581edo: Difference between revisions

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As an equal temperament, it [[tempering out|tempers out]] [[2401/2400]], [[33554432/33480783]], and [[48828125/48771072]] in the 7-limit; [[3025/3024]], [[19712/19683]], [[234375/234256]] in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]] in the 13-limit. It [[support]]s and gives a good tuning for [[newt]], the {{nowrap| 270 & 311 }} microtemperament, which features a neutral-third generator.

It notably achieves [[diamond monotone]] in the 71-odd-limit with the 581jks [[val]] (s is the [[wart]] for prime 67), which is a large improvement from the previous record of the 59-odd-limit, held by [[571edo]] using its [[patent val]].

=== Prime harmonics ===

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| 582.44

| 7/5

| [[Neptune]] (7-limit)

| [[Neptune (temperament)|Neptune]] (7-limit)

|-

| 1

| 285\581

| 588.64

| ~~{{Monzo| -14 15 -4 }}~~

| 351/250

| [[~~Countritonic~~]] ~~(5-limit)~~

| [[Garitritonic]]

|}

<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:Newt]]

@@ Line 6: / Line 6: @@
 As an equal temperament, it [[tempering out|tempers out]] [[2401/2400]], [[33554432/33480783]], and [[48828125/48771072]] in the 7-limit; [[3025/3024]], [[19712/19683]], [[234375/234256]] in the 11-limit; [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]] in the 13-limit. It [[support]]s and gives a good tuning for [[newt]], the {{nowrap| 270 & 311 }} microtemperament, which features a neutral-third generator.
+It notably achieves [[diamond monotone]] in the 71-odd-limit with the 581jks [[val]] (s is the [[wart]] for prime 67), which is a large improvement from the previous record of the 59-odd-limit, held by [[571edo]] using its [[patent val]].
 === Prime harmonics ===
@@ Line 123: / Line 125: @@
 | 582.44
 | 7/5
-| [[Neptune]] (7-limit)
+| [[Neptune (temperament)|Neptune]] (7-limit)
 |-
 | 1
 | 285\581
 | 588.64
-| {{Monzo| -14 15 -4 }}
+| 351/250
-| [[Countritonic]] (5-limit)
+| [[Garitritonic]]
 |}
 <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:Newt]]