Simple Deterministic Algorithms for Generating “Good” Musical Rhythms

Abstract

The most economical representation of a musical rhythm is as a binary sequence of symbols that represent sounds and silences, each of which have a duration of one unit of time. Such a representation is eminently suited to objective mathematical and computational analyses, while at the same time, and perhaps surprisingly, provides a rich enough structure to inform both music theory and music practice. A musical rhythm is considered to be ``good'' if it belongs to the repertoire of the musical tradition of some culture in the world, is used frequently as an ostinato or timeline, and has withstood the test of time. Here several simple deterministic algorithmsAlgorithmsfor generating musical rhythms are reviewed and compared in terms of their computational complexity, applicability, and capability to capture "goodness".