Classification and Phylogenetic Analysis of African Ternary Rhythm Timelines

A combinatorial classification and a phylogenetic analysis of the ten 12/8 time, seven-stroke bell rhythm timelines in African and Afro-American music are presented. New methods for rhythm classification are proposed based on measures of rhythmic oddity and off-beatness. These combinatorial classifications reveal several new uniqueness properties of the Bembé bell pattern that may explain its widespread popularity and preference among the other patterns in this class. A new distance measure called the swap-distance is introduced to measure the non-similarity of two rhythms that have the same number of strokes. A swap in a sequence of notes and rests of equal duration is the location interchange of a note and a rest that are adjacent in the sequence. The swap distance between two rhythms is defined as the minimum number of swaps required to transform one rhythm to the other. A phylogenetic analysis using Splits Graphs with the swap distance shows that each of the ten bell patterns can be derived from one of two “canonical” patterns with at most four swap operations, or from one with at most five swap operations. Furthermore, the phylogenetic analysis suggests that for these ten bell patterns there are no “ancestral” rhythms not contained in this set.