57edt
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Prime factorization
3 × 19
Step size
33.3676¢
Octave
36\57edt (1201.23¢) (→12\19edt)
Consistency limit
8
Distinct consistency limit
8
| ← 56edt | 57edt | 58edt → |
57 divisions of the third harmonic (57edt) is related to 36edo (sixth-tone tuning), but with the 3/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 33.3676 cents. It is consistent to the 9-integer-limit. In comparison, 36edo is only consistent up to the 8-integer-limit.
Lookalikes: 36edo, 93ed6, 101ed7, 21edf
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 33.368 | |
| 2 | 66.735 | 27/26, 28/27 |
| 3 | 100.103 | 18/17 |
| 4 | 133.471 | |
| 5 | 166.838 | 32/29 |
| 6 | 200.206 | 9/8 |
| 7 | 233.573 | 8/7 |
| 8 | 266.941 | 7/6 |
| 9 | 300.309 | 19/16, 31/26 |
| 10 | 333.676 | 17/14, 23/19 |
| 11 | 367.044 | 21/17, 26/21 |
| 12 | 400.412 | 24/19, 29/23, 34/27 |
| 13 | 433.779 | 9/7 |
| 14 | 467.147 | 17/13, 21/16 |
| 15 | 500.514 | 4/3 |
| 16 | 533.882 | |
| 17 | 567.25 | 18/13, 32/23 |
| 18 | 600.617 | 17/12, 24/17 |
| 19 | 633.985 | 13/9 |
| 20 | 667.353 | 28/19 |
| 21 | 700.72 | 3/2 |
| 22 | 734.088 | 26/17, 29/19 |
| 23 | 767.456 | 14/9 |
| 24 | 800.823 | 27/17 |
| 25 | 834.191 | 21/13, 34/21 |
| 26 | 867.558 | 28/17 |
| 27 | 900.926 | 32/19 |
| 28 | 934.294 | 12/7 |
| 29 | 967.661 | 7/4 |
| 30 | 1001.029 | |
| 31 | 1034.397 | |
| 32 | 1067.764 | 13/7 |
| 33 | 1101.132 | 17/9 |
| 34 | 1134.499 | 27/14 |
| 35 | 1167.867 | |
| 36 | 1201.235 | 2/1 |
| 37 | 1234.602 | |
| 38 | 1267.97 | 27/13 |
| 39 | 1301.338 | 17/8 |
| 40 | 1334.705 | 13/6 |
| 41 | 1368.073 | |
| 42 | 1401.441 | 9/4 |
| 43 | 1434.808 | 16/7 |
| 44 | 1468.176 | 7/3 |
| 45 | 1501.543 | 19/8, 31/13 |
| 46 | 1534.911 | 17/7 |
| 47 | 1568.279 | |
| 48 | 1601.646 | |
| 49 | 1635.014 | 18/7 |
| 50 | 1668.382 | 21/8, 34/13 |
| 51 | 1701.749 | 8/3 |
| 52 | 1735.117 | |
| 53 | 1768.484 | |
| 54 | 1801.852 | 17/6 |
| 55 | 1835.22 | 26/9 |
| 56 | 1868.587 | |
| 57 | 1901.955 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.2 | +0.0 | +2.5 | +16.6 | +1.2 | +1.3 | +3.7 | +0.0 | -15.6 | -13.7 | +2.5 |
| Relative (%) | +3.7 | +0.0 | +7.4 | +49.7 | +3.7 | +3.9 | +11.1 | +0.0 | -46.6 | -41.2 | +7.4 | |
| Steps (reduced) |
36 (36) |
57 (0) |
72 (15) |
84 (27) |
93 (36) |
101 (44) |
108 (51) |
114 (0) |
119 (5) |
124 (10) |
129 (15) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | +2.5 | +16.6 | +4.9 | +0.1 | +1.2 | +7.7 | -14.3 | +1.3 | -12.5 | +10.6 |
| Relative (%) | -7.9 | +7.6 | +49.7 | +14.8 | +0.3 | +3.7 | +23.2 | -42.9 | +3.9 | -37.5 | +31.9 | |
| Steps (reduced) |
133 (19) |
137 (23) |
141 (27) |
144 (30) |
147 (33) |
150 (36) |
153 (39) |
155 (41) |
158 (44) |
160 (46) |
163 (49) | |