A Mathematical Model of Tonal Function (II): Modulation

Abstract:

This work is the second part of a research into mathematical models of tonal function. In the first paper, we presented a mathematical model based on optimal voice leadings for chords with the same number of notes. We gave several examples for classical music in the common practice period. In this second paper, we generalize the model to jazz music and music from the extended common practice and we remove the constraint on the number of voices, allowing the classification of chords with a different number of notes. Furthermore, modulation within this mathematical model is also explored and a classification of modulation between major and minor scales is constructed.

Año de publicación:

2022

Keywords:

• Cadence endomorphisms
• Voice-leadings
• Tonal function
• Nabla distance
• Characteristic polynomials
• Modal interchange
• modulation
• Optimal voice-leadings

Fuente:

scopus