  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.
