A Graph-Theoretic Approach to Efficient Voice-Leading

TL;DR

This paper applies graph theory and complex network analysis to study voice-leading in music, quantifying chord importance and connectivity within harmonic networks to better understand musical flow.

Contribution

It introduces a novel graph-theoretic framework for analyzing voice-leading, combining classical and modern network measures to assess chord significance.

Findings

No triad is more isolated than others in common scales.

Complex network measures identify key chords for harmonic flow.

Different centrality measures provide insights into chord importance.

Abstract

We study the Neo-Riemannian principle of parsimonious voice-leading using tools and techniques from classical graph theory and the modern field of complex networks. We quantify the relative importance of particular chords within this framework. The graph-theoretic notion of eccentricity suggests that when working in a harmonic scheme dictated by any common musical scale, no triad is any more isolated than any other. Complex network theory refines this idea, and in this context provides measures of how important particular triads might be for the flow of chord progressions through the harmonic network. We review and compare several different such measures of centrality and communicability.