It is well-known that while mathematics plays a role in music-making, most musicians do not necessarily engage with it in an explicit manner. In the case of Hindustani music, a student’s engagement with mathematics takes place from the formative stages. Depending on the teacher’s proclivity to this aspect, a student is put through graded musical exercises that focus on rhythm. Various cross-rhythmic patterns are taught to enable the student to get a grip on the taal cycle. Percussionists are taught more complex rhythmic structures. On the melodic side, permutations and combinations of swaras or notes are created as per formulae.

The test for a sensitive performer is to integrate this information into the larger body of knowledge that he or she imbibes, and to then use it judiciously in performance practice. While some vocalists and instrumentalists engage in the mathematical aspect in an obvious fashion, there are others who almost completely eschew any cross-rhythmic interplay or avoid vigorous dialogues with their percussionists. But even in the case of the latter, they cannot ignore this element completely, as this would create anarchy in their musical presentation.

Importantly, however, a disproportionate tilt towards the mathematical part could adversely affect the expressive quality of the music that performers would normally hope to realise. A good guru demonstrates how a balance can be achieved, but it is equally possible that the disciple may choose to deviate and focus on this aspect.

Mathematics of rhythm

Having said that, there have been rare exceptions of practitioners who have immersed themselves in the mathematics of music, or rather, the mathematics of rhythm.

Goa-born pakhawaj and tabla player Khaprumama Parvatkar (1880-1953), an iconic figure in this context, made this a lifelong passion. From using all four limbs to tap out different taals simultaneously while reciting yet another or even reciting intricate compositions, to placing cross-rhythmic patterns accurately over taals having fractional matras or time units, Parvatkar achieved what seemed humanly impossible.

He was publicly felicitated for his presentations and the best-known percussionists showered praise on him for his command over the mathematics of rhythm. In fact, he was awarded the title Layabhaskar or the “sun of rhythm” to acknowledge his prowess.

Parvatkar’s wizardry was captured on 78 rpm recordings that have been made available by scholar-musician Rajan Parrikar: