Musical stylistic analysis: a study of intervallic transition graphs via persistent homology

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 quantitative study of stylistic trends. As a first illustration, we analyse 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. 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.