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| Line 1,250: |
Line 1,250: |
| [[Comma list]]: 24576/24389 | | [[Comma list]]: 24576/24389 |
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| [[Mapping]]: [{{val|1 2 5}}, {{val|0 3 -1}}]
| | {{Mapping|legend=2| 1 2 5 | 0 3 -1 }} |
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| [[CTE tuning|CTE generator]]: ~32/29 = 166.067 | | [[Optimal tuning]]s ([[CTE]]): ~32/29 = 166.067{{c}} |
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| {{Optimal ET sequence|legend=1| 7, 22, 29, 94, 123, 152j, 275jj, 427jjj }} | | {{Optimal ET sequence|legend=1| 7, 22, 29, 94, 123, 152j, 275jj, 427jjj }} |
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| === Sematology === | | === Sematology === |
| This temperament tempers out 4107/4096 and thus equates 2 [[37/32]]'s with [[4/3]]. | | This temperament tempers out [[4107/4096]] and thus equates a stack of two [[37/32]]'s with [[4/3]]. |
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| [[Subgroup]]: 2.3.37 | | [[Subgroup]]: 2.3.37 |
| Line 1,263: |
Line 1,263: |
| [[Comma list]]: 4107/4096 | | [[Comma list]]: 4107/4096 |
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| [[Gencom]]: [2 37/32; 4107/4096]
| | {{Mapping|legend=2| 1 1 5 | 0 -2 1 }} |
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| [[Mapping]]: [{{val|1 1 5}}, {{val|0 -2 1}}] | | [[Optimal tuning]]s ([[POTE]]): ~37/32 = 249.075{{c}} |
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| [[POTE generator]]: ~[[37/32]] = 249.075 | |
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| {{Optimal ET sequence|legend=1| 5, 14, 19, 24, 53, 77, 130 }} | | {{Optimal ET sequence|legend=1| 5, 14, 19, 24, 53, 77, 130 }} |
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| ==== 2.3.7.37 subgroup ====
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| [[Subgroup]]: 2.3.7.37
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| [[Comma list]]: 4107/4096, 259/256
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| [[Gencom]]: [2 37/32; 4107/4096 259/256]
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| [[Mapping]]: [{{val|1 1 1 5}}, {{val|0 -2 -1 1}}]
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| [[POTE generator]]: ~[[37/32]] = 247.782
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| {{Optimal ET sequence|legend=1| 5, 14, 19, 24, 53d }}
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| ==== 2.3.5.37 subgroup ====
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| It is difficult to extend sematology to include 5, due the 5th harmonic being quite high-complexity.
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| [[Subgroup]]: 2.3.5.37
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| [[Comma list]]: 4107/4096, 17592186044416/17562397269605
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| [[Gencom]]: [2 37/32; 4107/4096 17592186044416/17562397269605]
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| [[Mapping]]: [{{val|1 1 4 5}}, {{val|0 -2 -8 1}}]
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| [[POTE generator]]: ~[[37/32]] = 251.393
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| {{Optimal ET sequence|legend=1| 5, 14c, 19, 43, 62 }}
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| ===== 2.3.5.7.37 subgroup =====
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| [[Subgroup]]: 2.3.5.7.37
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| [[Comma list]]: 4107/4096, 17592186044416/17562397269605, 259/256
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| [[Gencom]]: [2 37/32; 4107/4096 17592186044416/17562397269605 259/256]
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| [[Mapping]]: [{{val|1 1 4 1 5}}, {{val|0 -2 -8 -1 1}}]
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| [[POTE generator]]: ~[[37/32]] = 251.204
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| {{Optimal ET sequence|legend=1| 5, 14c, 19 }}
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| === Reversed mavila === | | === Reversed mavila === |
| Line 1,317: |
Line 1,274: |
| [[Comma list]]: 81/74 | | [[Comma list]]: 81/74 |
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| [[Gencom]]: [2 4/3; 81/74]
| | {{Mapping|legend=2| 1 1 0 | 0 -1 12 }} |
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| [[Mapping]]: [{{val|1 1 0}}, {{val|0 -1 12}}] | | [[Optimal tuning]]s ([[POTE]]): ~4/3 = 521.397{{c}} |
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| [[POTE generator]]: ~4/3 = 521.397 | |
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| {{Optimal ET sequence|legend=1| 5l, 7l, 9, 16l }} | | {{Optimal ET sequence|legend=1| 5l, 7l, 9, 16l }} |
| Line 1,328: |
Line 1,283: |
| {{Main| Reversed meantone }} | | {{Main| Reversed meantone }} |
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| Subgroup: 2.3.41 | | [[Subgroup]]: 2.3.41 |
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| [[Comma list]]: 82/81 | | [[Comma list]]: 82/81 |
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| [[Gencom]]: [2 4/3; 82/81]
| | {{Mapping|legend=2| 1 2 7 | 0 -1 -4 }} |
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| [[Mapping|Sval mapping]]: [{{val|1 2 7}}, {{val|0 -1 -4}}] | | [[Optimal tuning]]s ([[POTE]]): ~4/3 = 494.509{{c}} |
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| [[Tp tuning|POL2 generator]]: ~4/3 = 494.509 | |
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| {{Optimal ET sequence|legend=1| 5, 12, 17 }} | | {{Optimal ET sequence|legend=1| 5, 12, 17 }} |
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| ==== 2.3.7.41 subgroup ====
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| Subgroup: 2.3.7.41
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| [[Comma list]]: 64/63, 82/81
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| [[Gencom]]: [2 4/3; 64/63 82/81]
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| [[Mapping|Sval mapping]]: [{{val| 1 2 2 7 }}, {{val| 0 -1 2 -4 }}]
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| [[POTE generator]]: ~4/3 = 490.0323
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| [[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029
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| {{Optimal ET sequence|legend=1| 5, 12, 17, 22, 49 }}
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| ==== 2.3.7.11.41 subgroup ====
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| Subgroup: 2.3.7.11.41
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| [[Comma list]]: 64/63, 82/81, 99/98
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| [[Gencom]]: [2 4/3; 64/63 82/81 99/98]
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| [[Mapping|Sval mapping]]: [{{val| 1 2 2 1 7 }}, {{val| 0 -1 2 6 -4 }}]
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| [[POTE generator]]: ~4/3 = 492.1787
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| [[TOP tuning|TOP generator]]s: ~2 = 1197.9683, ~4/3 = 491.3454
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| {{Optimal ET sequence|legend=1| 5, 12, 17, 22, 39d }}
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| [[Category:Temperament collections]] | | [[Category:Temperament collections]] |
| [[Category:Subgroup temperaments]] | | [[Category:Subgroup temperaments]] |
| [[Category:Rank 2]] | | [[Category:Rank 2]] |