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 'SRGM' repeated twice, forming the complete Saptak. (PDNS' are actually, SRGM from P) The secret must be here, I thought, and one day, I started studying the interrelationships between these 4 notes. Out of these notes, S and M were "Natural" and welldefined 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) 
Table shows Basic Mathematical percentages creating 22 Shrutis : the differences in Natural S, R, G, M ; and Natural S, M, and Mathematical R and G 
My findings were 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) 
Table shows SRGM based Derivation of 22 Shrutis (based on % difference values between S,R,G,M, which are 5.35, 6.66, 11.11, and 12.5 respectively) 
S' of course is 200. Interestingly, the distance between m2P; and N2S' was also exactly 5.35% confirming that the 22 Shrutis were fitting snugly and mathematically in the space between 100 and 200. JigSaw puzzle was solved. There were no extra pieces, and no extra space.


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