Sengic family: Difference between revisions

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 == Sengic ==
-[[Comma]]: 686/675
+Subgroup: 2.3.5.7
-[[Mapping]]: {{lbrack}} {{val| 1 0 2 1 }}, {{val| 0 1 0 1 }}, {{val| 0 0 3 2 }} {{rbrack}}
+[[Comma list]]: [[686/675]]
-[[POTE tuning|POTE generators]]: 2, ~3/2 = 704.154, ~15/14 = 129.824
+[[Mapping]]: [{{val| 1 0 2 1 }}, {{val| 0 1 0 1 }}, {{val| 0 0 3 2 }}]
-[[Optimal GPV sequence]]: {{Vals| 9, 10, 18, 19, 27, 46 }}
+Mapping generators: ~2, ~3, ~15/14
-[[Badness]]: 0.000320
+[[POTE generator]]s: ~3/2 = 704.154, ~15/14 = 129.824
-[[Projection pair]]s: ~5 = 3375/686 ~7 = 675/98 to 2.3.7/5
+{{Val list|legend=1| 9, 10, 18, 19, 27, 46 }}
+[[Badness]]: 0.320 × 10<sup>-3</sup>
+[[Projection pair]]s: ~5 = 3375/686, ~7 = 675/98 to 2.3.7/5
 == Demeter ==
-Comma list: 441/440, 686/675
+Subgroup: 2.3.5.7.11
+[[Comma list]]: 441/440, 686/675
-Mapping: {{lbrack}} {{val| 1 0 2 1 -3 }}, {{val| 0 1 0 1 4 }}, {{val| 0 0 3 2 1 }} {{rbrack}}
+[[Mapping]]: [{{val| 1 0 2 1 -3 }}, {{val| 0 1 0 1 4 }}, {{val| 0 0 3 2 1 }}]
-POTE generators: 2, ~3/2 = 705.518, ~15/14 = 130.039
+[[POTE generator]]s: ~3/2 = 705.518, ~15/14 = 130.039
-Optimal GPV sequence: {{Vals| 10, 17c, 19e, 27e, 29, 46 }}
+{{Val list|legend=1| 10, 17c, 19e, 27e, 29, 46 }}
-Projection pairs: ~5 = 2725888/531441, ~7 = 15488/2187 to 2.3.11
+[[Projection pair]]s: ~5 = 2725888/531441, ~7 = 15488/2187 to 2.3.11
 === 13-limit ===
+Subgroup: 2.3.5.7.11.13
 Comma list: 91/90, 169/168, 352/351
-Mapping: {{lbrack}} {{val| 1 0 2 1 -3 2 }}, {{val| 0 1 0 1 4 1 }}, {{val| 0 0 3 2 1 1 }} {{rbrack}}
+Mapping: [{{val| 1 0 2 1 -3 2 }}, {{val| 0 1 0 1 4 1 }}, {{val| 0 0 3 2 1 1 }}]
-POTE generators: 2, ~3/2 = 705.113, ~13/12 = 129.673
+POTE generators: ~3/2 = 705.113, ~14/13 = 129.673
-Optimal GPV sequence: {{Vals| 10, 17c, 19e, 27e, 29, 46 }}
+Optimal GPV sequence: {{Val list| 10, 17c, 19e, 27e, 29, 46 }}
 Projection pairs: ~5 = 2725888/531441, ~7 = 15488/2187, ~13 = 352/27 to 2.3.11
 === 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
 Comma list: 91/90, 136/135, 154/153, 169/168
-Mapping: {{lbrack}} {{val| 1 0 2 1 -3 2 -1 }}, {{val| 0 1 0 1 4 1 3 }}, {{val| 0 0 3 2 1 1 3 }} {{rbrack}}
+Mapping: [{{val| 1 0 2 1 -3 2 -1 }}, {{val| 0 1 0 1 4 1 3 }}, {{val| 0 0 3 2 1 1 3 }}]
-POTE generators: 2, ~3/2 = 705.147, ~13/12 = 129.700
+POTE generators: ~3/2 = 705.147, ~14/13 = 129.700
-Optimal GPV sequence: {{Vals| 10, 17cg, 19eg, 27eg, 29g, 46 }}
+Optimal GPV sequence: {{Val list| 10, 17cg, 19eg, 27eg, 29g, 46 }}
 Projection pairs: ~5 = 2725888/531441, ~7 = 15488/2187, ~13 = 352/27, ~17 = 340736/19683 to 2.3.11
 == Krypton ==
-Comma list: 56/55, 540/539
+Subgroup: 2.3.5.7.11
-Mapping: {{lbrack}} {{val| 1 0 2 1 2 }}, {{val| 0 1 0 1 1 }}, {{val| 0 0 3 2 -1 }} {{rbrack}}
+[[Comma list]]: 56/55, 540/539
-POTE generators: 2, ~3/2 = 705.978, ~12/11 = 132.544
+[[Mapping]]: [{{val| 1 0 2 1 2 }}, {{val| 0 1 0 1 1 }}, {{val| 0 0 3 2 -1 }}]
-Optimal GPV sequence: {{Vals| 8d, 9, 10, 17c, 19, 27e, 36 }}
+[[POTE generator]]s: ~3/2 = 705.978, ~12/11 = 132.544
-Badness: 0.000856
+{{Val list|legend=1| 8d, 9, 10, 17c, 19, 27e, 36 }}
-Projection pairs: ~5 = 6912/1331 ~7 = 854/121 to 2.3.11
+[[Badness]]: 0.856 × 10<sup>-3</sup>
+[[Projection pair]]s: ~5 = 6912/1331, ~7 = 854/121 to 2.3.11
 === 13-limit ===
+Subgroup: 2.3.5.7.11.13
 Comma list: 56/55, 78/77, 91/90
-Mapping: {{lbrack}} {{val| 1 0 2 1 2 2 }}, {{val| 0 1 0 1 1 1 }}, {{val| 0 0 3 2 -1 1 }} {{rbrack}}
+Mapping: [{{val| 1 0 2 1 2 2 }}, {{val| 0 1 0 1 1 1 }}, {{val| 0 0 3 2 -1 1 }}]
-POTE generators: 2, ~3/2 = 706.029, ~12/11 = 132.428
+POTE generators: ~3/2 = 706.029, ~14/13 = 132.428
-Optimal GPV sequence: {{Vals| 8d, 9, 10, 17c, 19, 27e, 36 }}
+Optimal GPV sequence: {{Val list| 8d, 9, 10, 17c, 19, 27e, 36 }}
-Badness: 0.000727
+Badness: 0.727 × 10<sup>-3</sup>
 Projection pairs: ~5 = 6912/1331, ~7 = 854/121, ~13 = 144/11 to 2.3.11
-[[Category:Theory]]
 [[Category:Temperament families]]
-[[Category:Sengic]]
+[[Category:Sengic family| ]] <!-- main article -->
+[[Category:Rank 3]]