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Orwellismic family: Difference between revisions

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The orwellismic family of [[rank_three_temperaments|rank three temperaments]] tempers out the orwellisma, 1728/1715.
The '''orwellismic family''' of rank three temperaments tempers out the orwellisma, [[1728/1715]].


[[Comma|Comma]]: 1728/1715
= Orwellismic =
[[Comma]]: 1728/1715


[[7-limit|7-]] and [[9-limit|9-limit]] [[minimax|minimax]]
[[7-odd-limit|7-]] and [[9-odd-limit|9-limit]] [[minimax tuning|minimax]]


[<1 0 0 0|, <0 1 0 0|, <3/2 3/4 3/4 -3/4|,  
[<1 0 0 0|, <0 1 0 0|, <3/2 3/4 3/4 -3/4|,  
Line 10: Line 11:
<3/2 3/4 -1/4 1/4|]
<3/2 3/4 -1/4 1/4|]


[[Eigenmonzo|Eigenmonzo]]s: 2, 4/3, 7/5
[[Eigenmonzo]]s: 2, 4/3, 7/5


Lattice basis: 7/6 0.7526 3/2 1.3931
Lattice basis: 7/6 0.7526 3/2 1.3931
Line 18: Line 19:
Map to lattice: [<0 0 -3 1|, <0 1 0 1|]
Map to lattice: [<0 0 -3 1|, <0 1 0 1|]


[[Map|Map]]: [<1 0 0 2|, <0 1 0 1|, <0 0 3 -1|]
[[Map]]: [<1 0 0 2|, <0 1 0 1|, <0 0 3 -1|]


[[generator|Generator]]s: 2, 3, 12/7
[[Generator]]s: 2, 3, 12/7


Edos: [[9edo|9]], [[14edo|14]], [[17edo|17]], [[18edo|18]], [[22edo|22]], [[26edo|26]], [[27edo|27]], [[31edo|31]], [[49edo|49]], [[53edo|53]], [[58edo|58]], [[80edo|80]], [[84edo|84]], [[111edo|111]], [[142edo|142]], [[164edo|164d]], [[306edo|306d]], [[417edo|417cd]]
{{EDOs|legend=1| 9, 14, 17, 18, 22, 26, 27, 31, 49, 53, 58, 80, 84, 111, 142, 164d, 306d, 417cd }}


[[Badness|Badness]]: 0.000187
[[Badness]]: 0.000187


[[Projection_pair|Projection pair]]: 5 1728/343 to 2.3.7
[[Projection pair]]: 5 1728/343 to 2.3.7


[[scale|Scale]]s: [[Orwellismic9|orwellismic9]]
[[Scale]]s: [[orwellismic9]]


=Orwellian=
= Orwellian =
Commas: 99/98, 385/384
Commas: 99/98, 385/384


Map: [<1 0 0 2 5|, <0 1 0 1 0| <0 0 3 -1 -2|]
Map: [<1 0 0 2 5|, <0 1 0 1 0| <0 0 3 -1 -2|]


EDOs: 22, 31, 53, 84e, 163e, 194e, 247cde, 278bdee
{{EDOs|legend=1| 22, 31, 53, 84e, 163e, 194e, 247cde, 278bdee }}


Badness: 0.000715
Badness: 0.000715


=Guanyin=
= Guanyin =
[[Comma|Comma]]s: 176/175, 540/539
[[Comma]]s: 176/175, 540/539


[[11-limit|11-limit]] [[minimax|minimax]]
[[11-limit]] [[minimax tuning|minimax]]


[<1 0 0 0 0|, <-2/9 0 -5/9 5/9 4/9|, <4/3 0 1/3 -1/3 1/3|,  
[<1 0 0 0 0|, <-2/9 0 -5/9 5/9 4/9|, <4/3 0 1/3 -1/3 1/3|,  
Line 48: Line 49:
<4/3 0 -2/3 2/3 1/3|, <0 0 0 0 1|]
<4/3 0 -2/3 2/3 1/3|, <0 0 0 0 1|]


[[Eigenmonzo|Eigenmonzo]]s: 2, 11/8, 7/5
[[Eigenmonzo]]s: 2, 11/8, 7/5


Lattice basis: 7/6 0.5167 3/2 1.3055
Lattice basis: 7/6 0.5167 3/2 1.3055
Line 56: Line 57:
Map to lattice: [<0 0 -3 1 -5|, <0 1 0 1 1|]
Map to lattice: [<0 0 -3 1 -5|, <0 1 0 1 1|]


[[Map|Map]]: [<1 0 0 2 -2|, <0 1 0 1 1|, <0 0 3 -1 5|]
[[Map]]: [<1 0 0 2 -2|, <0 1 0 1 1|, <0 0 3 -1 5|]


[[generator|Generator]]s: 2, 3, 12/7
[[Generator]]s: 2, 3, 12/7


EDOs: [[9edo|9]], [[22edo|22]], [[31edo|31]], [[53edo|53]], [[58edo|58]], [[80edo|80]], [[111edo|111]], [[280edo|280cd]], [[391edo|391cd]]
{{EDOs|legend=1| 9, 22, 31, 53, 58, 80, 111, 280cd, 391cd }}


[[Badness|Badness]]: 0.000411
[[Badness]]: 0.000411


[[Projection_pair|Projection pair]]s: 5 1728/343 11 186624/16807 to 2.3.7
[[Projection pair]]s: 5 1728/343 11 186624/16807 to 2.3.7


[[scale|Scale]]s: [[guanyin22|guanyin22]]
[[Scale]]s: [[guanyin22]]


Music:  
Music:  


[http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297 Trio for SoftSaturn, NebulaSing and TromBonehead]  [http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3 play] by [[Gene_Ward_Smith|Gene Ward Smith]]
* [http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297 Trio for SoftSaturn, NebulaSing and TromBonehead]  [http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3 play] by [[Gene Ward Smith]]


==[[13-limit|13-limit]]==
== 13-limit ==
[[Comma|Comma]]s: 176/175, 351/350, 540/539
[[Comma]]s: 176/175, 351/350, 540/539


[[Map|Map]]: [<1 0 0 2 -2 3|, <0 1 0 1 1 -2|, <0 0 3 -1 5 5|]
[[Map]]: [<1 0 0 2 -2 3|, <0 1 0 1 1 -2|, <0 0 3 -1 5 5|]


EDOs: [[22edo|22]], [[31edo|31]], [[53edo|53]], [[58edo|58]], [[80edo|80]], [[111edo|111]], [[280edo|280cdf]], [[391edo|391cdf]]
{{EDOs|legend=1| 22, 31, 53, 58, 80, 111, 280cdf, 391cdf }}


[[Badness|Badness]]: 0.000758
[[Badness]]: 0.000758


Projection pairs: 5 1728/343 11 186624/16807 221184/16897 to 2.3.7
Projection pairs: 5 1728/343 11 186624/16807 221184/16897 to 2.3.7


==Georgian==
== Georgian ==
[[Comma|Comma]]s: 144/143, 176/175, 196/195
[[Comma]]s: 144/143, 176/175, 196/195


[[Map|Map]]: [<1 0 0 2 -2 6|, <0 1 0 1 1 1|, <0 0 3 -1 5 -5|]
[[Map]]: [<1 0 0 2 -2 6|, <0 1 0 1 1 1|, <0 0 3 -1 5 -5|]


EDOs: [[9edo|9]], [[31edo|31]], [[46edo|46f]], [[48edo|48c]], [[58edo|58]]
{{EDOs|legend=1| 9, 31, 46, 48, 58 }}


[[Badness|Badness]]: 0.000904
[[Badness]]: 0.000904


Projection pairs: 5 1728/343 11 186624/16807 16807/1296 to 2.3.7
Projection pairs: 5 1728/343 11 186624/16807 16807/1296 to 2.3.7
Line 96: Line 97:
[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Orwell]]
[[Category:Orwellismic]]
[[Category:Orwellismic]]
[[Category:Guanyin]]
[[Category:Rank 3]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Guanyin]]
Retrieved from "https://en.xen.wiki/w/Orwellismic_family"