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Thought and Play in Musical Rhythm

i Thought and Play in Musical Rhythm

Asi A n, Afric A n, A nd Euro- Am E ric A n P E rs PE ctiv E s

Edited by Richard K. Wolf, Stephen Blum, and Christopher Hasty

1

Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries.

Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America.

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Paperback printed by Marquis, Canada Hardback printed by Bridgeport National Bindery, Inc., United States of America

i Contents

List of Figures and Tables vii

Preface xiii

List of Contributors xv

About the Companion Website xvii

Introduction 1

Richard K. Wolf, Stephen Blum, and Christopher Hasty

1. Thinking With and About Rhythm 20

Christopher Hasty

2. Formative Processes of Durational Projection in “Free Rhythm” World Music 55

John Roeder

3. Meter and Rhythm in the Sung Poetry of Iranian Khorasan 75

Stephen Blum

4. An Approach to Musical Rhythm in Agbadza 100

David Locke

5. Rhythm and the Physical 146

Eugene Montague

6. Modern Drum Solos Over Ostinatos 174

Fernando Benadon

7. Temporal and Density Flow in Javanese Gamelan 196

Sumarsam

8. Layers and Elasticity in the Rhythm of Noh Songs: “Taking Komi” and Its Social Background 212

Takanori Fujita

9. Rhythmic Metamorphoses: Botanical Process Models on the Atlas Mountains of Morocco 232

Miriam Rovsing Olsen

10. Mapping a Rhythmic Revolution Through Eighteenth- and Nineteenth- Century Sources on Rhythm and Drumming in North India 253

James Kippen

11. Time Changes: Heterometric Music in South Asia 273

Richard Widdess

12. “Rhythm,” “Beat,” and “Freedom” in South Asian Musical Traditions 314

Richard K. Wolf

13. New Music—New Rhythm 337

Christopher Hasty

Glossary 381

Bibliography 393

Index 415

i

Figures and Tables

Figures

1.1. From a) two to b) three claps and the possibility c) of two larger events. 36

1.2. Joseph Haydn, String Quartet Op. 76 no. 4 (“Sunrise”), second movement, bs. 1–16. 39

1.3. Josquin des Prez, Missa pange lingua, the opening of Pleni sunt coeli, t.1–24. 42

1.4. Josquin des Prez, Missa pange lingua, the opening of Pleni sunt coeli, repetitions in altus, t.13–23. 46

2.1. Some temporal sensations associated with durational projection and realization. Adapted from Hasty, Meter as Rhythm (1997, 87–89). 57

2.2. Projective analysis of the introduction (darāmad) to the classical Persian chant (āvāz) of an extract from Bīdād from dastgāh homāyun, sung by Afsāne Ziā’i with Hoseyn Omumi, ney. 58

2.3. Projective analysis of the first seven cycles of “Flute,” performed by Zinzir, tatarore. 63

2.4. Two possible kinds of realized durational projections in “Flute” (under the assumption of parallelism). 64

2.5: Projective analysis of the opening (0:07–0:55) of the ālāp on rāga PūriyāKalyān performed by Budhaditya Mukherjee, sitar. Transcribed by Richard Widdess, adapted and annotated by John Roeder. 68

3.1. One quantitative poetic meter as represented in (a) the system of Arabic and Persian prosody, and (b) a simplified notation of attacks and durations in rhythmic cycles, which can also be used for poetic meters. 79

3.2. Moḥammad Ḥoseyn Yegāneh (d. 1992) singing a Persian quatrain to Šāh Xaṭā’i. 81

3.3. Initial quatrain of a monājāt (an intimate communication with God). 82

3.4. The guše of Šāh Xaṭā’i in the dastgāh of Navā, as sung by Maḥmud Karimi. 83

3.5. Quatrain from the story of Šāh Esmā‘il, sung by Moxtār Zambilbāf, 1972 (AWM RL 16245). 85

3.6. Quatrain from the story of Šāh Esmā‘il, sung by Moxtār Zambilbāf, 1972 (AWM RL 16245). 85

3.7. Two lines from Ferdowsi’s Šāh-nāma, sung to a 12-beat cycle by Ḥāj Ḥoseyn Xān Yāvari (age ca. 60) of Xarv Olyā (AWM RL 16234). 88

3.8 One verse of a fable from the Būstān of Sa‘di as sung by two naqqāls: (a) Ṣādeq ‘Ali Šāh (AWM RL 16211, and Naqqāli in Northern Khorāsān, track 6, 4:23–4:35); (b) Moḥammad Ḥasan Naqqāl (AWM RL 16225). 89

3.9. Two verses from the Šāh Nāma, sung by Sayyed Ḥasan Naqib Zāde (age 43), the moršed of a zur-xāna (men’s athletic club) in Sabzevār, 1995. 90

3.10. The same verses as in Figure 3.9, sung by Ḥasan Salaḥšur (age 18), a naqqāl active in tea houses of Bojnurd, 1969 (AWM RL 16208). 91

4.1. Rhythm of Agbadza dance movement. 103

4.2. Resultant rhythm of bell phrase with four- feel and six- feel beats. 109

4.3. Support drum function: articulation of offbeats. 110

4.4. Support drum phrase: accentuation in the metric matrix. 111

4.5. Music setting of drum language of the time parts. 112

4.6. Response drum themes for items 1–25. 114

4.7. Response theme, item 24: motion and accentuation “in four” and “in six.” 119

4.8. Lead drum: key to notation of strokes. 120

4.9. Lead drum themes for items 1–25. 121

4.10. Lead drum form: excerpt from complete score of item 1. 126

4.11. Modes of anhemitonic pentatonic scale. 131

4.12. Modes of hemitonic pentatonic scales. 132

4.13. Song-drum affinity in item 19: time-point 1.2. 137

4.14. Song: drum interaction in item 15. 139

4.15. Song and drums in item 16: cascading entrances, reinforcement of lexical meaning. 140

5.1. Eight ways to notate the son clavé rhythm, after Toussaint (2005). 149

5.2. A score of the first page of “Pianistes” from Saint- Saëns, Le carnaval des animaux. 153

5.3. A rhythmic analysis of the Piano I part at the opening of “Pianistes.” 154

5.4. A gestural-rhythmic analysis of the opening of Chopin, Étude in C major, Op. 10 no. 1. 158

5.5. Spans of the right hand in Chopin’s etude. 159

5.6. Calculating the stretch of each handspan in the basic instrumental gesture of Chopin, Op. 10 no. 1. 160

5.7. Stretching the hand: relative stretches of each of the three handspans A, B, and C in the first three phrases of Chopin, Op. 10 no. 1, measures 1–8, 9–16, and 17–24. 161

5.8. Three- voice counterpoint (bass line plus span C, the topmost two in Chopin, Op. 10 no. 1, measures 1–8). 162

5.9. A diagrammatic representation of the drummer’s gestures in a typical measure of “Straight Edge” by Minor Threat. 164

5.10. An interpretation of the metrical structure of the first four lines of “Straight Edge.” 166

5.11. An interpretation of the metrical structure of Mackaye’s performance of “Straight Edge.” 166

5.12. An interpretation of the durational structures of Mackaye’s performance of “Straight Edge.” 167

5.13. A rough alignment of the drum and vocal rhythms in the opening lines of “Straight Edge.” 167

5.14. A general analysis of the rhythmic relationships between voice and drums in the first section of “Straight Edge.” 168

6.1. Configurations in “synchronization space” for three- and two-element groups. Elements inside a circle are in synchrony with each other; d = drums, m = meter, o = ostinato. 175

6.2. Steve Gadd, “Quartet No. 2, Part II” (9:14). 177

6.3. Trilok Gurtu, “Belo Horizonte” (3:49). 181

6.4. Gurtu’s accent placements in the measure cycle. 182

6.5. Dave Weckl, “Master Plan” (3:12). 183

6.6. Vinnie Colaiuta, “Live at Catalina’s” (2:51). 184

6.7a–b. Vinnie Colaiuta, “Live at Catalina’s” (2:11). 185

6.8a–d. Jojo Mayer, “Jabon” (5:09, 5:19, 5:56, 6:11). 187

6.9. Gadd, clave solo (2:21). 189

6.10. Ostinato (top) vs. polymeter (staggered 2+3 pairs) vs. meter (vertical lines) in the first five measures of Figure 6.9. 191

6.11. Gadd’s 15- subdivision group and two “rational” approximations. 193

6.12. Drum notation key. 194

7.1a. A song for accompanying a deer dance: the original song. 199

7.1b. A song for accompanying a deer dance: Sindusawarno’s version of the melodic skeleton of the song. 200

7.2a. Example of the melodies of elaborating instruments (rebab, gender, bonang) and kendhang (drum) in irama dadi. 205

7.2b. Example of the melodies of elaborating instruments (rebab, gender, bonang) and kendhang (drum) in irama wilet: gendèr rangkep, bonang imbal, kendhang ciblon. 205

8.1. Original configuration of poetic syllables in hira-nori rhythm (a song from Noh Ataka). 213

8.2. Su-utai performed by amateur singers, at the amateur recital held on August 9, 2009, at the Noh theater in Otsu city. 215

8.3a. The libretto notation of a song in Ataka by Kita school published in 1924. 216

8.3b. Singer’s rhythm image of a song in Ataka. At the syllables with accent signs (⋏), choral singers have to extend the syllables to go with drumming pattern. 217

8.4a. Mitsuji pattern of o- tsuzumi and ko- tsuzumi. 218

8.4b. Tsuzuke pattern by o- tsuzumi and ko- tsuzumi. 218

Figures and Tables x i

8.5a. “Waving” modification of a drumming pattern in the dance music kakeri. 219

8.5b. “Contraction” of beats 2 and 4 in the entrance music shidai. 220

8.5c. Mitsuji pattern in “blur” modification, norazu. 221

8.6. Analysis of a hira-nori song in Ataka. 223

8.7. Alternation model of synchronization and detachment in a passage. 226

8.8. An amateur woman dancing with professional musicians at the back and choral singers at the side of the stage July 31, 2011, at the Noh theater in Otsu city. 228

9.1. The beginning of amarg sung by a soloist. 249

9.2. Amḫllf. The beginning of the two female choirs. 249

9.3. Amḫllf. Introduction of the first verse in the female choirs. 249

9.4. Amḫllf. Beginning of the drum ming and the dancing. 250

9.5. Tamssust. The same tune as before is sung alternately by the two choirs. 250

9.6. Tamssust. Rhythmic transition in the percussion instruments. 250

9.7. Tamssust. Introduction of a new melody. 251

11.1. Dāphā song He Śiva Bhairava as sung by the Dattātreya and Bhairavnāth temple dāphā groups, Bhaktapur, Nepal. 282

11.2. Singers of the Bhairavnāth temple dāphā group singing He Śiva Bhairava at the start of the Biskāḥ festival. The chariot of Bhairav can be seen in the background. Bhaktapur, Nepal, 2003. 283

11.3. Changes of metrical cycle in dāphā song He Śiva Bhairava. 285

11.4. Dāphā song Girīhe nandinī as sung by the Dattātreya temple dāphā group, Bhaktapur, Nepal. 287

11.5. The Dattātreya temple dāphā group, Bhaktapur, Nepal, 2012. 289

11.6. Proportional structure in dāphā song Girīhe nandinī. 290

11.7. Maṇḍala of Cakrasaṃvara. Painting on cloth, Nepal, c. 1100. 293

11.8. Singers making time-keeping gestures while performing Mahārudra Gvārā. Ikhālakhu Nekujātrā and Matayājātrā group, Patan, Nepal, 2011. 295

11.9. Proportional structure in Mahārudra Gvārā. 296

11.10. Structure of pāṇikā song. 299

11.11. The Ikhālakhu Nekujātrā and Matayājātrā group, Patan, Nepal, 2011. 306

11.12. Page from a modern notation-book showing heterometric structure of a gvārā song (Śākya 1995). 309

12.1. Ādi tāla with 2 kaḷā. 319

12.2. 12.2a: Tiruganāṭ basic version on tabaṭk, “one-beat” (or aṛy).

12.2b: Tiruganāṭ variation on tabaṭk, “two-beat” (eyṛ aṛy). 12.2c: Tiruganāṭ variation on tabaṭk, “three-beat” (mūṇḍ aṛy). 322

12.3. 12.3a: Do mār. 12.3b: Tīn mār. 324

12.4. The kalmah, a beat pattern corresponding to the Muslim statement of faith in one god. 329

12.5. Approximate oscillation rhythm on svara ma in nīlāmbari. 334

12.6. Approximate oscillation rhythm on svara ma in śankarābharaṇam. 334

Figures and Tables j xi

13.1a–b. Scheme for simple durational projection. 340

13.2a–e. Schemes for compound projections. 342

13.3. Scheme for triple unequal projection (deferral). 344

13.4. Pierre Boulez, Le Marteau sans maître, no. 9, “bel edifice et les pressentiments” double bs. 1–4. 349

13.5. Anton von Webern, Six Bagatelles for String Quartet, Op. 9 no. 6, bars 1–6. 350

13.6a–b. Lewin’s representation of a) Bamberger’s stimulus and b) her subjects’ interpretation (modified). 351

13.7a–b. Toru Takemitsu, Rain Tree, a) second section bs.1–8 (bottom of page 6); b) interpretation of figure X. 352

13.8. Salvatore Sciarrino, Muro d’orizzonte bs. 13–22. 355

13.9. Salvatore Sciarrino, Muro d’orizzonte bs. 1–12. 357

13.10. Toru Takemitsu, Rain Tree, first section bs. 30–45 (page 5 of score). 360

13.11. Toru Takemitsu, Rain Tree, opening bs. 1–29. 363

13.12. Morton Feldman, Spring of Chosroes bs. 1–7. 367

13.13. Morton Feldman, Crippled Symmetry first system (bs. 1–9). 369

13.14. Morton Feldman, De Kooning first system. 370

13.15. Morton Feldman, De Kooning final system. 372

Tables

2.1. Distribution of ratios of successive durations marked by grace-notegroup onsets. 71

2.2. Distribution of ratios of successive durations marked by long-note onsets. 72

4.1. Agbadza dance cadence “in four.” 104

4.2. Agbadza dance cadence “in six.” 104

4.3. Supporting instruments: implicit Ewe texts. 107

4.4. Agbadza kidi phrases: patterns of bounce and press strokes. 117

4.5. Lead drum: palette of strokes. 120

4.6. Agbadza songs: musical form, call-and-response, and duration in bell cycles. 133

4.7. Agbadza songs: nuanced form of melody with call-and-response. 134

5.1. The lyrics of Minor Threat’s “Straight Edge.” 166

9.1. Temporal development of a “womens’ aḥwaš”: the order of contributions to the performance. 246

9.2. The sung poetry reconstructed in its literary form from the performance of the aḥwaš. 247

9.3. The sung poetry transcribed as expressed in performance. 248

10.1. The three categories of tāl in the Sharḥ-i risāla-yi qawā’id-i tabla. 263

11.1. Levels of pulsation in Tīntāl (cardinality 16). 275

11.2. Levels of pulsation in Jhaptāl (cardinality 10). 276

11.3. Text and translation of dāphā song He Śiva Bhairava. 284

Figures and Tables

11.4. Text and translation of dāphā song Girīhe nandinī. 288

11.5. Proportional structure in Girīhe nandinī. 291

11.6. Proportional structure in Mahārudra Gvārā. 297

12.1. Beat structure of cāls performed by ḍhol group in Hyderabad, Sindh, Pakistan. 325

Preface

Earlier versions of the essays collected here were presented at a Conference on Rhythm held at Harvard University, March 3 and 4, 2012. The conference was planned in conjunction with a seminar on cross- cultural rhythm taught by Richard Wolf and Christopher Hasty during the spring semester of 2012; Stephen Blum was also involved in organizing the conference. We are grateful for financial support for the conference provided by the Harvard University Department of Music, the Provostial Fund for Arts and Humanities at Harvard, the Reischauer Institute of Japanese Studies at Harvard University, and the South Asia Initiative (now South Asia Institute) at Harvard.

We first conceived of the introduction as a conversation among the three of us, which we began to draft the day after the conference. When that plan proved unworkable, Richard Wolf made an outline of six topics that seemed to draw together themes from all the chapters, and these served as the basis of the introduction as it appears here. The opening section and the treatment of “Representations” and “Qualities” are Wolf’s work; Blum wrote the sections on “Units” and “Interactions”; and Hasty those on “Periodicity and Cycle” and “Meter.” Some topics are necessarily discussed in more than one section, just as the three of us are continually returning to them in our conversations.

We would like to thank the Harvard University Music Department for support during all stages of this project, and particularly Lesley Bannatyne, who assisted preparing the final manuscript.

RKW, SB, CFH

Contributors

Fernando Benadon is Professor of Music at American University.

Stephen Blum is Professor of Music Emeritus at the City University of New York Graduate Center.

Takanori Fujita is Professor of Ethnomusicology at the Research Centre for Japanese Traditional Music at Kyoto City University of Arts.

Christopher Hasty is Walter W. Naumburg Professor of Music at Harvard University.

James Kippen is Professor of Ethnomusicology at the University of Toronto.

David Locke is Professor at the Music Department of Tufts University.

Eugene Montague is Associate Professor of Music at the George Washington University.

Miriam Rovsing Olsen is Associate Professor Emeritus of Ethnomusicology and Member of the Center for Research in Ethnomusicology (CREM-LESC) at the University of Paris Nanterre.

John Roeder is Professor at the University of British Columbia School of Music.

Sumarsam is Winslow-Kaplan Professor of Music at Wesleyan University.

Richard Widdess is Professor of Musicology at SOAS University of London.

Richard K. Wolf is Professor of Music and South Asian Studies at Harvard University.

About the Companion Website

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Thought and Play in Musical Rhythm

Introduction

Richard

K. Wolf, Stephen Blum, and Christopher Hasty

Thought and Play in Musical Rhythm seeks to explore representations, ideal types, and implicit theorizing of rhythm in relation to aspects of performance that “play”— that pull against these ideal types, resist objectification, and/or are elastic. Our aim has been to incorporate a diversity of musical traditions and scholarly approaches, embracing those of performers, music theorists, and music ethnographers. The performance dynamic implicit in “thought and play” can, with some imagination, be recast in terms of a larger dynamic in scholarly discourse on rhythm and music more generally— that between “universalizing” and “local” approaches. The former include efforts to create overarching models that accommodate the diversity of music and to gain insight into human cognition generally, as well as craft terminologies (meter, beat, etc.) that apply cross- culturally. Local, by contrast, signals attention to musical systems and practices as they are constituted in one region, however narrowly or broadly defined; attention focuses on the specifics of musical interaction, uses of language, and regional histories. Most music scholars attempt to bring out the historical and regional specificity of what they study while also contributing to general knowledge about musical process.

One of the first challenges in writing about and teaching “rhythm” is constituting rhythm as an object of study in the first place. Some concepts of rhythm rely on the presence of regular, perceivable recurrences, making possible such statements as “X is more rhythmic than Y.” When rhythm is understood as the patterning of events in time, all music has rhythm and the problem is to describe or represent rhythm when the patterning is less than obvious. The commonplace elision of two senses of the word—“rhythm” as a structural abstraction and “rhythms” as specific instance— creates another form of confusion in definition, particularly when what is meant by

“rhythms” is “drumming patterns.” The challenge of commonplace terminologies remains for the authors of this volume, who do not always agree to use terms in the same ways. For this reason, we provide a glossary highlighting not only local-language terms, but also some differences in usage for English words across the volume.

Etymologies (in various languages) have stimulated imaginative thinking about rhythm. For example, the derivation of “rhythm” from the word “to flow” in Greek supports, via the image of “waves,” intuitive ideas of rhythm as regular, yet elastic and full of movement (see also Stephen Blum’s chapter in this volume). Émile Benveniste has revealed the flaws in this etymology, pointing out that the term in question for “flow” was used at the time in Greek for the movement of a river or a stream and not for the recurrence of waves in the sea (Benveniste 1971, 281–82). Benveniste suggests that a modern sense of rhythm can be traced back in Greek at least to the time of Plato’s Socratic dialogue Philebus (4th c. b.c.e.), which draws an analogy between “intervals” in music and the timing of bodily movements, the numerical regulation of which was called “rhythm” and “measure” (Benveniste 1971, 286).

Despite its dubious historical veracity, the “wave” etymology resonates with various intuitions about rhythm shared by many writers on music and time. It may call forth the tensions between “pure duration” versus “measurable time” in Henri Bergson’s formulation (Bergson 1965 [1922], 50), “inner time” versus “outer time” in that of Alfred Schütz (1951), and time without parts versus time with parts in the Maitri Upaniṣad (6.15–15, cited in Rowell 1992b, 180). The unbroken motion of water in a wave is analogous to the continuity and absence of articulation in inner time, while the sound of each wave lapping onto a piece, boat, or segment of shoreline, creating semiperiodic attacks, may suggest a form of time measurement and division. In understanding rhythm as both a musical and cultural phenomenon, then, it is helpful to keep both operational definitions and local ideologies closely in mind.

This idea of moving among different views on rhythm could fruitfully spill over into more holistic accounts of music generally. Unfortunately, in music textbooks one commonly encounters rhythm, alongside harmony and melody, represented as an “element” of music. This fundamental act of separating rhythm from musical process is, in our opinion, detrimental to understanding the fullness of musical experience. In a similar vein, in Rhythm and Tempo Curt Sachs alludes to “pure melody”—a melody that can recur with different rhythmic settings (Sachs 1953, 18; compare with a similar move by Sindusawarno as discussed by Sumarsam in this volume). But does pure melody exist? In each and every instance melody must have a rhythmic form. Without accounting for the passage of time, “pure melody” could be no more than an ordered set of pitches— though it is hardly possible to think about “order” without invoking time or space. The point is that no actual passage in music is possible without rhythm.1 It would be equally problematic to suggest that rhythm could exist without sounding vehicles that produce sameness and difference in timbre, tone, and vertical relations (harmony, etc.). An account of rhythm that embraces musical experience requires attention to much more than the relations among abstracted points in time. It may call for analysis of attack and decay, envelope, interactions among musicians, physical

gestures overlapping parts, microtiming, silent reckoning of beats and pulses, and so forth. Africanist scholars of rhythm, accustomed to the subtleties of interaction among instrumentalists, dancers, and singers, have long recognized rhythm’s many facets— what David Locke has called “simultaneous multidimensionality.” But the musical traditions of Africa merely provide salient examples of what is more generally the case. We wish to highlight the many ways musical rhythm persists multidimensionally. A responsible account of rhythm in any one case will allude to this, while recognizing that certain kinds of reduction in complexity are inevitable in putting pen to page.

The authors of the present volume explore what rhythm is and can be across a spectrum of musical traditions. In rejecting the kind of abstraction that removes “rhythm” from musical process and experience, we nevertheless recognize that the very consideration of rhythm as a topic involves a set of terminologies, methodologies, assumptions, efforts at generalizing, and yes, abstracting that point toward a music- field- wide effort to understand rhythm better per se. In this sense, the “universalizing” writings of Justin London, Michael Tenzer, Jeff Pressing, and others who seek overarching ways of representing rhythm as part of human music-making and cognition provide useful reference points for inspiration as well as resistance. Counterposing these efforts are those of some ethnomusicologists and theorists who have elaborated theories of rhythm or time specific to one civilization, region, or culture— such scholars as Alan Merriam, Ruth Stone, Simha Arom, and Meki Nzewi for Africa; Lewis Rowell for India; Judith Becker for Indonesia; José Maceda for Southeast Asia more generally; and a host of anthropologists with regard to time in a broader range of cultural behaviors and institutions. Clifford Geertz (e.g., 1973) and Nancy Munn (e.g., 1986) provide salient examples of culturally constructed time (and space), while Alfred Gell argues against notions of different kinds of time (Gell 1992). In thematizing the universalistversus-local tension we ask the reader to question what is to be gained in emphasizing one end of the spectrum or another at any given analytical moment.

Rather than introduce the chapters one by one, we will discuss aspects of these contributions in terms of six broad topics pertinent to the universalist-local dynamic:

Representations, Units, Periodicity and Cycle, Meter, Qualities, and Interactions.

Representations

Representations of rhythm and its parts highlight this dynamic, for the choice of an analytic vocabulary shared by a scholarly community accomplishes something quite different from highlighting the terms, metaphors, or myths drawn from a particular repertoire.

Many of the discussions negotiate broad and focused views on rhythm via forms of “translation.” “Rhythm,” already multifaceted in English, may have similarly multifaceted analogues in other languages or no analogues at all. Rhythm may also play a relatively major or minor part in the way a particular repertoire is identified and

valued— whether by practitioners themselves or by broader reputation. African music has long been identified with rhythm in the popular imagination—especially in the Western world. Despite the enticing potentials of the tabla and other drums, rhythm is subordinated to melody in the world of South Asian classical music because of a longstanding ideology there favoring the voice. At a more local level, Sumarsam explains, the melodic identity of particular pieces in Javanese gamelan resides in particular levels of rhythmic texture and density (irama).

Terms such as rhythm in English, laya in Indic languages, īqā‘ in Arabic, and irama in Javanese operate synecdochically, referring to one part or aspect of a musical structure as well as to a more abstract, general idea of rhythm. The fact that performers in many traditions use some version of the English word “rhythm” does not make it a transparent term for cross- cultural analysis, but it does alert us to the kinds of translations taking place all the time when performers put musical process into words.

In understanding the regulative role of cycles, whether in Javanese gamelan (Sumarsam), folk drumming (Richard Wolf), African time-lines (Locke), or ostinatos (Fernando Benadon), as well as their hierarchical implications, we engage theories of meter, but it remains an open question as to how we translate local representations of such structures. In Indian musical studies, opinions vary on the extent to which the regulative cyclic framework of tāla ought itself to be considered as musical meter. Richard Widdess and James Kippen do allow for this equation. Taking a narrower frame of analysis: mātra in South Asian music refers to a subdivision of the tāla, a unit of a cycle. Sumarsam cites a Javanese usage of mātra (and also gatra) as meter, the ordering of alternating movements with contrasting weight. These usages pinpoint segments of contrasting length. The possibility of a mātra being akin to meter would depend on how short it is.2 If two levels of grouping exist below that of the mātra (e.g., beat and pulse), one might view it as metric in the sense developed by London (2012, 46–47).

Commonplace understandings of meter in Western classical music rely on the listener’s inference of repeating units differentiated by strong and weak beats. In Indian classical music, strong and weak beats in the music are not necessarily meant to be guided by claps in the tāla. Justin London’s “many meters hypothesis” (meter as skilled behavior involving many context- specific, expressively nuanced tempo-metrical types) takes in expressive microtiming at lower levels of the metric hierarchy and questions the dichotomy of structure- versus-expression. Hence, at different tempi and in different styles, a meter with X number of beats can vary considerably. In the case of tāla, were one to grant metric status to the structure in an ordinary sense, how might one account for different feel patterns of a single tāla? In North India, the ṭhekā allows for such variation and yields differently named tāls. In South India, one particularly common groove within the 8- count ādi tāla has its own name, deśādi, which would seem to support London’s more inclusive concept of meter, but in South India generally, groove patterns are not considered part of the definition of tāla. Beat remains a difficult concept to translate across various musical styles. Determining the placement of “beats” is essential in attempts to employ Western staff

notation, and is usually important in representing meter as well. In Locke’s analysis dance movements determine the beat, and he uses beat numbers to indicate the location of every pulse in the musical flow. This makes it possible to allude to timesignature-like representations of meter: “this piece is ‘in four.’ ” Widdess regards the beat as an isochronous division of the metric cycle while Miriam Rovsing Olsen allows for a drum pattern of 5 beats of equal or unequal length. Some nonisochronous notions of beat derive from the more fundamental idea of a “strike,” with some implication of accent within a larger structure, but not necessarily implying a regularly recurring pattern (Kippen, Wolf). The term becomes even more problematic in Japanese, when we learn that terms for beat need not refer to attacks, but also to time points to which performers attend as well as to the interval between one time point and the next (Takanori Fujita).

Representations of rhythm often involve metaphorical projections that extend beyond notation. Here we mention three: body, space, and object. For Eugene Montague, Rovsing Olsen, Widdess, and others, rhythm is the product of bodily agency. Reminiscent of Hornbostel’s early insights into African rhythm as composed of physical movements as well as sounds, Montague argues that rhythm and its notation carry traces of the physical gestures with which they were learned, and on down the line so that any pattern implicates a history of gestures. In Rovsing Olsen’s analysis, the complexity of Berber rhythmic texture arises from principles of bodily movement, “shifting/intertwining” and “trembling/restlessness.” This latter principle militates against “shifting” and is marked by a stop or jolt.

Considering the relation between attacks and pauses (or sustained durations) turns out to be fundamental to rhythmic thinking in many societies including those of South Asia (laya: Wolf, Kippen) and Java (irama: Sumarsam), and West Asia (e.g., in the rhythmic practices discussed by the Central Asian polymath Al-Fārābī in the tenth century c.e.; Sawa 2009, and Blum this volume). On a small scale, these representations of rhythm are linear. But rhythmic representations often project into space. For example, according to Locke, African teachers emphasize circular conceptions of time that tend to destabilize a single notion of beat 1 in a cycle. Yet the time-line also extends forward in virtual horizontal space—it is linear, while sustaining “vertical” relations with other parts in 3:2 proportions. One can hardly mention “projection” without taking into account Christopher Hasty’s theory of rhythm, which involves the listener or player predicting durations based on ones heard before. In thinking through the potentials of this theory, as John Roeder does in this volume, it is almost inevitable to spatialize time in the form of diagrams.

A third type of metaphorical projection relates rhythm to concrete objects, organs, or figures. Fujita, for instance, points to a rushing stream and the relation of lord to servant as prominent rhythmic metaphors in Noh. Rovsing Olsen describes models of barley and date-palm growth as fundamental to Berber rhythmic ideas. And Sumarsam notes Javanese instances of widespread tendencies to describe rhythm in relation to breath and heartbeat. This selection of metaphorical projections provides a sliding scale of relations between the universal and the particular.