DANIELOU'S "UNIVERSAL SCALE" COMPARED TO 72 TONE EQUAL TEMPERAMENT

David Canright has prepared the following chart, comparing Danielou's "Universal Scale" to it's approximations in 72-tET.

This scale can be found in: Danielou, Alain, Music and the Power of Sound, The Influence of Tuning and Interval on Consciousness, Inner Traditions, Rochester, Vermont, USA 1995, p42.

 

Note Indian solfege sruti ratio, cents error, note, key
1 Sa 0 1/1 +0.0 0 0:0
2 81/80 +4.8 1 1:0
46/45 +4.7 2 2:0
3 128/125 +7.7 2 2:0
31/30 +6.8 3 3:0
4 1 25/24 +4.0 4 4:0
256/243 +6.9 5 5:0
5 135/128 -7.8 6 0:1
6 2 16/15 -4.9 7 1:1
2187/2048 -3.0 7 1:1
7 27/25 -0.1 8 2:1
135/124 -2.9 9 3:1
8 800/729 -5.8 10 4:1
11/10 -1.7 10 4:1
9 3 10/9 -0.9 11 5:1
10 Re 4 9/8 +3.9 12 0:2
11 256/225 +6.8 13 1:2
8/7 -2.2 14 2:2
2187/1900 -6.5 15 3:2
12 15/13 -2.3 15 3:2
93/80 -6.0 16 4:2
13 75/64 +7.9 16 4:2
14 5 32/27 -5.9 18 0:3
15 6 6/5 -1.0 19 1:3
75/62 -3.8 20 2:3
243/200 +3.8 20 2:3
16 8000/6561 -6.7 21 3:3
17 100/81 -1.9 22 4:3
18 Ga 7 5/4 +3.0 23 5:3
19 8 81/64 +7.8 24 0:4
19/15 -7.4 25 1:4
20 32/25 -6.0 26 2:4
31/24 -6.9 27 3:4
21 125/96 +7.0 27 3:4
22 320/243 -6.8 29 5:4
23 Ma 9 4/3 -2.0 30 0:5
24 10 27/20 +2.9 31 1:5
25 512/375 +5.8 32 2:5
2187/1600 +7.7 32 2:5
62/45 +4.8 33 3:5
26 25/18 +2.1 34 4:5
7/5 -0.8 35 5:5
27 11 45/32 +6.9 35 5:5
28 12 64/45 -6.9 37 1:6
29 36/25 -2.1 38 2:6
45/31 -4.8 39 3:6
19/13 +7.0 39 3:6
30 375/256 -5.8 40 4:6
31 40/27 -2.9 41 5:6

 

 

 

 

Note Indian solfege sruti ratio cents error, note key
32 Pa 13 3/2 +2.0 42 0:7
33 243/160 +6.8 43 1:7
34 192/125 -7.0 45 3:7
19683/12800 -5.0 45 3:7
31/20 -7.9 46 4:7
35 25/16 +6.0 46 4:7
36 14 128/81 -7.8 48 0:8
19/12 -4.4 48 0:8
37 15 8/5 -3.0 49 1:8
50/31 -5.7 50 2:8
38 81/50 +1.9 50 2:8
39 400/243 -3.8 52 4:8
40 Dha 16 5/3 +1.0 53 5:8
41 17 27/16 +5.9 54 0:9
42 128/75 -7.9 56 2:9
12/7 -0.2 56 2:9
31/18 +7.8 56 2:9
43 125/72 +5.0 57 3:9
7/4 +2.2 58 4:9
44 225/128 -6.8 59 5:9
45 18 16/9 -3.9 60 0:10
46 19 9/5 +0.9 61 1:10
29/16 -3.8 62 2:10
729/400 +5.8 62 2:10
47 4000/2187 -4.7 63 3:10
48 50/27 +0.1 64 4:10
13/7 +5.0 64 4:10
49 Ni 20 15/8 +4.9 65 5:10
21 256/135 +7.8 66 0:11
50 243/128 -6.9 67 1:11
51 48/25 -4.0 68 2:11
60/31 -6.8 69 3:11
31/16 -5.0 69 3:11
52 125/64 -7.7 70 4:11
53 160/81 -4.8 71 5:11
1 Sa 22 2/1 +0.0 72 0:12

Each entry includes the ratio, cents error relative to nearest tempered (so, for example, 3/2 is +2.0c relative to note #42), tempered note # (0-71), keyboard # (0-5), key # (0-11), where keyboards 1 -5 are~ assumed progressively [17 globally] sharper relative to keyboard 0 [which are all 12-tET].

Tues., 1 May 2001 from "Canright, David"

www.alaindanielou.org

 

SRUTI

 

PAUL ERLICH'S 17-LIMIT TABLE

NOTE NUMBERS

TEMPERAMENT

DAVID CANRIGHT PUBLICATIONS

DAVID CANRIGHT PERSONAL WEBPAGE

IMPROVISATION IN CANRIGHTS 13-LIMIT 12 TONE SCALE

TUNING PAGE

Maurice Courant allows himself to write: "Needless to say, the sixty degrees in the octave are scarcely perceptible and are difficult to realize, a slight difference of temperature bringing a significant variation in the sound compared with the interval of two successive degrees. Such a scale can never be accurate." Courant, Maurice. "Chine et Corée, essai historique sur la musique classique des chinois." In Encylopédie de la musique et dictionnaire du Conservatoire. Paris: Delagrave, 1922., in Daniélou, Alain, Music and The Power of Sound, Inner Traditions, Rochester, VT, 1995, p55]

. . . We should not forget that the problem is not to play intervals of one comma in succession but to play intervals with an accuracy of one comma. A difference of one comma in a fifth or an octave is not only perceptible but extremely disagreeable even to an untrained ear. The same difference in a third or in a major second (it is then the difference between the major and the minor tone) completely changes the color of the note and its expression. One can even say, as a rule, that such differences are the very basis of vocal and melodic expression, . . . . [Daniélou, Alain, Music and The Power of Sound, Inner Traditions, Rochester, VT, 1995, p55]

 

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December 4, 2003
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