Analysing Music with Point-Set Compression Algorithms

Several point-set pattern-discovery and compression algorithms designed for analysing music are reviewed and evaluated. Each algorithm takes as input a point-set representation of a score in which each note is represented as a point in pitch-time space. Each algorithm computes the maximal translatable patterns (MTPs) in this input and the translational equivalence classes (TECs) of these MTPs, where each TEC contains all the occurrences of a given MTP. Each TEC is encoded as a 〈pattern,vector set〉 pair, in which the vector set gives all the vectors by which the pattern can be translated in pitch-time space to give other patterns in the input dataset. Encoding TECs in this way leads, in general, to compression, since each occurrence of a pattern within a TEC (apart from one) is encoded by a single vector, that has the same information content as one point. The algorithms reviewed here adopt different strategies aimed at selecting a set of MTP TECs that collectively cover (or almost cover) the input dataset in a way that maximizes compression. The algorithms are evaluated on two musicological tasks: classifying folk song melodies into tune families and discovering repeated themes and sections in pieces of classical music. On the first task, the best-performing algorithms achieved success rates of around 84%. In the second task, the best algorithms achieved mean F1 scores of around 0.49, with scores for individual pieces rising as high as 0.71. 13.1 Music Analysis and Data Compression A musical analysis represents a particular way of understanding certain structural aspects of a musical object, where such an object may be any quantity of music, ranging from a motive, chord or even a single note through to a complete work or even an entire corpus of works (cf. Bent, 1987, p. 1). In the spirit of the theory of David Meredith Department of Architecture, Design and Media Technology, Aalborg University, Aalborg, Denmark e-mail: [email protected]