The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good?

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CRC Press, 19 abr. 2016 - 365 páginas

The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good? is the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explains how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly disparate fields. For the music community, the book also introduces the distance approach to phylogenetic analysis and illustrates its application to the study of musical rhythm. Accessible to both academics and musicians, the text requires a minimal set of prerequisites.

Emphasizing a visual geometric treatment of musical rhythm and its underlying structures, the author—an eminent computer scientist and music theory researcher—presents new symbolic geometric approaches and often compares them to existing methods. He shows how distance geometry and phylogenetic analysis can be used in comparative musicology, ethnomusicology, and evolutionary musicology research. The book also strengthens the bridge between these disciplines and mathematical music theory. Many concepts are illustrated with examples using a group of six distinguished rhythms that feature prominently in world music, including the clave son.

Exploring the mathematical properties of good rhythms, this book offers an original computational geometric approach for analyzing musical rhythm and its underlying structures. With numerous figures to complement the explanations, it is suitable for a wide audience, from musicians, composers, and electronic music programmers to music theorists and psychologists to computer scientists and mathematicians. It can also be used in an undergraduate course on music technology, music and computers, or music and mathematics.

 

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Índice

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 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 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
Chapter 14 Necklaces and Bracelets
73
Chapter 15 Rhythmic Oddity
85
Chapter 16 OffBeat Rhythms
99
Chapter 17 Rhythm Complexity
107
Chapter 18 Dispersion Problems and Maximally Even Rhythms
121
Chapter 19 Euclidean Rhythms
129
The Rhythm of the Stars
137
Chapter 21 Approximately Even Rhythms
143
Chapter 30 Symmetric Rhythms
225
Chapter 31 Odd Rhythms
237
Chapter 32 Other Representations of Rhythm
243
Chapter 33 Rhythmic Similarity and Dissimilarity
247
Chapter 34 Regular and Irregular Rhythms
257
Chapter 35 Evolution and Phylogenesis of Musical Rhythm
265
Chapter 36 Rhythmic Combinatorics
275
Chapter 37 What Makes the Clave Son Such a Good Rhythm?
279
Chapter 38 The Origin Evolution and Migration of the Clave Son
293
Epilogue
305
References
311
Back Cover
337
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