Mathematical and Geometrical Analysis and Representation of North Indian Musical Rhythms Based on Multi Polygonal Model

One of the universal languages which transcends all barriers of country, race or religion is music. Sometimes it is said that music is the language of the soul. To identify the underlying properties of music we have to understand its basic element and the basic element of music is rhythm. Identifying the structure of musical rhythm and performing similarity measurement between them is important in computational musicology. It also becomes as an interesting and challenging problem in computer science. No music can run without rhythm and rhythm is the combination of some claps and waves with some bols (speech or syllables). In this paper most commonly used north Indian rhythms are analyzed and represented in binary format where dasia1psila (black dot) indicates the clap and dasia0psila (empty field) indicates the wave. The mathematical and geometrical analysis is also performed to build a classification system that cans categories these rhythms. Here the multi polygonal model is used to represent the north Indian rhythm and various distance matrixes are generated using the turning function. Based on this distance matrix a number of phylogenetic trees are also used to represent the classification trees of the north Indian rhythm.