Continuum fingerboard

I'm sure there is somebody playing Indian classical music using these.

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Fretboard map of 22 sruti layout

I tried a few major and minor triads on this instrument and was quite pleased with the results. (maybe I'm biased after investing significant resources on this) I wanted to see what triads could be reached when this instrument is tuned in perfect fourths with six strings. I've used Indian note names 's R G m P D N' to represent the notes of the major scale. s and p are case insensitive, whereas the rest are case-sensitive. Lower case stands for the flatter note. In the key of C, here is roughly how the notes map. s - C, r - Db, R - D, g - Eb, G - E, m - F, M - F#, p - G, d - Ab, D - A, n - Bb, N - B In earlier posts I've named 4 srutis of a note using number suffixes like R1, R2, R3, R4 etc. In a fretboard map since numbers may be useful for fingers, I've named the 22 srutis as s, r, r+, R, R+, g, g+, G, G+, m, m+, M, M+, p, d, d+, D, D+, n, n+, N, N+ Numbering the strings from top to bottom the 4th string starts as 'S'. There are 11...
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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...
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Very interesting interpretation of 22 srutis

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The computed values below are surprisingly close to the ones computed using cycle of fifths. I've used a string length of 9*13*4 = 468 to have integer units for the vibrating string lengths. Sruti - Sruti Number VSL - Vibrating sring length. Ratio = String Length / VSL SA Grama - Ratios and corresponding Swara positions in Bharata's SA Grama MA Grama - Ratios and corresponding Swara positions in Bharata's MA Grama Sruti VSL Ratio SA Grama MA Grama 0 468 1.0000 1.7778 N 1.1852 G 1 455 1.0286 1.8286 1.2190 2 442 1.0588 1.8824 1.2549 3 429 1.0909 1.9394 1.2929 4 416 1.1250 1.0000 S 1.3333 M 5 403 1.1613 1.0323 1.3763 6 390 1.2000 1.0667 1.4222 7 377 1.2414 1.1034 R 1.4713 P 8 364 1.2857 1.1429 1.5238 9 351 1.3333 1.1852 G 1.5802 10 342 1.3684 1.2164 1.62...
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