Efficient extraction of closed motivic patterns in multi-dimensional symbolic representations of music

An efficient model for discovering repeated patterns in symbolic representations of music is presented. Combinatorial redundancy inherent in the pattern discovery paradigm is commonly filtered using global selective mechanisms, based on pattern frequency and length. We propose an alternate approach founded on the concept of closed pattern and enabling detailed analyses through adaptive selection of most specific descriptions in a multidimensional parametric space. A notion of cyclic pattern is introduced, enabling an adapted filtering of another form of combinatorial redundancy caused by successive repetitions of patterns. The use of cyclic patterns implies a necessary chronological scanning of the piece, and the addition of mechanisms formalizing particular Gestalt principles. This study shows therefore that automated analysis of music cannot rely on simple mathematical or statistical approaches, but needs rather complex and detailed modeling of the cognitive system ruling listening processes. The resulting algorithm is able to offer for the first time compact and relevant motivic analyses of simple monodies, and may therefore be applied to automated indexing of symbolic music databases. Numerous additional mechanisms need to be added in order to consider all aspects of music expression, including polyphony and complex musical transformations.