Alain Daniélou (1907-1994), an expert of European musical intervals, had studied the Indian Classical music too (22 shrutis) for a large part of his life.
Danielou wanted to evolve a system that comes closer to many of the world music systems. Hence, he developed a musical scale of 53 notes, only using the ratios of the prime factors 2, 3 and 5, which is similar to the 22-Shruti system.
The attempt was of course laudable, but the Semantic Daniélou-53 system differs from 22 shrutis as shown below. Only 19 out of the 22 shrutis (shown in Red) are present in the Semantic Daniélou-53 system as shown in the following table.
The details of the 3 missed shrutis are given at the bottom of the table.
| Number | Note | Ratio | Cents | Interval (Shruti) |
| 0 | C | 1-Jan | 0 | Unison |
| 1 | C+ | 81/80 | 21,506 | Pramana shruti, syntonic comma |
| 2 | C++ | 128/125 | 41,059 | Diesis, small quartertone |
| 3 | Db- | 25/24 | 70,672 | 5-limit Lagu |
| 4 | Db | 135/128 | 92,179 | Major limma, 1st shruti |
| 5 | Db+ | 16/15 | 111,731 | Diatonic semitone, apotome (r2) |
| 6 | Db++ | 27/25 | 133,238 | Zarlino semitone |
| 7 | D-- | 800/729 | 160,897 | High neutral 2nd, Dlotkot |
| 8 | D- | 10-Sep | 182,404 | Minor whole tone (R1) |
| 9 | D | 9-Aug | 203,910 | Major whole tone (R2) |
| 10 | D+ | 256/225 | 223,463 | Double apotome |
| 11 | D++ | 144/125 | 244,969 | Low semifourth |
| 12 | Eb- | 75/64 | 274,582 | Low minor third |
| 13 | Eb | 32/27 | 294,135 | 3-limit minor third (g1) |
| 14 | Eb+ | 6-May | 315,641 | 5-limit minor third (g2) |
| 15 | Eb++ | 243/200 | 337,148 | Double Zalzal (54/49)^2 |
| 16 | E- | 100/81 | 364,807 | Double minor tone |
| 17 | E | 5-Apr | 386,314 | 5th harmonic major third (G1) |
| 18 | E+ | 81/64 | 407,820 | 3-limit major third (G2) |
| 19 | E++ | 32/25 | 427,373 | Supermajor third, Daghboc |
| 20 | F-- | 125/96 | 456,986 | Hypermajor third |
| 21 | F- | 320/243 | 476,539 | Biseptimal slendroic fourth |
| 22 | F | 4-Mar | 498,045 | 3-limit natural fourth (M1) |
| 23 | F+ | 27/20 | 519,551 | Fourth + pramana shruti (M2) |
| 24 | F++ | 512/375 | 539,104 | Fourth + diesis, Zinith |
| 25 | F#- | 25/18 | 568,717 | Major third + minor tone |
| 26 | F# | 45/32 | 590,224 | Diatonic tritone, 11th shruti (m1) |
| 27 | F#+ | 64/45 | 609,776 | High tritone, 12th shruti |
| 28 | F#++ | 36/25 | 631,283 | Double minor third |
| 29 | G-- | 375/256 | 660,896 | Narayana, reverse Zinith |
| 30 | G- | 40/27 | 680,449 | Fifth minus pramana |
| 31 | G | 3-Feb | 701,955 | 3rd harmonic perfect fifth (P) |
| 32 | G+ | 243/160 | 723,461 | Fifth plus pramana |
| 33 | G++ | 192/125 | 743,014 | Low trisemifourth |
| 34 | Ab- | 25/16 | 772,627 | Low minor sixth, double 5/4 |
| 35 | Ab | 128/81 | 792,180 | 3-limit minor sixth (d1) |
| 36 | Ab+ | 8-May | 813,686 | 5-limit minor sixth (d2) |
| 37 | Ab++ | 81/50 | 835,193 | Double Zalzal |
| 38 | A- | 400/243 | 862,852 | Double Daghboc |
| 39 | A | 5-Mar | 884,359 | 5-limit major sixth (D1) |
| 40 | A+ | 27/16 | 905,865 | 3-limit major sixth (D2) |
| 41 | A++ | 128/75 | 925,418 | Supermajor sixth |
| 42 | Bb-- | 125/72 | 955,031 | Reverse semifourth |
| 43 | Bb- | 225/128 | 976,537 | Low minor seventh |
| 44 | Bb | 16-Sep | 996,090 | 3-limit minor seventh (n1) |
| 45 | Bb+ | 9-May | 1,017,596 | 5-limit minor seventh (n2) |
| 46 | Bb++ | 729/400 | 1,039,103 | Low neutral seventh |
| 47 | B- | 50/27 | 1,066,762 | Reverse Zarlino semitone |
| 48 | B | 15-Aug | 1,088,269 | Major seventh, 15th harmonic (N1) |
| 49 | B+ | 256/135 | 1,107,821 | High major seventh, 21th shruti |
| 50 | B++ | 48/25 | 1,129,328 | Reverse 5-limit Lagu |
| 51 | C-- | 125/64 | 1,158,941 | Triple major third |
| 52 | C- | 160/81 | 1,178,494 | Octave minus pramana |
| 53 | C | 2-Jan | 1,200,000 | Octave (S’) |
It can be appreciated that 3 out of 22 shrutis are missing in the above table, namely, r1 (256/243), m2 (729/512) and N2 (243/128).
This is because the system does not ‘strictly’ follow the ‘Poorna-Praman-Nyuna’(mathematical ratios in a series) of the 22 shruti-system (See Diagram on our homepage), e.g., Danielou gives 135/128 (1.0546875) which is close to r1 (256/243 or 1.053497942), 64/45 (1.42222222) which is close to m2 (729/512 or 1.423828125),and 256/135 (1.8962962962) which is close to N2 (243/128 or 1.8984375).
The differences are small but there is no reason to have imperfect numbers for the 22 shrutis, when perfect numbers can be easily selected.
In short, the above Danielou’s 53-note system is close to 22 shrutis, but not perfect.
You are wrong about your statement regarding Danielou
The 22 shruti scheme published by Danielou in Music and the Power of Sound (1996) is identical to your scheme apart from the assignment of the fractional value for just one shruti 12, which Danielou assigns as the just tritone (64/45) and you the Pythagorean augmented fourth (729/512). These two notes differ by just 1.954 cents. Look at Fig 11 (p 80) and Fig 17 (p 142-145).
For shruti 1 he gives it (in that publication) as 256/243 – the Pythagorean limma just as you do , but with an alternative of 135/128. The same goes for shruti 21 243/128 with alternative 256/135. So these shrutis are not missing in that scheme published by Danielou. Also. these notes differ by just 1.953 cents, which are effectively indistinguishable by any normal mortal being.
I find it impossible to believe that Indian musicians can reproducibly produce these exact relative frequencies when singing or playing an instrument. In fact they can't and they don't as shown by Wim van der Meer. Every swara sung has a significant range of pitch, which depends on the artist, the raga, and the specific performance. So your efforts and everyone else's on this matter are merely academic and mathematical exercises.