The key concept here is the distribution of k. So, we have an average degree for the whole network. The number of links emerging from and converging at a node is called the “degree” of that node, usually denoted by k. If we consider a network of musical notes, then the nodes will be the individ- ual musical notes and a link between two nodes denotes that the two musical notes are neighbors in the score. A network is usually de fi ned as a collection of “nodes” connected by “links” or “edges”. As an interim trick, some rudimentary rules may come into play when selecting compositions. Of course, we do not know exactly how the brain does that. In composing a music, from a system’s viewpoint, our human brain would have automatically performed a processing step that allows only compositions that satisfy certain network properties to emerge and fi nally pick the best composition according to the composer’s subjective choice. We ba- sically fi nd that if the same network property is retained, it is possible to compose music arti fi cially and the remain- ing open problem is the choice of a particular sample from a large number of possible compositions. Our fi nal task in this paper is to make an attempt to create “reasonably good” music 1 from the network that has been formed from given compositions such as Bach’s and Mozart’s. Our results demon- strate, quite surprisingly, that different music types actu- ally share remarkably similar properties. The purpose is to make an attempt to fi nd out if different music would display uniformity or disparity in terms of network structure. Our approach is to treat a piece of music as a complex network and to evaluate the properties of the resulting network, such as degree distribution, mean degree, mean distance, clustering coef fi cient, etc. In this paper we analysis a few distinct types of music, including classical, Russian folks and our local pop.
Scalefree power-law distribution is a remarkable property that has been found across of a variety of connected communities – and is a key to optimal performance of networked systems. A key fi nding is that most networks involving man-made couplings and connection of people are naturally connected in a scalefree manner, which means that the number of connections follows a power-law distribution. The study of complex networks in physics has aroused a lot of interest across a multitude of application areas.
One fundamental question of interest is whether these different music share similar properties, and the implication of this question is whether a common pro- cess/rule exists in the human brain that is responsible for composing music. People from different parts of the world and in different eras have their own music. Music is a form of creative art which is often identi fi ed as a signature of a particular composer, a group of people, country and culture at different times in history. The newly created music from Mozart’s network will be played in the presentation, along with the original piece. 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. Power- law exponents of degree distributions, mean degrees, clustering coef fi cients, mean geodesic distances, etc. We observe remarkably similar properties in all networks constructed from the selected compositions. We analyze sample compositions from Bach, Mozart, Chopin, as well as other types of music including our local (Hong Kong) pop. Networks are constructed with nodes and edges corresponding to musical notes and their co-occurrences. In this paper we study the network structure in music and attempt to compose music arti fi cially.
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