Music analysis and point-set compression

A musical analysis represents a particular way of understanding certain aspects of the structure of a piece of music. The quality of an analysis can be evaluated to some extent by the degree to which knowledge of it improves performance on tasks such as mistake spotting, memorising a piece, attributing authorship, completing an unfinished work and so on. A traditional principle in science is "Occam's razor", which states that, given two conflicting successful explanations for the same data, one should choose the simpler alternative. This principle has been formalized in information theory as the minimum description length principle and relates closely to certain ideas in the theory of Kolmogorov complexity. Inspired by this general principle, the hypothesis explored in this paper is that the best ways of understanding (or explanations for) a piece of music are those that are represented by the shortest possible descriptions of the piece. With this in mind, two compression algorithms are presented, COSIATEC and SIATECCompress. Each of these algorithms takes as input an in extenso description of a piece of music as a set of points in pitch-time space representing notes. Each algorithm then losslessly compresses this set of points, producing an encoding in terms of a sequence of sets of translationally related patterns. The patterns found by the algorithms often correspond closely to those identified by music analysts as being structurally important. The analyses generated by the algorithms for a selection of pieces will be presented and discussed.