37ed8
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Prime factorization
37 (prime)
Step size
97.2973¢
Octave
12\37ed8 (1167.57¢)
Twelfth
20\37ed8 (1945.95¢)
Consistency limit
1
Distinct consistency limit
1
| ← 36ed8 | 37ed8 | 38ed8 → |
37ed8 is an equal tuning that divides the 8/1 ratio (triple-octave, octuple, twenty-second) 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.
| 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 | +45 | +33 | +36 | +12 | +38 | +0 | -10 | +3 | +33 | -21 | +36 | +4 | -18 | |
| 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, 52/49, 55/52 |
| 2 | 194.595 | 9/8, 10/9, 19/17, 28/25, 49/44, 55/49 |
| 3 | 291.892 | 13/11, 19/16, 20/17, 45/38, 85/72, 77/65 |
| 4 | 389.189 | 5/4 |
| 5 | 486.486 | 25/19, 45/34 |
| 6 | 583.784 | 7/5, 25/18, 45/32 |
| 7 | 681.081 | 28/19, 25/17 |
| 8 | 778.378 | 11/7, 14/9, 25/16 |
| 9 | 875.676 | 28/17 |
| 10 | 972.973 | 7/4, 44/25 |
| 11 | 1070.270 | 13/7, 35/19 |
| 12 | 1167.568 | 49/25, 35/18, 55/28 |
| 13 | 1264.865 | 35/17, 52/25 |
| 14 | 1362.162 | 11/5, 35/16 |
| 15 | 1459.459 | 44/19, 65/28 |
| 16 | 1556.757 | 22/9, 49/20, 32/13 |
| 17 | 1654.054 | 44/17, 49/19, 13/5, 34/13 |
| 18 | 1751.351 | 11/4, 36/13, 49/18, 52/19 |
| 19 | 1848.649 | 26/9, 32/11, 38/13, 49/17, 55/19 |
| 20 | 1945.946 | 34/11, 40/13, 49/16, 52/17, 55/18, 77/25 |
| 21 | 2043.243 | 13/4, 36/11, 55/17 |
| 22 | 2140.541 | 38/11, 55/16, 65/19 |
| 23 | 2237.838 | 40/11, 65/18, 91/25 |
| 24 | 2335.135 | 65/17, 77/20, 50/13 |
| 25 | 2432.432 | 65/16, 77/19 |
| 26 | 2529.730 | 56/13, 77/18 |
| 27 | 2627.027 | 32/7, 77/17, 50/11, 91/20 |
| 28 | 2724.324 | 34/7, 77/16, 91/19 |
| 29 | 2821.622 | 36/7, 56/11, 91/18 |
| 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, 50/7 |
| 36 | 3502.703 | 38/5, 68/9 |
| 37 | 3600.000 | 8/1 |