22nd-octave temperaments: Difference between revisions

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[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families. ~~Vigintiduo has the same 7-limit mapping as 22et with harmonic 11 mapped to an independent generator. Vigin has the same 11-limit mapping as 22et with harmonic 13 mapped to an independent generator.~~

[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families.

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-{{Fractional-octave navigation|22}}
+{{Technical data page}}
-[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families. Vigintiduo has the same 7-limit mapping as 22et with harmonic 11 mapped to an independent generator. Vigin has the same 11-limit mapping as 22et with harmonic 13 mapped to an independent generator.
+{{Infobox fractional-octave|22}}
+[[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families.
 See also:
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 == Vigintiduo ==
+''Vigintiduo'' has the same 7-limit mapping as 22et with harmonic 11 mapped to an independent generator.
 [[Subgroup]]: 2.3.5.7.11
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 == Vigin ==
+''Vigin'' has the same 11-limit mapping as 22et with harmonic 13 mapped to an independent generator.
 [[Subgroup]]: 2.3.5.7.11.13
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 == Major arcana ==
-Named after a subset of Tarot cards of which there is 22. Tempers out the {{monzo|-193 154 -22}} comma in the 5-limit. Can be conceptualized as a more precise version of icosidillic in the 5-limit and the 7-limit bearing the same [[pergen]] (P8/22, P5), however there's no single way to extend it to the 11-limit due to inconsistency.
+''Major arcana'' is named after a subset of Tarot cards of which there is 22. Tempers out the {{monzo|-193 154 -22}} comma in the 5-limit. Can be conceptualized as a more precise version of icosidillic in the 5-limit and the 7-limit bearing the same [[pergen]] (P8/22, P5), however there's no single way to extend it to the 11-limit due to inconsistency.
 Subgroup: 2.3.5
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 Mapping: [{{val|22 22 -39}}, {{val|0 1 7}}]
-Mapping generators: ~{{monzo|79 -63 9}}, ~3/2
+: mapping generators: ~{{monzo|79 -63 9}}, ~3/2
 Optimal tuning (CTE): ~3/2 = 701.942
-{{Optimal ET sequence|legend=1|176, 506, 836, 1342, 1848}}, ...
+[[Support]]ing [[ET]]s: {{EDOs|176, 330, 506, 836, 1342, 1848}}, ...
 === 7-limit ===
 Subgroup: 2.3.5.7
-Comma list: {{monzo|51 -24 -8 2}},  {{monzo|-20 41 -23 3}}
+Comma list: 14348907/14336000, {{monzo|39 11 -11 -11}}
-Mapping: [{{val|22 22 -39 -453}}, {{val|0 1 7 40}}]
+Mapping: [{{val|22 0 -193 271}}, {{val|0 1 7 -6}}]
-Mapping generators: ~16128/15625, ~3/2
+: mapping generators: ~8388608/8103375, ~3/2
-Optimal tuning (CTE): ~3/2 = 701.948
+Optimal tuning (CTE): ~3/2 = 702.014
-{{Optimal ET sequence|legend=1|506}}
+[[Support]]ing [[ET]]s: {{EDOs|176, 506, 682}}
-== Bibium ==
+== Titanium ==
-Bibium is named after an "extended provisional name" for the 22nd element [[wikipedia:titanium|titanium]], which is needed to resolve a name conflict as [[Titanium]] is already a temperament. It reaches [[11/8]] and [[7/6]] in one generator, and as a corollary tempers [[96/77]] to 7 steps of 22edo.
+''Titanium'' is named after the 22nd element after the previous temperament called "titanium" was found to be the same thing as [[beep]]. It reaches [[11/8]] and [[7/6]] in one generator, and as a corollary tempers [[96/77]] to 7 steps of 22edo.
 Subgroup: 2.3.5.7.11
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 [[Support]]ing [[ET]]s: {{EDOs|198, 616, 814, 1012, 1210}}
+{{Navbox fractional-octave}}
 {{Todo| cleanup }}