Polytopic reconfiguration: a graph-based scheme for the multiscale transformation of music segments and its perceptual assessment
Résumé
Music is a sequential process for which relations between adjacent elements play an important role. Expectation processes based on alternations of similarity and novelty contribute to the structure of the musical flow. In this work, we explore a polytopic representation of music, which accounts for expectation systems developing at several timescales in parallel. After recalling properties of polytopic representations for describing multi-scale implication processes , we introduce a scheme for recomposing musical sequences by simple transformations of their support poly-tope. A specific set of permutations (referred to as Primer Preserving Permutations or PPP) are of particular interest , as they preserve systems of analogical implications within musical segments. By means of a perceptual test, we study the impact of PPP-based transformations by applying them to the choruses of pop songs in midi format and comparing the result with Randomly Generated Permutations (RGP). In our test, subjects are asked to rate musical excerpts reconfigured by PPP-based transformations versus RGP-based ones in terms of musical consistency and of attractiveness. Results indicate that PPP-transformed segments score distinctly better than RGP-transformed for the two criteria, suggesting that the preservation of implication systems plays an important role in the subjective acceptability of the transformation. Additionally, from the perspective of building an automatic recomposition system for artistic creation purposes, we introduce, in appendix, the preliminary version of an automatic method for decomposing segments into low-scale musical elements, taking into account possible phase-shifts between the musical surface of the melody and the metrical information.
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