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A self-similar map of rhythmic components

A self-similar map of rhythmic components This paper defines a collection of rhythmic building blocks produced by generative operations that fuse metrical anticipation and parallelism. It connects aspects of musical expectation with Arthur Komar's constraints on the generation of rhythmic derivations. A correspondence between those constraints and the divisibility of binomial coefficients is used to map derived rhythmic elaborations and syncopations separately onto Pascal's triangle and jointly onto the Sierpinski gasket. This mapping provides concise means to directly enumerate and compare rhythmic configurations. An Online Supplement provides musical examples and discusses potential applications. It can be accessed at http://dx.doi.org/10.1080/17459737.2015.1136001. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis and Composition" Taylor & Francis

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References (16)

Publisher
Taylor & Francis
Copyright
© 2016 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1745-9745
eISSN
1745-9737
DOI
10.1080/17459737.2015.1136001
Publisher site
See Article on Publisher Site

Abstract

This paper defines a collection of rhythmic building blocks produced by generative operations that fuse metrical anticipation and parallelism. It connects aspects of musical expectation with Arthur Komar's constraints on the generation of rhythmic derivations. A correspondence between those constraints and the divisibility of binomial coefficients is used to map derived rhythmic elaborations and syncopations separately onto Pascal's triangle and jointly onto the Sierpinski gasket. This mapping provides concise means to directly enumerate and compare rhythmic configurations. An Online Supplement provides musical examples and discusses potential applications. It can be accessed at http://dx.doi.org/10.1080/17459737.2015.1136001.

Journal

"Journal of Mathematics and Music: Mathematical and Computational Approaches to Music Theory, Analysis and Composition"Taylor & Francis

Published: Jan 2, 2016

Keywords: rhythm; binary meter; syncopation; music prediction; rhythmic expectancy; rhythmic derivations; generative music; binomial coefficients; Pascal's triangle; Sierpinski gasket; 00A65; 60G18; 11Z05; sound and music computing

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