Pentacircle clan: Difference between revisions
m +links; update keys |
Update keys; +kujuku and restrict to the 11-limit |
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[[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 -4 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 1 }}] | [[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 -4 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 1 }}] | ||
[[Optimal tuning]] ([[POTE]]): ~3/2 = 703.8345, ~5/4 = 387.7585, ~7/4 = 969.8722 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.8345, ~5/4 = 387.7585, ~7/4 = 969.8722 | ||
{{Val list|legend=1| 12, 17c, 19e, 22, 34d, 39d, 41, 58, 80, 87, 99e, 121, 145, 167, 208, 266e, 699bbcdeee }} | {{Val list|legend=1| 12, 17c, 19e, 22, 34d, 39d, 41, 58, 80, 87, 99e, 121, 145, 167, 208, 266e, 699bbcdeee }} | ||
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[[Sval]] [[mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 -4 }}, {{val| 0 0 0 1 1 }}] | [[Sval]] [[mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 -4 }}, {{val| 0 0 0 1 1 }}] | ||
: sval mapping generators: ~2, ~3, ~7 | |||
[[Optimal tuning]] ([[POTE]]): ~3/2 = 703.8345, ~7/4 = 969.8722 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.8345, ~7/4 = 969.8722 | ||
{{Val list|legend=1| 12, 17, 36, 41, 58, 63, 104, 225e, 266e, 370bee, 699bbdeee }} | {{Val list|legend=1| 12, 17, 36, 41, 58, 63, 104, 225e, 266e, 370bee, 699bbdeee }} | ||
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Sval mapping: [{{val| 1 0 0 0 7 12 }}, {{val| 0 1 0 0 -4 -7 }}, {{val| 0 0 0 1 1 1 }}] | Sval mapping: [{{val| 1 0 0 0 7 12 }}, {{val| 0 1 0 0 -4 -7 }}, {{val| 0 0 0 1 1 1 }}] | ||
Optimal tuning (POTE): ~3/2 = 703.8563, ~7/4 = 969.9074 | Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.8563, ~7/4 = 969.9074 | ||
Optimal GPV sequence: {{Val list| 12f, 17, 41, 46, 58, 87, 104, 266ef, 329bef, 370beef, 474beef, 595bdeeeff, 699bbdeeeff }} | Optimal GPV sequence: {{Val list| 12f, 17, 41, 46, 58, 87, 104, 266ef, 329bef, 370beef, 474beef, 595bdeeeff, 699bbdeeeff }} | ||
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Sval mapping: [{{val| 1 0 0 0 7 12 -13 }}, {{val| 0 1 0 0 -4 -7 9 }}, {{val| 0 0 0 1 1 1 1 }}] | Sval mapping: [{{val| 1 0 0 0 7 12 -13 }}, {{val| 0 1 0 0 -4 -7 9 }}, {{val| 0 0 0 1 1 1 1 }}] | ||
Optimal tuning (POTE): ~3/2 = 704.0315, ~7/4 = 970.6051 | Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.0315, ~7/4 = 970.6051 | ||
Optimal GPV sequence: {{Val list| 12f, 17g, 29g, 41g, 46, 58, 75e, 104, 121, 225e }} | Optimal GPV sequence: {{Val list| 12f, 17g, 29g, 41g, 46, 58, 75e, 104, 121, 225e }} | ||
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[[Mapping]]: [{{val| 1 0 0 -10 }}, {{val| 0 1 0 11 }}, {{val| 0 0 1 -2 }}] | [[Mapping]]: [{{val| 1 0 0 -10 }}, {{val| 0 1 0 11 }}, {{val| 0 0 1 -2 }}] | ||
: mapping generators: ~2, ~3, ~5 | |||
[[Optimal tuning]] ([[POTE]]): ~3/2 = 703.9571, ~5/4 = 386.8863 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.9571, ~5/4 = 386.8863 | ||
{{Val list|legend=1| 41, 80, 87, 121, 167, 208, 329b, 375b, 537b, 583b, 704bd }} | {{Val list|legend=1| 41, 80, 87, 121, 167, 208, 329b, 375b, 537b, 583b, 704bd }} | ||
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[[Mapping]]: [{{val| 1 0 0 -10 -3 }}, {{val| 0 1 0 11 7 }}, {{val| 0 0 1 -2 -2 }}] | [[Mapping]]: [{{val| 1 0 0 -10 -3 }}, {{val| 0 1 0 11 7 }}, {{val| 0 0 1 -2 -2 }}] | ||
[[Optimal tuning]] ([[POTE]]): ~3/2 = 704.0412, ~5/4 = 387.2927 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.0412, ~5/4 = 387.2927 | ||
{{Val list|legend=1| 41, 80, 87, 121, 167, 208, 334be, 375be, 542bce }} | {{Val list|legend=1| 41, 80, 87, 121, 167, 208, 334be, 375be, 542bce }} | ||
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Mapping: [{{val| 1 0 0 -10 -3 2 }}, {{val| 0 1 0 11 7 4 }}, {{val| 0 0 1 -2 -2 -2 }}] | Mapping: [{{val| 1 0 0 -10 -3 2 }}, {{val| 0 1 0 11 7 4 }}, {{val| 0 0 1 -2 -2 -2 }}] | ||
Optimal tuning (POTE): ~3/2 = 703.9605, ~5/4 = 386.9831 | Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.9605, ~5/4 = 386.9831 | ||
Optimal GPV sequence: {{Val list| 41, 46, 80, 87, 121, 167, 208, 375be, 583bef }} | Optimal GPV sequence: {{Val list| 41, 46, 80, 87, 121, 167, 208, 375be, 583bef }} | ||
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Mapping: [{{val| 1 0 0 -10 -3 2 8 }}, {{val| 0 1 0 11 7 4 -1 }}, {{val| 0 0 1 -2 -2 -2 -1 }}] | Mapping: [{{val| 1 0 0 -10 -3 2 8 }}, {{val| 0 1 0 11 7 4 -1 }}, {{val| 0 0 1 -2 -2 -2 -1 }}] | ||
Optimal tuning (POTE): ~3/2 = 704.0831, ~5/4 = 387.3269 | Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.0831, ~5/4 = 387.3269 | ||
Optimal GPV sequence: {{Val list| 41, 46, 75e, 80, 87, 121, 167, 288beg }} | Optimal GPV sequence: {{Val list| 41, 46, 75e, 80, 87, 121, 167, 288beg }} | ||
Badness: 0.982 × 10<sup>-3</sup> | Badness: 0.982 × 10<sup>-3</sup> | ||
== Kujuku == | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 896/891, 14700/14641 | |||
[[Mapping]]: [{{val| 1 0 0 -13 -6 }}, {{val| 0 2 0 17 9 }}, {{val| 0 0 1 1 1 }}] | |||
: mapping generators: ~2, ~121/70, ~5 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~121/70 = 951.8367, ~5/4 = 386.4048 | |||
{{Val list|legend=1| 24, 29, 34d, 53d, 58, 87, 121, 145, 179e, 208, 266e }} | |||
[[Badness]]: 2.26 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 352/351, 364/363, 676/675 | |||
Mapping: [{{val| 1 0 0 -13 -6 -1 }}, {{val| 0 2 0 17 9 3 }}, {{val| 0 0 1 1 1 1 }}] | |||
Optimal tuning (CTE): ~2 = 1\1, ~121/70 = 951.8367, ~5/4 = 386.4048 | |||
Optimal GPV sequence: {{Val list| 24, 29, 34d, 53d, 58, 87, 121, 179ef, 208, 266ef, 474beef }} | |||
Badness: 1.06 × 10<sup>-3</sup> | |||
Complexity spectrum: 15/13, 4/3, 13/10, 9/8, 13/11, 15/11, 12/11, 11/9, 11/8, 14/11, 16/13, 16/15, 11/10, 13/12, 9/7, 5/4, 18/13, 7/6, 6/5, 8/7, 10/9, 14/13, 15/14, 7/5 | |||
== Terrapyth == | == Terrapyth == | ||
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[[Mapping]]: [{{val| 1 0 -31 0 7 }}, {{val| 0 1 21 0 -4 }}, {{val| 0 0 0 1 1 }}] | [[Mapping]]: [{{val| 1 0 -31 0 7 }}, {{val| 0 1 21 0 -4 }}, {{val| 0 0 0 1 1 }}] | ||
: mapping generators: ~2, ~3, ~7 | |||
[[Optimal tuning]] ([[POTE]]): ~3/2 = 704.1814, ~7/4 = 970.6217 | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.1814, ~7/4 = 970.6217 | ||
{{Val list|legend=1| 17c, 29, 46, 92de, 121, 167, 288be }} | {{Val list|legend=1| 17c, 29, 46, 92de, 121, 167, 288be }} | ||
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Mapping: [{{val| 1 0 -31 0 7 12 }}, {{val| 0 1 0 11 7 4 -7 }}, {{val| 0 0 1 -2 -2 -2 1 }}] | Mapping: [{{val| 1 0 -31 0 7 12 }}, {{val| 0 1 0 11 7 4 -7 }}, {{val| 0 0 1 -2 -2 -2 1 }}] | ||
Optimal tuning (POTE): ~3/2 = 704.1691, ~7/4 = 970.8432 | Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.1691, ~7/4 = 970.8432 | ||
Optimal GPV sequence: {{Val list| 17c, 29, 46, 75e, 92def, 121, 167, 288be }} | Optimal GPV sequence: {{Val list| 17c, 29, 46, 75e, 92def, 121, 167, 288be }} | ||
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Mapping: [{{val| 1 0 -31 0 7 12 -13 }}, {{val| 0 1 0 11 7 4 -7 9 }}, {{val| 0 0 1 -2 -2 -2 1 1 }}] | Mapping: [{{val| 1 0 -31 0 7 12 -13 }}, {{val| 0 1 0 11 7 4 -7 9 }}, {{val| 0 0 1 -2 -2 -2 1 1 }}] | ||
Optimal tuning (POTE): ~3/2 = 704.1628, ~7/4 = 970.6620 | Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.1628, ~7/4 = 970.6620 | ||
Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 75e, 92defg, 121, 167, 288beg }} | Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 75e, 92defg, 121, 167, 288beg }} | ||
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[[Category:Pentacircle clan| ]] <!-- main article --> | [[Category:Pentacircle clan| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
[[Category:Tolerant]] | [[Category:Tolerant]] | ||