57ed12
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Prime factorization
3 × 19
Step size
75.4729¢
Octave
16\57ed12 (1207.57¢)
Twelfth
25\57ed12 (1886.82¢)
Consistency limit
6
Distinct consistency limit
6
| ← 56ed12 | 57ed12 | 58ed12 → |
57ED12 is the equal division of the twelfth harmonic into 57 equal parts. It is similar to 16edo, but has the 12/1 tuned just instead of the octave. Octaves are stretched by 7.6 ¢ and the step size is 75.47 ¢. It can be used as a tuning for Mavila and also approximates Pelog tunings in Indonesian gamelan music.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 75.473 | 23/22, 24/23 |
| 2 | 150.946 | 12/11 |
| 3 | 226.419 | 8/7, 33/29 |
| 4 | 301.892 | 19/16, 25/21, 31/26 |
| 5 | 377.364 | |
| 6 | 452.837 | 13/10 |
| 7 | 528.31 | 19/14, 34/25 |
| 8 | 603.783 | 17/12 |
| 9 | 679.256 | 34/23 |
| 10 | 754.729 | 17/11, 31/20 |
| 11 | 830.202 | 21/13, 29/18, 34/21 |
| 12 | 905.675 | 32/19 |
| 13 | 981.148 | 30/17 |
| 14 | 1056.621 | |
| 15 | 1132.093 | 25/13 |
| 16 | 1207.566 | |
| 17 | 1283.039 | 21/10 |
| 18 | 1358.512 | |
| 19 | 1433.985 | 16/7 |
| 20 | 1509.458 | |
| 21 | 1584.931 | 5/2 |
| 22 | 1660.404 | 34/13 |
| 23 | 1735.877 | 30/11 |
| 24 | 1811.349 | |
| 25 | 1886.822 | |
| 26 | 1962.295 | 31/10 |
| 27 | 2037.768 | 13/4 |
| 28 | 2113.241 | |
| 29 | 2188.714 | |
| 30 | 2264.187 | |
| 31 | 2339.66 | |
| 32 | 2415.133 | |
| 33 | 2490.606 | |
| 34 | 2566.078 | 22/5 |
| 35 | 2641.551 | 23/5 |
| 36 | 2717.024 | 24/5 |
| 37 | 2792.497 | |
| 38 | 2867.97 | 21/4 |
| 39 | 2943.443 | |
| 40 | 3018.916 | |
| 41 | 3094.389 | |
| 42 | 3169.862 | 25/4 |
| 43 | 3245.334 | |
| 44 | 3320.807 | 34/5 |
| 45 | 3396.28 | |
| 46 | 3471.753 | |
| 47 | 3547.226 | 31/4 |
| 48 | 3622.699 | |
| 49 | 3698.172 | |
| 50 | 3773.645 | |
| 51 | 3849.118 | |
| 52 | 3924.591 | 29/3 |
| 53 | 4000.063 | |
| 54 | 4075.536 | 21/2 |
| 55 | 4151.009 | 11/1 |
| 56 | 4226.482 | 23/2 |
| 57 | 4301.955 | 12/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.6 | -15.1 | +15.1 | +6.2 | -7.6 | +27.5 | +22.7 | -30.3 | +13.7 | -0.3 | +0.0 |
| Relative (%) | +10.0 | -20.1 | +20.1 | +8.2 | -10.0 | +36.4 | +30.1 | -40.1 | +18.2 | -0.4 | +0.0 | |
| Steps (reduced) |
16 (16) |
25 (25) |
32 (32) |
37 (37) |
41 (41) |
45 (45) |
48 (48) |
50 (50) |
53 (53) |
55 (55) |
57 (0) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.4 | +35.0 | -8.9 | +30.3 | +0.8 | -22.7 | +34.6 | +21.3 | +12.3 | +7.3 | +5.8 |
| Relative (%) | +16.4 | +46.4 | -11.9 | +40.1 | +1.0 | -30.1 | +45.9 | +28.2 | +16.3 | +9.6 | +7.7 | |
| Steps (reduced) |
59 (2) |
61 (4) |
62 (5) |
64 (7) |
65 (8) |
66 (9) |
68 (11) |
69 (12) |
70 (13) |
71 (14) |
72 (15) | |