Hemimage family: Difference between revisions
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= | The '''hemimage family''' of temperaments are rank-3 temperaments tempering out [[10976/10935]]. | ||
[[ | |||
= Hemimage = | |||
[[Comma]]: hemimage 10976/10935 | |||
7-limit minimax | 7-limit minimax | ||
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|5/8 -7/8 7/8 3/8>, |0 0 0 1>] | |5/8 -7/8 7/8 3/8>, |0 0 0 1>] | ||
[[Eigenmonzo | [[Eigenmonzo]]s: 2, 8/7, 6/5 | ||
9-limit minimax | 9-limit minimax | ||
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|10/9 -14/9 7/9 2/3>, |0 0 0 1>] | |10/9 -14/9 7/9 2/3>, |0 0 0 1>] | ||
[[Eigenmonzo | [[Eigenmonzo]]s: 2, 10/9, 8/7 | ||
Map: [<1 0 2 -1|, <0 1 2 3|, <0 0 -3 -1|] | Map: [<1 0 2 -1|, <0 1 2 3|, <0 0 -3 -1|] | ||
[[ | [[Generator]]s: 2, 3, 27/14 | ||
[[EDO|Edos]]: 14, 19, 41, 58, 77, 80, [[99edo|99]], [[118edo|118]], [[140edo|140]], [[217edo|217]], [[316edo|316]], [[338edo|338]], [[357edo|357]], [[415edo|415]], [[456edo|456]], [[654edo|654]], [[695edo|695]] | [[EDO|Edos]]: 14, 19, 41, 58, 77, 80, [[99edo|99]], [[118edo|118]], [[140edo|140]], [[217edo|217]], [[316edo|316]], [[338edo|338]], [[357edo|357]], [[415edo|415]], [[456edo|456]], [[654edo|654]], [[695edo|695]] | ||
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Badness: 0.000199 | Badness: 0.000199 | ||
[[ | [[Projection pair]]: 5 10976/2187 to 2.3.7 | ||
= Uni = | |||
[[Comma | [[Comma]]s: 540/539, 896/891 | ||
[[ | [[Minimax tuning]] | ||
[|1 0 0 0 0>, |16/11 6/11 1/11 0 -3/11>, | [|1 0 0 0 0>, |16/11 6/11 1/11 0 -3/11>, | ||
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|32/11 -10/11 2/11 0 5/11>] | |32/11 -10/11 2/11 0 5/11>] | ||
[[Eigenmonzo | [[Eigenmonzo]]s: 2, 11/9, 5/4 | ||
Map: [<1 0 2 -1 6|, <0 1 2 3 -1|, <0 0 -3 -1 -1|] | Map: [<1 0 2 -1 6|, <0 1 2 3 -1|, <0 0 -3 -1 -1|] | ||
[[ | [[Generator]]s: 2, 3, 27/14 | ||
[[EDO|Edos]]: [[19edo|19]], [[22edo|22]], [[41edo|41]], [[58edo|58]], [[80edo|80]], [[121edo|121]] | [[EDO|Edos]]: [[19edo|19]], [[22edo|22]], [[41edo|41]], [[58edo|58]], [[80edo|80]], [[121edo|121]] | ||
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Badness: 0.000702 | Badness: 0.000702 | ||
== 13-limit == | |||
Commas: 352/351, 364/363, 540/539 | Commas: 352/351, 364/363, 540/539 | ||
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Badness: 0.00106 | Badness: 0.00106 | ||
== Tin == | |||
Commas: 144/143, 196/195, 729/728 | Commas: 144/143, 196/195, 729/728 | ||
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Badness: 0.00107 | Badness: 0.00107 | ||
= Turan = | |||
[[Comma | [[Comma]]s: 441/440, 10976/10935 | ||
[[ | [[Minimax tuning]] | ||
[|1 0 0 0 0>, |19/12 -2/3 1/12 0 1/4>, | [|1 0 0 0 0>, |19/12 -2/3 1/12 0 1/4>, | ||
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|19/6 -10/3 1/6 0 3/2>] | |19/6 -10/3 1/6 0 3/2>] | ||
[[Eigenmonzo | [[Eigenmonzo]]s: 2, 10/9, 11/9 | ||
Map: [<1 0 2 -1 -7|, <0 1 2 3 6|, <0 0 -3 -1 1|] | Map: [<1 0 2 -1 -7|, <0 1 2 3 6|, <0 0 -3 -1 1|] | ||
[[ | [[Generator]]s: 2, 3, 27/14 | ||
[[EDO|Edos]]: [[41edo|41]], [[58edo|58]], [[118edo|118]], [[159edo|159]], [[217edo|217]], [[335edo|335]] | [[EDO|Edos]]: [[41edo|41]], [[58edo|58]], [[118edo|118]], [[159edo|159]], [[217edo|217]], [[335edo|335]] | ||
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[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Hemimage]] | [[Category:Hemimage]] | ||
[[Category:Rank 3]] | |||
Revision as of 05:26, 6 January 2021
The hemimage family of temperaments are rank-3 temperaments tempering out 10976/10935.
Hemimage
Comma: hemimage 10976/10935
7-limit minimax
[|1 0 0 0>, |5/8 1/8 -1/8 3/8>, |5/8 -7/8 7/8 3/8>, |0 0 0 1>]
Eigenmonzos: 2, 8/7, 6/5
9-limit minimax
[|1 0 0 0>, |5/9 2/9 -1/9 1/3>, |10/9 -14/9 7/9 2/3>, |0 0 0 1>]
Eigenmonzos: 2, 10/9, 8/7
Map: [<1 0 2 -1|, <0 1 2 3|, <0 0 -3 -1|]
Generators: 2, 3, 27/14
Edos: 14, 19, 41, 58, 77, 80, 99, 118, 140, 217, 316, 338, 357, 415, 456, 654, 695
Badness: 0.000199
Projection pair: 5 10976/2187 to 2.3.7
Uni
Commas: 540/539, 896/891
[|1 0 0 0 0>, |16/11 6/11 1/11 0 -3/11>, |0 0 1 0 0>, |19/11 14/11 6/11 0 -7/11>, |32/11 -10/11 2/11 0 5/11>]
Eigenmonzos: 2, 11/9, 5/4
Map: [<1 0 2 -1 6|, <0 1 2 3 -1|, <0 0 -3 -1 -1|]
Generators: 2, 3, 27/14
Badness: 0.000702
13-limit
Commas: 352/351, 364/363, 540/539
Map: [<1 0 2 -1 6 11|, <0 1 2 3 -1 -4|, <0 0 -3 -1 -1 -1|]
EDOs: 22, 41, 58, 80, 121
Badness: 0.00106
Tin
Commas: 144/143, 196/195, 729/728
Map: [<1 0 2 -1 6 -2|, <0 1 2 3 -1 3|, <0 0 -3 -1 -1 1|]
EDOs: 19, 36, 41, 58
Badness: 0.00107
Turan
Commas: 441/440, 10976/10935
[|1 0 0 0 0>, |19/12 -2/3 1/12 0 1/4>, |19/6 -10/3 7/6 0 1/2>, |37/12 -8/3 7/12 0 3/4>, |19/6 -10/3 1/6 0 3/2>]
Eigenmonzos: 2, 10/9, 11/9
Map: [<1 0 2 -1 -7|, <0 1 2 3 6|, <0 0 -3 -1 1|]
Generators: 2, 3, 27/14
Edos: 41, 58, 118, 159, 217, 335
Badness: 0.000936