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.
Highlights
One of the core questions in music research concerns the structural regularities within and across historical styles and cultures
This article presents a empirical characterization of tonal harmony, the core organization system of Western music
We do not claim that these dimensions provide an exhaustive characterization of tonal music, as we leave other structural aspects such as meter, rhythm, voice-leading, and hierarchical syntax out of account
Summary
One of the core questions in music research concerns the structural regularities within and across historical styles and cultures. In the field of music theory, manifold attempts have been made to characterize these structures and their underlying rule systems, from antiquity up to the present [1,2,3,4,5,6,7,8,9]. Previous music theoretical approaches addressing tonal harmony suffer from a lack of empirical foundation. The empirical study of sophisticated concepts related to tonal harmony depends on tractable representations of musical structure. Since symbolic representations of musical pieces are scarce, large-scale analyses have been hindered due to the lack of large symbolic corpora
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