I was struggling hard to decifer the mathematics behind 22 shrutis.

As days and months passed by in tedious calculations, I was becoming certain that there had to be a 'simpler' method to get to the Shrutis, and I was not succeeding probably because of only trying the difficult paths.

One day, I went back to basics.

The Saptak was 'S-R-G-M' repeated twice, forming the complete Saptak (P-D-N-S' are actually, S-R-G-M from P).

The secret must be here, I thought, and one day, I started studying the inter-relationships between these 4 notes.

Out of these notes, **S and M were "Natural"** and well-defined by Nature at 100 and 133.33 % respectively. The notes **R and G were different "in Nature" and "as arrived Mathematically"** (By Pythagoras), giving the following differences. (Refer to following table)

My findings were as follows:

- 1The distances between Natural S and Natural R was
**12.5%.** - 2The distance between Natural R and Natural G was
**11.11%.** - 3The distance between Natural G and Natural M was
**6.66%.** - 4The distance between Mathematical G and Natural M was
**5.35%.**

The figure of 5.35 struck a note in my mind, as, earlier, I had also studied the Pythagorean Octave where he had found that 5.35 was the famous Pythagorean Limma!

The notes S, R, G, and M are identified and easily sung even by small children without any musical training.

There must be a natural "setting' in the brain to differentiate these distances, I thought. It occurred to me that surely, this must be the starting point.

And, when I rearranged the above distances, 5.35%, 6.66%,11.11%, and 12.5%, and starting from S taken (as 100 hz), the 22 Shrutis unearthed themselves accurately to my astonishment. (Refer to following table)

S' of course is 200. Interestingly, the distance between m2-P; and N2-S' was also exactly 5.35% confirming that the 22 Shrutis were fitting snugly and mathematically in the space between 100 and 200.

###### THE JigSaw puzzle was solved!

There were no extra pieces, and no extra space.