Modeling the Evolution of Tonal Complexity: A Statistical Analysis from Renaissance to Baroque.

Abstract

Studying musical evolution using time-consuming traditional methods can be a nearly impossible task due to the large datasets required. Computational methods, however, provide a useful alternative, as large amounts of data can be processed in a short time. One such approach is multiple f0 extraction from audio recordings, which was applied in this study. The aim was to examine the evolution of tonal complexity, a measure that captures how pitch class content is distributed along the circle of fifths. The period of interest was from the Renaissance to the Baroque (c. 1450–1750), an era marked by the transition from modality to tonality, which saw a rise in the importance of chords, key centres, and modulations. Based on a dataset of 469 compositions from 1450 to 1750, regression analysis with Beta Generalized Linear Mixed Models was executed, in which a distinction was made for musical function (sacred versus secular), as well as for performance type (vocal versus instrumental versus mixed). The results revealed how tonal complexity evolved across different temporal resolutions, from milliseconds to entire compositions. Tonal complexity calculated over entire compositions (‘global’), showed an upward trend over time, as well as tonal complexity calculated over 8-second sliding windows (‘medium’), although less substantial. Reflecting vertical harmonies, tonal complexity for the smallest window size possible (‘local’) did not show a change over time. While the distinction for musical function and performance type did not show different trends, it was revealed that secular music as well as vocal and mixed music had a higher global and medium tonal complexity than, respectively, sacred and instrumental music, which corroborates existing musical knowledge. The consistency with established research strengthens the validity of the results and supports the robustness of the methods used.