ABSTRACT

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.

chapter CHAPTER 1|6 pages

What is Rhythm?

chapter CHAPTER 2|4 pages

Isochrony, Tempo, and Performance

chapter CHAPTER 3|6 pages

Timelines, Ostinatos, and Meter

chapter CHAPTER 4|2 pages

The Wooden Claves

chapter CHAPTER 5|4 pages

The Iron Bells

chapter CHAPTER 6|4 pages

The Clave Son

A Ubiquitous Rhythm

chapter CHAPTER 7|4 pages

Six Distinguished Rhythm Timelines

chapter CHAPTER 8|6 pages

The Distance Geometry of Rhythm

chapter CHAPTER 9|4 pages

Classification of Rhythms

chapter CHAPTER 10|4 pages

Binary and Ternary Rhythms

chapter CHAPTER 13|6 pages

Syncopated Rhythms

chapter CHAPTER 14|10 pages

Necklaces and Bracelets

chapter CHAPTER 15|10 pages

Rhythmic Oddity

chapter CHAPTER 16|6 pages

Offbeat Rhythms

chapter CHAPTER 17|12 pages

Rhythm Complexity

chapter CHAPTER 18|20 pages

Meter and Metric Complexity

chapter CHAPTER 19|6 pages

Rhythmic Grouping

chapter CHAPTER 20|10 pages

Dispersion Problems

Perfectly Even, Maximally Even, and Balanced Rhythms

chapter CHAPTER 22|4 pages

Lunisolar Rhythms

Leap Year Patterns

chapter CHAPTER 23|6 pages

Almost Maximally Even Rhythms

chapter CHAPTER 24|6 pages

Homometric Rhythms and Crystallography

chapter CHAPTER 25|8 pages

Complementary Rhythms

chapter CHAPTER 26|8 pages

Flat Rhythms and Radio Astronomy

chapter CHAPTER 27|10 pages

Deep Rhythms

chapter CHAPTER 28|10 pages

Shelling Rhythms

chapter CHAPTER 29|8 pages

Phase Rhythms

The “Good,” the “Bad,” and the “Ugly”

chapter CHAPTER 30|10 pages

Phantom Rhythms

chapter CHAPTER 32|6 pages

Toggle Rhythms

chapter CHAPTER 33|10 pages

Symmetric Rhythms

chapter CHAPTER 34|6 pages

Rhythms with an Odd Number of Pulses

chapter CHAPTER 36|8 pages

Rhythmic Similarity and Dissimilarity

chapter CHAPTER 38|6 pages

Regular and Irregular Rhythms

chapter CHAPTER 40|4 pages

Rhythm Combinatorics

chapter CHAPTER 43|4 pages

Epilogue