114edt: Difference between revisions

(3 intermediate revisions by the same user not shown)

Line 3:

== Theory ==

114edt is related to [[72edo]], but with the 3/1 rather than the 2/1 being just~~, resulting in octaves being~~ stretched by about 1.~~2347~~ cents. Like 72edo, 114edt is [[consistent]] to the [[integer limit|18-integer-limit]], and significantly ~~improves on~~ 72edo~~'s approximation to 13~~.

114edt 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=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 }}.

== Intervals ==

Line 15:

Line 18:

* [[72edo]] – relative edo

* [[186ed6]] – relative ed6

* [[258ed12]] – relative ed12

@@ Line 3: / Line 3: @@
 == Theory ==
-edt is related to [[72edo]], but with the 3/1 rather than the 2/1 being just, resulting in octaves being stretched by about 1.2347 cents. Like 72edo, 114edt is [[consistent]] to the [[integer limit|18-integer-limit]], and significantly improves on 72edo's approximation to 13.
+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 }}.
 == Intervals ==
@@ Line 15: / Line 18: @@
 * [[72edo]] – relative edo
 * [[186ed6]] – relative ed6
+* [[258ed12]] – relative ed12