Euclidean Rhythm with Palindromic Rests

Through a deep inspection of the rhythmic structures used in Indian Classical music, one can easily see how frequently Euclidean rhythms are used. There is a particular kind of Euclidean rhythm that is used very frequently: the rhythms in which the rests have a palindromic structure. In this paper, we characterize this family of rhythms. We look at the structural and geometric properties of such rhythms using tools that are very frequently used in live performances of Indian Classical music. Most of the properties have a certain combinatorial interest as well. The results we prove can be seen to be quite relevant in the context of Indian Classical music. We show how operations can be defined on such rhythms to construct a larger family of rhythms. Towards the end of the paper, we show applications of these rhythms in contemporary Indian Classical music.