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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]] |
| | * ''[[Quintakwai]]'', {5120/5103, 9765625/9680832} → [[Quindromeda family #Quintakwai|Quindromeda family]] |
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| == Buzzard == | | == Buzzard == |
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| Badness: 0.034837 | | Badness: 0.034837 |
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| == Quintakwai ==
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| {{See also| 28ed5 #Regular temperaments }}
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| The ''quintakwai'' temperament (12&193) tempers out the hemifamity comma (5120/5103) and the compass comma (9765625/9680832, quinruyoyo) in the 7-limit; 1375/1372 and 4375/4356 in the 11-limit. In the 2.3.5.7.17.19 subgroup, 225/224 (the difference between 15/14 and 16/15), 256/255 (between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), and 361/360 (between 19/18 and 20/19) are equated together, and 400/399 (between 20/19 and 21/20) is tempered out. The name ''quintakwai'' is so named because the generator is 1/5 of the [[Mirkwai clan #Kwai|kwai]] fourth (~4/3, about 497.4 cents).
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 5120/5103, 9765625/9680832
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| [[Mapping]]: [{{val|1 2 0 -2}}, {{val|0 -5 28 58}}]
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| {{Multival|legend=1|5 -28 -58 -56 -106 -56}}
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| [[POTE generator]]: ~625/588 = 99.483
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| {{Val list|legend=1| 12, 169, 181, 193 }}
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| [[Badness]]: 0.155536
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 1375/1372, 4375/4356, 5120/5103
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| Mapping: [{{val|1 2 0 -2 -4}}, {{val|0 -5 28 58 90}}]
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| POTE generator: ~35/33 = 99.472
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| Vals: {{Val list| 12, 181, 193, 374, 567ce }}
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| Badness: 0.073158
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 325/324, 1375/1372, 1575/1573, 4096/4095
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| Mapping: [{{val|1 2 0 -2 -4 10}}, {{val|0 -5 28 58 90 -76}}]
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| POTE generator: ~35/33 = 99.468
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| Vals: {{Val list| 12, 181, 193, 374, 567ce, 941bce }}
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| Badness: 0.062737
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 325/324, 375/374, 595/594, 1275/1274, 4096/4095
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| Mapping: [{{val|1 2 0 -2 -4 10 5}}, {{val|0 -5 28 58 90 -76 -11}}]
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| POTE generator: ~18/17 = 99.469
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| Vals: {{Val list| 12, 181, 193, 374, 567ce, 941bceg }}
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| Badness: 0.037855
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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: 325/324, 375/374, 400/399, 595/594, 1216/1215, 1275/1274
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| Mapping: [{{val|1 2 0 -2 -4 10 5 4}}, {{val|0 -5 28 58 90 -76 -11 3}}]
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| POTE generator: ~18/17 = 99.469
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| Vals: {{Val list| 12, 181, 193, 374, 567ce, 941bcegh, 1508bccdeegghh }}
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| Badness: 0.025861
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| === Quinkwai ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 352/351, 847/845, 1375/1372, 4375/4356
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| Mapping: [{{val|1 2 0 -2 -4 -5}}, {{val|0 -5 28 58 90 105}}]
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| POTE generator: ~35/33 = 99.456
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| Vals: {{Val list| 12f, 169e, 181 }}
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| Badness: 0.061873
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 352/351, 375/374, 595/594, 833/832, 1375/1372
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| Mapping: [{{val|1 2 0 -2 -4 -5 5}}, {{val|0 -5 28 58 90 105 -11}}]
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| POTE generator: ~18/17 = 99.458
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| Vals: {{Val list| 12f, 169e, 181, 374ff, 555cff }}
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| Badness: 0.043506
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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: 352/351, 375/374, 400/399, 495/494, 595/594, 1375/1372
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| Mapping: [{{val|1 2 0 -2 -4 -5 5 4}}, {{val|0 -5 28 58 90 105 -11 3}}]
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| POTE generator: ~18/17 = 99.459
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| Vals: {{Val list| 12f, 169e, 181, 374ff, 555cff }}
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| Badness: 0.031313
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| === Quintakwoid ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 364/363, 625/624, 1375/1372, 5120/5103
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| Mapping: [{{val|1 2 0 -2 -4 -6}}, {{val|0 -5 28 58 90 117}}]
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| POTE generator: ~35/33 = 99.484
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| Vals: {{Val list| 12f, 181f, 193 }}
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| Badness: 0.057357
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 364/363, 375/374, 442/441, 595/594, 5120/5103
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| Mapping: [{{val|1 2 0 -2 -4 -6 5}}, {{val|0 -5 28 58 90 117 -11}}]
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| POTE generator: ~18/17 = 99.484
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| Vals: {{Val list| 12f, 181f, 193 }}
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| Badness: 0.039289
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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: 364/363, 375/374, 400/399, 442/441, 595/594, 1216/1215
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| Mapping: [{{val|1 2 0 -2 -4 -6 5 4}}, {{val|0 -5 28 58 90 117 -11 3}}]
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| POTE generator: ~18/17 = 99.485
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| Vals: {{Val list| 12f, 181f, 193 }}
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| Badness: 0.028101
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| == Quinticosiennic == | | == Quinticosiennic == |