441edo: Difference between revisions

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~~The '''441 equal divisions of the octave''' ('''441edo'''), or the '''441(-tone) equal temperament''' ('''441tet''', '''441et''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO|~~equal division of the octave]] into~~ 441 ~~parts of about 2.72 [[cent]]s each.~~

== Theory ==

441edo is a very strong [[7-limit]] system; strong enough to qualify as a [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta peak edo]]. It is also very strong simply considered as a 5-limit system; it is the first division past [[118edo|118]] with a lower [[5-limit]] [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. In the 5-limit It [[tempering out|tempers out]] the [[hemithirds comma]], {{monzo| 38 -2 -15 }}, the [[ennealimma]], {{monzo| 1 -27 18 }}, whoosh, {{monzo| 37 25 -33 }}, and egads, {{monzo| -36 -52 51 }}. In the 7-limit it tempers out [[2401/2400]], [[4375/4374]], [[420175/419904]] and [[250047/250000]], so that it [[support]]s [[Ragismic microtemperaments #Ennealimmal|ennealimmal temperament]]. In the [[11-limit]] it tempers out [[4000/3993]], and in the 13-limit, [[1575/1573]], [[2080/2079]] and [[4096/4095]]. It provides the [[optimal patent val]] for 11- and [[13-limit]] [[Ragismic microtemperaments #Ennealimmal|semiennealimmal temperament]], and the 7-limit 41&359 temperament. Since it tempers out 1575/1573, the nicola, it allows the [[nicolic tetrad]].

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One step of 441edo is also of a size close to [[625/624]], the tunbarsma.

~~441 factors into primes as 32 × 72, and has divisors {{EDOs|3, 7, 9, 21, 49, 63 and 147}}.~~

=== Prime harmonics ===

=== Subsets and supersets ===

441 factors into primes as 32 × 72, and has divisors {{EDOs| 3, 7, 9, 21, 49, 63 and 147 }}.

== Selected intervals ==

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== 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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|+Table of rank-2 temperaments by generator

! Periods per 8ve

! Generator (~~reduced~~)

! Generator (Reduced)

! Cents (~~reduced~~)

! Cents (Reduced)

! Associated ~~ratio~~

! Associated Ratio

! Temperaments

|-

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== Music ==

* [https://www.youtube.com/watch?v=j3sq5jkFjUE Etude in G Akjayland for Piano and Tribal Pan, Op. 1, No. 3~~] by [[Eliora]~~]

; [[Eliora]]

* [https://www.youtube.com/watch?v=j3sq5jkFjUE ''Etude in G Akjayland for Piano and Tribal Pan'', Op. 1, No. 3]

~~[[Category:441edo]]~~

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

[[Category:Ennealimmal]]

[[Category:Semienealimmal]]

[[Category:Luna]]

[[Category:Nicolic]]

~~[[Category:Zeta]]~~

[[Category:Akjayland]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''441 equal divisions of the octave''' ('''441edo'''), or the '''441(-tone) equal temperament''' ('''441tet''', '''441et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 441 parts of about 2.72 [[cent]]s each.
+{{EDO intro|441}}
 == Theory ==
 edo is a very strong [[7-limit]] system; strong enough to qualify as a [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta peak edo]]. It is also very strong simply considered as a 5-limit system; it is the first division past [[118edo|118]] with a lower [[5-limit]] [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. In the 5-limit It [[tempering out|tempers out]] the [[hemithirds comma]], {{monzo| 38 -2 -15 }}, the [[ennealimma]], {{monzo| 1 -27 18 }}, whoosh, {{monzo| 37 25 -33 }}, and egads, {{monzo| -36 -52 51 }}. In the 7-limit it tempers out [[2401/2400]], [[4375/4374]], [[420175/419904]] and [[250047/250000]], so that it [[support]]s [[Ragismic microtemperaments #Ennealimmal|ennealimmal temperament]]. In the [[11-limit]] it tempers out [[4000/3993]], and in the 13-limit, [[1575/1573]], [[2080/2079]] and [[4096/4095]]. It provides the [[optimal patent val]] for 11- and [[13-limit]] [[Ragismic microtemperaments #Ennealimmal|semiennealimmal temperament]], and the 7-limit 41&amp;359 temperament. Since it tempers out 1575/1573, the nicola, it allows the [[nicolic tetrad]].
@@ Line 9: / Line 8: @@
 One step of 441edo is also of a size close to [[625/624]], the tunbarsma.
-factors into primes as 3<sup>2</sup> × 7<sup>2</sup>, and has divisors {{EDOs|3, 7, 9, 21, 49, 63 and 147}}.
 === Prime harmonics ===
 {{Harmonics in equal|441|prec=3|columns=11}}
+=== Subsets and supersets ===
+factors into primes as 3<sup>2</sup> × 7<sup>2</sup>, and has divisors {{EDOs| 3, 7, 9, 21, 49, 63 and 147 }}.
 == Selected intervals ==
@@ Line 73: / Line 73: @@
 == 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 122: / Line 122: @@
 |+Table of rank-2 temperaments by generator
 ! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator<br>(Reduced)
-! Cents<br>(reduced)
+! Cents<br>(Reduced)
-! Associated<br>ratio
+! Associated<br>Ratio
 ! Temperaments
 |-
@@ Line 198: / Line 198: @@
 == Music ==
-* [https://www.youtube.com/watch?v=j3sq5jkFjUE Etude in G Akjayland for Piano and Tribal Pan, Op. 1, No. 3] by [[Eliora]]
+; [[Eliora]]
+* [https://www.youtube.com/watch?v=j3sq5jkFjUE ''Etude in G Akjayland for Piano and Tribal Pan'', Op. 1, No. 3]
-[[Category:441edo]]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Ennealimmal]]
 [[Category:Semienealimmal]]
 [[Category:Luna]]
 [[Category:Nicolic]]
-[[Category:Zeta]]
 [[Category:Akjayland]]