『The Geometry of Musical Rhythm: What Makes a “Good” Rhythm Good?』

Godfried T. Toussaint

(2013年1月刊行,The CRC Press, Boca Raton, xviii+347 pp., ISBN: 978-1-4665-1202-3 [pbk] → 版元ページ

音楽の「リズム」をどのように可視化・体系化するかが本書の中心テーマ.本書では伝統音楽の打楽器リズムを例に挙げながら,リズム・パターンのグラフ化と分類の方法を議論する.系統推定については後半に簡単に触れられているだけだが(距離法に基づく SplitsTree),前に:archief voor stambomen -「音楽リズムの系統推定」にも書いたように,本書の著者は音楽リズムの距離と形質状態に基づく系統推定の論文:Godfried T. Toussaint, Luke Matthews, Malcolm Campbell, and Naor Brown 2012. Measuring musical rhythm similarity: Transformation versus feature-based methods. Journal of Interdisciplinary Music Studies, volume 6, issue 1, art. #12060102, pp. 23-53, spring 2012 → journal website | paper pdf [open access] をすでに発表している.この論文ではリズムの系統推定にあたって,距離法(「feature-based method」)としてはユークリッド距離とマンハッタン距離を,一方,形質状態行列については MrBayes を用いたベイズ系統推定(「transformation method」)を行なっている.結論として,音楽学における系統推定では,距離法ではなくベイズ法がすぐれていると主張する.

【目次】
Prolegomenon xi
Author xvii
Chapter 1. What Is Rhythm? 1
Chapter 2. A Steady Beat 9
Chapter 3. Timelines, Ostinatos, and Meter 13
Chapter 4. The Wooden Claves 17
Chapter 5. The Iron Bells 19
Chapter 6. The Clave Son 23
Chapter 7. Six Distinguished Rhythm Timelines 27
Chapter 8. The Distance Geometry of Rhythm 33
Chapter 9. Classification of Rhythms 39
Chapter 10. Binary and Ternary Rhythms 45
Chapter 11. The Isomorphism of Rhythm and Scale 51
Chapter 12. Binarization, Ternarization, and Quantization of Rhythms 57
Chapter 13. Syncopated Rhythms 67
  Keith’s Measure of Syncopation 70
Chapter 14. Necklaces and Bracelets 73
Chapter 15. Rhythmic Oddity 85
Chapter 16. Off-Beat Rhythms 99
Chapter 17. Rhythm Complexity 107
  Objective, Cognitive, and Performance Complexities 109
  Lempel-Ziv Complexity 117
  Cognitive Complexity of Rhythms 119
  Irregularity and the Normalized Pairwise Variability Index 120
Chapter 18. Dispersion Problems and Maximally Even Rhythms 121
Chapter 19. Euclidean Rhythms 129
Chapter 20. Leap Years: The Rhythm of the Stars 137
Chapter 21. Approximately Even Rhythms 143
Chapter 22. Rhythms and Crystallography 151
Chapter 23. Complementary Rhythms 157
Chapter 24. Radio Astronomy and Flat Rhythms 165
Chapter 25. Deep Rhythms 175
Chapter 26. Shelling Rhythms 187
Chapter 27. Phantom Rhythms 195
Chapter 28. Reflection Rhythms and Rhythmic Canons 207
Chapter 29. Toggle Rhythms 217
Chapter 30. Symmetric Rhythms 225
  Hourglass Drums and Hourglass Rhythms 233
Chapter 31. Odd Rhythms 237
Chapter 32. Other Representations of Rhythm 243
  Alternating-Hands Box Notation 243
  Spectral Notation 244
  TEDAS and Chronotonic Notation 245
Chapter 33. Rhythmic Similarity and Dissimilarity 247
Chapter 34. Regular and Irregular Rhythms 257
Chapter 35. Evolution and Phylogenesis of Musical Rhythm 265
  Guajira 271
Chapter 36. Rhythmic Combinatorics 275
Chapter 37. What Makes the Clave Son Such a Good Rhythm? 279
  Maximal Evenness 279
  Rhythmic Oddity 280
  Off-Beatness 282
  Weighted Off-Beatness 283
  Metrical Complexity 283
  Main-Beat Onsets and Closure 283
  Distinct Durations 284
  Distinct Adjacent Durations 284
  Onset-Complexity and Distinct Distances 284
  Deep Rhythms, Deepness, and Shallowness 285
  Tallness 285
  Phylogenetic Tree Centrality 286
  Mirror Symmetry 286
  Shadow Contour Isomorphism 288
Chapter 38. The Origin, Evolution, and Migration of the Clave Son 293


Epilogue 305
References 311
Index 337