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

Abstract

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.

Keywords:

• Topological data analysis
• persistent homology
• string quartet
• intervallic transitions
• stylistic analysis

2020 Mathematics Subject Classifications:

• 55N31
• 62R40
• 05C90
• 00A65

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments that improved the quality of the manuscript. MM would like to thank CONACyT for the financial support. A. Bravetti acknowledges financial support by DGAPA-UNAM, programme PAPIIT, Grant No. IA-102823. PP would like to thank DGAPA (PASPA) and Clare Hall at the University of Cambridge.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

MM was supported by a CONACyT postdoctoral fellowship. PP would like to thank Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México (DGAPA (PASPA)) and Clare Hall at the University of Cambridge. The work of AB was partially supported by DGAPA-UNAM, programme PAPIIT, Grant No. IA-102823.