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The abstraction of musical structures (notes, melodies, chords, harmonic orrhythmic progressions, etc.) as mathematical objects in a geometrical space isone of the great accomplishments of contemporary music theory. Building on thisfoundation, I generalize the concept of musical spaces as networks and derivefunctional principles of compositional design by the direct analysis of thenetwork topology. This approach provides a novel framework for the analysis andquantification of similarity of musical objects and structures, and suggests away to relate such measures to the human perception of different musicalentities. Finally, the analysis of a single work or a corpus of compositions ascomplex networks provides alternative ways of interpreting the compositionalprocess of a composer by quantifying emergent behaviors with well-establishedstatistical mechanics techniques. Interpreting the latter as probabilisticrandomness in the network, I develop novel compositional design frameworks thatare central to my own artistic research.

Topology of Networks in Generalized Musical Spaces