Tonal harmony and the topology of dynamical score networks
This provides a novel computational method for music theory analysis and generative composition, addressing a domain-specific problem in music informatics.
The authors tackled the problem of analyzing tonal compositions by introducing dynamical score networks, where chords are nodes and progressions are links, enabling automatic identification of tonal regions using time series analysis without pre-determined references. They demonstrated that key features of tonal harmony emerge from the network's topology and scale-free properties, and used route optimization to abstract harmonic sequences for generative models.
We introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score is interpreted as a dynamical network where every chord is a node and each progression links successive chords. 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 tonal regions using time series analysis and change point detection without relying on comparisons with pre-determined reference sets or extensive corpora. We demonstrate that the essential features of tonal harmony, centricity, referentiality, directedness and hierarchy, emerge naturally from the network topology and its scale-free properties. Finally, solving for the minimal length path through a route optimization algorithm on these graphs provides an abstraction of harmonic sequences that can be generalized for the conception of generative models of tonal compositional design.