422edo: Difference between revisions

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== 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. It is also nearly consistent in the [[31-odd-limit]] with the only inconsistent intervals being [[29/27]] ~~and~~ [[29/21]] and their octave ~~compliments~~, and picks up only one extra inconsistent interval pair in the [[35-odd-limit]], [[35/29]] and its octave ~~compliment~~. 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]].

422edo is [[consistency|distinctly consistent]] through the [[27-odd-limit]], with [[harmonic]]s of 3 through 23 all tuned sharp. It is also nearly consistent in the [[31-odd-limit]] with the only inconsistent intervals being [[29/27]], [[29/21]] and their [[octave complement]]s, and picks up only one extra inconsistent interval pair in the [[35-odd-limit]], [[35/29]] and its octave complement. It is a [[zeta peak edo]].

As an equal temperament, it [[tempering out|tempers out]] the [[vishnu comma]], {{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 ===

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 == Theory ==
-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. It is also nearly consistent in the [[31-odd-limit]] with the only inconsistent intervals being [[29/27]] and [[29/21]] and their octave compliments, and picks up only one extra inconsistent interval pair in the [[35-odd-limit]], [[35/29]] and its octave compliment. 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]].
+edo is [[consistency|distinctly consistent]] through the [[27-odd-limit]], with [[harmonic]]s of 3 through 23 all tuned sharp. It is also nearly consistent in the [[31-odd-limit]] with the only inconsistent intervals being [[29/27]], [[29/21]] and their [[octave complement]]s, and picks up only one extra inconsistent interval pair in the [[35-odd-limit]], [[35/29]] and its octave complement. It is a [[zeta peak edo]].
+As an equal temperament, it [[tempering out|tempers out]] the [[vishnu comma]], {{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 ===