431edo: Difference between revisions

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~~The '''431 equal divisions of the octave''' ('''431edo'''), or the '''431(-tone) equal temperament''' ('''431tet''', '''431et''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO|~~equal division of the octave]] into~~ 431 ~~parts of about 2.78 [[cent]]s each.~~

== Theory ==

431edo is [[consistent]] to the [[15-odd-limit]], tempering out the [[schisma]] in the 5-limit; [[2401/2400]] in the 7-limit; [[5632/5625]] and [[8019/8000]] in the 11-limit; [[729/728]], [[1001/1000]], [[1716/1715]], [[4096/4095]], [[6656/6655]] and [[10648/10647]] in the 13-limit. It [[support]]s the [[sesquiquartififths]] temperament.

~~431edo is the 83rd [[prime edo]].~~

=== Prime harmonics ===

=== Subsets and supersets ===

431edo is the 83rd [[prime edo]].

== 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 8ve

! Generator (~~reduced~~)

! Generator (Reduced)

! Cents (~~reduced~~)

! Cents (Reduced)

! Associated ~~ratio~~

! Associated Ratio

! Temperaments

|-

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| [[Ostara]]

|}

~~[[Category:Equal divisions of the octave|###]] ~~

~~[[Category:Prime EDOs]]~~

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 {{Infobox ET}}
-The '''431 equal divisions of the octave''' ('''431edo'''), or the '''431(-tone) equal temperament''' ('''431tet''', '''431et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 431 parts of about 2.78 [[cent]]s each.
+{{EDO intro|431}}
 == Theory ==
 edo is [[consistent]] to the [[15-odd-limit]], tempering out the [[schisma]] in the 5-limit; [[2401/2400]] in the 7-limit; [[5632/5625]] and [[8019/8000]] in the 11-limit; [[729/728]], [[1001/1000]], [[1716/1715]], [[4096/4095]], [[6656/6655]] and [[10648/10647]] in the 13-limit. It [[support]]s the [[sesquiquartififths]] temperament.
-edo is the 83rd [[prime edo]].
 === Prime harmonics ===
 {{Harmonics in equal|431}}
+=== Subsets and supersets ===
+edo is the 83rd [[prime edo]].
 == 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 60: / Line 61: @@
 {| class="wikitable center-all left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per octave
+! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperaments
 |-
@@ Line 90: / Line 91: @@
 | [[Ostara]]
 |}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
-[[Category:Prime EDOs]]