Musical Stylistic Analysis: A Study of Intervallic Transition Graphs via Persistent Homology

TL;DR

This paper introduces a novel topological data analysis method using persistent homology to analyze and compare musical styles based on pitch transition graphs, revealing stylistic differences among composers and genres.

Contribution

The paper develops a new approach to represent weighted directed graphs as metric spaces and applies persistent homology for stylistic analysis of musical compositions.

Findings

Haydn is the most conservative composer.

Beethoven is the most innovative.

Minuet is the most stable genre form.

Abstract

Topological data analysis has been recently applied to investigate stylistic signatures and trends in musical compositions. A useful tool in this area is Persistent Homology. In this paper, we develop a novel method to represent a weighted directed graph as a finite metric space and then use persistent homology to extract useful features. We apply this method to weighted directed graphs obtained from pitch transitions information of a given musical fragment and use these techniques to the study of stylistic trends. In particular, we are interested in using these tools to make quantitative stylistic comparisons. As a first illustration, we analyze a selection of string quartets by Haydn, Mozart and Beethoven and discuss possible implications of our results in terms of different approaches by these composers to stylistic exploration and variety. We observe that Haydn is stylistically the most conservative, followed by Mozart, while Beethoven is the most innovative, expanding and modifying the string quartet as a musical form. Finally we also compare the variability of different genres, namely minuets, allegros, prestos and adagios, by a given composer and conclude that the minuet is the most stable form of the string quartet movements.