Harmonic structures of Beethoven quartets: a complex network approach – Archive ouverte HAL

Théo Frottier 1 Bertrand Georgeot 1 Olivier Giraud 2

Théo Frottier, Bertrand Georgeot, Olivier Giraud. Harmonic structures of Beethoven quartets: a complex network approach. The European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2022, 95, pp.103. ⟨s10051-022-00368-z⟩. ⟨hal-03540963⟩

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 the 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.

  • 1. LPT – Laboratoire de Physique Théorique
  • 2. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques

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