The Mathematical Foundations
of Indian Rhythm
is a program that will demonstrate various ways of visualizing rhythms using mathematical proportions, employing symmetric musical shapes, and calculating musical combinations and possibilities. The lessons will be curated and compiled by Rajna Swaminathan (a mrudangam artist representing the South Indian Carnatic tradition), Ganavya Doraiswamy (a vocalist also trained in South Indian Carnatic tradition, who recently pubilshed a work titled Fundamentals of Indian Music for Berklee College of Music), and Miles Okazaki (a guitarist well versed in both jazz and Indian rhythmic techniques, author of Fundamentals of Guitar).
Through exposure to these creative methods of using mathematics, students will gain a richer understanding of the aesthetics of mathematical principles and start to visualize and even hear proportions, additive combinations, and juxtapositions. By distilling the fundamental elements of the Indian rhythmic traditions, this program will provide an entry point into experiencing how musicians can use mathematics to create an infinite compositional and improvisational palette. The lessons can be useful for students working on a variety of skills: basic arithmetic, fractions and ratios, geometry, algebra, or permutations and combinations.
Karnatik music has its origins in South India, but is now practiced in many parts of the world. Music in India has undergone many changes over the centuries, and at each stage, people have tried to record the rules and practices in various theoretical treatises. Karnatik music as we know it was codified most recently in the 20th century, as India gained independence as a democratic nation. However, the essence of the music is considered an oral tradition: while its grammar has been written down throughout history, much of the musical meaning and expressivity is handed down and transformed from generation to generation by ear.
This emphasis on the oral tradition has honed a time-tested educational approach that encourages the student to understand the concepts in multiple ways – visually and aurally – leading to an embodied knowledge makes musical memory and skill feel like second nature. By harnessing this “hands-on” aspect of Karnatik music, we hope that the mathematical ideas covered here can become embedded in students’ daily embodied understandings, as well as in their conceptualization of the world they inhabit and its diverse cultures.
These still in-progress lesson plans, created exlusively for the Thelonious Monk Institute's International Jazz Day Program and Outreach Inititative, demonstrate how the pedagogical methods of Karnatik music can help a student work with mathematical concepts in a tangible manner.