Chapman and Hall/CRC
312 pages | 300 B/W Illus.
The original edition of The Geometry of Musical Rhythm was the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explained how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly disparate fields. The book also introduced the distance approach to phylogenetic analysis and illustrated its application to the study of musical rhythm. The new edition retains all of this, while also adding 100 pages, 93 figures, 225 new references, and six new chapters covering topics such as Meter and Metric Complexity, Rhythmic Grouping, Expressive Timbre and Timing in Rhythmic Performance, and Evolutionary Phylogenetic Analysis of Ancient Greek Paeonic Rhythms. In addition, further context is provided to give the reader a fuller and richer insight into the historical connections between music and mathematics.
Praise for the previous edition
"Toussaint’s Geometry presents a whirlwind tour of the world’s rhythms … For a reader interested in musical rhythm, Geometry is a great introduction to the computer science and mathematics of rhythm. For a reader interested in algorithms and mathematical reasoning, the musical focus provides compelling examples lying at the intersection of the arts and the sciences."
—William A. Sethares, Journal of Mathematics and the Arts, 2014
"… a delightful, informative, and innovative study in the geometric interpretation of rhythm. … It is a pleasure to find an author who has such good command of mathematics and music and who can explain their interconnections with such literary skill. I recommend this book wholeheartedly to every serious student of geometry and music."
—Ilhan M. Izmirli, Mathematical Reviews, March 2014
"This dynamic fluid presentation of mathematics is exactly what our undergraduate and graduate students need. … I would highly recommend this book for everyone."
—Russell Jay Hendel, MAA Reviews, May 2013
Preface to First Edition
Preface to Second Edition
1. What is Rhythm
2. Isochrony, Tempo, and Performance
3. Timelines, Ostinatos and Meter
4. The Wooden Claves
5. The Iron Bells
6. The Clave Son: A Ubiquitous Rhythm
7. Six Distinguished Rhythm Timelines
8. The Distance Geometry of Rhythm
9. Classification of Rhythms
10. Binary and Ternary Rhythms
11. The Isomorphism Between Rhythms and Scales
12. Binarization, Ternarization, and Quantization of Rhythms
13. Syncopated Rhythms
14. Necklaces and Bracelets
15. Rhythmic Oddity
16. Off-Beat Rhythms
17. Rhythm Complexity
18. Meter and Metric Complexity
19. Rhythmic Grouping
20. Dispersion Problems: Perfectly Even, Maximally Even, and Balanced Rhythms
21. Euclidean Rhythms, Euclidean Strings, and Well-Formed Rhythms
22. Lunisolar Rhythms: Leap Year Patterns
23. Almost Maximally Even Rhythms
24. Homometric Rhythms and Crystallography
25. Complementary Rhythms
26. Flat Rhythms and Radio Astronomy
27. Deep Rhythms
28. Shelling Rhythms
29. Phase Rhythms: The "Good," the "Bad," and the "Ugly"
30. Phantom Rhythms
31. Reflection Rhythms, Elastic Rhythms, and Rhythmic Canons
32. Toggle Rhythms
33. Symmetric Rhythms
34. Rhythms with an Odd Number of Pulses
35. Visualization and Representation of Rhythms
36. Rhythm Similarity and Dissimilarity
37. Grouping and Meter as Features of Rhythm Similarity
38. Regular and Irregular Rhythms
39. Evolution and Phylogenetic Analysis of Musical Rhythms
40. Rhythm Combinatorics
41. What Makes the Clave Son Such a "Good" Rhythm?
42. On the Origin, Evolution, and Migration of the Clave Son