A Mathematical Analysis of African, Brazilian, and Cuban Clave Rhythms

Godfried Toussaint
Bridges: Mathematical Connections in Art, Music, and Science (2002)
Pages 157–168


Several geometric, graph theoretical and combinatorial techniques useful for the teaching, analysis, generation and automated recognition of rhythms are proposed and investigated. The techniques are illustrated on the six fundamental 4/4 time clave and bell rhythm timelines most frequently used in African, Brazilian and Cuban music. It was found that Pressing's measure of rhythm complexity agrees well with the difficulty of performing these clave rhythms whereas the Lempel-Ziv measure appears to be useless. An analysis of the rhythms with several similarity measures reveals that the clave Son is most like all the other clave rhythms and perhaps provides an explanation for its worldwide popularity. Finally, a combinatorial technique based on permutations of multisets suggests a fruitful approach to automated generation of new rhythms.