Modulation in Tetradic Harmony and its Role in Jazz

TL;DR

This paper explores Mazzola's quantum modulation model applied to tetradic harmony in jazz, highlighting its relevance and classical foundations within the equal temperament system.

Contribution

It extends Mazzola's quantum modulation model from triadic to tetradic interpretation, emphasizing its significance in jazz harmony analysis.

Findings

Tetradic harmony can be modeled using Mazzola's quantum framework.

Classical objects relevant to jazz are recovered within this model.

The study enhances understanding of jazz harmony through mathematical modeling.

Abstract

After a quick exposition of Mazzola's quantum modulation model for the so-called triadic interpretation of the major scale within the equal temperament, we study the model for the tetradic interpretation of the same scale. It is known that tetrads are fundamental for jazz music, and some classical objects for this kind of music are recovered.