Derivation of 22 srutis of indian music as a fret spacing problem
In Indian music the tonic (1/1) is called Sa (S) and the perfect fifth (3/2) is called Pa (P). Indian music being monophonic, S and P are the only notes that are allowed to be heard along with any other note. So strings are tuned in S - P relationship only. That way even if the strings are accidentally struck not much harm is done. In my view, 22 srutis appear as the solution to a problem of identifying the optimal number of fret positions in a fixed fret ( straight frets perpendicular to strings ) - stringed instrument, tuned to S (1/1 ) - P (3/2) , while satisfying the following constraints. - The notes should be consonant with both strings S - P - It should be possible to play the scale assuming either string as the tonic, in which case the string relationship is S (1/1) - M ( 4/3 ) - Exploit octave complements, since we have to live with them - example S - P, P - 2 S This places the following mathematical constraints on the solution set which is a set of d...