  The structure of the Euclidean algorithm can be used to generate a very large
family of rhythms. In this paper, we explore a very specific family of
Euclidean rhythms, the Euclidean rhythms in which the rests have a palindromic
structure. We look at the structural and geometric properties of such rhythms;
most of the properties have a certain combinatorial interest. We also show how
operations can be defined on such rhythms to construct a larger family of
rhythms. Towards the end of the paper, we also show applications of these
rhythms in contemporary Indian Classical music.
