Complex Networks in Music Compositions

Music to Network

The study of complex network has lighted researchers in various fields including large system, power system and bio systems. Here we try to apply complex network theory in music compositions and try to compose music artificially from the networks. We consider each distinct music note as a network node and co-occurrence of music notes as network edges. A sample network formed from Bach's solo violin works looks like this.

Figure: Sample network graph modeled from Bach's Well Tempered Clavier Book II.
The deeper red a node has, the higher degree it holds.
The darker color an edge has, the more weighted it is.

Network to Music

We compose music by selecting network nodes from music network and string these music notes together to form a piece of music.
The selection process starts with a arbitrarily chosen node (the probability is proportional to its degree). Then we choose the next one from those which are linked to the previous one. The probability a node been chosen is according to its

• weight of edge connects with previous one
• node degree
• node weight (summation of all edges' weight)

corresponding to our three algorithms of Biased Random Walk. Samples of music is free to download.

• Original music (one piece from Bach's solo violin)
• sample of Algorithm 1
• sample of Algorithm 2
• sample of Algorithm 3

A packed collection of recompositions can be downloaded here.