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The geometry of musical rhythm : what makes a "good" rhythm good?

Author: Godfried T Toussaint
Publisher: Boca Raton, FL : CRC Press, Taylor & Francis Group, ©2013.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"{U2026} 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  Read more...
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Document Type: Book
All Authors / Contributors: Godfried T Toussaint
ISBN: 9781466512023 1466512024
OCLC Number: 825990490
Notes: "A Chapman & Hall book."
Description: xvii, 347 pages : illustrations ; 26 cm
Contents: Prolegomenon --
Author --
What is rhythm? --
A steady beat --
Timelines, ostinatos, and meter --
The wooden claves --
The iron bells --
The clave son --
Six distinguished rhythm timelines --
The distance geometry of rhythm --
Classification of rhythms --
Binary and ternary rhythms --
The isomorphism of rhythm and scale --
Binarization, ternarization, and quantization of rhythms --
Syncopated rhythms : Keith's measure of syncopation --
Necklaces and bracelets --
Rhythmic oddity --
Off-beat rhythms --
Rhythm complexity : Objective, cognitive, and performance complexities ; Lempel-ziv complexity ; Cognitive complexity of rhythms ; Irregularity and the normalized pairwise variability index --
Dispersion problems and maximally even rhythms --
Euclidean rhythms --
Leap years: the rhythm of the stars --
Approximately even rhythms --
Rhythms and crystallography --
Complementary rhythms --
Radio astronomy and flat rhythms --
Deep rhythms --
Shelling rhythms --
Phantom rhythms --
Reflection rhythms and rhythmic canons --
Toggle rhythms --
Symmetric rhythms : Hourglass drums and hourglass rhythms --
Odd rhythms --
Other representations of rhythm : Alternating-hands box notation ; Spectral notation ; Tedas and chronotonic notation --
Rhythmic similarity and dissimilarity --
Regular and irregular rhythms --
Evolution and phylogenesis of musical rhythm : Guajira --
Rhythmic combinatorics --
What makes the clave son such a good rhythm? : Maximal evenness ; Rhythmic oddity ; Off-beatness ; Weighted off-beatness --
Metrical complexity --
Main-beat onsets and closure ; Distinct durations ; Distinct adjacent durations ; Onset-complexity and distinct distances ; Deep rhythms, deepness, and shallowness ; Tallness ; Phylogenetic tree centrality ; Mirror symmetry ; Shadow contour isomorphism --
The origin, evolution, and migration of the clave son --
Epilogue.
Responsibility: Godfried T. Toussaint ; illustrative drawings by Yang Liu.
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Abstract:

"{U2026} 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{u2014}an eminent computer scientist and music theory researcher{u2014}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."--Provided by publisher.

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"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 Read more...

 
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