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| * [[Misty]] (+3136/3125 or 5120/5103) → [[Misty family]] | | * [[Misty]] (+3136/3125 or 5120/5103) → [[Misty family]] |
| * ''[[Term (temperament)|Term]]'' (+32805/32768) → [[Schismatic family #Term|Schismatic family]] | | * ''[[Term (temperament)|Term]]'' (+32805/32768) → [[Schismatic family #Term|Schismatic family]] |
| | * ''[[Sextile]]'' (+33554432/33480783) → [[Garischismic clan #Sextile|Garischismic clan]] |
| * ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]] | | * ''[[Tritricot]]'' (+{{monzo| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot|Alphatricot family]] |
| * [[Compton]] (+225/224) → [[Compton family #Compton|Compton family]] | | * [[Compton]] (+225/224) → [[Compton family #Compton|Compton family]] |
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| * ''[[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 septichrome, akjayland, pnict, atomic, slendscape, avicenna, sextile, zinc, magnesium, poe, and chromium in the order of increasing [[badness]]. | | Considered below are septichrome, akjayland, pnict, atomic, slendscape, avicenna, zinc, magnesium, poe, and chromium in the order of increasing [[badness]]. |
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| == Septichrome == | | == Septichrome == |
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| ==== 17-limit ==== | | ==== 17-limit ==== |
| Subgroup: 2.3.5.7.11.13 | | Subgroup: 2.3.5.7.11.13.17 |
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| Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 61965/61952 | | Comma list: 936/935, 1701/1700, 1716/1715, 2025/2023, 61965/61952 |
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| Badness (Sintel): 0.928 | | Badness (Sintel): 0.928 |
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| == Sextile ==
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| : ''For the 5-limit version, see [[Schismic–commatic equivalence continuum #Sextile (5-limit)]].''
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| Sextile tempers out the [[garischisma]] with a 1/6-octave period and is the {{nowrap| 12 & 270 }} temperament.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 250047/250000, 33554432/33480783
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| {{Mapping|legend=1| 6 0 71 150 | 0 1 -6 -14 }}
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| : mapping generators: ~4096/3645, ~3
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| [[Optimal tuning]]s:
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| * [[WE]]: ~4096/3645 = 199.9828{{c}}, ~3/2 = 702.1521{{c}}
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| : [[error map]]: {{val| -0.103 +0.094 +0.173 -0.088 }}
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| * [[CWE]]: ~4096/3645 = 200.0000{{c}}, ~3/2 = 702.2187{{c}}
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| : error map: {{val| 0.000 +0.264 +0.374 +0.112 }}
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| {{Optimal ET sequence|legend=1| 12, …, 258, 270, 1362c, 1632c, …, 2442bc, 2712bc }}
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| [[Badness]] (Sintel): 1.77
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 5632/5625, 9801/9800, 151263/151250
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| Mapping: {{mapping| 6 0 71 150 230 | 0 1 -6 -14 -22 }}
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| Optimal tunings:
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| * WE: ~55/49 = 199.9817{{c}}, ~3/2 = 702.1383{{c}}
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| * CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2080{{c}}
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| {{Optimal ET sequence|legend=0| 12, …, 258e, 270, 822, 1092, 1362c }}
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| Badness (Sintel): 0.981
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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, 5632/5625, 10648/10647
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| Mapping: {{mapping| 6 0 71 150 230 279 | 0 1 -6 -14 -22 -27 }}
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| Optimal tunings:
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| * WE: ~55/49 = 199.9804{{c}}, ~3/2 = 702.1260{{c}}
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| * CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2001{{c}}
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| {{Optimal ET sequence|legend=0| 12f, …, 258ef, 270, 552, 822, 1092, 1914cde }}
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| Badness (Sintel): 0.788
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 936/935, 1701/1700, 1716/1715, 5632/5625, 7744/7735
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| Mapping: {{mapping| 6 0 71 150 230 279 -4 | 0 1 -6 -14 -22 -27 3 }}
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| Optimal tunings:
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| * WE: ~55/49 = 199.9669{{c}}, ~3/2 = 702.0643{{c}}
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| * CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.1869{{c}}
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| {{Optimal ET sequence|legend=0| 12f, 270, 552g }}
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| Badness (Sintel): 1.06
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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: 936/935, 1216/1215, 1701/1700, 1716/1715, 2376/2375, 4200/4199
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| Mapping: {{mapping| 6 0 71 150 230 279 -4 35 | 0 1 -6 -14 -22 -27 3 -1 }}
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| Optimal tunings:
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| * WE: ~55/49 = 199.9711{{c}}, ~3/2 = 702.0829{{c}}
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| * CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.1890{{c}}
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| {{Optimal ET sequence|legend=0| 12f, 270, 552g, 822gg }}
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| Badness (Sintel): 0.948
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| === Sextilia ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 1001/1000, 4096/4095, 4459/4455, 20449/20412
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| Mapping: {{mapping| 6 0 71 150 230 -149 | 0 1 -6 -14 -22 18 }}
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| Optimal tunings:
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| * WE: ~55/49 = 199.9975{{c}}, ~3/2 = 702.2196{{c}}
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| * CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2285{{c}}
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| {{Optimal ET sequence|legend=0| 12, 258e, 270 }}
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| Badness (Sintel): 1.62
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 715/714, 1001/1000, 1701/1700, 4096/4095, 4459/4455
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| Mapping: {{mapping| 6 0 71 150 230 -149 -4 | 0 1 -6 -14 -22 18 3 }}
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| Optimal tunings:
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| * WE: ~55/49 = 199.9862{{c}}, ~3/2 = 702.1714{{c}}
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| * CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2207{{c}}
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| {{Optimal ET sequence|legend=0| 12, 258e, 270 }}
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| Badness (Sintel): 1.95
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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: 715/714, 1001/1000, 1216/1215, 1701/1700, 1729/1728, 2912/2907
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| Mapping: {{mapping| 6 0 71 150 230 -149 -4 35 | 0 1 -6 -14 -22 18 3 -1 }}
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| Optimal tunings:
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| * WE: ~55/49 = 199.9866{{c}}, ~3/2 = 702.1731{{c}}
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| * CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 702.2208{{c}}
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| {{Optimal ET sequence|legend=0| 12, 258e, 270 }}
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| Badness (Sintel): 1.53
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| == Zinc == | | == Zinc == |