422edo: Difference between revisions

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== Theory ==

422edo is a [[zeta peak edo]], though not zeta integral nor zeta gap. It is [[distinctly consistent]] through the [[27-odd-limit]], with [[harmonic]]s of 3 through 23 all tuned sharp. It [[tempers out]] the [[vishnuzma]], {{monzo| 23 6 -14 }} and the countritonic comma, {{monzo| 33 -34 9 }}, in the 5-limit; [[4375/4374]] and [[589824/588245]] in the 7-limit; [[3025/3024]], [[5632/5625]], and [[9801/9800]] in the 11-limit; [[1716/1715]], [[2080/2079]], and [[2200/2197]] in the 13-limit; [[1156/1155]], [[1275/1274]], and [[2431/2430]] in the 17-limit; [[1216/1215]], [[1331/1330]], [[1445/1444]], and [[2432/2431]] in the 19-limit; and [[736/735]], [[1496/1495]], and [[1863/1862]] in the 23-limit. It [[support]]s provides the [[optimal patent val]]s for [[gamera]] in the 7-limit and [[hemigamera]] in the 13-limit. Other notable temperaments it supports are [[vishnu]], [[semisupermajor]], and [[countritonic]].

422edo is a [[zeta peak edo]], though not zeta integral nor zeta gap. It is [[consistency|distinctly consistent]] through the [[27-odd-limit]], with [[harmonic]]s of 3 through 23 all tuned sharp. As an equal temperament, it [[tempering out|tempers out]] the [[vishnuzma]], {{monzo| 23 6 -14 }} and the countritonic comma, {{monzo| 33 -34 9 }}, in the 5-limit; [[4375/4374]] and [[589824/588245]] in the 7-limit; [[3025/3024]], [[5632/5625]], and [[9801/9800]] in the 11-limit; [[1716/1715]], [[2080/2079]], and [[2200/2197]] in the 13-limit; [[1156/1155]], [[1275/1274]], and [[2431/2430]] in the 17-limit; [[1216/1215]], [[1331/1330]], [[1445/1444]], and [[2432/2431]] in the 19-limit; and [[736/735]], [[1496/1495]], and [[1863/1862]] in the 23-limit. It [[support]]s provides the [[optimal patent val]]s for [[gamera]] in the 7-limit and [[hemigamera]] in the 13-limit. Other notable temperaments it supports are [[vishnu]], [[semisupermajor]], and [[countritonic]].

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 422 factors into ~~{{factorization|422}}~~, 422edo has subset edos [[2edo]] and [[211edo]].

Since 422 factors into 2 × 211, 422edo has subset edos [[2edo]] and [[211edo]].

== Regular temperament properties ==

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|422}}
+{{ED intro}}
 == Theory ==
-edo is a [[zeta peak edo]], though not zeta integral nor zeta gap. It is [[distinctly consistent]] through the [[27-odd-limit]], with [[harmonic]]s of 3 through 23 all tuned sharp. It [[tempers out]] the [[vishnuzma]], {{monzo| 23 6 -14 }} and the countritonic comma, {{monzo| 33 -34 9 }}, in the 5-limit; [[4375/4374]] and [[589824/588245]] in the 7-limit; [[3025/3024]], [[5632/5625]], and [[9801/9800]] in the 11-limit; [[1716/1715]], [[2080/2079]], and [[2200/2197]] in the 13-limit; [[1156/1155]], [[1275/1274]], and [[2431/2430]] in the 17-limit; [[1216/1215]], [[1331/1330]], [[1445/1444]], and [[2432/2431]] in the 19-limit; and [[736/735]], [[1496/1495]], and [[1863/1862]] in the 23-limit. It [[support]]s provides the [[optimal patent val]]s for [[gamera]] in the 7-limit and [[hemigamera]] in the 13-limit. Other notable temperaments it supports are [[vishnu]], [[semisupermajor]], and [[countritonic]].
+edo is a [[zeta peak edo]], though not zeta integral nor zeta gap. It is [[consistency|distinctly consistent]] through the [[27-odd-limit]], with [[harmonic]]s of 3 through 23 all tuned sharp. As an equal temperament, it [[tempering out|tempers out]] the [[vishnuzma]], {{monzo| 23 6 -14 }} and the countritonic comma, {{monzo| 33 -34 9 }}, in the 5-limit; [[4375/4374]] and [[589824/588245]] in the 7-limit; [[3025/3024]], [[5632/5625]], and [[9801/9800]] in the 11-limit; [[1716/1715]], [[2080/2079]], and [[2200/2197]] in the 13-limit; [[1156/1155]], [[1275/1274]], and [[2431/2430]] in the 17-limit; [[1216/1215]], [[1331/1330]], [[1445/1444]], and [[2432/2431]] in the 19-limit; and [[736/735]], [[1496/1495]], and [[1863/1862]] in the 23-limit. It [[support]]s provides the [[optimal patent val]]s for [[gamera]] in the 7-limit and [[hemigamera]] in the 13-limit. Other notable temperaments it supports are [[vishnu]], [[semisupermajor]], and [[countritonic]].
 === Prime harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-Since 422 factors into {{factorization|422}}, 422edo has subset edos [[2edo]] and [[211edo]].
+Since 422 factors into 2 × 211, 422edo has subset edos [[2edo]] and [[211edo]].
 == Regular temperament properties ==