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| * ''[[Hendecatonic (temperament)|Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic|Porwell temperaments]] | | * ''[[Hendecatonic (temperament)|Hendecatonic]]'' (+6144/6125 or 10976/10935) → [[Porwell temperaments #Hendecatonic|Porwell temperaments]] |
| * [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard|Marvel temperaments]] | | * [[Wizard]] (+225/224) → [[Marvel temperaments #Wizard|Marvel temperaments]] |
| | * ''[[Witcher]]'' (+1600000/1594323) → [[Amity family #Witcher|Amity family]] |
| * [[Oolong]] (+126/125) → [[Starling temperaments #Oolong|Starling temperaments]] | | * [[Oolong]] (+126/125) → [[Starling temperaments #Oolong|Starling temperaments]] |
| * [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]] | | * [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal|Septiennealimmal clan]] |
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| * ''[[Decavish]]'' (+2202927104/2197265625) → [[Vishnuzmic family #Decavish|Vishnuzmic family]] | | * ''[[Decavish]]'' (+2202927104/2197265625) → [[Vishnuzmic family #Decavish|Vishnuzmic family]] |
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| Considered below are qak, tokko, tertiathirds, and witcher. | | Considered below are qak, tokko, and tertiathirds, in the order of increasing [[badness]]. |
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| == Qak == | | == Qak == |
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| Badness (Sintel): 0.950 | | Badness (Sintel): 0.950 |
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| == Witcher ==
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| {{See also| Amity family }}
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| Witcher tempers out the wizma (420175/419904) and the amity comma (1600000/1594323). It may be described as the {{nowrap| 99 & 166 }} temperament.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 420175/419904, 1600000/1594323
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| {{Mapping|legend=1| 1 -7 -20 -2 | 0 25 65 14 }}
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| : mapping generators: ~2, ~80/63
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1199.8698{{c}}, ~80/63 = 412.0531{{c}}
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| : [[error map]]: {{val| -0.130 +0.283 -0.260 +0.178 }}
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| * [[CWE]]: ~2 = 1200.0000{{c}}, ~80/63 = 412.0956{{c}}
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| : error map: {{val| 0.000 +0.435 -0.100 +0.512 }}
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| {{Optimal ET sequence|legend=1| 32c, 67c, 99, 265, 364, 463, 562, 1025 }}
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| [[Badness]] (Sintel): 2.04
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 540/539, 4375/4356, 1240029/1239040
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| Mapping: {{mapping| 1 -7 -20 -2 -35 | 0 25 65 14 112 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9909{{c}}, ~80/63 = 412.0758{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~80/63 = 412.0788{{c}}
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| {{Optimal ET sequence|legend=0| 99e, 166, 265 }}
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| Badness (Sintel): 2.73
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 540/539, 729/728, 4375/4356, 10648/10647
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| Mapping: {{mapping| 1 -7 -20 -2 -35 -43 | 0 25 65 14 112 136 }}
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| Optimal tunings:
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| * WE: ~2 = 1200.0660{{c}}, ~33/26 = 412.0928{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~33/26 = 412.0709{{c}}
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| {{Optimal ET sequence|legend=0| 99ef, 166, 265 }}
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| Badness (Sintel): 2.40
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| === Semiwitcher ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 9801/9800, 41503/41472, 585640/583443
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| Mapping: {{mapping| 2 -14 -40 -4 -13 | 0 25 65 14 29 }}
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| : mapping generators: ~99/70, ~80/63
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| Optimal tunings:
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| * WE: ~99/70 = 599.9717{{c}}, ~80/63 = 412.0766{{c}}
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| * CWE: ~99/70 = 600.0000{{c}}, ~80/63 = 412.0951{{c}}
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| {{Optimal ET sequence|legend=0| 32c, 166, 198, 364, 562, 926 }}
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| Badness (Sintel): 2.92
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280
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| Mapping: {{mapping| 2 11 25 10 16 24 | 0 25 65 14 29 53 }}
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| Optimal tunings:
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| * WE: ~99/70 = 599.9666{{c}}, ~33/26 = 412.0726{{c}}
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| * CWE: ~99/70 = 600.0000{{c}}, ~33/26 = 412.0944{{c}}
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| {{Optimal ET sequence|legend=0| 32cf, 166, 198, 364, 562, 926 }}
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| Badness (Sintel): 1.57
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| === Hitch ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 3025/3024, 117649/117612, 1600000/1594323
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| Mapping: {{mapping| 1 -32 -85 -16 31 | 0 50 130 28 -41 }}
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| : mapping generators: ~2, ~891/560
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| Optimal tunings:
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| * WE: ~2 = 1199.8455{{c}}, ~891/560 = 805.9457{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~891/560 = 806.0488{{c}}
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| {{Optimal ET sequence|legend=0| 67c, 198, 463, 661, 1124bde }}
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| Badness (Sintel): 3.09
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323
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| Mapping: {{mapping| 1 -32 -85 -16 31 -134 | 0 50 130 28 -41 205 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.8415{{c}}, ~891/560 = 805.9451{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~891/560 = 806.0508{{c}}
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| {{Optimal ET sequence|legend=0| 198, 463, 661 }}
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| Badness (Sintel): 2.51
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| ==== Hitcher ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561
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| Mapping: {{mapping| 1 -32 -85 -16 31 -1 | 0 50 130 28 -41 7 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.7690{{c}}, ~78/49 = 805.8958{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~78/49 = 806.0500{{c}}
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| {{Optimal ET sequence|legend=0| 67c, 198, 463f, 661ff }}
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| Badness (Sintel): 2.46
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| [[Category:Temperament collections]] | | [[Category:Temperament collections]] |
| [[Category:Wizmic microtemperaments| ]] <!-- main article --> | | [[Category:Wizmic microtemperaments| ]] <!-- main article --> |
| [[Category:Rank 2]] | | [[Category:Rank 2]] |