37ed8: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
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...."
 
Dummy index (talk | contribs)
Line 54: Line 54:
|-
|-
| 16 || 1556.757
| 16 || 1556.757
| 22/9
| 22/9, 49/20
|-
|-
| 17 || 1654.054
| 17 || 1654.054
| 44/17, 13/5
| 44/17, 49/19, 13/5
|-
|-
| 18 || 1751.351
| 18 || 1751.351
| 11/4, 52/19
| 11/4, 49/18, 52/19
|-
|-
| 19 || 1848.649
| 19 || 1848.649
| 26/9, 55/19
| 49/17, 26/9, 55/19
|-
|-
| 20 || 1945.946
| 20 || 1945.946
| 52/17, 55/18
| 49/16, 52/17, 55/18
|-
|-
| 21 || 2043.243
| 21 || 2043.243
| 13/4, 55/17
| 13/4, 55/17
|-
|-
| ||  
| 22 || 2140.541
|  
| 55/16, 65/19
|-
|-
| ||  
| 23 || 2237.838
|  
| 65/18
|-
| 24 || 2335.135
| 65/17, 77/20
|-
| 25 || 2432.432
| 65/16, 77/19
|-
| 26 || 2529.730
| 77/18
|-
| 27 || 2627.027
| 32/7, 77/17
|-
| 28 || 2724.324
| 34/7, 77/16
|-
| 29 || 2821.622
| 36/7, 56/11
|-
| 30 || 2918.919
| 38/7, 91/17
|-
| 31 || 3016.216
| 40/7, 91/16
|-
| 32 || 3113.514
| 85/14
|-
|-
| 33 || 3210.811
| 33 || 3210.811
| 32/5
| 32/5, 45/7
|-
|-
| 34 || 3308.108
| 34 || 3308.108
| 88/13, 34/5
| 34/5, 88/13
|-
|-
| 35 || 3405.405
| 35 || 3405.405

Revision as of 15:27, 4 August 2023

← 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, 49/20
17 1654.054 44/17, 49/19, 13/5
18 1751.351 11/4, 49/18, 52/19
19 1848.649 49/17, 26/9, 55/19
20 1945.946 49/16, 52/17, 55/18
21 2043.243 13/4, 55/17
22 2140.541 55/16, 65/19
23 2237.838 65/18
24 2335.135 65/17, 77/20
25 2432.432 65/16, 77/19
26 2529.730 77/18
27 2627.027 32/7, 77/17
28 2724.324 34/7, 77/16
29 2821.622 36/7, 56/11
30 2918.919 38/7, 91/17
31 3016.216 40/7, 91/16
32 3113.514 85/14
33 3210.811 32/5, 45/7
34 3308.108 34/5, 88/13
35 3405.405 36/5, 64/9
36 3502.703 38/5, 68/9
37 3600.000 8/1