Topology of Networks in Generalized Musical Spaces

TL;DR

This paper introduces a novel network topology framework for analyzing musical structures, enabling quantification of similarity, perception, and compositional processes through complex network analysis and statistical mechanics techniques.

Contribution

It generalizes musical spaces as networks and derives principles for compositional design, linking network topology to musical perception and creation.

Findings

Network topology quantifies musical similarity.

Complex network analysis reveals compositional patterns.

Statistical mechanics models interpret musical randomness.

Abstract

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 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 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.