# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1905.01842