Topology of Networks in Generalized Musical Spaces

Marco Buongiorno Nardelli (1, 2, 3)

1 PRISM - Perception, Représentations, Image, Son, Musique
2 IMéRA - Institute for Advanced Studies - Aix-Marseille University
3 UNT - University of North Texas

The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this foundation, I generalize the concept of musical spaces as networks and derive functional principles of compositional design 15 by the direct analysis of the network topology. This approach provides a novel framework for the analysis and quantification of similarity of musical objects and structures, and suggests a way to relate such measures to the human perception of different musical entities. Finally, the analysis of a single work or a corpus of compositions as complex networks provides alternative ways of interpreting the compositional process of a composer by quantifying emergent behaviors with 20 well-established statistical mechanics techniques. Interpreting the latter as probabilistic randomness in the network, I develop novel compositional design frameworks that are central to my own artistic research. One Sentence Summary: Network theory is an innovative tool for the classification of generalized musical spaces and provides a framework for the discovery or generation of functional 25 principles of compositional design.

Domaines: Musique, musicologie et arts de la scène; Son [cs.SD]; Acoustique [physics.class-ph]; Machine Learning [stat.ML]; Algorithme et structure de données [cs.DS]

Marco Buongiorno Nardelli. Topology of Networks in Generalized Musical Spaces. 2019. ⟨hal-02271490⟩