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.


Website inaugurated on the 2nd, 3rd February, 2008 by Achyut Godbole, Dr.N.Rajam and Pt. D.K.Datar.
©20082012, 22shruti.com  All rights reserved. 