Topology of Networks in Generalized Musical Spaces
This work addresses the problem of understanding and creating music through mathematical modeling for music theorists and composers, but it appears incremental as it builds on existing abstractions of musical structures.
The paper tackles the problem of analyzing and quantifying musical structures by generalizing musical spaces as networks and analyzing their topology, resulting in a novel framework for measuring similarity and relating it to human perception, and developing compositional design frameworks using statistical mechanics.
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.