57edt: Difference between revisions

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 {{Infobox ET}}
-'''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]].
+{{ED intro}}
-Lookalikes: [[36edo]], [[93ed6]], [[101ed7]], [[21edf]]
+== Theory ==
+edt is related to [[36edo]] (sixth-tone tuning), but with the 3/1 rather than the 2/1 being just. This stretches the octave by about 1.2347 [[cent]]s. It is consistent to the [[9-odd-limit|9-integer-limit]], whereas 36edo is only consistent up to the [[7-odd-limit|8-integer-limit]] due to a discrepancy with approximating 9/5, although 57edt barely manages to achieve this since it almost completely misses [[5/1]].
-== Harmonics ==
+=== Harmonics ===
-{{Harmonics in equal|57|3|1}}
+{{Harmonics in equal
+| steps = 57
+| num = 3
+| denom = 1
+| intervals = integer
+}}
+{{Harmonics in equal
+| steps = 57
+| num = 3
+| denom = 1
+| start = 12
+| collapsed = 1
+| intervals = integer
+}}
+== Intervals ==
+{{Interval table}}
+== See also ==
+* [[21edf]] – relative edf
+* [[36edo]] – relative edo
+* [[93ed6]] – relative ed6
+* [[101ed7]] – relative ed7
+* [[129ed12]] – relative ed12, close to the zeta-optimized tuning for 36edo
+[[Category:36edo]]