For a long time, I found the tani avartanam to be the most alienating part of the concert. Beyond the thrill of the rhythmic table tennis between the mridangam player and the supporting percussionists, I didn't get what was happening. I would keep tala during the longer rounds, often slipping and looking at the main artiste to get back on track, but I never understood when or why the audience sighed, why the main artiste exclaimed a "Besh!" suddenly, how each performer knew when his round started, and how the main artiste knew exactly when to jump in with the song again.

Then, I had no one to guide me to the answers to these questions. I attended most concerts alone or with people who understood even less than me. Each concert, I tried to make sense of the human spectacle before me — four or five musicians on stage, revelling in what seemed like a fun session of musical mathematics, cracking in-jokes and being all nudge-nudge-wink-wink with each other.

While drum solos in most forms of music coax the audience to clap along to the beat, Carnatic percussionists challenge their audience to keep beat. Educated audiences, of course, are more than willing to take up the challenge. Look around the hall, and there are always some people, nonchalantly counting, with this knowing expression on their face that almost says, "I know what's coming."

The tani isn't easy to follow because the emphasis is not on the beat itself, but on how to split that time interval between beats and fill the gaps between them, how to spin variations on rhythmic themes and build on them. The tani is as much about rhythm cycles as it is about patterns and structures. It is an intellectual exercise, as much as it is a musical one. You can be clever, you can be witty. You can be impenetrable, you can be arcane.

I felt like I was being excluded from a club that I desperately wanted to be in. This egged me to crack the code.

Unwinding the knot

After some years of intense listening and furious mental note-taking, I noticed that there were portions when the rhythmic structures wove a little knot around the beat I was keeping. I would concentrate and keep tala till this knot unwound itself, which it did, every time, on the "samam", where the tala began, or the "edam", where the composition began. I was able to identify that a phrase that formed the refrain of this knot repeated or underwent small variations to make the knot. Then, I found that the structural knot almost always repeated itself three times and that even the elements that made up this knot were often grouped in threes. Three, therefore, was some sort of magic number. This "knot", a friend told me, is the "korvai".

There were times when the tala and the patterns being played were in sync — the nuances were, I surmised, in how they were kept in sync. I just christened this part of the tani "flow". In the best tani avartanams, the "flow" morphs seamlessly into the "knot", almost as if the latter were an extension of the former.

After the percussionists trade shorter and shorter phrases before joining in for the crescendo, they play together. Here, my ears discerned a recurring theme that signalled one last set-piece before the home stretch – a joyous hurrah that was a part of nearly every tani avartanam. The theme landed, I realised, on another knot — the main korvai — at the end of which, the melody section broke out into song.

Tani avartanam-s, like all other aspects of improvisational music, vary in terms of their form and structure, but pretty much every tani is made of these very building blocks — the "knots" (korvai), the "flows", the "table tennis" (kuraippu), and the "home stretch" (periya mohra and korvai). Their names and the solkattu syllables change from region to region and school to school. The technique of rendering them might also differ. But the underlying elements remain the same.

The world where music and mathematics collide is fascinating, and the tani avartanam is both a meditation and celebration of this space.

It might seem distancing at first, but learning to enjoy one takes only a little bit of close listening (a postponement of one's coffee break, perhaps) and some inputs from a knowledgeable friend, teacher or that veritable modern-day guru, Baba Googlenath.

(The author is a flautist, writer and a practising lawyer.)