422edo: Difference between revisions

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The '''422 equal division of the octave''' divides the octave into 422 equal parts of 2.844 [[cent]]s each.

422edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap~~, and~~ is distinctly [[consistent]] through the [[27-odd-limit]]. In the 5-limit it tempers out the [[vishnuzma]], {{monzo| 23 6 -14 }}; and in the 7-limit [[4375/4374]] and 589824/588245 so that it [[support]]s the [[gamera]] temperament, and provides its [[optimal patent val]], and also supports the [[vishnu]] temperament. A basis for the 11-limit is 3025/3024, 4375/4374, 5632/5625 and 825000/823543.

422edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap. It is distinctly [[consistent]] through the [[27-odd-limit]], with harmonics of 3 through 23 all tuned sharp. In the 5-limit it tempers out the [[vishnuzma]], {{monzo| 23 6 -14 }}; and in the 7-limit [[4375/4374]] and 589824/588245 so that it [[support]]s the [[gamera]] temperament, and provides its [[optimal patent val]], and also supports the [[vishnu]] temperament. A basis for the 11-limit is 3025/3024, 4375/4374, 5632/5625 and 825000/823543.

=== Prime harmonics ===

[[Category:Equal divisions of the octave]]

[[Category:Gamera]]

[[Category:Vishnu]]

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 The '''422 equal division of the octave''' divides the octave into 422 equal parts of 2.844 [[cent]]s each.
-edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap, and is distinctly [[consistent]] through the [[27-odd-limit]]. In the 5-limit it tempers out the [[vishnuzma]], {{monzo| 23 6 -14 }}; and in the 7-limit [[4375/4374]] and 589824/588245 so that it [[support]]s the [[gamera]] temperament, and provides its [[optimal patent val]], and also supports the [[vishnu]] temperament. A basis for the 11-limit is 3025/3024, 4375/4374, 5632/5625 and 825000/823543.
+edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]], though not zeta integral nor zeta gap. It is distinctly [[consistent]] through the [[27-odd-limit]], with harmonics of 3 through 23 all tuned sharp. In the 5-limit it tempers out the [[vishnuzma]], {{monzo| 23 6 -14 }}; and in the 7-limit [[4375/4374]] and 589824/588245 so that it [[support]]s the [[gamera]] temperament, and provides its [[optimal patent val]], and also supports the [[vishnu]] temperament. A basis for the 11-limit is 3025/3024, 4375/4374, 5632/5625 and 825000/823543.
+=== Prime harmonics ===
+{{Harmonics in equal|422|columns=11}}
 [[Category:Equal divisions of the octave]]
 [[Category:Gamera]]
 [[Category:Vishnu]]