The ancient logic on how different musical notes are created in a Saptak is very insightful and relevant. The fundamental notes in music are S and P and the Tanpura is tuned to these notes for the same reason. Other than P, the next important note is M because, the upper S' becomes the P of it.
The natural ratio of the frequencies of S:P is 100:150, and of S:M is 100:133.33333. These are obtainable after an analysis of an extremely welltuned Tanpura. In other words, from any musical note (taken as 100), the note at 133.33333 % is it's Madhyam, and the note at 150 % is it's Pancham. Therefore, beginning from any Shadja, if we continue the S:P cycle ahead by adding 50 % to the frequency of the earlier note, we shall complete the cycle, coming back to S' and giving 12 positions or places. And similarly, if we continue the S:M cycle ahead by adding 33.33333 % to the earlier note, we shall complete the cycle, coming back to S' giving 12 additional positions or places. In total, 24 places or 24 musical notes are obtained. (Refer to following figure)
