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The Geometry of Musical Rhythm 2nd Edition by Godfried Toussaint 0815370970 9780815370970

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Product details:

ISBN 10: 0815370970
ISBN 13: 9780815370970
Author: Godfried T. Toussaint
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 evolution 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.

Table of contents:

CHAPTER 1 What is Rhythm?

CHAPTER 2 Isochrony, Tempo, and Performance

CHAPTER 3 Timelines, Ostinatos, and Meter

CHAPTER 4 The Wooden Claves

CHAPTER 5 The Iron Bells

CHAPTER 6 The Clave Son: A Ubiquitous Rhythm

CHAPTER 7 Six Distinguished Rhythm Timelines

CHAPTER 8 The Distance Geometry of Rhythm

CHAPTER 9 Classification of Rhythms

CHAPTER 10 Binary and Ternary Rhythms

CHAPTER 11 The Isomorphism Between Rhythms and Scales

CHAPTER 12 Binarization, Ternarization, and Quantization of Rhythms

CHAPTER 13 Syncopated Rhythm

CHAPTER 14 Necklaces and Bracelets

CHAPTER 15 Rhythmic Oddity

CHAPTER 16 Offbeat Rhythms

CHAPTER 17 Rhythm Complexity

CHAPTER 18 Meter and Metric Complexity

CHAPTER 19 Rhythmic Grouping

CHAPTER 20 Dispersion Problems: Perfectly Even, Maximally Even, and Balanced Rhythms

CHAPTER 21 Euclidean Rhythms, Euclidean Strings, and Well-Formed Rhythms

CHAPTER 22 Lunisolar Rhythms: Leap Year Patterns

CHAPTER 23 Almost Maximally Even Rhythms

CHAPTER 24 Homometric Rhythms and Crystallography

CHAPTER 25 Complementary Rhythms

CHAPTER 26 Flat Rhythms and Radio Astronomy

CHAPTER 27 Deep Rhythms

CHAPTER 28 Shelling Rhythms

CHAPTER 29 Phase Rhythms: The “Good,” the “Bad,” and the “Ugly”

CHAPTER 30 Phantom Rhythms

CHAPTER 31 Reflection Rhythms, Elastic Rhythms, and Rhythmic Canons

CHAPTER 32 Toggle Rhythms

CHAPTER 33 Symmetric Rhythms

CHAPTER 34 Rhythms with an Odd Number of Pulses

CHAPTER 35 Visualization and Representation of Rhythms

CHAPTER 36 Rhythmic Similarity and Dissimilarity

CHAPTER 37 Grouping and Meter as Features of Rhythm Similarity

CHAPTER 38 Regular and Irregular Rhythms

CHAPTER 39 Evolution and Phylogenetic Analysis of Musical Rhythms

CHAPTER 40 Rhythm Combinatorics

CHAPTER 41 What Makes the Clave Son Such a Good Rhythm?

CHAPTER 42 On the Origin, Evolution, and Migration of the Clave Son

CHAPTER 43 Epilogue

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