Statistical characteristics of tonal harmony: A corpus study of Beethoven's string quartets

PLoS One. 2019 Jun 6;14(6):e0217242. doi: 10.1371/journal.pone.0217242. eCollection 2019.


Tonal harmony is one of the central organization systems of Western music. This article characterizes the statistical foundations of tonal harmony based on the computational analysis of expert annotations in a large corpus. Using resampling methods, this study shows that 1) the rank-frequency distribution of chords resembles a power law, i.e. few chords govern a large proportion of the data; 2) chord transitions are referential and chord predictability is significantly affected by distinguished chord features; 3) tonal harmony conveys directedness in time; and 4) tonal harmony operates differently at the hierarchical levels of chords and keys. These results serve to characterize tonal harmony on empirical grounds and advance the methodological state-of-the-art in digital musicology.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Music*
  • Pitch Perception
  • Statistics as Topic*

Grants and funding

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (GA N° 760081). Further funding was provided by the Volkswagen Foundation within the scope of the project "From Bach to the Beatles: Exploring compositional building blocks and style change with hermeneutic and computational methods”, and the École Polytechnique Fédérale de Lausanne (EPFL). The authors thank Claude Latour for supporting this research through the Latour Chair of Digital and Cognitive Musicology at EPFL.