|
|
| (One intermediate revision by the same user not shown) |
| Line 1: |
Line 1: |
| {{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.
| |
| | |
| Temperaments discussed elsewhere are:
| |
| * [[Blackwood]] (+28/27 or 49/48) → [[Limmic temperaments #Septimal blackwood|Limmic temperaments]]
| |
| * [[Cloudtone]] (+81/80) → [[Meantone family #Cloudtone|Meantone family]]
| |
| * [[Pental (temperament)|Pentacloud]] (+245/243) → [[Quintile family #Pentacloud|Quintile family]]
| |
| * [[Sengasec]] (+686/675) → [[Quintosec family #Sengasec|Quintosec family]]
| |
| * [[Warlock]] (+3125/3072) → [[Magic family #Warlock|Magic family]]
| |
| | |
| == Decic ==
| |
| {{Main| Decic }}
| |
| | |
| 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.
| |
| | |
| [[Subgroup]]: 2.3.5.7
| |
| | |
| [[Comma list]]: 225/224, 16807/16384
| |
| | |
| {{Mapping|legend=1| 10 0 39 28 | 0 1 -1 0 }}
| |
| : mapping generators: ~15/14, ~3
| |
| | |
| [[Optimal tuning]]s:
| |
| * [[WE]]: ~15/14 = 120.1837{{c}}, ~3/2 = 699.7654{{c}} (~49/48 = 21.3366{{c}})
| |
| : [[error map]]: {{val| +1.837 -0.353 -0.753 -3.683 }}
| |
| * [[CWE]]: ~15/14 = 120.0000{{c}}, ~3/2 = 698.8236{{c}} (~49/48 = 21.1764{{c}})
| |
| : error map: {{val| 0.000 -3.131 -5.137 -8.826 }}
| |
| | |
| {{Optimal ET sequence|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}
| |
| | |
| [[Badness]] (Sintel): 2.26
| |
| | |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 225/224, 385/384, 3087/3025
| |
| | |
| Mapping: {{mapping| 10 0 39 28 3 | 0 1 -1 0 2 }}
| |
| | |
| Optimal tunings:
| |
| * WE: ~15/14 = 120.1406{{c}}, ~3/2 = 697.6075{{c}} (~56/55 = 23.2360{{c}})
| |
| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.0142{{c}} (~56/55 = 22.9858{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 10, 40, 50 }}
| |
| | |
| Badness (Sintel): 2.11
| |
| | |
| ==== 13-limit ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 105/104, 144/143, 196/195, 2200/2197
| |
| | |
| Mapping: {{mapping| 10 0 39 28 3 37 | 0 1 -1 0 2 0 }}
| |
| | |
| Optimal tunings:
| |
| * WE: ~15/14 = 120.1166{{c}}, ~3/2 = 697.6705{{c}} (~78/77 = 23.0289{{c}})
| |
| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.1492{{c}} (~78/77 = 22.8508{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 10, 40, 50 }}
| |
| | |
| Badness (Sintel): 1.52
| |
| | |
| ==== 17-limit ====
| |
| Subgroup: 2.3.5.7.11.13.17
| |
| | |
| Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
| |
| | |
| Mapping: {{mapping| 10 0 39 28 3 37 25 | 0 1 -1 0 2 0 1 }}
| |
| | |
| Optimal tunings:
| |
| * WE: ~15/14 = 120.1262{{c}}, ~3/2 = 697.8185{{c}} (~78/77 = 22.9388{{c}})
| |
| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 697.2757{{c}} (~78/77 = 22.7243{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 10, 40, 50 }}
| |
| | |
| Badness (Sintel): 1.28
| |
| | |
| === Splendecic ===
| |
| 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''.
| |
| | |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 225/224, 1617/1600, 2401/2376
| |
| | |
| Mapping: {{mapping| 10 0 39 28 82 | 0 1 -1 0 -3 }}
| |
| | |
| Optimal tunings:
| |
| * WE: ~15/14 = 120.1874{{c}}, ~3/2 = 699.6085{{c}} (~99/98 = 21.5156{{c}})
| |
| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3531{{c}} (~99/98 = 21.6469{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de, 170cddee }}
| |
| | |
| Badness (Sintel): 1.98
| |
| | |
| ==== 13-limit ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 105/104, 196/195, 1001/1000, 1188/1183
| |
| | |
| Mapping: {{mapping| 10 0 39 28 82 37 | 0 1 -1 0 -3 0 }}
| |
| | |
| Optimal tunings:
| |
| * WE: ~15/14 = 120.1565{{c}}, ~3/2 = 699.2756{{c}} (~91/90 = 21.6631{{c}})
| |
| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.2480{{c}} (~91/90 = 21.7520{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 10e, 40e, 50, 60e, 110de }}
| |
| | |
| Badness (Sintel): 1.57
| |
| | |
| ==== 17-limit ====
| |
| Subgroup: 2.3.5.7.11.13.17
| |
| | |
| Comma list: 105/104, 170/169, 196/195, 289/288, 375/374
| |
| | |
| Mapping: {{mapping| 10 0 39 28 82 37 25 | 0 1 -1 0 -3 0 1 }}
| |
| | |
| Optimal tunings:
| |
| * WE: ~15/14 = 120.1571{{c}}, ~3/2 = 699.2892{{c}} (~91/90 = 21.6536{{c}})
| |
| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 698.3144{{c}} (~91/90 = 21.6856{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 10e, 50, 60e, 110deg }}
| |
| | |
| Badness (Sintel): 1.33
| |
| | |
| === Prodecic ===
| |
| 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''.
| |
| | |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 225/224, 441/440, 5929/5832
| |
| | |
| Mapping: {{mapping| 10 0 39 28 -13 | 0 1 -1 0 3 }}
| |
| | |
| Optimal tunings:
| |
| * WE: ~15/14 = 120.2024{{c}}, ~3/2 = 701.3908{{c}} (~55/54 = 19.8237{{c}})
| |
| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.5235{{c}} (~55/54 = 19.4765{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 10, 50e, 60e }}
| |
| | |
| Badness (Sintel): 2.20
| |
| | |
| ==== 13-limit ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 105/104, 196/195, 275/273, 5929/5832
| |
| | |
| Mapping: {{mapping| 10 0 39 28 -13 37 | 0 1 -1 0 3 0 }}
| |
| | |
| Optimal tunings:
| |
| * WE: ~15/14 = 120.1654{{c}}, ~3/2 = 701.4683{{c}} (~91/90 = 19.5242{{c}})
| |
| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.7175{{c}} (~91/90 = 19.2825{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 10, 50e, 60e }}
| |
| | |
| Badness (Sintel): 1.73
| |
| | |
| ==== 17-limit ====
| |
| Subgroup: 2.3.5.7.11.13.17
| |
| | |
| Comma list: 105/104, 154/153, 170/169, 196/195, 289/288
| |
| | |
| Mapping: {{mapping| 10 0 39 28 -13 37 25 | 0 1 -1 0 3 0 1 }}
| |
| | |
| Optimal tunings:
| |
| * WE: ~15/14 = 120.1577{{c}}, ~3/2 = 701.3950{{c}} (~91/90 = 19.5514{{c}})
| |
| * CWE: ~15/14 = 120.0000{{c}}, ~3/2 = 700.6932{{c}} (~91/90 = 19.3068{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 10, 50e, 60e }}
| |
| | |
| Badness (Sintel): 1.41
| |
| | |
| == Pentadecal ==
| |
| : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Pentadecal]].''
| |
| | |
| 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.
| |
| | |
| [[Subgroup]]: 2.3.5.7
| |
| | |
| [[Comma list]]: 875/864, 16807/16384
| |
| | |
| {{Mapping|legend=1| 15 0 11 42 | 0 1 1 0 }}
| |
| : mapping generators: ~21/20, ~3
| |
| | |
| [[Optimal tuning]] ([[POTE]]): ~21/20 = 80.000{{c}}, ~3/2 = 700.223{{c}} (~126/125 = 19.777{{c}})
| |
| | |
| {{Optimal ET sequence|legend=1| 15, 45, 60 }}
| |
| | |
| [[Badness]] (Smith): 0.114833
| |
| | |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 100/99, 385/384, 1372/1331
| |
| | |
| Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}
| |
| | |
| Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 702.733{{c}} (~56/55 = 17.267{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 15, 45, 60, 75de, 135de }}
| |
| | |
| Badness (Smith): 0.077420
| |
| | |
| ==== 13-limit ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 100/99, 105/104, 144/143, 1372/1331
| |
| | |
| Mapping: {{mapping| 15 0 11 42 52 8 | 0 1 1 0 0 2 }}
| |
| | |
| Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 701.715{{c}} (~91/90 = 18.285{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 15, 45f, 60, 135de, 195cddee }}
| |
| | |
| Badness (Smith): 0.051740
| |
| | |
| === Quindecal ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 121/120, 441/440, 875/864
| |
| | |
| Mapping: {{mapping| 15 0 11 42 28 | 0 1 1 0 1 }}
| |
| | |
| Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 700.318{{c}} (~126/125 = 19.682{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 15, 45e, 60e }}
| |
| | |
| Badness (Smith): 0.044405
| |
| | |
| ==== 13-limit ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 121/120, 196/195, 352/351, 875/864
| |
| | |
| Mapping: {{mapping| 15 0 11 42 28 103 | 0 1 1 0 1 -2 }}
| |
| | |
| Optimal tuning (POTE): ~21/20 = 80.000{{c}}, ~3/2 = 701.647{{c}} (~65/64 = 18.353{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 15f, 45e, 60e }}
| |
| | |
| Badness (Smith): 0.055361
| |
| | |
| == Quinkee ==
| |
| 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 & 40 }} temperament. It was named by [[Xenllium]] in 2021.
| |
| | |
| [[Subgroup]]: 2.3.5.7
| |
| | |
| [[Comma list]]: 1029/1000, 6144/6125
| |
| | |
| {{Mapping|legend=1| 5 9 12 14 | 0 -3 -1 0 }}
| |
| | |
| [[Optimal tuning]] ([[POTE]]): ~8/7 = 240.000{{c}}, ~5/4 = 393.439{{c}} (~25/24 = 86.561{{c}})
| |
| | |
| {{Optimal ET sequence|legend=1| 15, 40, 55, 125cd, 180ccdd }}
| |
| | |
| [[Badness]] (Smith): 0.184222
| |
| | |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 121/120, 176/175, 1029/1000
| |
| | |
| Mapping: {{mapping| 5 9 12 14 18 | 0 -3 -1 0 -2 }}
| |
| | |
| Optimal tuning (POTE): ~8/7 = 240.000{{c}}, ~5/4 = 393.438{{c}} (~22/21 = 86.562{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 15, 40, 55, 125cd, 180ccdde }}
| |
| | |
| Badness (Smith): 0.065192
| |
| | |
| === 13-limit ===
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 66/65, 105/104, 121/120, 637/625
| |
| | |
| Mapping: {{mapping| 5 9 12 14 18 20 | 0 -3 -1 0 -2 -4 }}
| |
| | |
| Optimal tuning (POTE): ~8/7 = 240.000{{c}}, ~5/4 = 392.798{{c}} (~22/21 = 87.202{{c}})
| |
| | |
| {{Optimal ET sequence|legend=0| 15, 40, 55 }}
| |
| | |
| Badness (Smith): 0.048440
| |
| | |
| [[Category:Temperament clans]]
| |
| [[Category:Cloudy clan| ]] <!-- main article -->
| |
| [[Category:Cloudy| ]] <!-- key article -->
| |
| [[Category:Rank 2]]
| |