Inferring Tonality from Note Distributions - Why Models Matter

Abstract

The present approach aims at bridging mathematical music theory and computational music analysis by combining formal models of tonal space and statistical analyses of symbolic musical corpora in different representations (neutral and tonal pitch classes). Computational music analysis necessarily relies on quantified musical data. Although numerical representations of pieces are inevitably reductive, they have the advantage to allow for objective statistical statements under given assumptions. One of the most common avenues in empirical approaches to music analysis is to study note distributions of pieces or collections of pieces, for instance in applications such as automated key or mode finding, or genre classification. Typically, notes are translated into pitch classes in twelve-tone equal temperament and represented by integers ranging from 0 to 11, allowing for convenient treatment of many digital music resources, such as MIDI databases. Other formats, such as MusicXML, allow for a richer representation of pitches and pitch classes.. This paper argues that the choice of the representation of notes and hence the associated models of tonal spaces fundamentally affects the discovery, analysis, and interpretation of patterns in note distributions (sometimes called ‘tone profiles’). It contrasts historical and contemporary models of tonal space, such as the line of fifths, the circle of fifths, and the Tonnetz, and it demonstrates how different representations influence the results. This is shown by (1) comparing a number of individual pieces marking different stages in the history of tonality, and (2) inspecting a musical dataset of more than 1,500 pieces (more than two million notes) ranging from the Renaissance to late Romantic periods, with a strong focus on the nineteenth century. The results reveal large-scale historical changes in the usage of tonal material that would not be visible in reduced pitch representations.

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.