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.

{{Infobox ET

| Prime factorization = 2 × 211

| Step size = 2.84360¢

| Fifth = 247\422 (702.37¢)

| Semitones = 41:31 (116.59¢ : 88.15¢)

| Consistency = 27

}}

The '''422 equal divisions of the octave''' ('''422edo'''), or the '''422(-tone) equal temperament''' ('''422tet''', '''422et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 422 [[equal]] parts of 2.84 [[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. 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.

@@ Line 1: / Line 1: @@
-The '''422 equal division of the octave''' divides the octave into 422 equal parts of 2.844 [[cent]]s each.
+{{Infobox ET
+| Prime factorization = 2 × 211
+| Step size = 2.84360¢
+| Fifth = 247\422 (702.37¢)
+| Semitones = 41:31 (116.59¢ : 88.15¢)
+| Consistency = 27
+}}
+The '''422 equal divisions of the octave''' ('''422edo'''), or the '''422(-tone) equal temperament''' ('''422tet''', '''422et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 422 [[equal]] parts of 2.84 [[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. 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.