Multi-scale and multi-dimensional modelling of music structure using polytopic graphs

Abstract : In this thesis, we approach these questions by defining and implementing a multi-scale model for music segment structure description, called Polytopic Graph of Latent Relations (PGLR). In our work, a segment is the macroscopic constituent of the global piece. In pop songs, which is the main focus here, segments usually correspond to a chorus or a verse, lasting approximately 15 seconds and exhibiting a clear beginning and end. Under the PGLR scheme, relationships between musical elements within a musical segment are assumed to be developing predominantly between homologous elements within the metrical grid at different scales simultaneously. This approach generalises to the multi-scale case the System&Contrast framework which aims at describing, as a 2×2 square matrix, the logical system of expectation within a segment and the surprise resulting from that expectation. For regular segments of 2^n events, the PGLR lives on a n-dimensional cube (square, cube, tesseract, etc...), n being the number of scales considered simultaneously in the multi-scale model. Each vertex in the polytope corresponds to a low-scale musical element, each edge represents a relationship between two vertices and each face forms an elementary system of relationships. The estimation of the PGLR structure of a musical segment can then be obtained computationally as the joint estimation of : the description of the polytope (as a more or less regular n-polytope) ; the nesting configuration of the graph over the polytope, reflecting the flow of dependencies and interactions as elementary implication systems within the musical segment, the set of relations between the nodes of the graph. The aim of the PGLR model is to both describe the time dependencies between the elements of a segment and model the logical expectation and surprise that can be built on the observation and perception of the similarities and differences between elements with strong relationships. The approach is presented conceptually and algorithmically, together with an extensive evaluation of the ability of different models to predict unseen data, measured using the cross-perplexity value. These experiments have been conducted both on chords sequences, rhythmic and melodic segments extracted from the RWC POP corpus. Our results illustrate the efficiency of the proposed model in capturing structural information within such data.
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Corentin Louboutin. Multi-scale and multi-dimensional modelling of music structure using polytopic graphs. Sound [cs.SD]. Université Rennes 1, 2019. English. ⟨NNT : 2019REN1S012⟩. ⟨tel-02149728⟩

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