Summary
International Symposium on Nonlinear Theory and its Applications
2008
Session Number:A1L-B
Session:
Number:A1L-B2
Analyzing and Composing Music with Complex Networks: Finding Structures in Bach’s, Chopin’s and Mozart’s
Chi K. Tse, Xiaofan Liu, Michael Small,
pp.-
Publication Date:2008/9/7
Online ISSN:2188-5079
Summary:
In this paper we study the network structure in music and attempt to compose music artificially. Networks are constructed with nodes and edges corresponding to musical notes and their co-occurrences. We analyze sample compositions from Bach, Mozart, Chopin, as well as other types of music including our local (Hong Kong) pop. We observe remarkably similar properties in all networks constructed from the selected compositions. Power-law exponents of degree distributions, mean degrees, clustering coefficients, mean geodesic distances, etc. are reported. With the network constructed, music can be created by using a biased random walk algorithm, which begins with a randomly chosen note and selects the subsequent notes according to a simple set of rules that compares the weights of the edges and/or the relative degrees of nodes. The newly created music from Mozart’s network will be played in the presentation, along with the original piece.