Sengic family: Difference between revisions
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'''Sengic family''' is a collection of the [[planar temperament]]s tempering out the | '''Sengic family''' is a collection of the [[planar temperament]]s tempering out the senga comma, [[686/675]]. | ||
[[Comma]]: 686/675 | [[Comma]]: 686/675 | ||
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[[Map]]: {{lbrack}} {{val| 1 0 2 1 }}, {{val| 0 1 0 1 }}, {{val| 0 0 3 2 }} {{rbrack}} | [[Map]]: {{lbrack}} {{val| 1 0 2 1 }}, {{val| 0 1 0 1 }}, {{val| 0 0 3 2 }} {{rbrack}} | ||
[[EDO]]s: | [[POTE tuning|POTE generators]]: 2, ~3/2 = 704.154, ~15/14 = 129.824 | ||
[[EDO]]s: {{Vals| 9, 10, 18, 19, 27, 46 }} | |||
[[Badness]]: 0.000320 | [[Badness]]: 0.000320 | ||
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[[Projection pair]]s: 5 3375/686 7 675/98 to 2.3.7/5 | [[Projection pair]]s: 5 3375/686 7 675/98 to 2.3.7/5 | ||
== Krypton | = Demeter = | ||
Commas: 441/440, 686/675 | |||
Map: {{lbrack}} {{val| 1 0 2 1 -3 }}, {{val| 0 1 0 1 4 }}, {{val| 0 0 3 2 1 }} {{rbrack}} | |||
POTE generators: 2, ~3/2 = 705.518, ~15/14 = 130.039 | |||
EDOs: {{Vals| 10, 17c, 19e, 27e, 29, 46 }} | |||
== 13-limit == | |||
Commas: 91/90, 169/168, 352/351 | |||
Map: {{lbrack}} {{val| 1 0 2 1 -3 2 }}, {{val| 0 1 0 1 4 1 }}, {{val| 0 0 3 2 1 1 }} {{rbrack}} | |||
POTE generators: 2, ~3/2 = 705.113, ~13/12 = 129.673 | |||
EDOs: {{Vals| 10, 17c, 19e, 27e, 29, 46 }} | |||
= Krypton = | |||
Commas: 56/55, 540/539 | Commas: 56/55, 540/539 | ||
Map: {{lbrack}} {{val| 1 0 2 1 2 }}, {{val| 0 1 0 1 1 }}, {{val| 0 0 3 2 -1 }} {{rbrack}} | Map: {{lbrack}} {{val| 1 0 2 1 2 }}, {{val| 0 1 0 1 1 }}, {{val| 0 0 3 2 -1 }} {{rbrack}} | ||
EDOs: 9, 10, 19, | POTE generators: 2, ~3/2 = 705.978, ~12/11 = 132.544 | ||
EDOs: {{Vals| 8d, 9, 10, 17c, 19, 27e, 36 }} | |||
Badness: 0.000856 | Badness: 0.000856 | ||
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Projection pairs: 5 6912/1331 7 854/121 to 2.3.11 | Projection pairs: 5 6912/1331 7 854/121 to 2.3.11 | ||
== 13-limit == | |||
Commas: 56/55, 78/77, 91/90 | Commas: 56/55, 78/77, 91/90 | ||
Map: {{lbrack}} {{val| 1 0 2 1 2 2 }}, {{val| 0 1 0 1 1 1 }}, {{val| 0 0 3 2 -1 1 }} {{rbrack}} | Map: {{lbrack}} {{val| 1 0 2 1 2 2 }}, {{val| 0 1 0 1 1 1 }}, {{val| 0 0 3 2 -1 1 }} {{rbrack}} | ||
EDOs: 9, 10, 19, 36 | POTE generators: 2, ~3/2 = 706.029, ~12/11 = 132.428 | ||
EDOs: {{Vals| 8d, 9, 10, 17c, 19, 27e, 36 }} | |||
Badness: 0.000727 | Badness: 0.000727 | ||
Revision as of 12:55, 3 April 2021
Sengic family is a collection of the planar temperaments tempering out the senga comma, 686/675.
Comma: 686/675
Map: [ ⟨1 0 2 1], ⟨0 1 0 1], ⟨0 0 3 2] ]
POTE generators: 2, ~3/2 = 704.154, ~15/14 = 129.824
Badness: 0.000320
Projection pairs: 5 3375/686 7 675/98 to 2.3.7/5
Demeter
Commas: 441/440, 686/675
Map: [ ⟨1 0 2 1 -3], ⟨0 1 0 1 4], ⟨0 0 3 2 1] ]
POTE generators: 2, ~3/2 = 705.518, ~15/14 = 130.039
EDOs: 10, 17c, 19e, 27e, 29, 46
13-limit
Commas: 91/90, 169/168, 352/351
Map: [ ⟨1 0 2 1 -3 2], ⟨0 1 0 1 4 1], ⟨0 0 3 2 1 1] ]
POTE generators: 2, ~3/2 = 705.113, ~13/12 = 129.673
EDOs: 10, 17c, 19e, 27e, 29, 46
Krypton
Commas: 56/55, 540/539
Map: [ ⟨1 0 2 1 2], ⟨0 1 0 1 1], ⟨0 0 3 2 -1] ]
POTE generators: 2, ~3/2 = 705.978, ~12/11 = 132.544
EDOs: 8d, 9, 10, 17c, 19, 27e, 36
Badness: 0.000856
Projection pairs: 5 6912/1331 7 854/121 to 2.3.11
13-limit
Commas: 56/55, 78/77, 91/90
Map: [ ⟨1 0 2 1 2 2], ⟨0 1 0 1 1 1], ⟨0 0 3 2 -1 1] ]
POTE generators: 2, ~3/2 = 706.029, ~12/11 = 132.428
EDOs: 8d, 9, 10, 17c, 19, 27e, 36
Badness: 0.000727
Projection pairs: 5 6912/1331 7 854/121 13 144/11 to 2.3.11