Representing melodic relationships using network science.

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 modelling 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) judgements 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.