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Tonal harmony and the topology of dynamical score networks

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Document pages: 33 pages

Abstract: We introduce the concept of dynamical score networks for the representationand analysis of tonal compositions: a score is interpreted as a dynamicalnetwork where every chord is a node and each progression links successivechords. This network can be viewed as a time series of a non-stationary signal,and as such, it can be partitioned for the automatic identification of tonalregions using time series analysis and change point detection without relyingon comparisons with pre-determined reference sets or extensive corpora. Wedemonstrate that the essential features of tonal harmony, centricity,referentiality, directedness and hierarchy, emerge naturally from the networktopology and its scale-free properties. Finally, solving for the minimal lengthpath through a route optimization algorithm on these graphs provides anabstraction of harmonic sequences that can be generalized for the conception ofgenerative models of tonal compositional design.

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