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| {{Technical data page}}
| | #redirect [[Cloudy comma]] |
| The '''cloudy clan''' tempers out the [[cloudy comma]], 16807/16384, thus splitting the octave into 5 equal parts and mapping the harmonic 7 to 4\5.
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| Temperaments discussed elsewhere are:
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| * [[Blackwood]] (+28/27 or 49/48) → [[Limmic temperaments #Septimal blackwood|Limmic temperaments]]
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| * [[Cloudtone]] (+81/80) → [[Meantone family #Cloudtone|Meantone family]]
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| * [[Pental (temperament)|Pentacloud]] (+245/243) → [[Quintile family #Pentacloud|Quintile family]]
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| * [[Sengasec]] (+686/675) → [[Quintosec family #Sengasec|Quintosec family]]
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| * [[Warlock]] (+3125/3072) → [[Magic family #Warlock|Magic family]]
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| == Decic ==
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| {{Main| Decic }}
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| Named by [[Xenllium]] in 2021, decic tempers out the [[cloudy comma]], 16807/16384 and the [[marvel comma]], 225/224 in the 7-limit, as well as the [[linus comma]], {{monzo| 11 -10 -10 10 }}. It maybe described as the {{nowrap| 50 & 60 }} temperament, [[support]]ed by [[10edo|10-]], [[50edo|50-]], and [[60edo]]. It can be extended naturally to the 11-, 13-, and 17-limit by adding [[385/384]], [[105/104]], and [[170/169]] to the comma list in this order.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 225/224, 16807/16384
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| {{Mapping|legend=1| 10 0 39 28 | 0 1 -1 0 }}
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| : mapping generators: ~15/14, ~3
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| [[Optimal tuning]]s:
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| * [[WE]]: ~15/14 = 120.1837{{c}}, ~3/2 = 699.7654{{c}} (~49/48 = 21.3366{{c}})
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| : [[error map]]: {{val| +1.837 -0.353 -0.753 -3.683 }}
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| * [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 698.8236{{c}} (~49/48 = 21.1764{{c}})
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| : error map: {{val| 0.000 -3.131 -5.137 -8.826 }}
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| {{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}
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| [[Badness]] (Sintel): 2.26
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 225/224, 385/384, 3087/3025
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| Mapping: {{mapping| 10 0 39 28 3 | 0 1 -1 0 2 }}
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| Optimal tunings:
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| * WE: ~15/14 = 120.1406{{c}}, ~3/2 = 697.6075{{c}} (~56/55 = 23.2360{{c}})
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| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.0142{{c}} (~56/55 = 22.9858{{c}})
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| {{Optimal ET sequence|legend=0| 10, 40, 50 }}
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| Badness (Sintel): 2.11
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 105/104, 144/143, 196/195, 2200/2197
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| Mapping: {{mapping| 10 0 39 28 3 37 | 0 1 -1 0 2 0 }}
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| Optimal tunings:
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| * WE: ~15/14 = 120.1166{{c}}, ~3/2 = 697.6705{{c}} (~78/77 = 23.0289{{c}})
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| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.1492{{c}} (~78/77 = 22.8508{{c}})
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| {{Optimal ET sequence|legend=0| 10, 40, 50 }}
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| Badness (Sintel): 1.52
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
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| Mapping: {{mapping| 10 0 39 28 3 37 25 | 0 1 -1 0 2 0 1 }}
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| Optimal tunings:
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| * WE: ~15/14 = 120.1262{{c}}, ~3/2 = 697.8185{{c}} (~78/77 = 22.9388{{c}})
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| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.2757{{c}} (~78/77 = 22.7243{{c}})
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| {{Optimal ET sequence|legend=0| 10, 40, 50 }}
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| Badness (Sintel): 1.28
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| === Splendecic ===
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| Splendecic (50 & 60e) is an alternative extension of decic, tempering out 1617/1600, 2401/2376 and 4375/4356 in the 11-limit. As a temperament of the [[fantastic]] rank-3 temperament, its name is a portmanteau of ''splendid'' and ''decic''.
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| Subgroup: 2.3.5.7.11
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| Comma list: 225/224, 1617/1600, 2401/2376
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| Mapping: {{mapping| 10 0 39 28 82 | 0 1 -1 0 -3 }}
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| Optimal tunings:
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| * WE: ~15/14 = 120.1874{{c}}, ~3/2 = 699.6085{{c}} (~99/98 = 21.5156{{c}})
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| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3531{{c}} (~99/98 = 21.6469{{c}})
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| {{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de, 170cddee }}
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| Badness (Sintel): 1.98
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 105/104, 196/195, 1001/1000, 1188/1183
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| Mapping: {{mapping| 10 0 39 28 82 37 | 0 1 -1 0 -3 0 }}
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| Optimal tunings:
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| * WE: ~15/14 = 120.1565{{c}}, ~3/2 = 699.2756{{c}} (~91/90 = 21.6631{{c}})
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| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.2480{{c}} (~91/90 = 21.7520{{c}})
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| {{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de }}
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| Badness (Sintel): 1.57
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 105/104, 170/169, 196/195, 289/288, 375/374
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| Mapping: {{mapping| 10 0 39 28 82 37 25 | 0 1 -1 0 -3 0 1 }}
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| Optimal tunings:
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| * WE: ~15/14 = 120.1571{{c}}, ~3/2 = 699.2892{{c}} (~91/90 = 21.6536{{c}})
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| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3144{{c}} (~91/90 = 21.6856{{c}})
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| {{Optimal ET sequence|legend=0| 10e, 50, 60e, 110deg }}
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| Badness (Sintel): 1.33
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| === Prodecic ===
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| Prodecic (50e & 60e) is an alternative extension of decic, tempering out 441/440, 1375/1372 and 4375/4356 in the 11-limit. As a temperament of the [[prodigy]] rank-3 temperament, its name is a portmanteau of ''prodigy'' and ''decic''.
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| Subgroup: 2.3.5.7.11
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| Comma list: 225/224, 441/440, 5929/5832
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| Mapping: {{mapping| 10 0 39 28 -13 | 0 1 -1 0 3 }}
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| Optimal tunings:
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| * WE: ~15/14 = 120.2024{{c}}, ~3/2 = 701.3908{{c}} (~55/54 = 19.8237{{c}})
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| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.5235{{c}} (~55/54 = 19.4765{{c}})
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| {{Optimal ET sequence|legend=0| 10, 50e, 60e }}
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| Badness (Sintel): 2.20
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 105/104, 196/195, 275/273, 5929/5832
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| Mapping: {{mapping| 10 0 39 28 -13 37 | 0 1 -1 0 3 0 }}
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| Optimal tunings:
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| * WE: ~15/14 = 120.1654{{c}}, ~3/2 = 701.4683{{c}} (~91/90 = 19.5242{{c}})
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| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.7175{{c}} (~91/90 = 19.2825{{c}})
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| {{Optimal ET sequence|legend=0| 10, 50e, 60e }}
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| Badness (Sintel): 1.73
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| ==== 17-limit ====
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| Subgroup: 2.3.5.7.11.13.17
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| Comma list: 105/104, 154/153, 170/169, 196/195, 289/288
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| Mapping: {{mapping| 10 0 39 28 -13 37 25 | 0 1 -1 0 3 0 1 }}
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| Optimal tunings:
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| * WE: ~15/14 = 120.1577{{c}}, ~3/2 = 701.3950{{c}} (~91/90 = 19.5514{{c}})
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| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.6932{{c}} (~91/90 = 19.3068{{c}})
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| {{Optimal ET sequence|legend=0| 10, 50e, 60e }}
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| Badness (Sintel): 1.41
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| == Pentadecal ==
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| : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Pentadecal]].''
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| Named by [[Xenllium]] in 2021, pentadecal tempers out the 15-5/3-comma ({{monzo| -11 -15 15 }}) in the 5-limit. This temperament can be described as {{nowrap| 15 & 60 }} temperament, tempering out the [[cloudy comma]], 16807/16384 and the [[keema]], 875/864 in the 7-limit.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 875/864, 16807/16384
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| {{Mapping|legend=1| 15 0 11 42 | 0 1 1 0 }}
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| : mapping generators: ~21/20, ~3
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| [[Optimal tuning]]s:
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| * [[WE]]: ~21/20 = 80.1141{{c}}, ~3/2 = 700.2213{{c}} (~126/125 = 19.8053{{c}})
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| : [[error map]]: {{val| +1.711 +0.977 -2.127 -4.035 }}
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| * [[CWE]]: ~21/20 = 80.0000{{c}}, ~3/2 = 701.2357{{c}} (~126/125 = 19.7643{{c}})
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| : error map: {{val| 0.000 -0.719 -5.078 -8.826 }}
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| {{Optimal ET sequence|legend=1| 15, 45, 60 }}
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| [[Badness]] (Sintel): 2.91
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 100/99, 385/384, 1372/1331
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| Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}
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| Optimal tunings:
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| * WE: ~21/20 = 80.0213{{c}}, ~3/2 = 702.9194{{c}} (~56/55 = 17.2721{{c}})
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| * CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 702.8751{{c}} (~56/55 = 17.1249{{c}})
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| {{Optimal ET sequence|legend=0| 15, 45, 60, 75de, 135de }}
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| Badness (Sintel): 2.56
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 100/99, 105/104, 144/143, 1372/1331
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| Mapping: {{mapping| 15 0 11 42 52 8 | 0 1 1 0 0 2 }}
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| Optimal tunings:
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| * WE: ~21/20 = 80.0207{{c}}, ~3/2 = 701.8966{{c}} (~91/90 = 18.2900{{c}})
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| * CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 701.8545{{c}} (~91/90 = 18.1455{{c}})
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| {{Optimal ET sequence|legend=0| 15, 45f, 60, 135de, 195cddee }}
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| Badness (Sintel): 2.14
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| === Quindecal ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 121/120, 441/440, 875/864
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| Mapping: {{mapping| 15 0 11 42 28 | 0 1 1 0 1 }}
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| Optimal tunings:
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| * WE: ~21/20 = 80.1322{{c}}, ~3/2 = 701.4751{{c}} (~126/125 = 19.7148{{c}})
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| * CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 701.5453{{c}} (~126/125 = 18.4547{{c}})
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| {{Optimal ET sequence|legend=0| 15, 45e, 60e }}
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| Badness (Sintel): 1.47
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 121/120, 196/195, 352/351, 875/864
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| Mapping: {{mapping| 15 0 11 42 28 103 | 0 1 1 0 1 -2 }}
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| Optimal tunings:
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| * WE: ~21/20 = 80.1015{{c}}, ~3/2 = 702.5374{{c}} (~126/125 = 18.3763{{c}})
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| * CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 701.8504{{c}} (~126/125 = 18.1496{{c}})
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| {{Optimal ET sequence|legend=0| 15f, 60e, 135deef }}
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| Badness (Sintel): 2.29
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| == Quinkee ==
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| Quinkee has a period of 1/5 octave and tempers out the [[keega]] (1029/1000), from which it derives its name. It may be described as the {{nowrap| 15 & 55 }} temperament. It was named by [[Xenllium]] in 2021.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 1029/1000, 6144/6125
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| {{Mapping|legend=1| 5 0 9 14 | 0 3 1 0 }}
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| : mapping generators: ~8/7, ~10/7
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| [[Optimal tuning]]s:
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| * [[WE]]: ~8/7 = 240.0512{{c}}, ~10/7 = 633.5744{{c}} (~25/24 = 86.5794{{c}})
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| : [[error map]]: {{val| +0.256 -1.232 +7.722 -8.108 }}
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| * [[CWE]]: ~8/7 = 240.0000{{c}}, ~10/7 = 633.4834{{c}} (~25/24 = 86.5160{{c}})
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| : error map: {{val| 0.000 -1.505 +7.170 -8.826 }}
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| {{Optimal ET sequence|legend=1| 15, 40, 55 }}
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| [[Badness]] (Sintel): 4.66
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 121/120, 176/175, 1029/1000
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| Mapping: {{mapping| 5 0 9 14 12 | 0 3 1 0 2 }}
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| Optimal tunings:
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| * WE: ~8/7 = 240.0916{{c}}, ~10/7 = 633.6802{{c}} (~22/21 = 86.5947{{c}})
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| * CWE: ~8/7 = 240.0000{{c}}, ~10/7 = 633.5204{{c}} (~22/21 = 86.4796{{c}})
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| {{Optimal ET sequence|legend=0| 15, 40, 55 }}
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| Badness (Sintel): 2.16
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 66/65, 105/104, 121/120, 637/625
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| Mapping: {{mapping| 5 9 12 14 18 20 | 0 3 1 0 2 4 }}
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| Optimal tunings:
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| * WE: ~8/7 = 240.0392{{c}}, ~10/7 = 632.9013{{c}} (~22/21 = 87.2162{{c}})
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| * CWE: ~8/7 = 240.0000{{c}}, ~10/7 = 632.8351{{c}} (~22/21 = 87.1649{{c}})
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| {{Optimal ET sequence|legend=0| 15, 40, 55 }}
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| Badness (Sintel): 2.00
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| [[Category:Temperament clans]]
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| [[Category:Cloudy clan| ]] <!-- main article -->
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| [[Category:Cloudy| ]] <!-- key article -->
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| [[Category:Rank 2]]
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