114edt: Difference between revisions

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-{{Stub}}
 {{Infobox ET}}
-'''[[Edt|Division of the third harmonic]] into 114 equal parts''' (114EDT) is related to [[72edo|72 edo]], 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 16.6838 cents. It is consistent to the [[17-odd-limit|18-integer-limit]], and significantly improves on 72edo's approximation to 13.
+{{ED intro}}
+== Theory ==
+edt is related to [[72edo]], but with the [[3/1|perfect twelfth]] rather than the [[2/1|octave]] being just. The octave is stretched by about 1.23 cents. Like 72edo, 114edt is [[consistent]] to the [[integer limit|18-integer-limit]]. While its approximations to 2, [[7/1|7]] and [[11/1|11]] are sharp, the [[5/1|5]] and [[17/1|17]] are nearly pure, and the [[13/1|13]] is significantly improved compared to 72edo, although the [[19/1|19]] becomes much worse.
+=== Harmonics ===
+{{Harmonics in equal|114|3|1|intervals=integer|columns=11}}
+{{Harmonics in equal|114|3|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 114edt (continued)}}
+=== Subsets and supersets ===
+Since 114 factors into primes as {{nowrap| 2 × 3 × 19 }}, 114edt contains subset edts {{EDs|equave=t| 2, 3, 6, 19, 38, and 57 }}.
-Lookalikes: [[72edo]], [[186ed6]]
 == Intervals ==
 {{Interval table}}
-== Harmonics ==
+== See also ==
-{{Harmonics in equal
+* [[72edo]] – relative edo
-| steps = 114
+* [[186ed6]] – relative ed6
-| num = 3
+* [[258ed12]] – relative ed12
-| denom = 1
-}}
-{{Harmonics in equal
-| steps = 114
-| num = 3
-| denom = 1
-| start = 12
-| collapsed = 1
-}}
-[[Category:Edt]]
-[[Category:Edonoi]]