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.

~~==Icosidillic==~~

~~Main article~~: [[Porwell temperaments#Icosidillic]]

Temperaments discussed elsewhere include:

* ''Icosidillic'', → [[Porwell temperaments#Icosidillic|Porwell temperaments]]

==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, however there's no single way to extend it to the 11-limit due to inconsistency.

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Optimal tuning (CTE): ~3/2 = 701.948

== Bibium ==

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.

Subgroup: 2.3.5.7.11.13

Comma list: 2401/2400, 9801/9800, 67392/67375, 142884/142805

Mapping: [{{val|22 2 10 33 72 28}}, {{val|0 8 10 7 1 3}}]

Mapping generators: ~65/63 = 1\22, 338/297 = 224.100

Optimal tuning (CTE): ~338/297 = 224.100

[[Support]]ing [[ET]]s: {{EDOs|198, 616, 814, 1012, 1210}}

[[Category:22edo]]

[[Category:Temperament collections]]

[[Category:Rank 2]]

@@ Line 1: / Line 1: @@
 [[22edo]] is a notable tuning system, and as such it gives rise to some fractional-octave temperaments.
-==Icosidillic==
-Main article: [[Porwell temperaments#Icosidillic]]
+Temperaments discussed elsewhere include:
+* ''Icosidillic'', → [[Porwell temperaments#Icosidillic|Porwell temperaments]]
 ==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, however there's no single way to extend it to the 11-limit due to inconsistency.
@@ Line 29: / Line 31: @@
 Optimal tuning (CTE): ~3/2 = 701.948
+==  Bibium ==
+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.
+Subgroup: 2.3.5.7.11.13
+Comma list: 2401/2400, 9801/9800, 67392/67375, 142884/142805
+Mapping: [{{val|22 2 10 33 72 28}}, {{val|0 8 10 7 1 3}}]
+Mapping generators: ~65/63 = 1\22, 338/297 = 224.100
+Optimal tuning (CTE): ~338/297 = 224.100
+[[Support]]ing [[ET]]s: {{EDOs|198, 616, 814, 1012, 1210}}
 [[Category:22edo]]
 [[Category:Temperament collections]]
 [[Category:Rank 2]]