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

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

Author information

Digital and Cognitive Musicology Lab, Digital Humanities Institute, College of Humanities, École Polytechnique Fédérale de Lausanne, Lausanne, 1015 Vaud, Switzerland.


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.

Conflict of interest statement

The authors have declared that no competing interests exist.

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