Representing Melodic Relationships Using Network Science

Abstract

Music is a complex system consisting of many dimensions and hierarchically organized
information—the organization of which, to date, we do not fully understand. Network science
provides a powerful approach to representing such complex systems, from the social networks of
people to modelling the underlying network structures of different cognitive mechanisms. In the
present research, we explored whether network science methodology can be extended to model
the melodic patterns underlying expert improvised music. Using a large corpus of transcribed
improvisations, we constructed a network model in which 5-pitch sequences were linked
depending on consecutive occurrences, constituting 116,403 nodes (sequences) and 157,429
edges connecting them. We then investigated whether mathematical graph modeling relates to
musical characteristics in real-world listening situations via a behavioral experiment paralleling
those used to examine language. We found that as melodic distance within the network
increased, participants judged melodic sequences as less related. Moreover, the relationship
between distance and reaction time (RT) judgments was quadratic: participants slowed in RT up
to distance four, then accelerated; a parallel finding to research in language networks. This study
offers insights into the hidden network structure of improvised tonal music and suggests that
humans are sensitive to the property of melodic distance in this network. More generally, our
work demonstrates the similarity between music and language as complex systems, and how
network science methods can be used to quantify different aspects of its complexity.

Keywords: music, network science, improvisation