Towards a topological fingerprint of music

TL;DR

This paper introduces a novel topological approach to represent and analyze music by modeling harmonic relationships as polyhedral surfaces and using persistent homology to extract meaningful features for style classification.

Contribution

It proposes a new geometric-topological model of music based on the Tonnetz and applies persistent homology for music analysis and automatic style classification.

Findings

Topological fingerprints effectively distinguish different musical styles.

Persistent homology captures meaningful harmonic features.

Hierarchical clustering based on topological features classifies music styles.

Abstract

Can music be represented as a meaningful geometric and topological object? In this paper, we propose a strategy to describe some music features as a polyhedral surface obtained by a simplicial interpretation of the \textit{Tonnetz}. The \textit{Tonnetz} is a graph largely used in computational musicology to describe the harmonic relationships of notes in equal tuning. In particular, we use persistent homology in order to describe the \textit{persistent} properties of music encoded in the aforementioned model. Both the relevance and the characteristics of this approach are discussed by analyzing some paradigmatic compositional styles. Eventually, the task of automatic music style classification is addressed by computing the hierarchical clustering of the topological fingerprints associated with some collections of compositions.