Mathematical Representation and Analysis of Rhythms from Various Regions

Rhythm is one of the fundamental elements of music. Each piece of music follows a rhythm. It might be observed that music of various regions differ from each other. A basic question is-what are the underlying properties of music that cause this difference? In this paper, first we study mathematical representation of rhythms of various regions. And then we analyze these representations with a view to building a classification system that can categorize rhythms of various regions. Here we use basically the same mathematical representation given by Toussaint [3, 4]. Toussaint has also shown a way to classify African, Brazilian and Cuban rhythms based on various distance matrices. In this paper, apart from these rhythms, we also study North Indian rhythms, used in India and Bangladesh and use turning function [1], a function for polygon similarity measurement, to find out distance measures among various rhythms. Finally, we use various types of phylogenetic trees to build up a graphical classification system.