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441edo: Difference between revisions

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5- and 7-limit notability
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== Selected intervals ==
== Selected intervals ==
{| class="wikitable"
{| class="wikitable"
|+Selected intervals
|+ style="font-size; 105%;" | Selected intervals
|-
! Step
! Step
! Eliora's Naming System
! Eliora's Naming System
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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3.5
| 2.3.5
| {{monzo| 38 -2 -15 }}, {{monzo| 1 -27 18 }}
| {{monzo| 38 -2 -15 }}, {{monzo| 1 -27 18 }}
| {{mapping| 441 699 1024 }}
| {{mapping| 441 699 1024 }}
| -0.0297
| &minus;0.0297
| 0.0224
| 0.0224
| 0.82
| 0.82
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| 2401/2400, 4375/4374, {{monzo| 38 -2 -15 }}
| 2401/2400, 4375/4374, {{monzo| 38 -2 -15 }}
| {{mapping| 441 699 1024 1238 }}
| {{mapping| 441 699 1024 1238 }}
| -0.0117
| &minus;0.0117
| 0.0367
| 0.0367
| 1.35
| 1.35
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| 2401/2400, 4000/3993, 4375/4374, 131072/130977
| 2401/2400, 4000/3993, 4375/4374, 131072/130977
| {{mapping| 441 699 1024 1238 1526 }}
| {{mapping| 441 699 1024 1238 1526 }}
| -0.0708
| &minus;0.0708
| 0.1227
| 0.1227
| 4.51
| 4.51
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| 1575/1573, 2080/2079, 2401/2400, 4096/4095, 4375/4374
| 1575/1573, 2080/2079, 2401/2400, 4096/4095, 4375/4374
| {{mapping| 441 699 1024 1238 1526 1632 }}
| {{mapping| 441 699 1024 1238 1526 1632 }}
| -0.0720
| &minus;0.0720
| 0.1120
| 0.1120
| 4.12
| 4.12
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| 936/935, 1225/1224, 1575/1573, 1701/1700, 2025/2023, 4096/4095
| 936/935, 1225/1224, 1575/1573, 1701/1700, 2025/2023, 4096/4095
| {{mapping| 441 699 1024 1238 1526 1632 1803 }}
| {{mapping| 441 699 1024 1238 1526 1632 1803 }}
| -0.1025
| &minus;0.1025
| 0.1278
| 0.1278
| 4.70
| 4.70
|}
{{comma basis end}}
* 441et has a lower relative error than any previous equal temperaments in the 5-limit, past [[118edo|118]] and before [[559edo|559]].  
* 441et has a lower relative error than any previous equal temperaments in the 5-limit, past [[118edo|118]] and before [[559edo|559]].  
* 441et is also notable in the 7-limit, where it has a lower absolute error than any previous equal temperaments, past [[171edo|171]] and before [[612edo|612]].  
* 441et is also notable in the 7-limit, where it has a lower absolute error than any previous equal temperaments, past [[171edo|171]] and before [[612edo|612]].  


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
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| 91875/65536<br>(126/125)
| 91875/65536<br>(126/125)
| [[Akjayland]]
| [[Akjayland]]
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}


== Scales ==
== Scales ==
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* Balzano-200[9]: 77 41 41 41 77 41 41 41 41 ([[2L 7s]], generator = 200\441)
* Balzano-200[9]: 77 41 41 41 77 41 41 41 41 ([[2L 7s]], generator = 200\441)
* OEIS-A163205[11]: 9 12 24 4 44 12 84 28 8 156 60 (rank 10)
* OEIS-A163205[11]: 9 12 24 4 44 12 84 28 8 156 60 (rank 10)
* Lafa[14]: 34 34 27 34 34 27 34 34 27 34 34 27 34 27 - [[9L 5s]] (m-chro semiquartal)
* Lafa[14]: 34 34 27 34 34 27 34 34 27 34 34 27 34 27 &ndash; [[9L 5s]] (m-chro semiquartal)
* Ennealimmal[27]: 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 (18L 9s)
* Ennealimmal[27]: 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 (18L 9s)
* Akjayland[84]: 6 5 5 5, repeated 21 times
* Akjayland[84]: 6 5 5 5, repeated 21 times
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; [[Gene Ward Smith]]
; [[Gene Ward Smith]]
* ''Bodacious Breed'' (archived 2010) – [http://www.archive.org/details/BodaciousBreed details] | [http://www.archive.org/download/BodaciousBreed/Genewardsmith-BodaciousBreed.mp3 play] – breed in 441edo tuning
* ''Bodacious Breed'' (archived 2010) &ndash; [http://www.archive.org/details/BodaciousBreed details] | [http://www.archive.org/download/BodaciousBreed/Genewardsmith-BodaciousBreed.mp3 play] &ndash; breed in 441edo tuning


[[Category:Akjayland]]
[[Category:Ennealimmal]]
[[Category:Ennealimmal]]
[[Category:Semienealimmal]]
[[Category:Listen]]
[[Category:Luna]]
[[Category:Luna]]
[[Category:Nicolic]]
[[Category:Nicolic]]
[[Category:Akjayland]]
[[Category:Semienealimmal]]
[[Category:Listen]]
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