57edt: Difference between revisions
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''' | '''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 [[cent]]s stretched and the step size is about 33.3676 cents. It is consistent to the [[9-odd-limit|9-integer-limit]]. In comparison, 36edo is only consistent up to the [[7-odd-limit|8-integer-limit]]. | ||
Lookalikes: [[36edo]], [[93ed6]], [[101ed7]], [[21edf]] | Lookalikes: [[36edo]], [[93ed6]], [[101ed7]], [[21edf]] | ||
=== Harmonics === | |||
{{Harmonics in equal|57|3|1}} | |||
Revision as of 11:31, 3 January 2023
| ← 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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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) | |