Comparison of musical sequences

摘要

Concepts from the theory of sequence comparison are adapted to measure the overall similarity or dissimilarity between two musical scores. A key element is the notion of consolidation and fragmentation, different both from the deletions and insertions familiar in sequence comparison, and from the compressions and expansions of time warping in automatic speech recognition. The measure of comparison is defined so as to detect similarities in melodic line despite gross differences in key, mode or tempo. A dynamic programming algorithm is presented for calculating the measure, and is programmed and applied to a set of variations on a theme by Mozart. Cluster analysis and spatial representation of the results confirm subjective impressions of the patterns of similarities among the variations. A generalization of the algorithm is presented for detecting locally similar portions in two scores, and is then applied.