Analyzing and composing music with complex networks : finding structures in Bach, Chopin and Mozart

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. Powerlaw 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.