat projection. Projection is enhanced, not weakened, by becoming more variable—​free to respond to context (more possibilities for performance, more challenging to perform, rewarding more attentiveness and experimentation). For iambic pentameter, a fifth beat offers a sixth relatively little. The sixth beat here begins a new line and is thus a new first beat. Felt as a new beginning, the second line-​event can (perhaps must) escape local projective obligations arising at the end of the first line (rather as beat II can escape Q’). This is a crucial moment for timing, a movement to a new event. Some such crossings are difficult and take some practice to enact successfully. In performance, they can be a provocation to test or experiment with the poetic sequence or flow. Meeting this challenge repeatedly will develop poetic skill. Rather than of exceptions (with their threat of de-​ formation) we might think of poetic refinements, enrichments of the art (technical refinements) that open new dimensions. Within the constraints of iambic pentameter, how many ways can line elision (ending into beginning) be plausibly done, i.e., how many forms/​styles of elision are there, which are particularly stylish, when? Each line presents its own problems/​opportunities for articulation involving many factors—​the rhythm of the preceding line; the rhyming of the line ending; the semantic connection of lines; local inflection (volume or stress, pitch contour, as well as timing). An ending may be enhanced by suppressing a fifth beat in a “triple ending” (dactylic | \ \) as in lines 2, 4, and 10 where the final (tenth) syllable is continuative. Here the following anacrusis, beginning the next line, can have even less to go on, with a feeling of slowing down in the fourth beat’s lengthening. Notice that line 4 ending in peacefulness (| \ \) closes the first large clause with the new beginning, Who . . . (corresponding to the initial whose but moving the next step closer to the god: from attributes/​possessions to actions, verbs). At the end of line 2, the triple overshadoweth is by contrast, an opening, crucial in that it must be held all the way to peacefulness (doth hang . . . and overshadoweth . . . in heavy peacefulness). In this long stretch, a sort of pausing, holding up, or holding onto overshadoweth helps make the syntactic/​semantic connection. In line 10, overgrowth (| \ \) ends the next large clause which initiates the intimate address, Bethinking thee, leading to Pan’s naming. Notice that the next line is broken by hiatus (||, a dissolution of projection)

14 To see this potential, try saying the two lines of recomposed verse on page 241, hearing the two-​beat projections, and then returning to Keats’ pentameter line. It may take some effort to get back into the pentameter—​the tetrameter has a very strong pull.

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252   The Philosophy of Rhythm with the delay of do thou now (with stress on the do to carry into the imperative Hear in the final line), which initiates a departure from iambic pentameter into trimeter, preparing, two lines later, the turn to dimeter. This metrical change could be prepared by the enjambment of line 11 and 12 motivated by syntax (loth Thou wast) in the emergence of continuous beats across the lines (loth Thou wast to lose | /​| /​|), thus providing an acceleration to fair Syrinx as an end. (The end rhyme growth-​loth is weakened by the clause division and perhaps more immediately by the alliterative connection of loth and lose.) In any case, the hiatus (||) opens the possibility for a shift (perhaps ecstatic) to a “displaced” or especially urgent and risky new pentameter line, Do thou now, By thy love’s milky brow. The rhyme now-​brow would argue by “rule” (de jure), but rhythm always asks for much more than rule. In fact, such a transitional displacement may again be turned in hearing the (possibly accelerated) expansion from By thy love’s milky brow to By all the trembling mazes that she ran. How long to wait to say line 15, when will the time be just right? In attending to these line-​articulations, much more context was taken into account than that of adjacent beats, but still less than the situation requires. The emergence of a new line from the old is predicated on there being, or rather becoming, a new pentameter line, which cannot happen immediately. The promised line takes time to emerge, even if we decide to make it happen. (Try, for example, beginning the second line and stopping with trunks, noticing the tendency of the new line fragment to attach to the first line as a continuation). Potential is continuous, not incremental but spread through the whole duration.

V The preceding discussion of quantitative-​durational projection or meter took syntax and, to a lesser extent, semantics, explicitly into account—​the distinction of the two, certainly in poetry, is not clear-​cut. Since rhythm involves all these categories (and more) we must consider more specifically the role of syntax and semantics. Seeing projections of durational quantity or meter as fluid and cumulative, rather than as a series of discrete moves, helps us view this sort of projection as continuous with syntactic and semantic projection. This is not the place to develop a temporalized syntax or semantics; theorizing them in terms of rhythm would require new categories replacing products with process.15 But in closing I would like to trace some contributions that syntax and semantics make to the rhythm of Keats’ stanza, thus suggesting further work along these lines. Let’s begin with the first four lines heard/​read as an event that is ended with Who lov’st to see as a new beginning (a sort of |) that nonetheless continues a larger event 15 Numerous resources explore linguistic and semiotic process. See, for example, the systemic functional linguistics of Michael Halliday and his followers. Relevant also might be the interdisciplinary work of Jay Lemke, Stanley Salthe, and Paul Thibault that integrates dynamic systems theory and more or less Peircean semiotics.

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begun in the first line, O thou . . . (rather as beat 2 in Figure 15.8 continues beat 1). I say that the lines 1–​4 event is ended with the new beginning, Who lov’st to see . . . , because lines could have been continued, if, for example, a fifth line were to begin, In silence. Line 1 is left open with hang. “Hang” asks for something more—​ a qualifier (where? how?) answered in From jagged trunks which also moves us (and Pan) downward from mighty palace-​roof. Opening again from doth hang, and overshadoweth moves us farther down this vegetative world to the forest floor, to flowers. This transitive verb (overshadoweth) leads to a great expansion in the next two lines—​from six syllables (doth to trunks) to twenty-​six. The syntactic expansion is accompanied by semantic expansion in a new topic introduced by Eternal. The new idea, which may take some time to figure out, could be paraphrased as follows: We now enter the eternal realm of Pan’s dominion, a place of endless cycles of birth and death, barely heard or seen (whispers, glooms), eternal because there is no one here to make distinctions of before and after, beginning and end; a place of nature passive, unconscious, asleep in heavy peacefulness. This sort of paraphrase is an R2 thinking about that carries us forward in the thought, but not necessarily outside it. When we return to saying, such an excursion can leave its traces in a new saying. If truly felt, this excursus affects the “prosodic” dimensions of sound and timing. The next event, Who lov’st to see . . . , brings Pan into the picture and moves us up again to the canopy (ruffled locks), no longer vegetative but animated by the hamadryads. Lines 7–​10 continue this event (with and), expanding it to six lines. Yet the immediate promise of continuation in the conjunction of lines 5–​6 and 7, complementing seeing with hearing, can gradually dissipate as we move into this darker, inward, emotional and musical world (of reeds and pipy hemlock, i.e., Pan’s pipes) that leads to memory (Bethinking thee) and to a pity that fully awakens Pan’s self-​consciousness in lines 11–​15. In this event, lines 5–​7 can function as a transition. The formation of larger syntactic/​semantic events is fluid; many events at various levels, involving all poetic dimensions, unfold together according to the unique exigencies of performance. The novelty, intensity, or vividness of performance is a measure of rhythmicity, and eventfulness. If the meaning of a poem is thought to reside exclusively in R2 paraphrasable “content,” rhythm will seem superfluous; and if rhythm is viewed from a customary R2 perspective, it will be equated with form and its study regarded as formalistic. From the revised R2 perspective I have been advancing, meaning is a rhythmic accomplishment (without rhythm no meaning), involving syntax and semantics no more nor less than (nor separated from) the “prosodic” or the “musical.” Paraphrase is, as is every R2, a sort of performance (a “reading” of the text), but because the semantic “content” seems extractable, holdable outside a reading of the poem’s words, we can forget that it is a performance, no less subjective, idiosyncratic, and evanescent than a reading of the poem’s words. Indeed, such “intellectual” content might be more evanescent because capable of breaking away from the sounding, sensible, “in-​time” making of poetry heard, said, and vividly imagined. What sort of

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254   The Philosophy of Rhythm R2 should we aim for that would value rhythm as temporal and experiential? There is no end of ways to proceed, and we engage them daily. If an R2, however fashioned, acknowledges its temporality and involvement in worlds of human activity and exchange, then the distinction between R1 and R2 becomes less clear-​cut, perhaps by being seen as Rhythm itself, in one of its irrepressible manifestations.16 The alternative—​to deny R1—​leaves us homeless, worldless: separated from our world and from one another.

Works Cited Abrams, M. H., The Fourth Dimension of a Poem, and Other Essays (New York, 2012). Attridge, Derrick, Poetic Rhythm (Cambridge, 1995). Easthope, Antony, Poetry as Discourse (London, 2002). Gendlin, Eugene, Experiencing and the Creation of Meaning: A Philosophical and Psychological Approach to the Subjective (Evanston, 1997). Gendlin, Eugene, A Process Model (Evanston, 2017). Hasty, Christopher, Meter as Rhythm (Oxford, 1997). Hasty, Christopher, “Rhythmusexperimente:  Halt und Bewegung,” in Christian Grüny and Matteo Nanni, eds, Rhythmus—​Balance—​Metrum (Bielefeld, 2014), 155–​207. Keats, John, “Hymn to Pan,” ll. 232–​46 of Endymion, in Complete Poems, ed. Jack Stillinger ([1818]; Cambridge, MA, 1986), 70. Polanyi, Michael, Knowing and Being, ed. Marjorie Grene (Chicago, 1969). Pred, Ralph, Onflow: Dynamics of Consciousness and Experience (Cambridge, MA, 2005). Rescher, Nicholas, Process Metaphysics: An Introduction to Process Philosophy (Albany, 1996).

16 Gendlin, Creation of Meaning, and A Process Model, give a processive semiotic. Polanyi, Knowing and Being, points to a “rhythmic” movement of focal and subsidiary awareness in learning and discovery.

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16 Encoded and Embodied Rhythm An Unprioritized Ontology Peter Cheyne

1.  Rhythmic description, not prescription Since Richard Wollheim’s Art and Its Objects appeared in 1968, philosophical aestheticians have debated the ontology of art objects in terms of the type–​token distinction, later joined by the work–​performance distinction between compositions and their historical instances.1 These analytic debates are foreshadowed by Sartre’s famous ontology of the musical work being an “unreal” object existing primarily in imagination—​the work being an ideal object that can be physically and historically instantiated indefinitely within loosely defined parameters.2 A contemporary position that prioritizes performance draws primarily from continental traditions, sometimes also drawing on process philosophy, to articulate an important line of thought about the intricacy of performed rhythm. While I think that position can often be misleading, it comes at root from a perennial experiential insight that I would hate to see go undefended. Indeed, if it were not promoted by exponents in this volume such as Christopher Hasty and Deniz Peters,3 and elsewhere by musicologists such as Nicholas Cook,4 I should give it more defence myself as an expression of the vital, human sense of subjective rhythm, though one that is very difficult to articulate logically and correctly. While rhythm that is heard and felt can rightly be described as the “flow” of performance, many qualities of this embodied, subjective sense starkly contrast with what I shall call encoded rhythm, or rhythm in an objective sense. Encoded rhythm refers to the signification of temporal patterning in such documents as musical scores, printed or manuscript poems, film screenplays and storyboards, dance notation, and so on. It is important that encoded rhythm (e.g., scores) be unlike embodied rhythm (e.g., performances), and, as I shall argue, keeping the encoded

1 Wollheim, Art and Its Objects; Davies, Works and Performances. 2 Sartre, The Imaginary. 3 See Chapter  15, Hasty, “Complexity and Passage”; and Chapter  7, Peters, “Rhythm, Preceding its Abstraction.” 4 Cook, Beyond the Score. Peter Cheyne, Encoded and Embodied Rhythm In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0017

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256   The Philosophy of Rhythm and embodied forms separate, rather than making the encoding more like the final performance, adds to performative freedom. Being a bipolar construction, what I  call the embodied–​encoded dichotomy comprises two opposite viewpoints, plus a third, which I shall defend, prioritizing neither pole but rather their interdependence. To take the viewpoint from the encoded pole is to prioritize the formalism and abstraction of theoretical, critical, and notational objects: the score, the outline, the written work, the analysis, etc. Defenders of the opposite viewpoint emphasize that only performed, embodied rhythm is actual rhythm, as opposed to potential. A corollary of this view is that while rhythm remains unperformed, encoded in conventional description, its non-​flowing timelessness means that it is held in a non-​dynamic state of limbo in which the encoded form lacks the necessarily temporal, felt features of embodied, performed, actual rhythm. Described, encoded rhythm, the argument goes, is abstract, and therefore secondary to performance, the concrete reality. More specifically, the concern is that conventional descriptions of rhythm such as the familiar musical score and objective analyses that focus on unit-​based constructions, cannot, as Hasty says, “capture an intricacy that is always on the move.”5 Indicating the essentially abstract nature of the description of rhythm, Hasty calls it an “intellectual construction . . . involving naming, description, analysis”6 whose inevitable atemporality debars it from what is most essential and alive in rhythmic performance, namely, the engaging course or flow of artistic works which he calls “the active and characterful creation of things or events.”7 His main complaint is that because traditional descriptions of rhythm lack the intricacy of rhythmic performance, they suggest a false notion of rhythm as a timeless element separable from actual rhythm, which latter he finds only in performance. Suggesting a wider importance to the debate, Hasty argues that conventional doctrine regarding the description of rhythm adamantly holds onto the dead part and denies the living, rhythmic performance. To remedy this complaint, he argues that the traditional priority of objective description (the conventional score; critical, theoretical abstraction) over the subjective interpretation given in performance gets things the wrong way round. One might object here that it is possible for a musical score to be drafted before any instance of its actual performance, and that the score therefore has at least chronological priority. However, Hasty is likely correct in observing that any codified composition in fact entails its own performance as it is actually being made. That is, the composer, as the original describer, must be doing something like hearing the rhythm in imagination, or tracing it rhythmically in the air by hand while composing–​–c​reating and transcribing–​–​the descriptive document. Yet, while it weakens arguments for the absolute priority of the score, the view of

5 Hasty, “Complexity and Passage,” 235. 6 Hasty, “Complexity and Passage,” 235. 7 Hasty, “Complexity and Passage,” 241.

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composition as imaginative transcription does not imply the straight reversal of ascribing necessary priority to performance; rather, it suggests objective–​subjective (score–​performance) co-​generation. While upholding an unprioritized view, my main concern is not primarily to dispute the logical and chronological priority of actual over described rhythm, or vice versa. I aim, rather, to defend the ability of conventional description to preserve the essentials of rhythm-​involving artworks, most notably, their flow, albeit in an encoded way. I shall further argue that conventional description favors intuitive and expressive interpretation, where more detailed prosodic or musical notation would be too strictly prescriptive for interpretive leeway. The current chapter, then, promotes an unprioritized view that emphasizes equally (a) the ability of conventional description to preserve musical works while keeping them open enough for creative and sensitive interpretation, and (b) the not only valuable but also necessary interpretation involved when performers bring a composition to life. I contend that while rhythm is perceived through the senses as patterned temporality (involving repetition, pause, continuation, return, etc.) that retains the past and moves towards a future, none of this intricacy need be lost in conventional codified description. It is therefore better to retain conventional description for its referencing advantages and the interpretive freedom it allows. The intricacy of the actual rhythm can as little prevent its description in objective form as it can prevent its performance by another skilled performer who is present and listening attentively. That is, if another musician can hear the performed rhythm and then perform it anew, it can also be encoded in objective form without requiring any revolutionary techniques of notation. The subtleties of performance can powerfully affect the listening (and performing) subject, but there is nothing capricious or magical about them. Or rather, as the nineteenth-​century pioneer of musical expression Matthis Lussy remarked, Composers, in accentuating their works, are obedient to sentiment—​to unknown laws, and not to caprice, though indeed, what is caprice but unconscious obedience to an impulse from some unknown cause?8

Nuances can be transcribed according to a formal system that relates discrete elements so that they become part of a flowing whole when performed by a sensitive and talented musician. The formal—​i.e., notateable, conventional, and coherent—​ properties of the structure as a whole outperform the sum of the parts taken as discrete units, in a way analogous to how the geometrical structure of an arch provides resilience ordinarily beyond that of the materials from which it is composed. Much as the resilience of an arched bridge or an egg maximizes that of its materials, an artwork taken as a compositional whole has a power that exceeds that of its parts. Both holistic property kinds—​structural resilience in the arch and compositional 8 Lussy, Musical Expression, 3.

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258   The Philosophy of Rhythm power in the artwork—​exist as formal, detectable properties in the respective objects themselves, though their existence is perceived only in experimental or experiential context, as when a bridge or egg undergoes a heavy load or when an artwork is performed to critical or popular acclaim. Intricacy, then, can be as much an objective quality of the description or encoding of rhythm as it is of the embodied performance. Thus, while performance-​priority proponents are right to caution against allowing discussion of rhythm obstinately to maintain the separable discreteness of its elementary units and thereby forget the flow that is its most essential characteristic, it would be misguided to replace traditional description—​e.g., the conventions of Western sheet music, or those of prosodic terminology—​with an alternative system of coding that added all the extra nuances of expression, timing, note grouping, accents, offbeat stresses, etc. that many composers in the nineteenth and early twentieth centuries increasingly tried to notate to ensure greater control. Here, in the tension between notation and interpretation, each with a rightful claim to intuition and expressivity, one must beware the siren call of a pseudo-​ problem–​–​as the Vienna Circle and Wittgensteinians would have said–​–​inherent in the nature of description, and what description of a practice must inevitably leave out. More precisely, while there is nothing in particular of a practice, of performance, that description must leave out, it is nonetheless inevitable that description must leave some things out and remain incomplete–​–​or open, depending on one’s viewpoint–​–a​ s the description necessarily cannot capture all the minutiae of what is described. For this, one has technique. Technique, as Adorno said, is how art thinks.9 In poetry, say, the particulars of form—​as specified as the sonnet or as spontaneous yet musically structured as free verse—​provide a metrical and compositional frame once a rhythm becomes established as a trellis over and around which ideas and feelings grow, take shape, and interact. Form does not constrain good poetry, nor is it merely an aid to get creativity going. Musical and poetic forms are rhythmic and experimental ways of thinking and working through problems of comprehension and expression, much as in philosophy syllogism, analysis, dialectic, and dialogue are ways of thinking and working through problems of understanding and knowledge. The formal structure (meter, rhythm, technique) and the living part expressed (ideas, feeling, mood) interpenetrate, preventing the two theoretical sides from being truly held apart in any simple dichotomy. Through technique, structured levels of meaning and enjoyment are created, inviting a discovery of thought in the work so that it is encountered as already thoughtful. Without technical structure imposed by the artist, such thought as the work does in fact contain could only be reached after considerable conceptual struggle. With the technically structured artwork, however, the composer presents the thought for more immediate aesthetic access, as the result of much thought is presented. The thought that the audience then discovers in the work gives a 9 Adorno, Aesthetic Theory, 129, 279, 283; Jarvis, “What Does Art Know?”

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seemingly miraculous intensity even to, indeed especially to, the simplest artworks. The understanding and refinement of this structure is the work of prosody, which reverse-​engineers creative technique and works out a more penetratingly perceptive system of commentary and annotation that can certainly aid appreciation of technical aspects in the work, and can sometimes help future composition through the insights into structure it provides. Yet this very precision, converting the organic expression into the structuring trellis it originally grew around, can if taken too far also stifle creative and appreciative possibilities. Rhythm makes content more accessible. Even when the ideas are not comprehended, entrance into the mood and aesthetic train of the music is more or less universal, so long as the listener has at least some cultural acquaintance with the forms and conventions used. Whether the rhythm is established solo or in concert with other performers, rhythmic expression allows easier access for participatory enjoyment, be it through dance, foot-​tapping, or head nods carried through or imperceptible. Awareness of rhythm in any communication, whether through art, games, conversation, or simply being together, embodies consideration of others and invites their fuller involvement. An unconcern for rhythm can lead to unkindness, neglecting the welcoming changes of tempo that make space for others to join in, and omitting those polite pauses for reflection and assent, which also permit considered disagreement, rephrasing, and repositioning. This is the open dance of give-​and-​take that rhythm creates. In the sense that it is created with the attentive participation of others in mind at even the most basic, bodily level, rhythm is, as Andy Hamilton argues, a humanistic phenomenon.10 On the other hand, an exhaustive, per impossibile, prosodic rendering would reduce the humanistic element of rhythm by limiting the freedom of access to the work to one highly specified interpretation. Although notational or prosodic instruction can lift barriers to sometimes difficult or archaic works, a tendency to increase the quantity of information encoded in a work, and the annotations to it, would create more barriers and constraints to performance than it removed, creating instead a jealous proto-​performance, i.e., a code permitting only one entrance and way of proceeding. An exhaustively complete rendering would be too “thick,” to use the parlance Stephen Davies borrows from ethics, in that the work would become overdetermined, i.e., too rigidly prescribed, allowing only one access to perform faithfully the “sonic detail of its accurate instances.”11 To be performed, embodied, more than once, a work must be encoded (even if only in memory, but more usually in a text). It would be doubly mistaken, however, to replace conventional ways of describing rhythm with ones that more exactingly aligned description to performance, adding ever-​infinitesimal detail. First, doing so would overload the description, creating an unwieldy apparatus. Secondly, this new descriptive system (the jealous proto-​performance) would be so radically

10 Hamilton, “Rhythm and Stasis.”

11 Davies, Works and Performances, 20.

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260   The Philosophy of Rhythm particularized that it would be far more prescriptive than any conventional score. It is in fact largely by not detailing every possible nuance of expression that conventional description leaves the variables of living rhythm open to the interpretative art of the actual performance. I am therefore arguing that the infinitesimal variations borne of living, performative expression are best left, as they are in traditional descriptive systems, to the intuitive sensitivity of the performer. The relative lack of complexity in traditional, abstract description–​–​relative, that is, to a more finely detailed account of the nuances of any specific performance–​–​constitutes the important quality of openness to interpretation that allows conventionally described works to be brought to life in so many different yet meaningfully expressive ways. The conventional description of rhythm thus avoids rigidly prescribing the very flow that comes alive only in the performance. The original artifact, the score, for example, or the poetic text, is therefore a descriptive document that supports innumerably many and different actual or possible performances. In virtue of this formal document, which is open to innumerable varieties of becoming actual, temporal performance, the original description has a priority over subsequent performances. But this is not the full story.

2.  An Unprioritized view An analogy between photography and music from the master photographer and printer Ansel Adams–​–a​ lso a proficient pianist–​–​illustrates this point about one original description supporting and encouraging many possible expressive interpretations in actual performance, where the encoded comes alive in the embodied: I have often said that the negative is similar to a musician’s score, and the print to the performance of that score. The negative comes to life only when ‘performed’ as a print.12

It should be noted that there is, and can be, no such thing as a “straight print” from a negative, just as there is, and can be, no such thing as a “straight performance” of a score. The duration of exposure to the overhead light is always a matter of judgment. The master printer in the darkroom might use a wand to prevent certain parts of the photographic paper from receiving too much light. He or she might use techniques such as feathering in certain areas and borders. The paper itself has to be chosen, and this choice affects qualities such as micro-​contrast and macro-​contrast. One might object, nonetheless, that in music a read-​through does in fact involve a “straight” playing, which consists in playing the notes without any pre-​considered

12 Adams, The Print, 2.

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interpretation. A  read-​through, however, unlike a performance for an audience, need not be done in real time, and often involves moving quickly through slower passages, and more slowly through rapid, or otherwise difficult sections. Perhaps sight-​reading–​–​performing a prima vista–​–​is more pertinent, but even then it is practically impossible to deliver a “straight performance.” Indeed, as Louis Armstrong described highly skilled musicians, “they might read a Fly Speck, if it get in the way.”13 Playing a prima vista must be done in real time, so even skipping notes, or playing wrong ones–​–​which itself involves interpretation–​–​would be more acceptable than losing the rhythm. There can, then, be no such thing as a straight print from a negative, a straight reading of a poem (however, characterless an actual reading might seem), or a straight performance from a score. Straight performance is impossible because any performance from a description requires an interpretation that necessarily contains a degree of openness. An exhibition that hung photographic negatives on the walls or a performance that consisted only in distributing the sheet music to the audience to imagine the work in relative silence might count as conceptual art, but the practice would not become conventional. Against those who argue that performance is primary, Adams’ analogy illuminates the mutual importance of the codified description (the negative or the musical score) that is necessarily the antecedent original and any rhythmic performances that are then produced. This is not to argue that performances are simply inferior copies of an archetypal and more perfect original. Even a photographic connoisseur who admires a negative for its exposure and composition does so with the understanding of how this serves the quality of the print, and much the same can be said of the admirer of a musical score. Like the negative, the score primarily has instrumental value, whereas the performance (like the print) has intrinsic value. But if the performance has intrinsic value, and the score has primarily instrumental value, does that not therefore mean that the performance has priority? The answer must be no, because of an inescapable asymmetry. While the performance depends on the score for its very existence, the score does not likewise depend on the performance for its existence. However, in the unprioritized view that I am presenting, while the score may be chronologically prior to performance (this is not true for improvisation, but even here there is often an initial idea and outline), it nevertheless depends upon performance for its actualization, which is in an aesthetic sense its completion. Although the score in itself, as a concrete artifact, has only instrumental value, it is the fundamental prerequisite that subsequent performances depend on before any intrinsic value can be realized. It is the work that has intrinsic value, and the musical composition as work of art is a composite of co-​dependent encoded form and actual or imagined performance. Perhaps the performance never entirely realizes the work, which is always, as Sartre suggested, held in “the imaginary”; thus it never quite exists concretely as accomplished, once and for all. If this view

13 Armstrong, His Own Words, 26.

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262   The Philosophy of Rhythm is correct, while the performance effects the completion of the work, it never quite achieves its perfection. The score, then, encodes, though necessarily incompletely, with gaps concerning expression, nuance, grouping. What one might call the arch-​performance is created by the composer in imagination and is ever and anew appreciated, rediscovered, in the imagination of the performers and the audience. The musical score and the photographic negative are both creations of their respective composing artists. As encoded, prototypical artifacts, they have a uniqueness that performances do not, in that the original encoded version is the one from which any number of performances develop. Note, however, that it is not because the score or the negative are each one, and only one, whereas the performances are many, that the prioritizing of performance is prevented. Copyright allowing, the score is often published and facsimiles can be reproduced from film negatives. Still, these copies remain multiplied tokens of the one prototype. A question also arises from multiple editions of the composer’s score leading to the quest for scholarly editions to construct an Ur-​text out of various manuscripts, proofs, and prints. The point concerning the uniqueness of the encoded prototype is that although performance-​prioritizing theorists wish the descriptive artifact to be understood as secondary, and although it is only as performance that the art achieves intrinsic (actual not potential) value, it is the encoded artifact that originates and inspires worthwhile performance. Accepting this co-​dependence of form and performance is key to the unprioritized view of encoded and embodied aesthetic qualities such as musical rhythm. My assertion of an unprioritized account amounts to defending encoded–​ embodied (description–​performance) co-​dependence. It is based on the argument that a conventional descriptive text holds open the possibility of many different performances that might embody it, rather than minutely describing expressive nuances such as the finer points of timing, note grouping, offbeat stresses, etc. Indeed, the method of increasingly minute and burgeoning description would, paradoxically and unfortunately, become the ideal if some original, authoritative performance were always prioritized over the encoded prototype. The job of such a minutely finessed, burgeoning description would be to convey every nuance and particular of that performance. While one can commend the scholarly quest to construct the most accurate description of the composer’s intentions, it should also be noted that those intentions often change as a composer returns to a score over many years, so further questions inevitably arise as to whether any one of these can have priority over another. Further, the existence of multiple editions might produce interesting historical and scholarly questions, but these are of lesser importance to the performing artist, who is, and ought to be, free to explore perceived nuances across different texts that variously suggest alternative expressive responses and resonances in the performer. Thus the unprioritized view has value here, being an account where the rights of the work are balanced in co-​dependence with the sensitive intuitions and expressive instincts of the interpretive performer.

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It could, however, be argued that the existence of multiple texts supports the opposite view, that particular performances have a uniqueness that is almost completely missed by the atemporality and universality of conventional description. Each performance is a one-​off event that that can be recorded but not repeated, while a musical score can easily be photocopied and is essentially repeated, with added nuance, by becoming embodied with each performance. Performances involve different maestros or even the same ones but on good and bad days; the synergy of all involved is such that small differences in some factors can affect the power of the whole. So while performances can rightly be said to be interpretive iterations of the score, they are necessarily unrepeatable in terms of the many particulars involved and how they add up to an aesthetic whole. Certainly analogue or digital reproduction is possible, but that is quite different from the (impossible) repetition of the event. The unity of the text, however, even if there are multiple versions from which to choose, is performance generative, without itself being in any normal sense of the word a performance. Performance, aside from improvisation, develops from code—​the text—​but the issue of priority is not such a vital quarrel. Each is necessary for the more-​or-​less faithful reproduction of embodied rhythm from an encoded composition. A good score never performed is wasted, almost a nullity. And a performance of a composition is equally dependent on the score, however radically the performer departs in expressive interpretation. Those who radically prioritize performance aim, quixotically, I believe, toward a reversal of values that not only promotes the particular and embodied (there is nothing wrong in that), but which also denigrates the powers of form as timeless agents of perpetual identity (which I consider to be tilting at windmills). But all this sounds like fighting an imaginary Platonic bogeyman,14 as if one should, like a good Nietzschean, fear shadows that threaten to engulf the living world of matter and bodies. What is really being opposed here? If the enduring identity of the text were instead to become, per impossibile, as unrepeatably nuanced as the temporal performance, then the text could not be the performance-​ generative artifact that it undoubtedly is. Nobody seriously argues that the score–​–​or any text intended to generate performance–​–​dictates or ought to dictate each detail and expressive nuance of every possible performance. As T. V. F. Brogan diplomatically but decisively judges the matter, with respect to poetry: It is natural to want to enrich scansion with other kinds of analyses which capture more of the phonological and syntactic structure of the line . . . But all such efforts exceed the boundary of strict metrical analysis, moving into descriptions of linguistic rhythm, and thus serve to blur or dissolve the distinction between

14 Cook, Beyond the Score, 8–​32, blames what he sees as the traditional prioritizing of score over performance on “Plato’s Curse.”

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264   The Philosophy of Rhythm meter and rhythm.  .  .  . Scansions which take account of more levels of metrical degree than two, or intonation, or the timing of syllables are all guilty of overspecification.15

Those who wish to enrich scansion all too easily end up “guilty of overspecification” through blurring the distinction between meter and rhythm and jealously prescribing not only precise timing, but also tongue movements, etc. Yet, though one might annotate a rhythmic, rather than just a metric, scansion, a greater freedom of experiment and expression in rhythm exists, perhaps counterintuitively, in remaining with the more basic, binary metrical scansion. Greater freedom is afforded by simple metrical scansion, marking only ictus (/​), i.e., the metric beat or pulse, and non-​ictus (˘, or ×), because by not prescribing any rhythm, the reciter is left free to experiment and discover rhythmic possibilities without needing to fixate on any particular one as the rhythm. This is not to deny that the lines strongly lend themselves to a particular rhythmic reading, indeed, I contend that reasons for favoring one reading over another already lie objectively in the text or in the cultural context. Yet it is equally true, however, that some lines are deliberately inflected with the ambiguity of multiple, contradictorily rhythmic readings. It therefore bears reflecting, against overspecified scansion and rhythm analysis, that, as William Empson said: “The machinations of ambiguity are among the very roots of poetry.”16 These insights return me to Adams’ analogy of the photographic negative, whereby the print is the performance, which serves well to show that the text (the score, or negative) is not a code that dictates exactly how the performance ought to turn out in each detail and in every instance. Could there be more at stake, then, in the argument for the living reality of actual, temporal, flowing presence than the apparently not very vital question of which of two necessary components is to be given priority? The foregoing discussion suggests that what is at stake is an assertion of personality, vitality, of spirit above the dead letter. My response is that such vitality requires an alternative to prioritizing terms on either side of the debate. An unprioritized theory of objective–​subjective, descriptive–​performative co-​dependence is free to pursue atemporal and temporal aspects of the artwork. The atemporal form is the imagined ideal, that which allowed Sartre to insist of Beethoven’s Seventh Symphony:  “I do not hear it actually,” because it is “outside existence,” such that “I listen to it in the imaginary,” where beauty is possible.17 The unprioritized, co-​dependence view of rhythm and other aesthetic qualities is at once common sense, in defending the openness and utility of traditional conventions, and dynamic (opposing merely static forms), in celebrating the fact that every new performance brings the ideal creation that is the



15 Brogan, “Scansion,” 1118.

16 Empson, Seven Types of Ambiguity, 21.

17 Sartre, The Imaginary, 193.

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artwork (Sartre’s “imaginary”) into an aesthetic, embodied reality that actualizes the power of the work to touch and move audiences intellectually and viscerally.

3.  The objective reality of rhythm With the unprioritized view, I am defending the sense of rhythm as a representable objective pattern. The fact that rhythm can be embodied across different forms and for different human senses–​–​sound, sight, and touch being the most pertinent–​–​ shows that it is an objective property perceivable by more than one sensory channel and that it is therefore quantitatively analyzable and describable. This objective sense is what Locke called a primary quality, one that exists objectively, can be expressed numerically, and consists in “Bulk, Figure, Number, Situation, and Motion, or Rest” of bodies, “whether we perceive them or no.”18 It is only because of this objective basis that rhythm in one art form perceivable primarily through one sensory channel can be translated into or illustrated by another, so that in ballet, contemporary, or popular dance, for example, the rhythm in the dance often corresponds to the rhythm in the music in the objective terms of magnitude, figure, number, situation, motion, and rest. These correspondences are intuitively apparent, but harder to explicate in words or formulae. Central to calculus, the mathematics of such transformation or correspondence is continuous as opposed to discrete, typically using “t” as the time axis moving from left to right. Magnitude is the simplest variable to measure with respect to time, and can also be done with sound (in decibels), light (in lux), and force (in pressure—​“P,” bars, or p.s.i.—​felt through touch). These are all objectively describable in terms of number and mathematical convention, as is figure (shape). The primary quality of figure, represented for instance by pirouettes or whirls in dance, resembles rapidly repeating phrases in music by a topological dynamics. The formulae underlying this continuous mapping of “various ‘repetitiveness’ properties”19 of the motion to the music would take considerable effort to calculate, yet would be superfluous to the audience, who need no proof of correspondences that they perceive and enjoy. An example of the highest one-​to-​one correspondence between rhythm as heard and as seen is the display of a graphic equalizer. These objective qualities are what would remain, in a recording for example, even in the absence of any living mind. One might not want to say that rhythm in such circumstances would remain “living,” but it would nonetheless remain real, as does the rhythm encoded in the score and other texts. To argue for the reality of objective rhythm and its importance is not to denigrate the subjective sense of rhythm, but only to emphasize that the subjective 18 Locke, Essay Concerning Human Understanding, Bk 2, Ch. 8, §23, 140. 19 Anosov, “Topological Dynamics.” McGinnis and Newe, “Topological Dynamics:  A Framework,” and Sutil, “Topological Movement,” discuss topological dynamics as a framework for dance notation, drawing on the pioneering choreography and movement notation of Rudolf Laban.

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266   The Philosophy of Rhythm depends upon the objective. Flow, or fluxion, the essence of rhythm, far from inaccessible to objective, mathematical analysis, is the very core of calculus. The connection between music and mathematics has been appreciated and often venerated since ancient times. There must first be a something heard, seen, or otherwise sensed before that thing is then felt in terms of meaning and value. Only then, with the objective rhythm established, can a subjective sense of it arise as the mode in which the rhythm affects the subject, prompting the subjective repetition of the rhythm. With this repetition, a meaningful quality with a felt value is added, such as calmness, solemnity, or jubilation, which is experienced at the same time as the rhythm. These subjective qualities or feels, however, are not themselves rhythmic, because what cannot be given quantitative analysis and description might be a response to rhythm, but cannot itself be rhythm. Thus while a rhythm may be calm or jubilant, calmness and jubilation are not rhythms. The foregoing argument can also be used against the subjectivist assertion that there is no rhythm without its actual appearance. To hold that there is no X without the actual appearance of X is a form of subjective idealism that is indefensible except when X is itself an appearance in the subject. For example, to say that a trumpet does not exist until someone hears it is indefensible, but to assert that the particular sensations that this trumpet creates in person Y exist only when person Y hears that trumpet is at least not logically indefensible. (It could be admitted, however, that stimulating a certain pattern on the subject’s auditory cortex might activate those particular sensations, or that a recording of the trumpet could produce the same effect.) To reiterate, a rhythm has objective qualities that exist in the absence of a subject. The fact that that the most aesthetically important effects of rhythm are its feeling, meaning, and value as felt by the subject does not give logical priority to the subjective sense of rhythm, which remains dependent on the objective qualities of the rhythm. That the subjective sense of rhythm depends on the objective sense (on the primary qualities of the series of events) is in fact the usual relation of subjective and objective qualities. The objective qualities exist first and their emotional, significant, or axiological resonance in the subject follows. This view is entirely consistent with agreeing, as I do, that meaning is found in the engaging course or flow of things. This meaning in rhythm is, I believe, a discovery of the harmonic resonance of things in the world within oneself. Indeed, to understand how music–​–​or any rhythmic happening or creation–​–​stimulates sensations and thoughts that refer to meaning and value is to have an at least implicit metaphysical understanding. Perhaps the historically first explicit metaphysical understanding of how the objective and subjective unite in musical phenomena remains the deepest, where the rational (ratio) is felt in the qualitative (quale). According to legend, Pythagoras, gripped in difficult mathematical thought of balance and measures,

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Encoded and Embodied Rhythm  267 walked by a smithy, and by divine chance, heard the hammers beating out iron on the anvil and giving off in combination sounds which were most harmonious with one another . . .20

Thus Pythagoras marveled, the story goes, at how objective mathematical ratios (of rods, pipes, and strings) are sensibly intuited across harmonious musical intervals. Each sonorous ringing is perfectly harmonized in the listener’s mind with the numerical ratio describing the placement of the grip that divided the rod into struck and unstruck portions. From this he understood that a law governs how change in the latter accounts for a correspondent change in the former and that this account is ultimately rational. The qualia and the numerical ratios are correspondences, resonances in fact, that are ultimately connected to the same nature, so that what in the subject is experienced as a musical note, is in the object the physical expression of a ratio. Yet one need not be a Pythagorean (mathematic or acousmatic)21 to hold that the objective in rhythm is prior to the subjective, such that quantitative properties precede qualitative ones insofar as the objective, mathematical properties of music determine what becomes the subjective sound of music and the qualities of its flowing parts. Another way of stating this is to say that subjective rhythm is how objective rhythm is experienced. This formulation allows a clearer view of the mind’s role, whether projective or intuitive, in the experience of emotional timbre in rhythm. Thus some rhythms promote a slow pensive mood, others light-​hearted moving around without much thought at all. Objective qualities in rhythms can make one piece of music stir one emotion, while another evokes a quite different mood. The meanings of progression and return, ascent and descent, and so on, are conveyed in objective rhythm and can be straightforwardly indicated. Return to a musical motive, for example, can convey a sense of remaining, or lingering, but with greater variation it will convey a similarity that progresses or one that regresses. It is quite natural, when experienced by a thinking being with life projects, that these objective qualities in rhythm will stir thoughts and feelings related to the advancing through, enjoyment of, regression to, or pensive dwelling around those life projects. The rhythm does not convey what is to be thought about, i.e., the content, but it influences the form and manner, which is to say the mode and the mood, of one’s thinking. Thus a very clipped performance that crisply enunciates the separation between each note or unit encourages a marching mood that does not linger on the past; emphasizing action over memory and thought, it thereby avoids being deeply affected. By contrast, a melody played rubato promotes a more comprehending, pensive mood in which less gets left behind. For instance, John Cage instructed 20 Nicomachus, Manual of Harmonics, 83, the earliest extant record of the account (83–​97). 21 The “mathematicians,” with their more scientific Pythagoreanism, opposed the “acousmatics,” who followed the sayings—​however cryptic—​of the master on authority without need of mathematical proof or reasoning: see Riedweg, Pythagoras, 107–​8. The acousmatic thesis in current aesthetic theory holds that music does not move, or if so, moves only metaphorically. The acousmatic theory is named in allusion to the Pythagorean acousmatics who heard the teachings of the master only through a veil or screen. Thus an acousmatic account of music makes no reference to anything beyond the sounds qua sonic phenomena.

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268   The Philosophy of Rhythm that his haunting, returning and gathering, composition “Dream” (1948) be performed Rubato: Always with resonance; no silence, tones . . . freely sustained, manually or with pedal, beyond noted durations . . .22

In such a gathering, synthesizing style, ideas build into a greater, cohering whole, with a wider, pulsing now retaining remembered presence. Understoodthus, rhythm does not present any specific content of thought or meditation, but instead presents thought or meditation itself. The fundamental meanings of departure and return, and of expectation and surprise, can be conveyed in the music, and can help comprise a basic, largely aesthetic comprehension of life, its necessities, and contingencies. These fundamental meanings, which are essentially musical, invite reflection, yet they are more basic and embodied than any conceptual assertion. Such meanings can be conveyed in musical and poetic structure, with elements such as tone, tempo, resonance, and pause adding significant nuances to the meaning. The meaning of rhythmic expression is directly related to its form, being composed of the formal, objective qualities already embedded in the description before they have become embodied in the performance with the addition of expressive elements added in the performer’s interpretive process. Remaining with the topic of merging and separateness in rhythmic flow, I return now to a specific contention in Hasty’s argument, to address his challenge against what he calls the “traditional construal of beats and offbeats as ultimately separate . . . entities.”23 Hasty wishes to replace this discourse of separate entities with a sense of each beat enduring through the arsic and anacrustic offbeats until their dynamism is passed on to the next beat. But is he not here challenging a straw man? It is already implicit in most understandings of musical rhythm that the beat commences a duration that endures until the next beat. And surely it is already generally accepted, certainly by those who hold that music in some sense “moves” (literally or metaphorically), that the pulsing of arses and anacruses propels the motive and the phrase in a movement that comes to life in the subjective sense of rhythm. This sense of the beat persisting through the movements of the offbeat until the next beat is not new. In 1874, Mathis Lussy published his theory of the formal qualities of rhythm as foundational for performative expression. To perfect expression, he required that nothing be added to the formal qualities of the musical phrase that was not capable of being generated from the formal description itself. Thus Lussy was an early demystifier of the processes of performative expression. One need not look for something mysterious or capricious in the soul of the performing artist to explain the intricacies and effects of the expression, as these are, rather, evolved

22 Cage, “Dream,” instructions at top of score. 23 Hasty, “Complexity and Passage,” 239.

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from the already objectively described phrasing itself. As Lussy puts it, “the cause of the expression resides and must be sought in the structure of the musical phrase,”24 so that even if the composer omitted all marks of expression and notated no slurs or accents, the true artist would play as if they were there, since their raison d’être would still exist. This is supported by logic, and daily confirmed by observation. As the generating causes of expression exist in the musical phrase, they must evidently act upon the purely material forms which are susceptible of observation and of submission to analysis and synthesis.25

The cause, then, of the expression would still exist objectively, even if only entailed by, rather than explicitly stated within, the musical score as read by a sensitive and talented performer. Comparable to the enduring of the beat through the offbeats, Lussy portrays rhythm as the music “breathing.” In his analogy, as the music “breathes,” the downbeats are the inevitable exhalation, his point being that rhythm is the pulsation of building up and relaxation, a process as vital to music as breath is to life. Each downbeat carries on the impulse from previous beats, passing them on through the offbeats in a continuous flow. So long as he or she has more than merely mechanical ability, the performer intuitively appreciates all this, even though the signs of expression—​the accents and so on—​may be absent from the score. Throughout his essay, Hasty asks a series of questions about the enduring of past events of a musical series in the present, i.e., the moment being performed right now. When is one to let go? Is that even possible? When to move to the next level or at least to a more fully new one? It is true that conventional descriptive models might seem to encourage “letting go,” but I contend that this only helps the performer to exercise sensitivity and tact. Conventional description in fact neither forces nor prevents the loosening and binding, the holding onto beats, phrases, motives, and other forms, that constitute the enduring, lifelike, breathing qualities of music that do not merely unfold time, but seem almost to enfold time, so that the past and the future are also in the present as resonance, memory, and expectation. But is one to believe, as Hasty argues, that conventional descriptive structures are in fact destructive, designed to prune natural growth, and cut off the past from living in the present? I have argued the contrary, that conventional descriptive structures leave enough openness in the system for performative expression and judgment by in fact not prescribing exactly where, when, and how to bind, loosen, cut, remember, and so on. Whether notation by the composer, or annotation by a critic or instructor, to create a new system of description that added so much extra information would be to prescribe too much. Such rigorous prescription made on behalf of

24 Lussy, Musical Expression, 2.

25 Lussy, Musical Expression, 3.

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270   The Philosophy of Rhythm “living rhythm” would be counterproductive, constraining the expressivity of the artist, reducing latitude for interpretation, and intruding on the performing artist’s sensitivity for what, as Lussy explained, already resides “in the structure of the musical phrase.” The existing conventions of description have evolved not to prune the outgrowths of memory, nor to excise the living rhythm, but rather to allow the artist at sensible or unexpected junctures to cut or not to cut and to bind or not to bind, according to a sensitive intuition of possibilities already there in the musical score. Thus Lussy celebrates, rather than bemoans the fact, that: “In music there are no special signs to mark the rhythm.”26 The reality is that such questions as when one should let go of a beat, let it peter out through its successors, or move onto the next level, are addressed afresh in each instance to the spontaneous artistic conscience. One should therefore resist giving prescriptive answers, let alone inscribe them as a new notational norm. If conventional descriptions and encodings such as traditional scores did indeed note where to let go of a beat and its memory, when to stop its pulse and begin a new level, and notate every accent and emphasis, etc., then that would stem experimental and creative performance and result in an artifact with much more information than is needed for an elegant encoding of music to be performed and thus embodied.

Works Cited Adams, Ansel, The Print ([1950]; New York, 1995). Adorno, Theodor W., Aesthetic Theory ([1970]; London, 2013). Armstrong, Louis, In His Own Words: Selected Writings, ed. Thomas Brothers (Oxford, 1999). Anosov, D. V., “Topological Dynamics,” in Michiel Hazewinkel, ed., Encyclopedia of Mathematics:  Supplement 3 (Dordrecht, 2002), 413–​ 14. Revd article:  https://​ www. encyclopediaofmath.org/​index.php?title=Topological_​dynamics&oldid=17008. Brogan, T. V.  F., “Scansion,” in Alex Preminger and T. V.  F. Brogan, eds, The New Princeton Encyclopedia of Poetry and Poetics, (3rd edn, Princeton, 1993), 1117–​20. Cage, John, “Dream” [1948], sheet music for solo piano, in Piano Works 1935–​48, EP 67830 (London, 1948). Cook, Nicholas, Beyond the Score: Music as Performance (Oxford, 2014). Davies, Stephen, Musical Works and Performances: A Philosophical Exploration (Oxford, 2001). Empson, William, Seven Types of Ambiguity ([1930]; 2nd revd edn, London, 1953). Hamilton, Andy, “Rhythm and Stasis:  A Major and Almost Entirely Neglected Philosophical Problem,” Proceedings of the Aristotelian Society, 111.1 (2011), 25–​42. Hasty, Christopher, “Complexity and Passage:  Experimenting with Poetic Rhythm,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C15. Locke, John, An Essay Concerning Human Understanding, ed. Peter H. Nidditch ([1690]; Oxford, 1998). Jarvis, Simon, “What Does Art Know?,” in Peter de Bolla and Stefan H. Uhlig, eds, Aesthetics and the Work of Art: Adorno, Kafka, Richter (New York, 2009), 57–​70. Lussy, Mathis, Musical Expression, Accents, Nuances, and Tempo, in Vocal and Instrumental Music, tr. M. E. von Glehn ([1874]; London, 1892).



26 Lussy, Musical Expression, 44.

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Encoded and Embodied Rhythm  271 McGinnis, Peter M. and K. M. Newe, “Topological Dynamics:  A Framework for Describing Movement and Its Constraints,” Human Movement Science, 1.4 (1982), 289–​305. Nicomachus, The Manual of Harmonics of Nicomachus the Pythagorean [Enchiridion harmonices], tr. Flora R. Levin ([c.100 ad]; Grand Rapids, 1994). Peters, Deniz, “Rhythm, Preceding Its Abstraction,” in Peter Cheyne, Andy Hamilton, and Max Paddison, eds, The Philosophy of Rhythm: Aesthetics, Music, Poetics (Oxford, 2019), C7. Riedweg, Christoph, Pythagoras: His Life, Teaching, and Influence, tr. Stephen Rendall ([2002]; Ithaca, 2005). Sartre, Jean-​Paul, The Imaginary: A Phenomenological Psychology of the Imagination, tr. Jonathan Webber ([1940]; London, 2004). Sutil, Nicolas Salazar, “Rudolf Laban and Topological Movement:  A Videographic Analysis,” Space and Culture, 16.2 (2013), 173–​93. Wollheim, Richard, Art and Its Objects: An Introduction to Aesthetics (London, 1968).

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17 Time, Rhythm, and Subjectivity The Aesthetics of Duration Max Paddison

Art manipulates our experience, and all art forms experiment with the ways we perceive time, space, and motion. This is particularly so with the experience of duration and rhythm in the temporal arts—​music, dance and also performed poetry and drama. And yet, this experience of temporality as a continuity is not in itself a given, but is something that we ourselves create. As Célestin Deliège has put it, “whatever our perception of time might be based upon, it is we who create this time, it remains always our work, our oeuvre.”1 This chapter starts from the position that the concept of rhythm needs to be understood in the context of its relation to time and subjectivity. The approach taken is phenomenological, with a focus on Gaston Bachelard’s phenomenology of time (via his critiques of Bergson and Husserl), together with the Bachelard-​influenced theory of musical time-​perception to be found in the work of Célestin Deliège. My argument falls into three parts. First, the case is made for an experiential concept of temporality through a brief survey of philosophies of time that takes Kantian subjectivity as its point of reference and argues that temporal experience is fundamentally subjective and exploratory. Second, attempts to define rhythm are placed in this context, with music as the focus. The argument is made for a concept of rhythm that also involves a large-​scale notion of “rhythmicized duration” as form, a concept that affords extended scope for an aesthetic experience of temporality that is also experimental in character. And third, I argue that the concepts of temporality, duration, and rhythm, which have a particular identity in the experience of music, are subject to historical change, and in the case of Western art music have functioned both normatively and metaphorically in different historical periods. It is suggested that there are different “aesthetic times”—​something reflected in the fact that paradigms of temporal experience in the arts shift2—​and that our experience of rhythm as structured duration is shaped by this. 1 Deliège, “Perception du temps musical,” 88 (my translation). 2 Thomas S. Kuhn, The Structure of Scientific Revolutions, 208, writes: “To the extent that the book portrays scientific developments as a succession of tradition-​bound periods punctuated by non-​cumulative breaks, its theses are undoubtedly of wide applicability . . . for they are borrowed from other fields. Historians of Max Paddison, Time, Rhythm, and Subjectivity In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0018

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1.  Time, duration, and the subjectivity of temporal experience How do we understand the experience of time and duration in the temporal arts? Before discussing rhythm directly, I want first to provide a context of basic arguments in the philosophy of time (Newton, Leibniz, Kant), which I shall outline as briefly as possible, before focusing on Bachelard’s phenomenology (particularly through his critiques of Bergson and Husserl), and on the concepts of subjectivity and the relationality of experience on which it is founded. The two fundamental historical positions on the philosophy of time normally referred to in this context are the “absolutist” and the “relationist” arguments. The first, associated particularly with Newton, argues that time is “absolute” and is an attribute of reality. True time flows, as he outlines it in the “Scholium” that introduces his Principia (1689), and does so independently of any other considerations, being independent of space, place and motion. Newton writes: Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.3

Thus Newton recognizes what he calls “relative time”—​the relativist or relationist position, which measures duration in relation to external factors like motion (the moving hands of a clock, for instance, or dividing the cycle of the year into twelve months)—​but he considers that this is only how time appears to us as human beings. True time—​that is, absolute time—​flows of itself, needs no external measure, and can only be understood through mathematics. Like time, space is also regarded by Newton as an absolute that exists apart from our perception of it. The second position, which is a critique of Newton’s argument, is associated particularly with Leibniz. It argues that time is only experienced through the relation between things or events in space, which makes time appear to flow, but it has no absolute reality in itself, is relative, and only perceived through motion. In a letter to Newton’s supporter Samuel Clarke in 1715 (his so-​called “Third Paper”) Leibniz writes: These gentlemen [including Newton] maintain, then, that space is a real absolute being . . . As for me, I have more than once stated that I held space to be something purely relative, like time; space being an order of co-​existences as time is an order of successions.4 literature, of music, of the arts, of political development, and of many other human activities have long described their subjects in the same way.” 3 Newton, Principia Mathematica, 6. 4 Leibniz, Philosophical Writings, 211.

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274   The Philosophy of Rhythm It is true to say that it is the relationist view that prevails today, particularly in the natural sciences since the theory of relativity,5 but also in the arts. It is therefore both significant and unexpected that the musicologist Christopher Hasty opts for the absolutist position on time,6 in the process appearing to raise a contradiction to which I shall return shortly. There is, however, a strong case that has been made in the cognitive sciences that our experience of time is dependent on our encounter with things and events either outside us (changes in the environment, the cycle of the seasons) or internal to us but largely independent of our volition (breathing, pulse).7 This lends support to the relationist rather than the absolutist position. Udo Will, for example, points out that we don’t actually possess a special internal organ that enables us to “sense” time directly as such, and can only experience time through our relationship to other things.8 It is true that this does not in itself disprove the “absolutist” case that time flows of its own accord, independently of space and whatever happens to be filling it or going on in it, but it does demonstrate that our perception of time as “flow” and “continuity” is contingent upon the motion of things and events, and that we have no other way of sensing it than through these relations. The claim that we only really perceive time through our perception of change as motion or movement of some kind I find persuasive. For example, while the experience of a piece of music (as an object or event “outside” us) might convince us that “time flows” of its own accord and that the “music flows” of itself and in some way “contains time,” the Bachelardian view taken here is that music and the temporal arts are constituted of discontinuous elements to which our consciousness lends continuity. Without an attentive mode of consciousness that makes connections as part of the experience of the music, the sense of temporal continuity collapses, as happens in distracted listening to extended pieces. The music then appears to us as a series of disconnected fragments. What the Newtonian and Leibnizian positions, and also empirical experiments in the cognitive sciences and neuro-​sciences, do not directly address is the nature of our subjective experience of time, and it is, of course, how time appears to us that is most significant in the experience of the temporal arts. Interestingly, given his “absolutist” stance on time, Christopher Hasty writes that [r]‌hythm, in our aesthetic sense, seems to refer to a time of subjectivity and human experience—​a world apart from the objective ‘absolute’ time of Newtonian physics (but perhaps not so far from quantum physics).9

5 In physics, the dominant view since Einstein’s theory of relativity has been that time is an illusion, the corresponding reality being “space-​time.” 6 Hasty, Meter as Rhythm, 7 n.1; also 9–​10. 7 E.g. Pöppel, “Temporal Perception”; Le Poidevin, “Perception of Time”; and Paddison “Musical Time,” 244–​52. 8 Will, “Rethinking Musical Time.” 9 Hasty, Meter as Rhythm, 7.

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The contradiction between the subjectivity of musical (that is, temporal) experience and the objectivity of the Newtonian position on “absolute” time stands revealed by Hasty, but is not addressed directly by him. It is precisely the issue of subjectivity and temporal experience that I now wish to pursue further. The problem of the subjectivity of our experience and its relation to objectivity is addressed most fundamentally by Kant. For Kant our empirical experience is of the appearance of things—​that is, how they appear to our minds. He writes, we dispute all claim of time to absolute reality, namely where it would attach to things absolutely as a condition or property even without regard to the form of our sensible intuition. Such properties, which pertain to things in themselves, can never be given to us through the senses.10

Kant does not, of course, deny the empirical reality of time, how it appears to us as experiencing subjects, but only its absolute reality—​that is to say, time is “empirical” because it is fundamental to the way we, as human beings, experience the world, the way it appears to us through our senses. Particularly significant, therefore, is Kant’s insistence that time is not an attribute of the object but is something brought to it by the experiencing subject. It is, however, important to note that “subjectivity” in this sense, does not refer to the everyday meaning of the term as entirely personal and a matter of individual choice, but refers instead to the subject side of the subject–​object relationship, and indeed to the subject’s relationship to the world.11 The Kantian position on the subjectivity of the experience of time is taken up by two of the most influential philosophers of temporality in the late nineteenth and early twentieth centuries: Henri Bergson and Edmund Husserl. I want to consider their positions here in brief overview, both as a preparation for my main methodological focus on Gaston Bachelard and phenomenology, and for the support they provide for the concepts of “rhythmicized duration” as form, and the subjectivity of temporal experience. In his Essai sur les données immédiates de la conscience (Time and Free Will) of 1889, Bergson makes a well-​known distinction between what he called temps durée and temps espace. He defines these terms again in his Introduction to Metaphysics (1903) as follows (and I paraphrase): temps durée (duration) is the flux of experience, fleeting, elusive, not measurable, and identified with intuition; temps espace—​as its designation clearly indicates—​identifies measured time, clock time, with space, and with intellect, reason and rationality. The former is characterized by continuity, the latter by discontinuity.12 Duration, as temps durée, is what underlies the continuity and persistence of consciousness of the self for Bergson, the connectedness of “lived moments.” Bergson claims that the experience of duration is characterized



10 Kant, Critique of Pure Reason, 164 (A36, B52).

11 Cox, “Tripartite Subjectivity,” 1 n.1.

12 Bergson, Introduction to Metaphysics, 9.

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276   The Philosophy of Rhythm by a simultaneity and multiplicity of different durations, and he writes in Durée et simultanéité (1922) that “different—​or rather I should say diversely rhythmicized—​ durations may coexist.”13 By this he means that duration may be structured in different ways by the rhythmic events that occur within it, and that several different “rhythmicized” durations may exist simultaneously and be experienced together. In the same passage Bergson also writes of consciousness itself as duration in the following terms: Such a consciousness would grasp in a single instantaneous perception multiple events situated at diverse points in space; simultaneity would be precisely the possibility for two or more events to enter into a single instantaneous perception.14

Even though this sense of the continuity of the self is also characterized by constant change from one minute to the next, it is memory, according to Bergson, that gives this duration its feeling of continuity, in spite of apparent discontinuities along the way. Underlying Bergson’s philosophy of time is the notion of the persistence of the self through change. He writes of a “self which endures,” or “a present which persists.”15 As he puts it: There is one reality, at least, which we all seize from within, by intuition and not by simple analysis. It is our own person in its flowing through time—​our self which endures.16

In spite of his references to “rhythmicized duration,” the musical metaphor for duration and continuity Bergson chooses to emphasize is that of melody, rather than rhythm. His expanded conception of duration has some significant implications, and has been influential not only on the phenomenology of temporal experience, but also on art itself, and especially on music and on conceptions of musical form. I shall return to the problem of defining Bergsonian “duration” in relation to music in Section 2. One of many ambiguities in Bergson concerns the nature of temporal experience. Husserl (who was a self-​confessed Bergsonian) appears to see Bergson as a proto-​phenomenologist.17 Taking Kant’s arguments for the subjectivity of time and consciousness as his point of reference, Husserl refers to what he calls “phenomenological time,” which he distinguished from “cosmic time,” or “objective time.”18 In his late, unfinished work, The Crisis of the European Sciences and Transcendental Phenomenology (1936) he writes that the world we live in, our



13 Bergson, Durée et simultanéité, 42–​3 (my translation). 14 Bergson, Durée et simultanéité (my translation).

15 Bergson, “La perception du changement,” 170 (my translation). 16 Bergson, Introduction to Metaphysics,  6–​7. 17 Winkler, “Husserl and Bergson,” 93. 18 Husserl, Ideas, 1: 155 (§81).

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“life-​world” (Lebenswelt), is a spatio-​temporal world, where “our focus on the world of perception gives us . . . only the temporal mode of the present.”19 We live in a present moment where only the content of our “lived experience” (Erlebnis) constantly changes, giving a sense of duration and continuity, and what he calls the “horizons” of this constantly changing present moment are a sense of a past, through recollection (“retention”), and a sense of a future, through anticipation (“protention”). For Husserl we experience the “flow” of time as a continuum through this process, and in this way we make sense of time in relation to the events that pass through our experience of the present moment. This extended experience of time, through retention and protention from the immediacy of the experience of lived time, can be designated, I propose, by the term Erfahrung (employed rather vaguely by Husserl himself), which I have identified elsewhere as mediated “interpretive experience” that understands the present moment (in a piece of music, for example), in relation to memory of what has already occurred and in anticipation of what may still be yet to come.20 I emphasize the significance of this conception of an extended experience of time beyond the immediate experience of the lived moment because it has important implications for our understanding of the temporal arts: that is, Erfahrung points to the experimental and exploratory aspects of artistic form. I argue that the development of extended structures as “emergent forms” has historically always gone hand-​in-​hand with the exploration of new possibilities for temporal experience. I now want to turn to Gaston Bachelard’s dialectical phenomenology as an approach that has particular relevance to the temporal arts, and especially music. Bachelard’s phenomenology of time is most immediately derived from Husserl and Bergson—​in particular from his critique of Bergson’s concepts of continuity, intuition, and duration in his The Dialectic of Duration (1936). Furthermore, the similarities to Husserl’s late philosophy are especially notable in Bachelard’s own late work The Poetics of Space (1958), which is methodologically indebted to Husserl. There are three aspects to Bachelard’s concept of time that I see as especially significant: (i) our sense of time is not inherent but is dependent on our relation to objects in space—​this he derives from the psychologist Pierre Janet;21 (ii) the experience of time is dialectical and not a psychic given—​indeed, it is made by us, and is not, as such, natural and intuitive; this emerges from his critique of Bergson’s concepts of duration and continuity, where he puts the emphasis on discontinuity and rhythm in place of Bergson’s emphasis on continuity and the metaphor of melody;22 and (iii) his emphasis on the concepts of form and causality, where he sees ideas of duration and continuity as metaphors constructed in reverse through the connections we make between discontinuous elements and a projected totality as “form.” Through 19 Husserl, Crisis of European Sciences, 168. 20 Paddison, Adorno’s Aesthetics of Music, 213–​16. 21 Pierre Janet (1859–​1947), French psychologist and psychotherapist who developed a theory of memory and of the concept of dissociation. 22 Corbier, “Bachelard, Bergson, Emmanuel,” 19.

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278   The Philosophy of Rhythm his critique of Bergson, Bachelard seeks critically and dialectically to demonstrate the lacunae in Bergson’s concept of duration, and argues for “the need to base complex life on a plurality of durations that have neither the same rhythm nor the same solidity in their sequence, nor the same power of continuity.”23 We have established that for Bachelard it is important to demonstrate that “psychic continuity is not a given but made.”24 It is precisely this aspect of the phenomenology of time that Bachelard sees as experimental in character—​something which derives initially from his critique of Bergson in his earlier writings and which is strengthened in his later turn to Husserl’s phenomenology; both of these can be traced back to Kant’s argument for the subjectivity of our experience of time and our re-​creation of the world out of our own subjectivity. That this constitutes the springboard for Bachelard’s conception of a phenomenological approach to the experience of duration as essentially experimental is made clear in his introduction to The Poetics of Space, where he argues for the experimental character of the oscillating relation between subject and object in the context of the poetic image. He writes that “the duality of subject and object is iridescent, shimmering, unceasingly active in its inversions. . . . In this union . . . the phenomenologist finds a field for countless experiments.”25 While Bachelard is talking here of the poetic image in relation to space, his argument applies equally to time and the temporal arts. The key issues are those of the experimental character of subjectivity and the centrality of the phenomenological experience. So, to summarize at this stage: Bachelard’s argument that the experience of time is dialectical in character in its “backward and forward” shifts provides the theoretical underpinning for the rest of this chapter, together with his claim that “it is rhythm, not melody . . . that can provide the real metaphors of a dialectical philosophy of duration.”26 This constitutes the larger context within which I locate the concepts of rhythm and “rhythmicized duration” and on which I shall now focus.

2.  Rhythm, duration, form Bachelard’s position is well represented in the thinking of Célestin Deliège, and informs his notion of the experience of the complexity of the musical work. Deliège writes: “In order to experience time, our faculties of perception are in need of a material of some kind, a canvas that allows it to flow.”27 This observation draws our attention again to the view that we experience time only in relation to something else, never “in itself,” and that we make objects that enable us to extend and experiment with our experience of time through the potential they afford for the perception

23 Bachelard, Dialectic of Duration, 19. 24 Bachelard, Dialectic of Duration, 19. 25 Bachelard, Poetics of Space, xv.

26 Bachelard, Dialectic of Duration, 134.

27 Deliège, “Perception du temps musical,” 87 (my translation).

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of complexity and simultaneity. It is these relationships and their structural articulation that constitute, so I argue, the large-​scale rhythmicized duration of the temporal arts. But first, some general considerations on rhythm. The composer Olivier Messiaen defines rhythm as “the ordering of movement.” He goes on: “This definition has the advantage of being applicable to dance, to words, and to music, but it’s incomplete.”28 As a definition this is interesting because it locates rhythm in movement in space and makes no mention of time.29 Messiaen’s enthusiastic utilization of ancient Greek theories of rhythm as well as Bergson’s philosophy of time in his own theory of time and rhythm in his Traité is, however, unusual and even confusing,30 not least because of his own tendency as a composer to treat time as space. What becomes again apparent is the overlap between temporal and spatial notions of rhythm—​something clearly so in the case of dance as the articulation of movement in space and time, but less obviously so in music because of the irreversibility of time. (Messiaen’s ideas of retrogradable rhythms as well as the idea of “cancrizans”—​retrogradable canons, as in Bach’s Musical Offering—​occupy an odd place in a temporal art like music.) But what about the attribution of rhythm to the non-​temporal spatial arts like painting, sculpture, and architecture? Roman Ingarden writes:  “Some interpret the phenomenon of rhythm so widely that according to them it is also present in nonmusical works like architecture and includes the ‘rhythm’ of arches and vaults.”31 Ingarden doubts the validity of these views, suggesting that they are merely arguing by analogy, that is to say, metaphorically. By this token, however, one would have to say that rhythm certainly has a spatial dimension because of the “measuring” function of meter within rhythm, as temps espace, although this is perhaps only literally present in dance as an art form that really does combine time, space, and motion. On the other hand, “space” could also be said to be a metaphor as could “motion,” in relation to music.32 Carl Dahlhaus has suggested that notions of tonal space and motion in music are highly problematic, particularly when we attempt to argue that pitches (or tones) “move” in tonal space. He asks how we might imagine motion without some agency that carries the motion, given that musical movement seems to lack such an agency: For it would be a questionable hypothesis to claim that it was a tone that moved in tonal space . . . A higher tone following a lower one is ‘another’ tone rather than ‘the same’ tone in another place.33



28 Messiaen, Music and Colour, 67.

29 Hamilton, “Rhythm and Stasis,” also argues a case for rhythm as movement in space. 30 Taylor, “Time and Eternity,” 256–​80. 31 Ingarden, Work of Music, 89.

32 Spitzer, Metaphor and Musical Thought, extends the discussion of metaphor theories applied to music.

33 Dahlhaus, Aesthetics of Music, 80.

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280   The Philosophy of Rhythm In his demolition of the notion that pitches can really “move,” and in his refusal to account for the importance of metaphor in the way we listen to music, Dahlhaus also underlines the frailty of the fictions that sustain the illusion of movement and continuity in music. He concludes, like Bachelard, that the appearance of motion in music is really only carried by rhythm: One can think a rhythm without any succession of tones, but not a succession of tones without some rhythm. This indicates that rhythm forms the basic component of the impression of musical motion. Time—​temps durée made into a firm temps espace—​is the primary dimension of tonal space; verticality is secondary.34

In view of all this, what do we mean by rhythm? It is not simply a regular pulse or meter, but also patterns that repeat, whether exactly, or in varied or developing shapes that retain something recognizable from the original patterns, though they may also depart from them in some way, whether suddenly or very gradually. Such patterns may also recur or develop at different “levels” (however literally or metaphorically that term may be understood). The tension between rhythm and meter (this term can be taken both as metrical scheme or as a sense of pulse) has been exploited to an extreme degree in music, and also in dance and to an extent in poetry. Christopher Hasty considers that meter and rhythm are not to be separated in reality, and that rhythm is really the combination of meter and the play against or departure from meter that constitutes a musical event. He argues that the word ‘rhythm’ speaks to us  .  .  .  of a time that is not other than the particular course of an event that we follow with interest—​a time that can be neither predicted nor recaptured, a time articulated not by points or segments but by the emergence of felt events.35

In this respect Hasty comes close to the large-​ scale notion of rhythm as “rhythmicized duration” that interests me here. The development of large-​scale rhythmically articulated forms goes back to antiquity, where it is inseparable from mimesis, understood as the mimetic impulse toward imitation as mimicking, whether of actions, emotions, or of narrative. Aristotle underlines the significance of the dynamic process of progressive innovation in the extension of form through improvisation: Given, then, that imitation [mimēsis] is natural to us, and also melody [melos] and rhythm [rhythmos] (it being obvious that verse-​forms are segments of rhythm), from the beginning those who had the strongest natural inclination towards



34 Dahlhaus, Aesthetics of Music, 80. 35 Hasty, Meter as Rhythm, 6.

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Time, Rhythm, and Subjectivity  281 these things generated poetry out of improvised activities by a process of gradual innovation.36

The unmediated and spontaneous rhythms of shorter popular forms as well as improvised extensions of them appear to have developed into the highly mediated and even contrived large-​scale “rhythms” of sectionalized epic poetry and tragedy. It is probable this would have involved initially a move from epic feats of memory to writing things down in order to record the extended structure for future performances. Rhythm as “form,” through its gradual disengagement from ritual and its involvement in innovation, could thus be said to have become historical and dynamic. Furthermore, the possibility of expanding our experience of increasing complexity can also be seen to have gone hand-​in-​hand historically with the development of technologies of writing, notation, score, and in due course electronic and digital modes of production and reproduction. This process—​a movement from the immediacy of direct and unmediated rhythm to the mediated character of the “rhythmicization” of large-​scale extended duration as structures—​has several important features. First, just as small-​scale rhythm is mimetic in its imitation of the repetitive aspects of actions and processes, so is large-​scale rhythmicization of duration mimetic through the imitation of longer-​term processes involving repetition, contrast, varied repetition, development, and so on. Second, there are technical and technological developments, as already suggested—​for example, techniques for developing the drama or the narrative, as outlined by Aristotle in the Poetics as mimetic, as well as technologies (i.e., writing) for recording and preserving it, because memory can no longer be entrusted with this, due to increasing complexity and the number of elements involved. Third, while time and memory are encapsulated in this process, they are in effect spatialized through being preserved, for example, on the written page.37 Fourth, as far as the performing arts are concerned, this spatialized time, reified as written page or score, has to be turned back into a “flow” of time available to experience through performance. Fifth, all of this, as the process of making (poiesis), serves to mark out a separate aesthetic sphere, a place for different experiences of time, as dramatic time, epic time, choreographic time, musical time (or rather, musical times, as I shall argue), where experiments in making elaborated and extended aesthetic objects have taken place, and where experiments in temporal experience can also be undertaken as a matter of course. But what of the counterargument that there is no necessary connection between these two concepts? Messiaen, for instance, insists on keeping the two strictly apart, as is brought out in the following exchange between the composer and his interviewer Claude Samuel. Messiaen has been talking of Debussy’s attempt to capture



36 Aristotle, Poetics, 7.

37 Adorno, Zu einer Theorie, 69–​72/​Towards a Theory, 52–​3, discusses this in a note dated June 20, 1946.

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282   The Philosophy of Rhythm the fleeting movement of nature in his music with his delicate use of subtly “irregular” rhythms and orchestral timbres: O.M. By dint of monitoring nature, Debussy understood its mobile aspect and its perpetual undulation, which he conveyed in his music. Thanks to this, he was one of the greatest rhythmicians of all time. C.S. Doesn’t this freedom of rhythm imply a renewal of form? Isn’t there a connection between the form of a work and this rhythmic treatment? O.M. I don’t think so; those are two distinct fields.38

It is obvious that Samuel thinks that rhythm informs every aspect of form—​ something that is clear to him in Debussy’s music. Messiaen, on the contrary, sees no connection at all between these two levels. For him, rhythms are one thing (he deals with them as if they are objects, and seeks to utilize them as such in his system of retrogradable and non-​retrogradable rhythms), while form is another thing (although he also treats “form,” and the sections that make up his forms, as objects in space). This seems to me to reveal a gap between (i) what artists consider they are doing in making a work, and (ii) how a work of art is actually experienced and what causal connections are made by an attentive consciousness. Messiaen manipulates his distinctive rhythms and his block forms as if they were quite separate compositional matters, but I suggest that in the experience of listening to Messiaen’s music the listener hears the larger formal connections derived from the juxtaposed and superimposed “rhythmicized” timbral blocks that typically characterize his work as also constituting a larger formal rhythmicized structure—​an example of this would be the Antistrophe I & II in his appropriately named orchestral work Chronochromie (“Time Colouration”) of 1960. In “musical time,” which is uni-​directional and where musical events must succeed each other, memory and anticipation in the listening experience seek causal relations that sustain a sense of continuity, even where the composer has sought to emphasize structural discontinuity. However, it is also the case that Messiaen’s music can disrupt the impression that time “flows,” to the extent that it often seeks to create the experience of time standing still. He sometimes does this through using extremely slow repeated rhythmic units against a continuous melodic line, as in the final movement of his Quatuour pour la fin du temps (1941), where there is a continuous, unbroken violin line lasting eight minutes or so, with what seems like an endlessly repeated and unvarying rhythmic motif in the accompanying piano chords. On the other hand, there is the sheer profusion and density of rapidly moving material derived from birdsong where the excess of rhythmic and melodic diversity acts to blot out all sense of difference, and as a consequence seems to arrest completely any perception of time passing, as in the sixth movement, Épode, of Chronochromie. I consider that these examples clearly demonstrate the close connection between small-​scale rhythm and large-​scale

38 Messiaen, Music and Colour, 70.

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“rhythmicized duration” as form in Messiaen’s music, and in our experience of it, in spite of the composer’s insistence that there is no connection between rhythm and form. Nevertheless, it is difficult to imagine that the composer would deny that such pieces certainly constitute clear examples of the manipulation of our perception of time, and to that extent they are experimental. Experimentation and innovation are particularly associated with twentieth-​ century modernism across the arts, and it was at the beginning of this period (which actually starts in the late nineteenth century) that Bergson’s vitalist ideas had their greatest influence. This is strikingly the case in music, as the musicologist Jann Pasler has argued in her work on temporality and the Bergsonian influence on Debussy, and later on the spectralist composers towards the end of the twentieth century in France (in particular Tristan Murail, Gérard Grisey, and Hugues Dufourt).39 I want to consider the example of Debussy’s ballet Jeux in this context, and in the light of Pasler’s comments on it, to clarify what I understand by the concept of “rhythmicized duration” in music. Debussy’s Jeux (1913) is a late work, written for Diaghilev and Nijinsky, and it represents the composer’s rhythmic and formal innovations at their most radical. As a ballet it takes as its point of departure the rather nebulous plot of a game of tennis and the constantly changing interrelations between the players—​a love triangle of two women and a man. It is usually performed as a concert work, however, and is a highly structured piece in its own right. It lasts about seventeen minutes. Pasler writes: “What gives Jeux its formal coherence is its overall rhythmic organization; recurrence of motives and timbres support this form rather than create it.”40 In each of the sections that make up the mosaic-​like structure of the work Debussy creates a distinct and self-​contained set of timbres, textures, and rhythmic motives. Pasler demonstrates this in her analysis, and emphasizes that “form is the rhythmicization of sections, each with their own colour and sense of time.”41 She points out that time for Debussy is seen as free-​flowing and in a state of flux, depending for its perception on what is filling it. This Bergsonian conception brings us to the point where we must now attempt to clarify what is meant by “rhythmicized duration” in relation to music, because the concept of “duration” is difficult to pin down in Bergson’s philosophy. For Bergson, as we have seen, duration is the indivisible flow of “becoming” that cannot be rationalized mechanistically, and can only be experienced intuitively. Bachelard had criticized this at a philosophical level. For Debussy, you could say that, while influenced by Bergson, he has no choice but offer a critique of Bergson’s ideas at a practical and technical level. For the artist as composer, involved at the poietic level in making musical works, the problem is how to make something that appears to embody the experience of this endless flux of time with its ebb and flow, 39 Pasler, “Debussy, Jeux,” 60–​75, discusses the influence of Bergson on Debussy, and the coexistence of different “rhythmicized durations.” See also Pasler, “Spectral Revolution,” 125–​40. 40 Pasler, “Debussy, Jeux,” 61. 41 Pasler, “Debussy, Jeux,” 63.

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284   The Philosophy of Rhythm its speeding up and slowing down, and its increasing and decreasing of intensity. This unavoidably involves calculation and artifice. Viewed in this context, I suggest that “duration” in music can be understood as the period of time taken up and animated by an event, in this case a musical event. Seen in this way, distinct durations can be made to shade into each other, be superimposed upon each other (for example, in simultaneously occurring different rhythms, as happens at many points in Jeux), and to overlap, creating a larger “rhythmicized duration” of which these individual events become the rhythmic elements. Debussy achieves this with such subtlety that we are not aware of his contrivance. Pasler cites from a letter Debussy wrote to his publisher Durand in 1907: Music is not, in its essence, a thing which can flow within a rigorous and traditional form. It is de couleurs et de temps rythmés [made of colours and rhythmicized time].42

As Pasler convincingly shows, Debussy captured the essence of the natural and intuitive by means of calculation and artifice. In Jeux his models were, on the one hand, games, and on the other hand the montage techniques of cinematography that Bergson himself had identified as the very opposite of the flux of durée, with its calculated intercutting, superimpositions, and juxtapositions employed to achieve the appearance of the ceaseless interactions of reality. In Jeux, Debussy structures duration through an infinitely subtle interplay of fluctuating rhythmic fragments that coalesce to build sections that in their turn serve to articulate the large-​scale form. However, “form” understood in this way as experimental and innovative, is not only a radical development of twentieth-​century modernism, or of Bergson’s concept of rhythmicized duration. “Form” as the rhythmicization and extension of duration has always been the arena for experimentation in the temporal arts, in spite of the historical and cultural tendency for particular forms to become standardized and normative.43 But experiments with duration as “aesthetic time” are not unique to the arts or by any means privileged in this respect, and we also experience other “times” as structured. We can talk, for instance, of the time of a football match, the time of a game of cards, or the time of a walk in the country. Each one of these, self-​contained and combined with elements of structure, play, and the unpredictability of improvisation, has a time of its own, different from other times. Interestingly, this raises the question: What might characterize the difference between the time of games as “play” and the “aesthetic time” of the experience of the art object or event? Both come under what has been identified by Gadamer as “transformation into structure” and into intentional object of experience.44 I argue that, if there is a distinction 42 Debussy to Durand, cited in Pasler, “Debussy, Jeux,” 71. 43 Spitzer, Metaphor and Musical Thought, on Heinrich Koch’s theory of form, is helpful in this respect, as is Clayton, Time in Indian Music, on the case of metric cycles and extended forms in Indian music. 44 Gadamer, Truth and Method, 110.

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to be made, it lies in the exploratory and innovative dimension of art and aesthetic experience that can also involve the breaking of rules or the invention of new ones. This in turn raises a further question: If we can distinguish in broad terms between the time of games, for instance, and the aesthetic time afforded by the structure of “rhythmicized” art objects, is there also a distinction to be made between different aesthetic times, especially in the temporal arts? I now want to address this through an expansion of the issues raised so far.

3.  Aesthetic time, historical time, experimental time I have argued for an experiential concept of temporality that is subjective in character, and have made a case for a concept of rhythm that also involves a large-​scale notion of “rhythmicized duration” that becomes objectified as artistic form, and which is exploratory and innovative. I now go on to argue that the experience of musical time, while distinctive, is not one kind of “aesthetic time” common to all music, but that there are different types of temporal experience characterized by the musical norms associated with different historical periods. I shall also argue that the gap that appears between innovation and normativity in the aesthetic experience of duration in the temporal arts takes on a critical character: innovation as critique of normativity. First, how might our experience of time through the temporal arts differ from our “normal” sense of time? Deliège claims that forms of art that need duration for their accomplishment are the most apt at abolishing our usual perception of time and leading it towards an experience of time that is richer, more complex, less easily analysable.45

He asks the question: If, from the moment an artform like the musical work slips between our consciousness and our usual experience of time [and] as a result a new quality of time experience offers itself to our consciousness, then does this not imply that it is indeed the art form itself that engenders its own time, a time conditioned by its organization, its rhythms and the hierarchy of its structures?46

This appears to claim that the work itself is the sole source of the complexity and richness of such an experience of time, that experience is merely shaped and directed by the complexity and richness of the structure of the musical work. But Deliège recognizes that this conclusion needs to be treated with caution. He



45 Deliège, “Perception du temps musical,” 87 (my translation).

46 Deliège, “Perception du temps musical,” 87–​8 (my translation).

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286   The Philosophy of Rhythm writes: “If a particular ‘time’ of the work of art does exist, then it belongs to our consciousness to make it real.”47 This is the most Bachelardian feature of Deliège’s theory. As Bachelard puts it: “Indeed, causality in its many forms brings many reasons for relations, links, and successions, and by doing so makes time and space organic.”48 Furthermore, the sense of continuity and duration we come to ascribe to “the music” is not necessarily the experience of the “innocent” first hearing. It is, rather, an experience constructed in reverse, the result of a combination of memory and expectation. In effect, the sense of the “form” of a work is as much the result of a psychological process of “re-​forming” and “reflux” as it is of the facticity of the work as structure “in itself.” Indeed, the continuity of the sounds themselves is illusory, according to Bachelard, and likely to break down at any moment. It is sustained only by our consciousness and our active attention through the process of making connections, through perceiving recurrences of groups of material, of rhythms, of motivic ideas. In a sense, therefore, the Bergsonian notions of duration and continuity are fictions. As Bachelard puts it: “In this way then, it gives us not really duration but the illusion of duration.”49 He concludes: “Music’s action is discontinuous; it is our emotional resonance that gives it continuity.”50 And yet, it also has to be argued that the facticity of the musical work and the potential it affords for a structured experience of time cannot be denied. Deliège, unlike Bachelard, cannot help but recognize the materiality of musical works. That is to say, works exist not only as successions of sounds given a sense of continuity by our consciousness, but also as “spatial” objects that can be read silently as scores, and where connections can be made both forwards and backwards as superimpositions of simultaneous levels, as similarities compared, as differences and contrasts recognized, and as the relationship of parts to whole seen as part of a process of increasing familiarity. Deliège restores the strong counterweight of the existence of the “work,” albeit as a work still to be re-​composed and re-​formed by an attentive consciousness, and in the process develops it further. The extent of his indebtedness to Bachelard nevertheless remains evident, which is to say, what it means to talk of the experience of time through music as specifically the perception of musical time. This is to be seen in a passage like the following, where Deliège writes: In effect, time is not a thing, but an experience where one lives time and constructs it at the same time; experience sufficiently fluid to accept its own disruption and provisional annihilation, all under the pressure of a simple fiction.51



47 Deliège, “Perception du temps musical,” 88 (my translation). 48 Bachelard, Dialectic of Duration, 73.

49 Bachelard, Dialectic of Duration, 123. 50 Bachelard, Dialectic of Duration, 124.

51 Deliège, “Perception du temps musical,” 90 (my translation).

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But our experience of time is dependent on the objects and events that occupy our consciousness. In this respect, musical works constitute a particular category of objects that can occupy our experience. That is to say, they are intentional objects, and as such tend to be highly structured with relationships between parts and whole that demand an attentive consciousness which also imbues such works with causality and continuity. Is the temporal experience afforded by any particular piece of music unique to that piece and different from the experience of any other piece? This raises the problem of nominalism (not addressed by Bachelard or Deliège), where any attempt to generalize from particular instances, and to establish universals is resisted by the uniqueness of each piece and the uniqueness of the experience of temporality. An example in support of this extreme position could be Edgard Varèse, each of whose works (there are fewer than a dozen) defies any attempt at generic categorization. To ask, therefore, whether there might be, on the contrary, a strong similarity between the experiences of temporaity enabled by most pieces of music regardless, would be to see composers like Varèse merely as exceptions to the rule, and to argue, untenably, that generic norms in music do indeed provide a sufficient similarity of experience across different historical periods. Deliège has to consider the problems raised by the implication in his argument that each work might indeed appear to imply its own unique experience of temporality. From a modernist perspective it could well be argued that this is to some extent the case. However, can extreme nominalism also be said to apply to musical works of earlier centuries? How might this apply, for example, to the Baroque, or to the early Classical period in Western art music? Deliège proposes that on one level, the experience of musical time is also always historical and cultural, because it involves culturally learned responses, expectations, and indeed, you might say, skills, that are to do with period, style, language and, one might add, idiom. Deliège draws two conclusions from this. The first is that, if a musical style or language underpins in some way the temporal structure of a musical work, then it is absolutely pointless to attempt to provide a single general definition of musical time that will apply in all cases and for all times. As he points out, the time of Machaut, of Handel, of Mozart, and of Wagner are not the same. He therefore proposes, quite reasonably, that there is a sort of “standard time” that characterizes the musical time of any particular period. It does not follow from this, however, that the experience of individual works will be similar, but only that general features of style, melodic phrasing, harmonic progressions, and characteristic rhythms will be familiar. Deliège’s second conclusion is that the concept of musical time is not one possessed by either the individual artist or by the art community, because these come down to the mediated relationship between listener and musical work, and this is largely a question of the acceptance or rejection of a dominant musical-​historical style or language, conditioned by, as he puts it, “four centuries of tonal polyphony.”52 He

52 Deliège, “Perception du temps musical,” 92–​3.

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288   The Philosophy of Rhythm concludes, therefore, that much of the temporal structure of music and of the musical consciousness of a particular period is a given, especially in relation to phraseology, which is itself the most obviously rhythmic aspect of melodic lines and also of harmonic progressions. It is this cultural, historical—​and indeed, ideological—​ dimension of musical time and rhythm that seems to me to be the important further development of Bachelard’s dialectic of duration, and his critique of Bergson in Deliège’s scheme. At the same time, the dialectical aspect of his approach also reveals itself yet further when, in talking about one important style period in the nineteenth century—​that of “developing variation”—​he moves back and forth between musical structure and listener demands to demonstrate how close and even fragile the relationship between them is. This suggests that ideas of continuity and coherence that we attribute to the musical work, and which we understand as belonging to the experience of musical time, are constructs, metaphors sustained by the norms of their historical period, and which are liable to disruption and change. Musical time is seen by Deliège as an “ingenious metaphor” that psychologically and ideologically we attribute to the work itself, and do so until the historical paradigm shifts and a different musical time takes its place. Deliège points out that this operates only as long as there is a degree of harmony between artists and listeners in a particular period. However, a crisis develops when such harmony breaks down through artistic innovation, and the gap between the musical time of innovators and the musical time of everyone else then widens, so that incomprehensibility results.53 What are the implications of such crises of comprehensibility between innovation and normativity in the experience of musical time? Viewed in the historical context of the crisis of musical modernism, Deliège distinguishes two antagonistic groups reflecting the kind of conflict of cultures of which “the state of crisis is the expression,” as he puts it.54 Group 1 is characterized by what he calls bi-​dimensional sonic processes, non-​ reversible, continuous and linear movement. The temporal structures hinge on the valuing of development and homogeneity. Group 2 opposes the linear and continuous values of the established culture, putting in its place “a non-​Euclidean geometrical space” that characterizes the contemporary imagination, so Deliège proposes, and the projection of “multiple dimensions in a succession of discontinuous instants favouring . . . a dynamic present.”55 These two antagonistic groups represent two distinctly different metaphors of time. The first group he suggests is characterized by the phraseological type of process organized according to the mode of development by variation. The second group is characterized by other modes of temporal organization like, for instance, moment forms, where the experience of continuity is constantly interrupted, as each “moment” is discontinuous with every other moment.56 Other forms of organization

53 Deliège, “Perception du temps musical,” 94–​5. 54 Deliège, “Perception du temps musical,” 95.

55 Deliège, “Perception du temps musical,” 95–​6. 56 Deliège, “Perception du temps musical,” 97.

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might also be included here, like labyrinth forms, with different routes through the structure, and mobile forms where different orderings of elements might be used in each new performance. You could therefore say that Deliège presents the second, the metaphor of discontinuity, as a critique of the first, the metaphor of continuity. Deliège takes Bachelard’s notion of a dialectical mode of experience of duration and attempts to sketch a critical theory of music and musical experience that has ramifications beyond Bachelard’s theory of rhythm, and is clearly influenced by Adorno.57

4.  In conclusion I have argued that rhythm needs to be understood not simply as an independent parameter but as a fundamentally structural dimension of the temporal arts, as “rhythmicized duration” as form. In this respect, moreover, innovations in the temporal arts afford us opportunities also to experiment with our perception of duration, extending our experience into areas of increasing complexity, simultaneity, and multiplicity. I have also made the claim that our ideas of rhythm, seen in this larger context, are historical and metaphorical in character, in that they have emerged in particular historical and cultural circumstances and have changed and developed over time. Underlying the position I have put forward is the argument that the aesthetics of rhythm in the temporal arts is concerned with an intensive experience of time that is essentially experimental in relation to the kinds of art works and events, as structured “rhythmicized forms,” made at any particular historical period. The aim has been to suggest the extent to which the creative and experimental impulse of the temporal arts has sought to extend the limits of our experience of time, to paraphrase Bachelard, through “the restoration of form” to rhythm.58

Works Cited Adorno, Theodor, Ästhetische Theorie, Gesammelte Schriften, vol. 7, ed. Rolf Tiedemann and Gretel Adorno (Frankfurt, 1970). Adorno, Theodor, Zu einer Theorie der muskalischen Reproduktion, ed. Henri Lonitz (Frankfurt, 2001). Tr. as Adorno, Towards a Theory of Musical Reproduction, tr. Wieland Hoban, ed. Henri Lonitz (Cambridge, 2006). Aristotle, Poetics, tr. Malcolm M. Heath (London, 1996). Bachelard, Gaston, The Poetics of Space, tr. Maria Jolas ([1957]; Boston, 1969). Bachelard, Gaston, The Dialectic of Duration, tr. Mary McAllester Jones ([1936]; Manchester, 2000). Bergson, Henri, Durée et simultanéité: A propos de la théorie d’Einstein ([1922]; Paris, 1968). 57 The connection is particularly striking, because Adorno, Ästhetische Theorie, 207, proposes that “musical time” acts as a critique of “empirical time.” 58 Bachelard, Dialectic of Duration, 133.

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290   The Philosophy of Rhythm Bergson, Henri, “La perception du changement,” in La pensée et le mouvant ([1911]; 15th edn, Paris, 2003), 143–​76. Bergson, Henri, An Introduction to Metaphysics, tr. T. E. Hulme ([1903]; London, 2007). Clayton, Martin, Time in Indian Music: Rhythm, Metre, and Form in North Indian Rag Performance (Oxford, 2000). Corbier, Christophe, “Bachelard, Bergson, Emmanuel: Mélodie, rythme et durée,” Archives de Philosophie, 75 (2012), 1–​19. Cox, Arnie, “Tripartite Subjectivity in Music Listening,” Indiana Theory Review, 30.1 (2012), 1–​43. Dahlhaus, Carl, Aesthetics of Music, tr. William Austin ([1967]; Cambridge, 1982). Deliège, Célestin, “Perception du temps musical,” in Invention musicale et idéologies, (Paris, 1986), 87–​100. Gadamer, Hans-​Georg, Truth and Method (1960), tr. Joel Weinsheimer and Donald G. Marshall (London, 2004). Hamilton, Andrew, “Rhythm and Stasis: A Major and Almost Entirely Neglected Philosophical Problem,” in Proceedings of the Aristotelian Society, 111.1 (2011), 25–​42. Hasty, Christopher, Meter as Rhythm (Oxford, 1997). Husserl, Edmund, Ideas for a Pure Phenomenology and Phenomenological Philosophy (1913), vol. 1 (of 2), tr. Daniel O. Dahlstrom (Indianapolis, 2014). Husserl, Edmund, The Crisis of European Sciences and Transcendental Phenomenology, tr. David Carr ([1936]; Evanston, 1970). Ingarden, Roman, The Work of Music and the Problem of Its Identity, tr. Adam Czerniawski, ed. Jean B. Harrell ([1973]; London, 1986). Kant, Immanuel, Critique of Pure Reason, tr. and ed. Paul Guyer and Allen W. Wood ([1781, 1787]; Cambridge, 1998). Kuhn, Thomas S., The Structure of Scientific Revolutions ([1962]; 3rd edn, Chicago, 1996). Leibniz, Gottfried Wilhelm, Philosophical Writings, tr. Mary Morris and G. H. R. Parkinson, ed. G. H. R. Parkinson (London, 1973). Le Poidevin, Robin, “The Experience and Perception of Time,” in Edward N. Zalta, ed., Stanford Encyclopedia of Philosophy, 2011:  https://​plato.stanford.edu/​archives/​fall2011/​entries/​time-​ experience/​. Messiaen, Olivier, Music and Colour: Conversations with Claude Samuel, tr. E. Thomas Glasow (Portland, 1994). Newton, Isaac, “Scholium to the Definitions,” in Philosophiae Naturalis Principia Mathematica [1689], tr. Andrew Motte (1729), revd Florian Cajori (Berkeley, 1934). Paddison, Max, Adorno’s Aesthetics of Music (Cambridge, 1993). Paddison, Max, “Adorno, Time, and Musical Time,” The Opera Quarterly, 29.3–​4 (2013), 244–​52. Pasler, Jann, “Debussy, Jeux: Playing with Time and Form,” 19th-​Century Music, 6.1 (1982), 60–​75. Pasler, Jann, “Resituating the Spectral Revolution:  French Antecedents and the Dialectic of Discontinuity and Continuity in Debussy’s Jeux,” Musicae Scientiae, special issue: Discussion Forum 3: Aspects du temps dans la création musicale (2004), 125–​40. Pöppel, Ernst, “A Hierarchical Model of Temporal Perception,” Trends in Cognitive Sciences, 1.2 (1997),  56–​61. Spitzer, Michael, Metaphor and Musical Thought (Chicago, 2004). Taylor, Benedict, “On Time and Eternity in Messiaen,” in Judith Crispin, ed., Messiaen:  The Centenary Papers (Newcastle-​upon-​Tyne, 2010), 256–​80. Will, Udo, “Rhythm, Time Experience and the Body:  Rethinking Musical Time,” conference paper (Institute of Advanced Study, Durham University, November 2012). Winkler, Rafael, “Husserl and Bergson on Time and Consciousness,” Analecta Husserliana, 90 (2006), 93–​115.

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18 Husserl’s Model of Time-​Consciousness, and the Phenomenology of Rhythm Salomé Jacob

1. Introduction This chapter examines the implications of Edmund Husserl’s model of temporal consciousness on the experience of musical rhythm. In Husserl’s phenomenology, temporality structures perception, but also memory and imagination. We visually perceive objects as enduring or moving through time. If our experience were only a succession of now-​points, the perception of endurance, movement, and change would be impossible. Husserl aims to account for the temporal structure of consciousness that renders possible these kinds of experiences. He argues that the living present—​any current moment of experience—​includes three phases: the retention of the just-​past; the primal-​impression which corresponds to the now-​point; and the protention, which is a short-​term anticipation of what is just about to come. The living present encompasses what has just happened and what is about to occur, thus enabling the experience of continuity and movement. The notion of rhythm is ambiguous; there is a tension between an objective and a subjective (or experiential) dimension of rhythm. In the first case, rhythm refers to the durational patterns of accented and unaccented sounds, as well as silences. This rhythm could be instantiated in other pieces; it seems to be repeatable as a type. In the experiential case however, rhythm is not studied as a pattern that can be instantiated, but rather in its particular experience. Rhythm as experienced—​which I shall term rhythm as lived—​involves the sensing of a flow, requiring a certain coherency in the events—​if the events occurred completely by chance, there would be no feeling of flow. Is there a real dichotomy between objective and subjective, experiential, rhythm?1 Christopher Hasty suggests that dictionaries and technical studies privilege the objective view of rhythm. However, I agree with his argument that one cannot think about rhythm in isolation from the temporal experience of it. Hasty claims that the reading of a score or a poem occurs in time, suggesting that it is in this sense a “performance”; we talk for instance of “the reading” of a 1 In this volume, Chapter 15, Hasty, “Complexity and Passage,” and Chapter 16, Cheyne, “Encoded and Embodied Rhythm,” present contrasting views on this question. Salomé Jacob, Husserl’s Model of Time- Consciousness, and the Phenomenology of Rhythm In: The Philosophy of Rhythm. Edited by: Peter Cheyne, Andy Hamilton, and Max Paddison. Oxford University Press (2019). © Oxford University Press. DOI: 10.1093/oso/9780199347773.003.0019

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292   The Philosophy of Rhythm poem. There is thus, even in the study of rhythm on a score, a certain experience of movement. It does not make sense to speak about rhythm as atemporal and non-​ experiential. This chapter aims to articulate rhythm as lived. Why is Husserl relevant in an examination of musical experience, and more specifically of musical rhythm? In his discussion on time, he provides the example of listening to a melody.2 Husserl examines the perception of change (how each tone heard is colored by the preceding and the following one) and duration (what it is to perceive a tone as having a certain duration). Why, then, concentrate on rhythmic experience specifically? The first motivation may be that rhythm seems more fundamental than melody, if melody is to be understood as pitched sounds organized in musical time. This temporal organization is precisely what we take to be musical rhythm. It is also possible to have rhythmic pieces which are not harmonic, although it is ambiguous whether we may have completely arrhythmic pieces.3 Simha Arom examines, for instance, pieces of “pure rhythmics” in the Central African Republic that can be produced on idiophones, membranophones, or by the human body, such as foot stamping.4 A second motivation is the intimate relation between lived rhythm and bodily movements. When listeners attend to rhythm, they often engage with it by tapping their foot, swaying their head, or balancing their body. As developed below, Husserl’s phenomenology of time strongly enables us to connect the experience of musical rhythm and the listener’ bodily movements. Yet, can Husserl’s model really say much about the distinctiveness of rhythmic experience? Given that it also applies to the perception of isochronous sounds, one may question the appeal to a Husserlian framework. I argue that Husserl’s analysis of time-​consciousness is particularly useful in a study of rhythm, although this analysis does not do justice to the full complexity of the phenomenology of rhythm. First, the dynamic structure of time-​consciousness, when applied to rhythm, suggests that listeners retain just-​past sounds and anticipate sounds to come based on what has been heard. Short-​term memory and short-​term anticipation should not thus be studied separately but in close interrelation. Second, I concentrate on bodily interaction with rhythm—​such as foot tapping—​and suggest that these movements are also intrinsically temporal in requiring an anticipation of where the movement is going, and how it will unfold. Experientially, rhythmic bodily movements encompass both the perception of musical rhythm and a bodily awareness of one’s own movements, both sharing the same structure of retention, primal-​impression, and protention. The anticipation in foot tapping, for instance, parallels anticipating when the next beat will occur, and suggests a particularly rich phenomenology of embodied rhythm. 2 Husserl, Internal Time,  24–​5. 3 By arrhythmic pieces, I do not mean pieces that are ametrical (see Section 2). Neither do I mean that there is no rhythmic structure specified on a score, even if, like John Cage’s “As Slow as Possible,” its performance (in this case, some notes lasting two years) prevents any experience of rhythm, and therefore of music. Similarly, a creation that has no temporal organization at all, i.e., notes with no sense of coherence between each duration, lacks a rhythm. I leave open the question whether or not such a piece may be experienced as musical. 4 Arom, African Polyphony, 233.

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In this chapter, I aim to illuminate Husserl’s phenomenology of temporality by putting together ideas on time from his 1904–​5 lectures with notions developed in the latter part of his career, e.g., the term “living present” (lebendige Gegenwart), first mentioned in the C-​manuscripts in 1929. These important Husserlian notions, I argue, demonstrate their full relevance in rhythm studies. However, the account of a temporal nature of bodily movement that I develop in Section 3, on the temporal nature of bodily movements, was not addressed by Husserl and is influenced by the work of more contemporary figures such as Shaun Gallagher and Evan Thompson.5

2. Rhythm In order to understand in what sense and to what extent Husserl’s analysis of time-​ consciousness may be relevant to a study of rhythmic experience, we need to say a bit more about rhythm first. Rhythm is rarely experienced in isolation from other musical features.6 We find in Edgar Varèse’s work, for example, a very close interaction between rhythm and timbre. In pieces such as “Arcana” and “Octandre,” rhythm is united with timbre to put different musical forces into tension. A passage in the first movement of “Octandre” (bars 19 to 21) exhibits a tension between the first pattern (horns, trumpets, trombone, and a double bass), consisting in a dotted semiquaver and a demisemiquaver rest, followed by four demisemiquaver notes, repeated four times. Varèse wrote on the score that it had to be “heavy and savage.” By opposition, the following pattern—​brief alternation of quaver rests and quavers—​exhibits very different timbral characteristics (piccolo flute, oboe, clarinet, and bassoon). In this passage, the sense of movement is not simply given by the rhythmic patterns but also by the timbral features. I assume in the rest of the chapter that rhythm can be conceptually distinguished from other musical features, even if it cannot always be separated from these features in our experience. Rhythm is often associated with meter. Meter involves alternation between stressed and unstressed beats—​regularly recurring divisions of time. The most commonly found time signatures in Western music are 3/​4, 4/​4, or 6/​8, and they usually remain stable throughout a piece. These signatures indicate the number of beats in each bar. The first beat of the bar, the downbeat, is traditionally the stressed one, but composers can—​and indeed often do—​play with this, as in the case of upbeat notes (the anticipatory note occurring before the first bar line), and in syncopations when the rhythmic stress is placed where it is not expected. The wide variety of durational note patterns, such as combinations of crochets, quavers, and demisemiquaver rests, corresponds to rhythm.

5 Gallagher and Zahavi, The Phenomenological Mind; Thompson, Mind in Life. 6 I do not hold a conservative position on what features are constitutive of musical works. I am not claiming in particular that a musical work necessarily involves pitched notes.

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294   The Philosophy of Rhythm Meter isn’t always regular. Composers in the twentieth century in particular have denied that meter ought to be the fixed framework within which rhythm can be heard. Luigi Dallapiccola, for example, developed what he termed a schwebender rhythmus, literally a “floating rhythm.” The idea is that there must be an interplay between meter and rhythm. Meter cannot simply be this rigid fragmentation of time. Schwebender rhythmus can occur thanks to three main characteristics: a meter that changes abruptly; phrases that go beyond the bar; and metrical superimposition. The first characteristic informs the main theme of Dallapiccola’s second “Due Liriche del Kalewala,” in which the time signature changes in each bar (4/​4, 3/​4, 2/​4, 7/​8, 4/​4, 7/​8,  4/​4).7 Dallapiccola’s work shows that meter can be more or less flexible. Some music may also be ametrical. Gregorian chants as well as a lot of non-​Western music, such as the Arabic taqsim, do not have a regular beat.8 I still want to maintain though that such pieces are rhythmical: the duration of each note is not completely aleatory; even if the temporal organization is minimal, the possibility to experience this organization grounds rhythmic experience. Crucially here is Hasty’s point (see Chapter 15 in this volume), that meter is also experienced and, as such, needs to be included in the study of rhythm as lived. It is mistaken, Hasty argues, to consider that meter is an unfelt, objective division in the score. As claimed below, beat induction does provide a feeling of the beat. The close interaction between rhythm and meter is particularly clear when examining the role of anticipation in rhythmic experience. Paul Fraisse writes that we say that there is rhythm when we can predict on the basis of what is perceived, or, in other words, when we can anticipate what will follow.9

The listener’s faculty to anticipate the sounds that will be heard depends on a relatively coherent rhythmic structure (and often includes a relatively stable beat). Admittedly, music plays with these forms of expectation, e.g., with syncopation. Anticipation occurs at various levels and can have a shorter or longer time-​lapse. Edward Large and Mari Riess Jones’s study claims that anticipation plays a central role in the perception of rhythm.10 They argue that a periodic pulse affords anticipation of when the next notes are likely to occur. Central to their theory—​ the dynamic attending theory—​is the role of entrainment. Entrainment happens when two or more autonomous rhythms interact, e.g., the human circadian rhythm entraining to the twenty-​four-​hour cycle of light and dark. In music, entrainment occurs for example when musicians play together in time.11 Large and Jones focus

7 Brown and Fabbri, “La Sperimentazione Ritmica,” 143.

8 The Arabic taqsim may have an ostinato pedal in a passage but would most often be ametrical. 9 Fraisse, “Rhythm and Tempo,” 153.

10 Large and Jones, “Dynamics of Attending.” 11 Clayton, “Entrainment, Ethnography.”

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on the entrainment between brain processes and music, more specifically between neural oscillators (called “attending rhythms”), and the periodicity in the music, i.e., beats and meter. Beats, however, are rarely isochronous; the interval between each beat may vary slightly. Attending rhythm must thus be capable of adapting itself to such variations. Large and Jones’ study points out that attending rhythm can be “tuned,” i.e., it is able to take into account the temporal alterations in the external stimuli.12 Their research suggests that tone grouping is facilitated by an accurate perception of strong and weak beats. In particular, the listener’s attention is more acute at strong metric positions. Entrainment to the beats thus facilitates the expectations one has with regards to rhythm: the beginning of a new rhythmic pattern, for instance, is expected to fall on the strong metric position. Entrainment to the beat can also be manifest in the synchronization of one’s body parts with the music, such as foot tapping.13 In such cases, the body movement occurs at the same time as the sound: stimulus and response are simultaneous. Fraisse emphasizes that this phenomenon is possible “only if the motor command is anticipated in regard to the moment when the stimulus is produced.”14 More precisely, the signal for the response is not the stimulus but the temporal interval between successive signals. Without anticipation of the sound stimuli to be heard, synchronization would not be possible. Fraisse stresses that synchronization is established very quickly, after the second or third sound. This means that it relies at most on short-​term memory (of the interval time between the sounds) and that the expectation process concerns quasi-​immediate events.15 Fraisse adds that synchronization can occur when the interval between two sound stimuli ranges from 200 to 1800ms, and it is most accurate for intervals from 400 to 800ms.16 Rhythmic anticipation is also crucial when one engages with the music, as in the case of dance and groove. Someone familiar with Chuck Berry’s “Johnny B. Goode” is likely to anticipate the development of the first succession of quavers running over five bars on a quick tempo. The bodily movement may follow this unfolding of the notes. Admittedly, one’s degree of familiarity with a musical piece or a musical genre can bring more or less determinate anticipations. It appears from the above that anticipation plays a fundamental role in the experience of rhythm, and does so at various levels. Listeners may not be actively aware of their anticipation of sounds but their bodily movements suggest that there is an implicit anticipation of coming notes. The following section brings in Husserl’s framework of time-​consciousness, which I think clarifies the anticipatory character of rhythmic experience.



12 Large and Jones, “Dynamics of Attending,” 149.

13 Fraisse, “Rhythm and Tempo”; Thaut, Rhythm, Music and the Brain. 14 Fraisse, “Rhythm and Tempo,” 154.

15 Section 4 develops the notion of short-​term memory. 16 Fraisse, “Rhythm and Tempo,” 155.

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296   The Philosophy of Rhythm

3.  Husserl’s Phenomenology of Time-​Consciousness Throughout his work, Husserl was concerned with the phenomenology of time, although his arguments on the topic developed and changed. Toine Kortooms identifies three main stages of Husserl’s thinking about time-​consciousness. The first stage corresponds to the fourth part of Husserl’s 1904–​5 lecture course; the second stage is mainly developed in the L-​manuscripts; and the later stage is found in the C-​manuscripts.17 I largely draw upon the second stage, notably the L-​manuscripts or Bernau manuscripts, named after the location in which they were written. Here, for the first time, the concept of protention becomes important. In addition, the dynamic account of the experience of time-​consciousness is particularly developed, as we will see. I also rely on Husserl’s 1904–​5 lectures and his Analysis Concerning Passive and Active Synthesis (1918–​26).

3.1  Retention, Primal-​Impression, and Protention One must suspend belief in objective time (e.g., the divisions between hours and minutes) in order to concentrate on the subjective apprehension of time, i.e., how time appears in experience. Husserl introduces the notions of retention, primal-​ impression, and protention to characterize the living present, i.e., the constitution of experience at a certain time:18 Perception is a process of streaming from phase to phase . . . In each phase we have primordial impression, retention and protention, and unity arises in this progression by the protention of each phase being fulfilled through the primordial impression of the phase that is continuously contiguous to it.19

It is important to note that these three phases do not occur successively in a temporal horizontal line. Rather, the Now is continuously colored by the retained perception of the just-​past and an openness towards what is just-​about-​to-​come. Thus retention and protention are simultaneous with the primal-​impression. In this continuously dynamic process, retention constantly colors the primal-​impression and partly shapes the protention itself, which in turn impacts on the new primal-​ impression as soon as it is fulfilled.

17 Kortooms, Phenomenology of Time, xiii–​iv. 18 The term “living present” (lebendige Gegenwart) is introduced in the C-​manuscripts. It is understood as a flowing present and replaces Husserl’s earlier term “primal stream.” It encompasses the phases of retention, primal-​impression and protention. 19 Lectures on Transcendental Logic, 107. Gallagher, “Phenomenology of Temporality,” 137, notes that Husserl was here influenced by William James’ concept of the specious present in his Principles of Psychology.

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Bp

Cp

Dp

A

B

C

D

Ar

Br

Cr

Dr

Ar’

Figure 18.1  Husserl’s structure of time-​consciousness

Husserl’s favorite example is that of listening to a melody.20 A  melody, like a rhythmic pattern, which it also involves, is a structure that is extended in time. To perceive its unity, each note must be heard in relation to the past and the coming ones. Husserl stresses that retention, primal-​impression, and protention allow for the creation of continuity and motion in sounds. Figure 18.1, borrowed from James Mensch,21 is useful in characterizing the relation between the three phases of the listener’s perception of music. The horizontal line corresponds to the continuum of perception. The vertical lines indicate the listener’s apprehension of temporal relations at each moment. For instance, the now-​point C is not experienced alone. The now-​point C is combined with the retention of B (Br), the more remote retention of A (Ar’), and the protention (short-​term anticipation) of D. The diagram shows that A does not disappear immediately but turns into Ar, then Ar’, and so on and so forth. Ar’ is a retention of a retention. A past note then fades away, while losing some of its vividness, as it dies out into the past. Our grasp of the just-​past tones gets weaker and weaker. Husserl spent more time developing the concept of retention than that of protention—​although in two of his Lectures on Transcendental Logic he insists on the crucial importance of protention.22 There is an important asymmetry between the two notions. Retentions are fulfilled intentions whose content has already been given. In contrast, protentions are unfulfilled intentions toward what is just about to come: their content increases in vividness as we get closer to the event. Husserl talks about “protentional continuity” or “directedness-​ahead.”23 This means that a constant intention towards what is about to be heard allows for the perception of

20 Husserl, Internal Time, 24–​5.

21 Mensch, “Husserl’s Conception.”

22 Husserl, Lectures on Transcendental Logic, 106–​21.

23 Lectures on Transcendental Logic, 116.

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298   The Philosophy of Rhythm continuity and change. Protention corresponds to the consciousness that there is a future continuity of tone phases, i.e., the consciousness that the music will carry on, at least in what is just about to come. Protentions are not necessarily devoid of content, but their degree of clarity varies. The following quote sheds light on the role of retention in shaping protentions: The further an event progresses, the more it offers in itself for more differentiated protentions, ‘the style of the past is projected into the future.’24

The more retentions there are, the more precise the protentions can get. If a rhythmic pattern has been unfolding for a couple of bars and has a predictable structure (such as the succession of three quavers played together with six semi-​ quavers in the opening of Chopin’s “Ballade No. 4”), the short-​term anticipations can have a better defined content. Husserl adds that any experience has a double intentionality. The term “intentionality” relates to the awareness of something, which is most often implicit: one does not reflect upon it. Any experience is the experience of an object, an event, etc., and the subject’s thought is directed towards this object or event. In the case of listening to a melody, one is aware of the melody itself. At the same time, however, one is also aware of one’s ongoing experience of that melody (see Section 4.2). The retention is not just the retention of the past-​note, but one also retains the just-​ past experience of this note. My experience thus has this temporal structure, which enables me to be aware both of the melody—​i.e., of temporally extended units—​and of my experience of this melody. Put differently, there is an implicit awareness that I am the subject undergoing the experience. This double-​intentionality also applies to protentions. While I can protend toward the notes which are about to be heard there is an implicit anticipatory sense that I will be the subject listening to these notes.25 Husserl’s purpose is thus two-​fold: to account for the experience of temporally extended objects and also to account for the experience of one’s ongoing stream of experiences.

3.2  Distinguishing Retention and Recollection, Protention and Expectation As stressed above, retentions and protentions are tied with primal-​impressions. They are part of a living present. These moments are not subject to our active contribution; they are involuntary and passive. Recollection and expectation differ considerably from retention and protention. They are not part of the perceptual experience. Recollection concerns events which fell out of the present experience;

24 Husserl, Bernau manuscripts (1917–​18), 20, cited in Kortooms, Phenomenology of Time, 178. 25 Gallagher and Zahavi, The Phenomenological Mind, 88.

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they are not in the just-​past but in a more remote past. Likewise, expectations are driven toward moments in a more distant future than just-​about-​to-​occur events. Husserl introduces the term “representation” (Vergegenwärtigung) to characterize how a past event appears in consciousness.26 Because recollection has lost the vividness of the just-​past, it requires that one brings this event to consciousness, thus reconstructing—​or “representing”—​it. In the L-​manuscripts, Husserl underlines that the structure retention/​primal-​ impression/​protention remains. An event is represented in relation to what was in the living present the just-​past and the just-​about-​to-​come. In other words, a recollection involves the memory of an event as rooted within a succession. Kortooms writes: In the original process, a unity has developed on the basis of retentions and protentions, for example in the unity of the melody that is heard, and this plays a role in the reproduction of the original process in recollection.27

The recollection of a past note thus involves, for instance, the representation, the awareness of the position of this note as part of a rhythmic pattern. Husserl does not expand much on the notion of expectation. Although it is unfulfilled like protentions, it does not structure the present experience the way protentions do. Familiarity with a musical piece may offer richer expectations, as in the case of the listener who anticipates the final chords of a passage. Following this examination of Husserlian time-​consciousness, the next section integrates the framework to rhythmic experience.

4.  Rhythm and Temporal Consciousness 4.1  Dynamic Process To reiterate, Husserl’s analysis does not say much about the experience of rhythm, given the ubiquity of the experiences that are grounded on the temporal structure of consciousness. But there are crucial aspects of his analysis that a phenomenology of rhythm should take into account. In particular, Husserl’s theory sheds light on the interaction between short-​term memory and short-​term anticipations. What is pervasive in the perception of rhythm is not just the anticipatory aspect but the full intrinsic temporality of the process. To clarify, the anticipation of when the next note or the next rhythmic pattern will be heard does not depend solely on the

26 Cited by Kortooms, Phenomenology of Time, 68, drawing from Husserl’s Nachlass (a manuscript on “Phantasy, Mental Images, and Memory”). 27 Kortooms, Phenomenology of Time, 199.

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300   The Philosophy of Rhythm anticipation of the listener, but the anticipation itself is shaped by the short-​term memory of the past notes or past rhythmic pattern. Let us first develop what short-​memory is and why I am relating this concept to Husserl’s notion of retention. Memory consists of three phases: echoic memory and early processing; short-​term memory; and long-​term memory. Each of these phases has a different time-​scale, although they may sometimes slightly overlap. Echoic memory usually fades away in less than a second: during this phase, the acoustical features of sounds, e.g., frequencies and timbre, are processed in the brain and grouped together to form coherent events.28 Short-​term memory lasts on average 3–​5 seconds. The information then gradually fall into long-​term memory. Bob Snyder writes that short-​term memory is the “memory of the immediate past.”29 He adds that it plays an essential role in perceiving duration. Long-​term memory falls beyond the 3–​5 seconds of short-​term memory. At this point, the events are not immediately present to consciousness but can be experienced only in retrospect: they must be “recollected.”30 Snyder’s terminology seems to echo Husserl’s, and the similarity requires further examination. Snyder stresses that short-​term memory is tied up with present experience, being “immediately available to conscious awareness at any given time.”31 He adds: Each frame persists for a time, fades, and is continuously related to others coming immediately after it while retaining its proper time order. At the same time, new memory and experiences are almost always fading in. In this way, separate ‘chunks’ of experience are integrated into an ongoing, unified world.32

Husserl’s framework is well suited for making sense of these processes. Information in short-​term memory is retained in the present experience, enabling the experience to be “unified,” as Snyder writes. As soon as a current moment falls into short-​ term memory, it fades away to then fall into long-​term memory. When it is no longer part of the just-​past, it must be “recollected” (a term used both by Husserl and Snyder). When we are listening to a whole musical piece, we can also make sense of the connections between certain passages—​e.g., echoes and modulations of a particular motif—​by having events coming back into awareness from the long-​ term memory.33

28 Snyder, Music and Memory, 48. 29 Snyder, Music and Memory. 30 Snyder, Music and Memory, 69. 31 Snyder, Music and Memory, 161. 32 Snyder, Music and Memory. 33 Snyder draws a distinction between voluntary recollection and spontaneous awareness of events/​objects from long-​term memory. Recollected memories require the voluntary bringing-​back-​into-​awareness of the subject. He distinguishes voluntary recollection from automatic reminding occurring from environmental cues, and also from recognition where an environmental event acts as its own cue: Snyder, Music and Memory, 70.

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Snyder argues that rhythm is perceived thanks to the role of short-​term memory: The length of short-​term memory is important in the definition of rhythm because to form a pattern, the component events of a rhythm must seem directly connected.34

Sequences of events within short-​term memory are perceived as being in the present and as forming patterns which can be integrated and experienced in their entirety.35 Husserl’s analysis illuminates the relation between just-​past events and the ones that are just about to come. It is not just the role of short-​term memory which is crucial, as Snyder suggests, but the full intrinsic temporality of the experience: short-​term memory is integrated to the anticipation of the sounds. Listeners experience rhythm because they can retain the notes and also anticipate the ones in the quasi-​immediate future. Unexpected rhythmic patterns, a sudden change in the tempo, etc., can occur, but Husserl’s analysis seems able to incorporate such unexpected events. As Lanei Rodenmeyer writes, this new situation will not be apprehended as fulfilled until it is part of retention, when the interrelation of retention and protention will once again allow me to form protentions towards the continuance of this new situation.36

Unexpected events then fall into retention and when they are retentions (and retentions of retentions etc., as Figure 18.1 in Section 3 indicates), they shape new protentions. To reiterate, the experience of every musical aspect—​melody, tone, rhythm—​is experienced within this temporal framework. Why develop Husserl’s argument specifically with regard to rhythm then? Husserl’s framework applies at all levels of rhythmic anticipation, mentioned in Section 2. It is particularly pertinent when we consider the listener’s bodily engagement with rhythm. Part of the process is enabled, I think, by the fact that the listener’s bodily movements have the same intrinsic temporality.

4.2  Rhythmic Experience, Time, and Bodily Movements Rhythm as lived often entails a bodily engagement on the part of the listener.37 Subjects may sway their head, tap their foot, or sway their whole body. The suggestion is that rhythm as lived encompasses both the perception of the musical rhythm 34 Snyder, Music and Memory, 70. 35 Snyder, Music and Memory, 70. 36 Rodemeyer, “Theory of Time-​Consciousness,” 139. 37 Bodily engagement, of course, also occurs on the part of the performer, an element that would be extremely interesting to develop, but this would extend the scope of this chapter.

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302   The Philosophy of Rhythm and a bodily awareness. There are different degrees of self-​awareness. For Husserl and later phenomenologists, Merleau-​Ponty in particular, there is always a minimal awareness of oneself. This minimal awareness corresponds to a pre-​reflective sense of mineness, also termed ipseity.38 “Pre-​reflective” here means that one’s sense of self is not explicitly posited as an I: the sense of self remains tacit and non-​ thematic. This ipseity is not additional to an experience, as if this could be taken away without altering the experience itself: rather, it is intrinsic to any experience. This corresponds to the double-​intentionality mentioned in Section 3. The perception of music is also accompanied by a tacit sense of selfhood, i.e., that I am the subject undergoing the experience. Husserl emphasizes the role of kinesthesis in any experience. My perception of the environment is structured by the way I orientate or move my body. I am constantly (pre-​reflectively) adjusting my body in relation to the surroundings. My eyes may focus on an object, which may involve a movement of the head. My posture may change if I am following the movement of an object. In the case of rhythmic perception, listeners are most often engaging with the music with their body. Movements such as foot tapping most often remain pre-​reflective, staying in the background of the experience as the listener attends to the rhythm. Joona Taipale points out that there are different levels of bodily awareness.39 Breathing and digestion are part of a primal sense of bodily awareness. When kinestheses are freely executed, such as foot tapping, jumping, swaying of the head, we talk of agency. If body movements are habitual (the activity remains implicit), as in the case of walking, which is a practical skill that remains implicit in the activity, the movements are “passively active.”40 This seems to correspond to foot tapping: subjects most often perform this movement habitually when they listen to music. This is something they do, but such an activity remains implicit. On the other hand, more full-​fledged movements, such as swaying one’s whole body when listening to a rhythm, may give a stronger sense of bodily-​awareness. These movements are not habitual the way foot tapping may be. This kind of movement may be accompanied by a slightly slower breathing and movements of the foot: ipseity, “passively active,” and active agency are not mutually exclusive, but they correspond to different modes of self-​awareness. These movements are also temporal. Gallagher stresses that temporality is found in all bodily movements and actions and that it manifests itself at the sub-​personal and at the personal levels.41 In the case of bodily synchronization to a beat, foot tapping along to the music requires a (pre-​reflective) retention of the initiation of the movement as well as an orientation toward the complete realization of this movement. What is interesting is that the temporal structure of this bodily movement interacts with the temporal structure of the music (in this case the beat). The anticipation of the body movement is grounded on the anticipation of the coming

38 Taipale, Phenomenology and Embodiment, 23.

39 Taipale, Phenomenology and Embodiment,  55–​9. 40 Taipale, Phenomenology and Embodiment, 57.

41 Gallagher, “Phenomenology of Temporality,” 142.

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beat. If the beat is late, the body needs to readjust itself as this late beat impacts on the bodily anticipation one had. The anticipation of the completion of the movement (raise the foot and finally hit the ground) corresponds to the occurrence of the anticipated beat. If the beat fails to occur at the expected time, then the bodily temporal structure is in asynchrony with the music and needs to readapt itself. Tiger Roholt’s quote is particularly pertinent: While moving to a pulse, late eighth notes are experienced—​not as late to a specific degree, not as so many instances of an ‘eighth note’—​but as pulling against the regularity of the movement of