A Comparison of Rhythmic Similarity Measures

Measuring the similarity between rhythms is a fundamental problem in computational music theory, with many applications such as music information retrieval and copyright infringement resolution. A common way to represent a rhythm is as a binary sequence where a zero denotes a rest (silence) and a one represents a beat or note onset. This paper compares various measures of rhythm similarity including the Hamming distance, the Euclidean interval-vector distance, the interval-dierence distance measure of Coyle and Shmulevich, the swap distance, and the chronotonic distance measures of Gustafson and Hofmann-Engl. Traditionally, rhythmic similarity measures are compared according to how well rhythms may be recognized with them, how ecien tly they can be retrieved from a data base, or how well they model human perception and cognition of rhythms. In contrast, here similarity measures are compared on the basis of how much insight they provide about the structural inter-relationships that exist within families of rhythms, when phylogenetic trees and graphs are computed from the distance matrices determined by these similarity measures. For two collections of rhythms, namely the 4/4 time and 12/8 time clave-bell time lines used in traditional African and Afro-American music, the chronotonic and swap distances appear to be superior to the other measures, and each has its own atractive features. The similarity measures are also compared according to their computational complexity.