A self-similar map of rhythmic components. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Hardesty, Jay
• Is Part Of: Journal of mathematics and music. Volume 10:Issue 1(2016)
• Page Start: 36
• Page End: 58
• Publication Date: 2016-01-02
• Subjects: 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; Music theory -- Periodicals; Music -- Mathematical models -- Periodicals; Music -- Mathematics -- Periodicals; 781.2
• DOI: 10.1080/17459737.2015.1136001
• Languages: English
• ISSNs: 1745-9737

Abstract

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 athttp://dx.doi.org/10.1080/17459737.2015.1136001 .