Intro; Preface; Contents; 1 Introduction; References; 2 Phenomenology of Rhythm and Meter; 2.1 Causality; 2.2 Definitions of Rhythm and Meter; 2.3 Organic Form; 2.3.1 The Cycle in Organic Form; 2.3.2 Breathing; References; 3 A Shorthand Notation for Musical Rhythm; 3.1 Introduction; 3.2 Overview of Rhythm Notation; 3.3 Chunks of Musical Time: A Shorthand Notation for Rhythm; 3.3.1 Rhythm and the Psychology of Chunking; 3.3.2 Subdivisions; 3.4 Examples; 3.4.1 The Ewe Rhythm; 3.4.2 Latin-American Music; 3.4.3 Greek Verse Rhythms; 3.4.4 Messiaen; 3.4.5 Beethoven; 3.4.6 Mussorgsky; 3.4.7 Debussy

3.4.8 Polyrhythm3.4.9 Conclusion of Examples; 3.5 Conclusion; References; 4 Partitions and Musical Sentences; 4.1 Introduction; 4.2 Integer Partitions; 4.2.1 Partitions into k Distinct Parts; 4.2.2 Partitions into Parts with an Arithmetic Progression; 4.3 Musical Sentences; 4.4 Asymmetric Sentences; 4.4.1 Stravinsky's Game with Metric Asymmetry; 4.4.2 Messiaen: The Birds as Teachers of Composition; 4.5 Measuring Metric Complexity; 4.6 The Resolution of Musical Sentences: Effects of Closure and Decline; 4.6.1 Shrinking Durations, or the Accelerando Technique

4.6.2 Triangular Rhythmic Phrases using Primes4.7 The Sentence Algorithm in Chunking; 4.7.1 Seven Categories of Rhythmic Patterns; 4.7.2 Transcription of Patterns and the Complete Sentence; 4.8 Conclusion; References; 5 The Use of the Burrows-Wheeler Transform for Analysis and Composition; 5.1 Introduction; 5.2 The BWT Algorithm; 5.2.1 The Inverse BWT Algorithm (iBWT); 5.2.2 A Rhythm Analysis Program Using the BWT; 5.2.3 Fragmentation Modelling by Using the iBWT Matrix; 5.3 Conclusion; References; 6 Christoffel Rhythms; 6.1 Introduction; 6.2 Christoffel Rhythms from Christoffel Words

6.2.1 Operations on Christoffel Rhythms6.3 The Burrows-Wheeler Transform as a Tool for Rhythm Analysis; 6.4 Rhythms from Various Music Cultures; 6.4.1 Euclidean Rhythms; 6.5 Conclusion; References; 7 The Farey Sequence as a Model for Musical Rhythm and Meter; 7.1 Introduction; 7.2 The Farey Sequence; 7.2.1 Building Consecutive Ratios Anywhere in Farey Sequences; 7.2.2 The Farey Sequence, Arnol'd Tongues and the Stern-Brocot Tree; 7.2.3 Farey Sequences and Musical Rhythms; 7.3 Filtered Farey Sequences; 7.3.1 Introduction; 7.3.2 Polyrhythms; 7.3.3 Rhythm Transformations

7.3.4 Greek Verse Rhythms7.3.5 Filters Based on Sequences of Natural Integers; 7.3.6 Filters Based on the Prime Number Composition of an Integer; 7.3.7 Metrical Filters; 7.4 Conclusion; References; 8 Models of Musical Meter, Temporal Perception and Onset Quantization; 8.1 Introduction; 8.2 Musical Meter; 8.2.1 Necklace Notation of Rhythm and Meter; 8.2.2 Meter and Entrainment; 8.3 Temporal Perception; 8.3.1 Shortest Timing Intervals; 8.3.2 The 100 ms Threshold; 8.3.3 Fastest Beats; 8.3.4 Slowest Beats; 8.3.5 The Perceptual Time Scale; 8.4 Onset Detection; 8.4.1 Manual Tapping