422edo: Difference between revisions
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== Theory == | == Theory == | ||
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 [[ | 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 and provides the [[optimal patent val]]s for [[gamera]] in the 7-limit, [[hemigamera]] in the 13-limit, and [[ragitritonic]] in the 11- and 13-limit. Other notable temperaments it supports are [[vishnu]] and [[semisupermajor]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|422}} | {{Harmonics in equal|422|columns=11}} | ||
{{Harmonics in equal|422|start=12|collapsed=1|title=Approximation of prime harmonics in 422edo (continued)}} | {{Harmonics in equal|422|columns=11|start=12|collapsed=1|title=Approximation of prime harmonics in 422edo (continued)}} | ||
{{Harmonics in equal|422|start=23|collapsed=1|title=Approximation of prime harmonics in 422edo (continued)}} | {{Harmonics in equal|422|columns=11|start=23|collapsed=1|title=Approximation of prime harmonics in 422edo (continued)}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
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| 588.63 | | 588.63 | ||
| 128/91 | | 128/91 | ||
| [[ | | [[Ragitritonic]] | ||
|- | |- | ||
| 2 | | 2 | ||
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| [[Semisupermajor]] | | [[Semisupermajor]] | ||
|} | |} | ||
<nowiki/>* [[Normal forms|Octave-reduced form]], reduced to the first half-octave, and [[normal forms|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
[[Category: | [[Category:Ragitritonic]] | ||
[[Category:Gamera]] | [[Category:Gamera]] | ||
[[Category:Vishnu]] | [[Category:Vishnu]] | ||