Musical rhythm and computational mathematics
Godfried T. Toussaint · 2005
Analysing the histograms of inter-onset duration intervals in rhythms yields interesting mathematical and computational problems, and suggests methods for the automatic generation of new rhythms that have specific properties. For example, a large class of noteworthy rhythms used in World music may be generated by the Euclidean algorithm originally proposed by Euclid for computing the greatest common divisor of two given integers. Viewing rhythms as sequences (or strings) of symbols, suggests using tools from bioinformatics to perform phylogenetic analyses of families of rhythms. Such tools allow us to “reconstruct” “ancestral” rhythms, which may be used in automatic music composition systems, or to test theories of the evolution of musical rhythms. These applications will be illustrated with examples from African, Latin-American, and Flamenco music. Most of the material relevant to this talk may be found scattered in: [?], [?] [?], [?], [?], [?], and [?].