Topology of Networks in Generalized Musical Spaces

Abstract

The abstraction of musical structures as mathematical objects in a geometrical space is one of the major accomplishments of contemporary music theory. The author generalizes the concept of musical spaces as networks and derives compositional design principles via network topology analysis. This approach provides a framework for analysis and quantification of similarity of musical objects and structures and suggests a way to relate such measures to human perception of different musical entities. Finally, network analysis provides alternative ways of interpreting the compositional process by quantifying emergent behaviors with well-established statistical mechanics. Interpreting the latter as probabilistic randomness in the network, the author develops novel compositional design frameworks.