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| * ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart|Quartonic family]] | | * ''[[Triquart]]'' (+117649/116640) → [[Quartonic family #Triquart|Quartonic family]] |
| * ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]] | | * ''[[Stearnscape]]'' (+118098/117649) → [[Stearnsmic clan #Stearnscape|Stearnsmic clan]] |
| * ''[[Domain (temperament)|Domain]]'' (645700815/645657712) → [[Minortonic family #Domain|Minortonic family]] | | * ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Domain|Vulture family]] |
| | * ''[[Domain (temperament)|Domain]]'' (+645700815/645657712) → [[Minortonic family #Domain|Minortonic family]] |
| * ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]] | | * ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]] |
| * ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments #Aemilic|159th-octave temperaments]] | | * ''[[Aemilic]]'' (+{{monzo|-84 53}}) → [[159th-octave temperaments #Aemilic|159th-octave temperaments]] |
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| Considered below are sextile, septichrome, pnict, atomic, avicenna, terture, slendscape, akjayland, magnesium, chromium, zinc, and poe. | | Considered below are sextile, septichrome, pnict, atomic, avicenna, slendscape, akjayland, magnesium, chromium, zinc, and poe. |
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| == Sextile == | | == Sextile == |
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| Badness (Sintel): 0.928 | | Badness (Sintel): 0.928 |
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| == Terture ==
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| {{See also| Vulture family }}
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| Named by [[Xenllium]] in 2021, terture may be described as the {{nowrap| 111 & 159 }} temperament.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 250047/250000, 359661568/358722675
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| {{Mapping|legend=1| 3 0 -18 -32 | 0 4 21 34 }}
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| : mapping generators: ~63/50, ~320/243
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| [[Optimal tuning]]s:
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| * [[WE]]: ~63/50 = 399.9723{{c}}, ~320/243 = 475.5221{{c}} (~392/375 = 75.5499{{c}})
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| : [[error map]]: {{val| -0.083 +0.134 +0.151 -0.185 }}
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| * [[CWE]]: ~63/50 = 400.0000{{c}}, ~320/243 = 475.5519{{c}} (~392/375 = 75.5519{{c}})
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| : error map: {{val| 0.000 +0.253 +0.276 -0.061 }}
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| {{Optimal ET sequence|legend=1| 111, 159, 270 }}
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| [[Badness]] (Sintel): 2.21
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 3025/3024, 19712/19683, 102487/102400
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| Mapping: {{mapping| 3 0 -18 -32 8 | 0 4 21 34 2 }}
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| Optimal tunings:
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| * WE: ~63/50 = 399.9902{{c}}, ~320/243 = 475.5383{{c}} (~392/375 = 75.5481{{c}})
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| * CWE: ~63/50 = 400.0000{{c}}, ~320/243 = 475.5490{{c}} (~392/375 = 75.5490{{c}})
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| {{Optimal ET sequence|legend=0| 111, 159, 270, 1239, 1509, 1779, 2049, 2319 }}
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| Badness (Sintel): 0.969
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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, 1001/1000, 3025/3024, 10985/10976
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| Mapping: {{mapping| 3 0 -18 -32 8 -21 | 0 4 21 34 2 27 }}
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| Optimal tunings:
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| * WE: ~63/50 = 399.9958{{c}}, ~154/117 = 475.5485{{c}} (~117/112 = 75.5527{{c}})
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| * CWE: ~63/50 = 400.0000{{c}}, ~154/117 = 475.5531{{c}} (~117/112 = 75.5531{{c}})
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| {{Optimal ET sequence|legend=0| 111, 159, 270 }}
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| Badness (Sintel): 0.771
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| === 17-limit ===
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913
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| Mapping: {{mapping| 3 0 -18 -32 8 -21 -2 | 0 4 21 34 2 27 12 }}
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| Optimal tunings:
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| * WE: ~34/27 = 399.9664{{c}}, ~112/85 = 475.5198{{c}} (~117/112 = 75.5534{{c}})
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| * CWE: ~34/27 = 400.0000{{c}}, ~112/85 = 475.5568{{c}} (~117/112 = 75.5568{{c}})
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| {{Optimal ET sequence|legend=0| 111, 159, 270 }}
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| Badness (Sintel): 0.953
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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: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615
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| Mapping: {{mapping| 3 0 -18 -32 8 -21 -2 -36 | 0 4 21 34 2 27 12 41 }}
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| Optimal tunings:
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| * WE: ~34/27 = 399.9665{{c}}, ~112/85 = 475.5198{{c}} (~95/91 = 75.5533{{c}})
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| * CWE: ~34/27 = 400.0000{{c}}, ~112/85 = 475.5568{{c}} (~95/91 = 75.5568{{c}})
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| {{Optimal ET sequence|legend=0| 111, 159, 270 }}
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| Badness (Sintel): 0.846
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| === 23-limit ===
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| Subgroup: 2.3.5.7.11.13.17.19.23
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| Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215
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| Mapping: {{mapping| 3 0 -18 -32 8 -21 -2 -36 10 | 0 4 21 34 2 27 12 41 3 }}
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| Optimal tunings:
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| * WE: ~34/27 = 400.0026{{c}}, ~112/85 = 475.5510{{c}} (~24/23 = 75.5485{{c}})
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| * CWE: ~34/27 = 400.0000{{c}}, ~112/85 = 475.5482{{c}} (~24/23 = 75.5482{{c}})
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| {{Optimal ET sequence|legend=0| 111, 159, 270 }}
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| Badness (Sintel): 1.07
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| == Slendscape == | | == Slendscape == |