94th-octave temperaments: Difference between revisions

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[[94edo]] is a "wheel" for some [[fractional-octave temperaments]] because of its excellent [[3/2|perfect fifth]].

[[94edo]] is a "wheel" for some [[fractional-octave temperaments]] because of its excellent [[3/2|perfect fifth]], which is a semiconvergent. Hence a natural option is to temper out the [[94-comma]] while leaving other generators as independent.

Not only 94edo is notable for its semiconvergent [[3/2|perfect fifth]], it is also the first ET [[consistent]] in the [[23-odd-limit]]. On top of that, [[282edo]], which is 94 × 3, is also consistent equally as far (on top of being the first distinctly consistent in it), thus providing natural octave-merger option.

Hence considered below is garistearn.

== Garistearn ==

~~The~~ garistearn temperament (94 & 282) tempers out the same commas as [[94edo]] in the [[2.3.7 subgroup]] while adding an independent generator for [[prime interval|prime]] [[5/1|5]].

Named by [[Xenllium]] in 2021, the garistearn temperament (94 & 282) tempers out the same commas as [[94edo]] in the [[2.3.7 subgroup]] while adding an independent generator for [[prime interval|prime]] [[5/1|5]].

[[Subgroup]]: 2.3.5.7

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Comma list: 540/539, 4000/3993, 33554432/33480783

~~Mapping:~~ {{~~mapping~~| 94 149 0 264 107 | 0 0 1 0 1 }}

Optimal tunings:

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Comma list: 540/539, 729/728, 1575/1573, 28672/28561

~~Mapping:~~ {{~~mapping~~| 94 149 0 264 107 348 | 0 0 1 0 1 0 }}

Optimal tunings:

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Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873

~~Mapping:~~ {{~~mapping~~| 94 149 0 264 107 348 166 | 0 0 1 0 1 0 1 }}

Optimal tunings:

@@ Line 1: / Line 1: @@
 {{Technical data page}}
 {{Infobox fractional-octave|94}}
-[[94edo]] is a "wheel" for some [[fractional-octave temperaments]] because of its excellent [[3/2|perfect fifth]].
+[[94edo]] is a "wheel" for some [[fractional-octave temperaments]] because of its excellent [[3/2|perfect fifth]], which is a semiconvergent. Hence a natural option is to temper out the [[94-comma]] while leaving other generators as independent.
+Not only 94edo is notable for its semiconvergent [[3/2|perfect fifth]], it is also the first ET [[consistent]] in the [[23-odd-limit]]. On top of that, [[282edo]], which is 94 × 3, is also consistent equally as far (on top of being the first distinctly consistent in it), thus providing natural octave-merger option.
+Hence considered below is garistearn.
 == Garistearn ==
-The garistearn temperament (94 & 282) tempers out the same commas as [[94edo]] in the [[2.3.7 subgroup]] while adding an independent generator for [[prime interval|prime]] [[5/1|5]].
+Named by [[Xenllium]] in 2021, the garistearn temperament (94 & 282) tempers out the same commas as [[94edo]] in the [[2.3.7 subgroup]] while adding an independent generator for [[prime interval|prime]] [[5/1|5]].
 [[Subgroup]]: 2.3.5.7
@@ Line 28: / Line 32: @@
 Comma list: 540/539, 4000/3993, 33554432/33480783
-Mapping: {{mapping| 94 149 0 264 107 | 0 0 1 0 1 }}
+{{Mapping|legend=0| 94 149 0 264 107 | 0 0 1 0 1 }}
 Optimal tunings:
@@ Line 43: / Line 47: @@
 Comma list: 540/539, 729/728, 1575/1573, 28672/28561
-Mapping: {{mapping| 94 149 0 264 107 348 | 0 0 1 0 1 0 }}
+{{Mapping|legend=0| 94 149 0 264 107 348 | 0 0 1 0 1 0 }}
 Optimal tunings:
@@ Line 58: / Line 62: @@
 Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873
-Mapping: {{mapping| 94 149 0 264 107 348 166 | 0 0 1 0 1 0 1 }}
+{{Mapping|legend=0| 94 149 0 264 107 348 166 | 0 0 1 0 1 0 1 }}
 Optimal tunings:

94th-octave temperaments: Difference between revisions

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