# Mathematical musings in art

Today during dance practice, I made a mistake. While keeping the beat for a song, I had switched from chaturashra Eka taaLa to aadi taaLa inadvertently. At the end of the song, I was surprised to find that I had not completed the taaLa at the correct position.

Later I got to thinking of this mistake and analysed the simple mathematics behind it. chaturashra Eka taaLa is a sequence of 4 beats while aadi taaLa is a sequence of 8 beats. Therefore, each aavartana of chaturashra Eka taaLa is comprised of 4 beats and each aavartana of aadi taaLa is comprised of 8 beats. The LCM of 4 and 8 is 8, so they will go in harmony if the total number of beats of the song is a common multiple.

All multiples of 8 are also multiples of 4, however, all multiples of 4 are not multiples of 8. From Figure 1, it is evident that odd multiples of 4 are those of 4 only and even multiples of 4 are also multiples of 8.

Figure 1 – Multiples of 4, multiples of 8 are highlighted

So, if the number of aavartanas in a song is an even multiple of 4, then the two taaLas will end at the correct position even if interchanged. If the number of aavartanas in a song is an odd multiple of 4, then the two taaLas will not end at the correct position if interchanged. Because the multiples of 8 is a subset of the set of multiples of 4, aadi taaLa can be swapped with chaturashra Eka taaLa without making a mistake. However, swapping chaturashra Eka taaLa with aadi taaLa will be inaccurate.

There is a lot of mathematics in music and dance, it is refreshing to make these connections on an everyday basis.

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#### Dr. Soumya Sreehari

Co-Founder and Specialist at NumberNagar®
Dr. Soumya is an Educator and Researcher with a passion for reading, writing and teaching. She holds a PhD in Chemistry (Michigan Technological University, Houghton, USA). Her experience as a student and a teacher in two countries led her to pursue a career in Education. Her core work at NumberNagar® involves quality delivery of product and services at every stage of the customer life cycle. She leads the team that makes this happen. Previously she has taught Chemistry to first year undergraduate students at Michigan Technological University. She is a voracious reader and challenges herself to read 50 books every year.