422edo: Difference between revisions

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== Theory ==

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~~.

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. The equal temperament 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. 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 ===

=== Subsets and supersets ===

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| 9/7

| [[Supermajor]]

|-

| 1

| 207\422

| 588.63

| 128/91

| [[Countritonic]]

|-

| 2

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[[Category:Gamera]]

[[Category:Vishnu]]

[[Category:Countritonic]]

@@ Line 3: / Line 3: @@
 == Theory ==
-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.
+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. The equal temperament 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. 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 ===
-{{Harmonics in equal|422|columns=11}}
+{{Harmonics in equal|422}}
 === Subsets and supersets ===
@@ Line 99: / Line 99: @@
 | 9/7
 | [[Supermajor]]
+|-
+| 1
+| 207\422
+| 588.63
+| 128/91
+| [[Countritonic]]
 |-
 | 2
@@ Line 121: / Line 127: @@
 [[Category:Gamera]]
 [[Category:Vishnu]]
+[[Category:Countritonic]]