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
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.23 | +0.00 | +2.47 | +16.57 | +1.23 | +1.30 | +3.70 | +0.00 | -15.57 | -13.73 | +2.47 | -2.63 | +2.54 | +16.57 | +4.94 |
| Relative (%) | +3.7 | +0.0 | +7.4 | +49.7 | +3.7 | +3.9 | +11.1 | +0.0 | -46.6 | -41.2 | +7.4 | -7.9 | +7.6 | +49.7 | +14.8 | |
| Steps (reduced) |
36 (36) |
57 (0) |
72 (15) |
84 (27) |
93 (36) |
101 (44) |
108 (51) |
114 (0) |
119 (5) |
124 (10) |
129 (15) |
133 (19) |
137 (23) |
141 (27) |
144 (30) | |