Lehmerismic temperaments: Difference between revisions
m -category as agreed upon |
m Cleanup and update keys |
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== Lehmerismic == | == Lehmerismic == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: [[3025/3024]] | [[Comma list]]: [[3025/3024]] | ||
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{{See also| Landscape family }} | {{See also| Landscape family }} | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 3025/3024, 102487/102400 | [[Comma list]]: 3025/3024, 102487/102400 | ||
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Mapping: [{{val| 3 0 0 4 8 -3 }}, {{val| 0 2 0 -4 1 3 }}, {{val| 0 0 1 2 0 1 }}] | Mapping: [{{val| 3 0 0 4 8 -3 }}, {{val| 0 2 0 -4 1 3 }}, {{val| 0 0 1 2 0 1 }}] | ||
Optimal GPV sequence: {{Val list| 15, 24d, 33cdff, 39df, 57f, 72, 111, 159, 183, 198, 270 }} | |||
Badness: 0.549 × 10<sup>-3</sup> | Badness: 0.549 × 10<sup>-3</sup> | ||
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== Skadi == | == Skadi == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 3025/3024, 703125/702464 | [[Comma list]]: 3025/3024, 703125/702464 | ||
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== Ganesha == | == Ganesha == | ||
=== 7-limit (quasiorwellismic) === | === 7-limit (quasiorwellismic) === | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 29360128/29296875 | [[Comma list]]: 29360128/29296875 | ||
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Mapping generators: ~2, ~3, ~5 | Mapping generators: ~2, ~3, ~5 | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.0901, ~5/4 = 386.6931 | ||
{{Val list|legend=1| 31, 87, 118, 152, 239, 270, 571, 723, 841, 993, 1263, 1564c, 1834c, 2104c }} | {{Val list|legend=1| 31, 87, 118, 152, 239, 270, 571, 723, 841, 993, 1263, 1564c, 1834c, 2104c }} | ||
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=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 3025/3024, 5632/5625 | [[Comma list]]: 3025/3024, 5632/5625 | ||
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[[Mapping]]: [{{val| 1 0 0 -22 -9 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 10 4 }}] | [[Mapping]]: [{{val| 1 0 0 -22 -9 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 10 4 }}] | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.2251, ~5/4 = 386.6908 | ||
{{Val list|legend=1| 31, 65d, 87, 118, 152, 239, 270, 962, 1232, 1502 }} | {{Val list|legend=1| 31, 65d, 87, 118, 152, 239, 270, 962, 1232, 1502 }} | ||
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== Hanuman == | == Hanuman == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 3025/3024, 4000/3993 | [[Comma list]]: 3025/3024, 4000/3993 | ||
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Mapping: [{{val| 1 2 0 -8 1 -6 }}, {{val| 0 -3 0 11 1 3 }}, {{val| 0 0 1 4 1 4 }}] | Mapping: [{{val| 1 2 0 -8 1 -6 }}, {{val| 0 -3 0 11 1 3 }}, {{val| 0 0 1 4 1 4 }}] | ||
Optimal GPV sequence: {{Val list| 15, 50d, 57f, 65d, 72, 87, 137, 152f, 224, 311, 535, 918c }} | |||
Badness: 0.653 × 10<sup>-3</sup> | Badness: 0.653 × 10<sup>-3</sup> | ||
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== Lux == | == Lux == | ||
=== 7-limit === | === 7-limit === | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 26843545600/26795786661 | [[Comma list]]: 26843545600/26795786661 | ||
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{{Multival|legend=1|rank=3| 5 2 13 30 }} | {{Multival|legend=1|rank=3| 5 2 13 30 }} | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.1152, ~40960/35721 = 235.5941 | ||
{{Val list|legend=1| 41, 87, 128, 142, 178, 183, 224, 270, 494, 764, 1034, 1798, 6428bcdd, 8226bbcddd }} | {{Val list|legend=1| 41, 87, 128, 142, 178, 183, 224, 270, 494, 764, 1034, 1798, 6428bcdd, 8226bbcddd }} | ||
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=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 3025/3024, 131072/130977 | [[Comma list]]: 3025/3024, 131072/130977 | ||
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{{Multival|legend=1|rank=3| 5 2 -4 13 -1 10 30 25 34 71 }} | {{Multival|legend=1|rank=3| 5 2 -4 13 -1 10 30 25 34 71 }} | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1/1, ~3/2 = 702.1117, ~55/48 = 235.5784 | ||
{{Val list|legend=1| 41, 87, 137, 178, 183, 224, 270, 494, 764, 1839, 2109, 2603, 3367d }} | {{Val list|legend=1| 41, 87, 137, 178, 183, 224, 270, 494, 764, 1839, 2109, 2603, 3367d }} | ||
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Mapping: [{{val| 1 0 0 6 5 6 }}, {{val| 0 1 4 -1 -3 -5 }}, {{val| 0 0 -5 -2 4 7 }}] | Mapping: [{{val| 1 0 0 6 5 6 }}, {{val| 0 1 4 -1 -3 -5 }}, {{val| 0 0 -5 -2 4 7 }}] | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.0674, ~55/48 = 235.5870 | ||
Optimal GPV sequence: {{Val list| 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }} | |||
Badness: 0.360 × 10<sup>-3</sup> | Badness: 0.360 × 10<sup>-3</sup> | ||
== Galaxy == | == Galaxy == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 3025/3024, 20614528/20588575 | [[Comma list]]: 3025/3024, 20614528/20588575 | ||
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{{Multival|legend=1| 9 -14 -16 -14 -20 5 34 35 6 21 }} | {{Multival|legend=1| 9 -14 -16 -14 -20 5 34 35 6 21 }} | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.9856, ~6125/3456 = 991.0688 | ||
{{Val list|legend=1| 46, 103, 121, 149, 167, 224, 270, 494, 764, 1631, 1901, 2395, 2665 }} | {{Val list|legend=1| 46, 103, 121, 149, 167, 224, 270, 494, 764, 1631, 1901, 2395, 2665 }} | ||
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Mapping: [{{val| 1 0 5 -4 -5 -4 }}, {{val| 0 1 3 -3 -3 -4 }}, {{val| 0 0 -9 14 16 17 }}] | Mapping: [{{val| 1 0 5 -4 -5 -4 }}, {{val| 0 1 3 -3 -3 -4 }}, {{val| 0 0 -9 14 16 17 }}] | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.9368, ~484/273 = 991.0597 | ||
Optimal GPV sequence: {{val list| 46, 75e, 103, 121, 149, 224, 270, 494, 764, 1137, 1258, 1361, 1631, 2125 }} | |||
Badness: 0.463 × 10<sup>-3</sup> | Badness: 0.463 × 10<sup>-3</sup> | ||
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Mapping: [{{val| 1 0 5 -4 -5 -4 -1 }}, {{val| 0 1 3 -3 -3 -4 -2 }}, {{val| 0 0 -9 14 16 17 10 }}] | Mapping: [{{val| 1 0 5 -4 -5 -4 -1 }}, {{val| 0 1 3 -3 -3 -4 -2 }}, {{val| 0 0 -9 14 16 17 10 }}] | ||
POTE | Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.1144, ~85/48 = 991.1035 | ||
Optimal GPV sequence: {{val list| 46, 75e, 103, 121, 149, 167, 224, 270, 494g }} | |||
Badness: 0.933 × 10<sup>-3</sup> | Badness: 0.933 × 10<sup>-3</sup> | ||