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基本説明
This book helps readers understand the general structure and evolution of musical rhythm. It focuses on a particular rhythm called the clave son, which is heard in music around the world and is best known in salsa dance music. Suitable for a wide audience, from musicians and composers to computer scientists and mathematicians, the book provides a visual geometric explanation of how this particular rhythm became the most popular rhythm in the world.
Full Description
The Geometry of Musical Rhythmfirst 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.
Contents
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 BraceletsRhythmic Oddity Off-Beat RhythmsRhythm 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 NotationSpectral Notation TEDAS and Chronotonic NotationRhythmic Similarity and Dissimilarity Regular and Irregular RhythmsEvolution and Phylogenesis of Musical Rhythm Guajira Rhythmic CombinatoricsWhat Makes the Clave Son Such a Good Rhythm? Maximal Evenness Rhythmic OddityOff-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 IsomorphismThe Origin, Evolution, and Migration of the Clave Son EpilogueReferencesIndex
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