A Mathematical Model of Tonal Function (I): Voice Leadings

Abstract:

This paper is the first in a series of two papers on mathematical models of tonal function. In this first paper, we present a mathematical model of tonal function whose scope is limited to classic music from the common practice period. After a formalization of some harmonic elements (pitch classes, chords, arrangements, voicings, voice leadings), the model of tonal function is described. Our model is based on voice leadings and the tonal function is defined in terms of them. A combinatorial optimization algorithm is used to determine the tonal function. In this work, only chords with the same number of voices are considered. The general case was left for the second paper of the series; in the second paper the model of tonal function is generalized.

Año de publicación:

2022

Keywords:

• Chord classification
• Nabla distance
• Optimal voice-leadings
• Chord progressions
• Distance functions
• Matrix algebra
• Voice-leadings
• Tonal function
• Characteristic polynomials

Fuente:

scopus