| Description |
1 online resource (xii, 187 pages) : illustrations (some color) |
| Contents |
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 |
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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 |
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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 |
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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 |
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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 |
| Summary |
This book presents the latest computational models of rhythm and meter that are based on number theory, combinatorics and pattern matching. Two computational models of rhythm and meter are evaluated: The first one explores a relatively new field in Mathematics, namely Combinatorics on Words, specifically Christoffel Words and the Burrows-Wheeler Transform, together with integer partitions. The second model uses filtered Farey Sequences in combination with specific weights that are assigned to inter-onset ratios. This work is assessed within the context of the current state of the art of tempo tracking and computational music transcription. Furthermore, the author discusses various representations of musical rhythm, which lead to the development of a new shorthand notation that will be useful for musicologists and composers. Computational Models of Rhythm and Meter also contains numerous investigations into the timing structures of human rhythm and metre perception carried out within the last decade. Our solution to the transcription problem has been tested using a wide range of musical styles, and in particular using two recordings of J.S. Bach's Goldberg Variations by Glenn Gould. The technology is capable of modelling musical rhythm and meter by using Farey Sequences, and by detecting duration classes in a windowed analysis, which also detects the underlying tempo. The outcomes represent human performances of music as accurate as possible within Western score notation |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed June 29, 2018) |
| Subject |
Musical meter and rhythm -- Data processing
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Computer modelling & simulation.
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Applied mathematics.
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Pattern recognition.
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MUSIC -- Instruction & Study -- Theory.
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| Form |
Electronic book
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| ISBN |
9783319762852 |
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3319762850 |
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