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.