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| * ''[[Kwai]]'', {5120/5103, 16875/16807} → [[Mirkwai clan #Kwai|Mirkwai clan]] | | * ''[[Kwai]]'', {5120/5103, 16875/16807} → [[Mirkwai clan #Kwai|Mirkwai clan]] |
| * ''[[Supers]]'', {5120/5103, 118098/117649} → [[Stearnsmic clan #Supers|Stearnsmic clan]] | | * ''[[Supers]]'', {5120/5103, 118098/117649} → [[Stearnsmic clan #Supers|Stearnsmic clan]] |
| | * ''[[Quintupole]]'', {5120/5103, 395136/390625} → [[Quintaleap family #Quintupole|Quintaleap family]] |
| * ''[[Quintakwai]]'', {5120/5103, 9765625/9680832} → [[Quindromeda family #Quintakwai|Quindromeda family]] | | * ''[[Quintakwai]]'', {5120/5103, 9765625/9680832} → [[Quindromeda family #Quintakwai|Quindromeda family]] |
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| Badness: 0.034837 | | Badness: 0.034837 |
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| == Quinticosiennic ==
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| {{See also| 16ed5/2 #Regular temperaments }}
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| The ''quinticosiennic'' temperament (12&145) tempers out the hemifamity comma (5120/5103) and 395136/390625 (trizo-aquadbigu) in the 7-limit; 441/440 (werckisma), 896/891 (pentacircle), and 78408/78125 (lolosepgu) in the 11-limit. The word "quinticosiennic" means 5 (quintuple) × 29 (είκοσι εννέα) = 145, and so named because 1/5 of [[29edo|29EDO]] fourth, i.e. 12\145, is a possible generator.
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 5120/5103, 395136/390625
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| [[Mapping]]: [{{val|1 2 1 -1}}, {{val|0 -5 16 46}}]
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| {{Multival|legend=1|5 -16 -46 -37 -87 -62}}
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| [[POTE generator]]: ~135/128 = 99.345
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| {{Val list|legend=1| 12, 133, 145, 157, 302c, 459bcc }}
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| [[Badness]]: 0.158041
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 441/440, 896/891, 78408/78125
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| Mapping: [{{val|1 2 1 -1 -2}}, {{val|0 -5 16 46 66}}]
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| POTE generator: ~35/33 = 99.318
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| Vals: {{Val list| 12, 133, 145 }}
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| Badness: 0.080674
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 196/195, 352/351, 364/363, 78408/78125
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| Mapping: [{{val|1 2 1 -1 -2 -3}}, {{val|0 -5 16 46 66 81}}]
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| POTE generator: ~35/33 = 99.307
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| Vals: {{Val list| 12f, 133, 145 }}
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| Badness: 0.052464
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| === 17-limit ===
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 196/195, 256/255, 352/351, 364/363, 3757/3750
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| Mapping: [{{val|1 2 1 -1 -2 -3 5}}, {{val|0 -5 16 46 66 81 -11}}]
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| POTE generator: ~18/17 = 99.308
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| Vals: {{Val list| 12f, 133, 145 }}
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| Badness: 0.037108
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| === 19-limit ===
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| Subgroup: 2.3.5.7.11.13.17.19
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| Comma list: 196/195, 256/255, 352/351, 361/360, 364/363, 476/475
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| Mapping: [{{val|1 2 1 -1 -2 -3 5 4}}, {{val|0 -5 16 46 66 81 -11 3}}]
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| POTE generator: ~18/17 = 99.303
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| Vals: {{Val list| 12f, 133, 145 }}
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| Badness: 0.028440
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| [[Category:Regular temperament theory]] | | [[Category:Regular temperament theory]] |