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Topological data analysis has been recently applied to investigate stylisticsignatures and trends in musical compositions. A useful tool in this area isPersistent Homology. In this paper, we develop a novel method to represent aweighted directed graph as a finite metric space and then use persistenthomology to extract useful features. We apply this method to weighted directedgraphs obtained from pitch transitions information of a given musical fragmentand use these techniques to the study of stylistic trends. In particular, weare 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 termsof different approaches by these composers to stylistic exploration andvariety. We observe that Haydn is stylistically the most conservative, followedby Mozart, while Beethoven is the most innovative, expanding and modifying thestring quartet as a musical form. Finally we also compare the variability ofdifferent genres, namely minuets, allegros, prestos and adagios, by a givencomposer and conclude that the minuet is the most stable form of the stringquartet movements.

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