Rhythm Similarity and Symbolic Dynamics

Terrence Richard Blackman and John Belcher
Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture (2014)
Pages 477–478 Short Papers


Measuring the similarity between two rhythms is of crucial importance in the field of music information retrieval. There has been an examination of the mathematical closeness of rhythms by means of a number of metrics: the Hamming distance, the Euclidean interval-vector distance, the interval-difference distance measure of Coyle and Shmulevich, the swap distance, and the chronotonic distance measures of Gustafson and Hofmann-Engl. This note proposes the use of the metric, $d(s,t) = \sum_{i=0}^{+\infty}\frac{|s_i-t_i|}{s^i}$, from symbolic dynamics to explore rhythmic closeness.