Tracing the History of Tonality with Note Distributions

Abstract

Pitch-class distributions are widely used in corpus-based Computational Musicology, e.g. to determine the mode or key of musical pieces, or to infer style-specific characteristics (De Clerq & Temperley, 2011; Broze & Shanahan, 2013). Unfortunately, research is often confined by specific representations of musical pieces due to MIDI-encoded data that renders, for instance, the distinction between enharmonically equivalent pitch classes (e.g. F# and Gb) and between diatonic and chromatic intervals (e.g. m2 and A1) impossible. Moreover, historical changes of these distributions are only recently being studied on a larger scale (Tymoczko, 2011; Albrecht & Huron, 2014; White, 2014; Yust, 2019), while many approaches assume more or less immutable abstract “tone profiles” (Krumhansl, 1990). These shortcomings are addressed by analyzing distributions of “tonal pitch classes” (TPCs; Temperley, 2000) in a large dataset of more than 2000 MusicXML-encoded pieces by 75 composers covering a historical range of almost 600 years. It is shown that the order on the line of fifths can be inferred both from TPC distributions of pieces as well as diachronically. Moreover, a mathematical model is used to show that composers progressively use third-based tonal relations in an increasingly explorative manner. Thus, the historically changing distributions of TPCs allow to expose large-scale changes in compositional practices. The present approach argues that adequate models for musical notes and pieces as well as the acknowledgement of historical changes are indispensable for the computational study of tonality.

Fabian C. Moss

Assistant Professor for Digital Music Philology and Music Theory

Fabian C. Moss is an assistant professor for Digital Music Philology and Music Theory at Julius-Maximilians University Würzburg (JMU), Germany.