Alain Daniélou (19071994), 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 22Shruti system. The attempt was of course laudable, but the Semantic Daniélou53 system differs from 22 shrutis as shown below. Only 19 out of the 22 shrutis (shown in Red) are present in the Semantic Daniélou53 system as shown in the following table. 
Number 
Note 
Ratio 
Cents 
Interval (Shruti) 
0 
C 
1/1 
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 
5limit 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 2^{nd}, Dlotkot 
8 
D 
10/9 
182,404 
Minor whole tone (R1) 
9 
D 
9/8 
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 
3limit minor third (g1) 
14 
Eb+ 
6/5 
315,641 
5limit 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 
5/4 
386,314 
5th harmonic major third (G1) 
18 
E+ 
81/64 
407,820 
3limit 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 
4/3 
498,045 
3limit 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, 11^{th} shruti (m1) 
27 
F#+ 
64/45 
609,776 
High tritone, 12^{th} 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 
3/2 
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 
3limit minor sixth (d1) 
36 
Ab+ 
8/5 
813,686 
5limit minor sixth (d2) 
37 
Ab++ 
81/50 
835,193 
Double Zalzal 
38 
A 
400/243 
862,852 
Double Daghboc 
39 
A 
5/3 
884,359 
5limit major sixth (D1) 
40 
A+ 
27/16 
905,865 
3limit 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 
16/9 
996,090 
3limit minor seventh (n1) 
45 
Bb+ 
9/5 
1017,596 
5limit minor seventh (n2) 
46 
Bb++ 
729/400 
1039,103 
Low neutral seventh 
47 
B 
50/27 
1066,762 
Reverse Zarlino semitone 
48 
B 
15/8 
1088,269 
Major seventh, 15^{th} harmonic (N1) 
49 
B+ 
256/135 
1107,821 
High major seventh, 21th shruti 
50 
B++ 
48/25 
1129,328 
Reverse 5limit Lagu 
51 
C 
125/64 
1158,941 
Triple major third 
52 
C 
160/81 
1178,494 
Octave minus pramana 
53 
C 
2/1 
1200,000 
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 ‘PoornaPramanNyuna’(mathematical ratios in a series) of the 22 shrutisystem (See Diagram on homepage), e.g., he 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 53note system is close to 22 shrutis, but not perfect. 

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