22 Shruti Research Topics


Topic 61. Difference between the Semantic Danielo-53 System and 22 shrutis


Dr. Vidyadhar Oke   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

1/1

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

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-

10/9

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

3-limit minor third (g1)

14

Eb+

6/5

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

5/4

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

4/3

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

3/2

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

3-limit minor sixth (d1)

36

Ab+

8/5

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

5/3

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

16/9

996,090

3-limit minor seventh (n1)

45

Bb+

9/5

1017,596

5-limit 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, 15th harmonic (N1)

49

B+

256/135

1107,821

High major seventh, 21th shruti

50

B++

48/25

1129,328

Reverse 5-limit 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 ‘Poorna-Praman-Nyuna’(mathematical ratios in a series) of the 22 shruti-system (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 53-note system is close to 22 shrutis, but not perfect.




Topic 60. Common Musical Scales and their equivalent in Indian Classical Music
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