Tonal harmony and the topology of dynamical score networks

TL;DR

This paper introduces dynamical score networks to analyze tonal compositions, revealing how key features of harmony naturally emerge from network topology and enabling generative models of tonal music.

Contribution

It presents a novel network-based approach to represent and analyze tonal music, using topology and scale-free properties to understand harmony and generate musical sequences.

Findings

Tonal features emerge from network topology

Scale-free properties characterize tonal networks

Path optimization models harmonic sequences

Abstract

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.