Music Analysis and Point-Set CompressionA 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. |