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