Harmonic structures of Beethoven quartets: a complex network approach

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.