Modes in modern music from a topological viewpoint

TL;DR

This paper applies topological and braid theory to analyze modern music modes, revealing new modal structures and providing a mathematical framework for understanding harmonic progressions and voice leadings.

Contribution

It introduces a topological approach to musical modes and develops a braid theoretical interpretation of harmonic progressions in modern music.

Findings

Existence of special modes not deducible by standard methods

Topological complexity measures for modal scales

Braid representations of harmonic progressions in a musical fragment

Abstract

The aim of this paper is twofold: on one side we review the classical concept of musical mode from the viewpoint of modern music, reading it as a superimposition of a base-chord (seventh chord) and a tension-chord (triad). We associate to each modal scale an oriented plane graph whose homotopy properties give a measure of the complexity of the base-chord associated to a certain mode. Using these graphs we prove the existence of special modes which are not deducible in the standard way. On the other side we give a more deep musical insight by developing a braid theoretical interpretation of some cadential harmonic progressions in modern music and we use braid theory in order to represent them and voice leadings among them. A striking application is provided by the analysis of an harmonic fragment from Peru by Tribal Tech We approximate the octatonic scale used in the improvisation by Scott Henderson, through the special mode myxolydian b2#4 and we finally associate a braid representation to the fragment we analysed.