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

Abstract

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
PLOS ONE, 14(6)
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Fabian C. Moss
Postdoctoral Researcher

Fabian C. Moss is a postdoctoral researcher in the Digital and Cognitive Musicology Lab (DCML) at École Polytechnique Fédérale de Lausanne (EPFL, Switzerland). He was born in Cologne, Germany, and studied Mathematics and Educational Studies at University of Cologne, and Music Education (Major Piano) and Musicology at Hochschule für Musik und Tanz, Köln. Working with large symbolic datasets of musical scores and harmonic annotations, he is primarily interested in Computational Music Analysis, Music Theory, Music Cognition, and their mutual relationship.