472edo: Difference between revisions

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472edo is [[consistent]] to the [[11-odd-limit]]. It is [[Enfactoring|enfactored]] in the 5-limit, with the same tuning as 118edo, defined by tempering out the [[schisma]] and the [[parakleisma]]. In the 7-limit, it tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256 , [[Support|supporting]] the [[Breedsmic temperaments #Maviloid|maviloid]] temperament, the [[Schismatic family #Bisesqui|bisesqui temperament]], and the [[Schismatic family #Octant|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.

It is a [[zeta peak integer edo]].

472edo is a [[zeta peak integer edo]].

=== Prime harmonics ===

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" | Subgroup

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~stretch~~ (¢)

! rowspan="2" | Optimal 8ve Stretch (¢)

! colspan="2" | Tuning ~~error~~

! colspan="2" | Tuning Error

|-

! [[TE error|Absolute]] (¢)

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{| class="wikitable center-all left-5"

|+Table of rank-2 temperaments by generator

! Periods per ~~octave~~

! Periods per Octave

! Generator (~~reduced~~)

! Generator (Reduced)

! Cents (~~reduced~~)

! Cents (Reduced)

! Associated ~~ratio~~

! Associated Ratio

! Temperaments

|-

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| 1

| 205\472

| ~~498~~.31

| 521.19

| 875/648

| [[Maviloid]]

@@ Line 11: / Line 11: @@
 edo is [[consistent]] to the [[11-odd-limit]]. It is [[Enfactoring|enfactored]] in the 5-limit, with the same tuning as 118edo, defined by tempering out the [[schisma]] and the [[parakleisma]]. In the 7-limit, it tempers out [[2401/2400]], 2460375/2458624, and 30623756184/30517578125; in the 11-limit, [[9801/9800]], 46656/46585, 117649/117612, and 234375/234256 , [[Support|supporting]] the [[Breedsmic temperaments #Maviloid|maviloid]] temperament, the [[Schismatic family #Bisesqui|bisesqui temperament]], and the [[Schismatic family #Octant|octant temperament]]. Using the [[patent val]], it tempers out [[729/728]], [[1575/1573]], [[2200/2197]], [[4096/4095]], and 21168/21125 in the 13-limit, so it also supports the 13-limit octant.
-It is a [[zeta peak integer edo]].
+edo is a [[zeta peak integer edo]].
 === Prime harmonics ===
-{{Harmonics in equal|472}}
+{{Harmonics in equal|472|columns=11}}
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" | Subgroup
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Comma list|Comma List]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve stretch (¢)
+! rowspan="2" | Optimal<br>8ve Stretch (¢)
-! colspan="2" | Tuning error
+! colspan="2" | Tuning Error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 54: / Line 54: @@
 {| class="wikitable center-all left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per octave
+! Periods<br>per Octave
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperaments
 |-
@@ Line 74: / Line 74: @@
 | 1
 | 205\472
-| 498.31
+| 521.19
 | 875/648
 | [[Maviloid]]