Harmonic structures of Beethoven quartets: a complex network approach

TL;DR

This paper introduces a complex network method to analyze Beethoven's quartets, revealing scale-free properties, community structures, and stylistic differences across periods in tonal harmony.

Contribution

It presents a novel network-based framework for studying harmonic structures in Western tonal music, applied specifically to Beethoven's string quartets.

Findings

Network is scale-free

Identifies community structures correlating with musical periods

Proposes statistical measures to distinguish stylistic differences

Abstract

We propose a complex network approach to the harmonic structure underpinning western tonal music. From a database of Beethoven's string quartets, we construct a directed network whose nodes are musical chords and edges connect chords following each other. We show that the network is scale-free and has specific properties when ranking algorithms are applied. We explore its community structure and its musical interpretation, and propose statistical measures stemming from network theory allowing to distinguish stylistically between periods of composition. Our work opens the way to a network approach of structural properties of tonal harmony.