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Geometry of Musical Rhythm by Godfried T. Toussaint (2019, Hardcover)

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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. Th also introduced the distance approach to phylogenetic analysis and illustrated its application to the study of musical rhythm.

About this product

Product Identifiers

PublisherCRC Press LLC

ISBN-100815370970

ISBN-139780815370970

eBay Product ID (ePID)21038706962

Product Key Features

Number of Pages352 Pages

Publication NameGeometry of Musical Rhythm

LanguageEnglish

Publication Year2019

SubjectInstruction & Study / General, Geometry / General, General, Recreations & Games

TypeTextbook

AuthorGodfried T. Toussaint

Subject AreaMathematics, Music

FormatHardcover

Dimensions

Item Height0.8 in

Item Length10.9 in

Item Width8.5 in

Additional Product Features

Edition Number2

Intended AudienceCollege Audience

ReviewsPraise 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

TitleLeadingThe

Dewey Edition23

IllustratedYes

Dewey Decimal781.2240285

Table Of ContentPreface to First Edition Preface to Second Edition 1. What is Rhythm 2. Isochrony, Tempo, and Performance Isochronous Rhythms Tempo 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 The Shiko Timeline The Clave Rumba The Soukous Timeline The Gahu Timeline The Bossa-Nova Timeline 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 Metrical Complexity Keith''s Measure of Syncopation 14. Necklaces and Bracelets 15. Rhythmic Oddity 16. Off-Beat Rhythms 17. Rhythm Complexity Objective, Cognitive and Performance Complexities The Lempel-Ziv Complexity The Cognitive Complexity of Rhythms Irregularity and the Normalized Pairwise Variability Index 18. Meter and Metric Complexity What is Meter? Does African Rhythm Possess Meter? Pulse Saliency Histograms in Renaissance and Common Practice Music African Rhythm Timelines and Western Music Keith''s Mathematical Measure of Meter Complexity The Interaction Between Meter and Rhythm Perception 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 Reflection Rhythms Paradiddle Method Alternating-Hands Method Elastic Rhythms Rhythmic Canons 32. Toggle Rhythms 33. Symmetric Rhythms Hourglass Rhythms Sub-Symmetries 34. Rhythms with an Odd Number of Pulses 35. Visualization and Representation of Rhythms Alternating-Hands Box Notation Spectral Notation TEDAS Notation Chronotonic Notation Phase Space Plots Tangle Diagrams 36. Rhythm Similarity and Dissimilarity Hamming Distance Swap Distance Directed Swap Distance Many-to-Many Assignment Distance Geometric Distance Edit Distance 37. Grouping and Meter as Features of Rhythm Similarity The Edit Distance with Grouping Information The Edit Distance with Meter Information 38. Regular and Irregular Rhythms 39. Evolution and Phylogenetic Analysis of Musical Rhythms Phylogenetic Analysis of Cultural Objects Phylogenetic Analysis of Flamenco Compás The Guajira Phylogenetic Analysis of Ancient Greek Paeonic Rhythms 40. Rhythm Combinatorics 41. What Makes the Clave Son Such a "Good" Rhythm? Evenness and Balance Rhythmic Oddity Off-Beatness Weighted Off-Beatness Metrical Complexity and Keith''s Measure of Syncopation Main-Beat Onsets and Closure Cardinality of Distinct Durations Cardinality of Distinct Adjacent Durations Onset-Complexity and Sum of Distinct Distances Deep Rhythms, Deepness, and Shallowness Tallness Prototypicality and Phylogenetic Tree Centrality Mirror Symmetry Pulse Sub-Symmetries IOI Duration Sub-Symmetries Area of Phase Space Plots Fractal Metric Hierarchy Shadow Contour Isomorphism 42. On the Origin, Evolution, and Migration of the Clave Son 43. Epilogue References Books, Book Chapters and Theses Journal Articles and Conference Proceedings

SynopsisThe 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.

LC Classification NumberMT42