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Line 4: |
| Temperaments discussed elsewhere are: | | Temperaments discussed elsewhere are: |
| * [[Superpyth]] (+64/63 or 245/243) → [[Archytas clan #Superpyth|Archytas clan]] | | * [[Superpyth]] (+64/63 or 245/243) → [[Archytas clan #Superpyth|Archytas clan]] |
| | * ''[[Gariwizmic]]'' (+33554432/33480783) → [[Garischismic clan #Gariwizmic|Garischismic clan]] |
| * ''[[Cloudtone]]'' (+81/80) → [[Meantone family #Cloudtone|Meantone family]] | | * ''[[Cloudtone]]'' (+81/80) → [[Meantone family #Cloudtone|Meantone family]] |
| * [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk|Schismatic family]] | | * [[Tsaharuk]] (+32805/32768) → [[Schismatic family #Tsaharuk|Schismatic family]] |
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Line 20: |
| * ''[[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, witcher, and gariwizmic. | | Considered below are qak, tokko, tertiathirds, and witcher. |
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| == Qak == | | == Qak == |
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| Badness (Sintel): 2.46 | | Badness (Sintel): 2.46 |
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| == Gariwizmic ==
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| Gariwizmic tempers out the wizma (420175/419904) and the garischisma ([[33554432/33480783]]), and may be described as the {{nowrap| 94 & 176 }} temperament. It assumes a [[semioctave]] period and a [[3/2|perfect fifth]] generator that is slightly sharp of just. It finds [[5/4]] 39 fifths away, shifted by a semioctave. It extends extremely well to the 2.3.5.7.11.13.19 subgroup.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 420175/419904, 33554432/33480783
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| {{Mapping|legend=1| 2 0 -119 50 | 0 1 39 -14 }}
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| : mapping generators: ~46305/32768, ~3
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| [[Optimal tuning]]s:
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| * [[WE]]: ~46305/32768 = 599.9657{{c}}, ~3/2 = 702.1765{{c}}
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| : [[error map]]: {{val|-0.069 +0.153 -0.021 -0.053 }}
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| * [[CWE]]: ~46305/32768 = 600.0000{{c}}, ~3/2 = 702.2161{{c}}
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| : error map: {{val| 0.000 +0.261 +0.114 +0.149 }}
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| {{Optimal ET sequence|legend=1| 94, 176, 270, 904, 1174, 1444, 1714, 3158b, 4872bbcd }}
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| [[Badness]] (Sintel): 2.22
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| ==== 11-limit ====
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| Subgroup: 2.3.5.7.11
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| Comma list: 9801/9800, 19712/19683, 41503/41472
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| Mapping: {{mapping| 2 0 -119 50 -66 | 0 1 39 -14 23 }}
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| Optimal tunings:
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| * WE: ~99/70 = 599.9790{{c}}, ~3/2 = 702.1938{{c}}
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| : error map: {{val| -0.042 +0.197 +0.106 -0.001 -0.440 }}
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| * CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.2179{{c}}
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| : error map: {{val| 0.000 +0.263 +0.185 +0.123 -0.306 }}
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| {{Optimal ET sequence|legend=0| 94, 176, 270, 1174, 1444, 1714, 1984e }}
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| Badness (Sintel): 1.01
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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, 4096/4095, 19712/19683
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| Mapping: {{mapping| 2 0 -119 50 -66 93 | 0 1 39 -14 23 -27 }}
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| Optimal tunings:
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| * WE: ~99/70 = 599.9958{{c}}, ~3/2 = 702.2096{{c}}
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| : error map: {{val| -0.008 +0.246 +0.035 +0.146 -0.412 -0.353 }}
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| * CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.2145{{c}}
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| : error map: {{val| 0.000 +0.260 +0.054 +0.170 -0.383 -0.321 }}
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| {{Optimal ET sequence|legend=0| 94, 176, 270, 634, 904, 1174 }}
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| Badness (Sintel): 0.822
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| ==== 2.3.5.7.11.13.19 subgroup ====
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| Subgroup: 2.3.5.7.11.13.19
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| Comma list: 1216/1215, 1540/1539, 1716/1715, 1729/1728, 2080/2079
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| Mapping: {{mapping| 2 0 -119 50 -66 93 -131 | 0 1 39 -14 23 -27 44 }}
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| Optimal tunings:
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| * WE: ~99/70 = 599.9969{{c}}, ~3/2 = 702.2114{{c}}
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| : error map: {{val| -0.006 +0.250 +0.057 +0.147 -0.394 -0.355 -0.079 }}
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| * CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.2150{{c}}
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| : error map: {{val| 0.000 +0.260 +0.070 +0.165 -0.374 -0.332 -0.055 }}
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| {{Optimal ET sequence|legend=0| 94, 176, 270, 634, 904, 1174 }}
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| Badness (Sintel): 0.655
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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]] |