22 Shruti Research Topics

Topic 21 : Discovery of 22 Shrutis from S-R-G-M

Dr. Vidyadhar Oke   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)

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

Basic Mathematical percentages creating 22 Shrutis

My findings were
1. The distances between Natural S and Natural R was 12.5%.
2. The distance between Natural R and Natural G was 11.11%.
3. The distance between Natural G and Natural M was 6.66%.
4. The 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)

Table shows S-R-G-M 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-R-G-M based Derivation of 22 Shrutis

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. Jig-Saw puzzle was solved. There were no extra pieces, and no extra space.

Topic 20 : Efforts made by 2 prominent Indian Researchers to find our Indian scale
END OF Topic 21.

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Topic 22 : Why are Shrutis 22 only ? : Natural Evolution
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