37ed8

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Revision as of 14:35, 4 August 2023 by Dummy index (talk | contribs) (Created page with "{{Infobox ET}} 37ed8 is an equal tuning that divides the 8/1 ratio (triple-octave, octuple, fifteenth) into 37 equal steps of approximately 97.297 cents. It stands out as a 8....")
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← 36ed8 37ed8 38ed8 →
Prime factorization 37 (prime)
Step size 97.2973 ¢ 
Octave 12\37ed8 (1167.57 ¢)
Twelfth 20\37ed8 (1945.95 ¢)
Consistency limit 2
Distinct consistency limit 2

37ed8 is an equal tuning that divides the 8/1 ratio (triple-octave, octuple, fifteenth) into 37 equal steps of approximately 97.297 cents. It stands out as a 8.9.10.14.22.26.17/2.19/2 subgroup tuning. This is an another approach for 97.5cET.

Approximation of harmonics in 37ed8
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Error Absolute (¢) -32.4 +44.0 +32.4 +35.3 +11.6 +36.6 +0.0 -9.3 +2.9 +32.5 -20.9 +35.1 +4.1 -18.0
Relative (%) -33.3 +45.2 +33.3 +36.3 +11.9 +37.6 +0.0 -9.6 +3.0 +33.4 -21.5 +36.1 +4.3 -18.5
Steps
(reduced)
12
(12)
20
(20)
25
(25)
29
(29)
32
(32)
35
(35)
37
(0)
39
(2)
41
(4)
43
(6)
44
(7)
46
(9)
47
(10)
48
(11)

Intervals

Steps Cents Ratio approximated
1 97.297 17/16, 18/17, 19/18, 20/19
2 194.595 9/8, 10/9, 19/17
3 291.892 13/11, 19/16, 20/17
4 389.189 5/4
5 486.486 25/19, 45/34
6 583.784 7/5
7 681.081 28/19
8 778.378 11/7, 14/9, 25/16
9 875.676 28/17
10 972.973 7/4
11 1070.270 13/7
12 1167.568 49/25, 35/18
13 1264.865 35/17, 52/25
14 1362.162 11/5
15 1459.459 44/19, 65/28
16 1556.757 22/9
17 1654.054 44/17, 13/5
18 1751.351 11/4, 52/19
19 1848.649 26/9, 55/19
20 1945.946 52/17, 55/18
21 2043.243 13/4, 55/17
33 3210.811 32/5
34 3308.108 88/13, 34/5
35 3405.405 36/5, 64/9
36 3502.703 38/5, 68/9
37 3600.000 8/1