A Framework for Topological Music Analysis (TMA)

TL;DR

This paper introduces a topological data analysis framework for music scores, using persistent homology and simplicial complexes to analyze musical fragments and compare stylistic features.

Contribution

It presents a novel application of topological data analysis techniques to music scores, including methods for analyzing chord sequences and musical events.

Findings

Effective topological features extracted from musical scores.

Successful stylistic comparison of classical and contemporary music fragments.

Demonstrated applicability to real musical works like Bach and Luna.

Abstract

In the present article we describe and discuss a framework for applying different topological data analysis (TDA) techniques to a music fragment given as a score in traditional Western notation. We first consider different sets of points in Euclidean spaces of different dimensions that correspond to musical events in the score, and obtain their persistent homology features. Then we introduce two families of simplicial complexes that can be associated with chord sequences, and leverage homology to compute their salient features. Finally, we show the results of applying the described methods to the analysis and stylistic comparison of fragments from three Brandenburg Concertos by J.S. Bach and two Graffiti by Mexican composer Armando Luna.