|
|
| (21 intermediate revisions by 8 users not shown) |
| Line 1: |
Line 1: |
| 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.
| | #redirect [[Cloudy comma]] |
| | |
| Temperaments discussed elsewhere are:
| |
| * [[Blacksmith]], {28/27, 49/48} → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
| |
| * [[Cloudtone]], {81/80, 16807/16384} → [[Meantone family #Cloudtone|Meantone family]]
| |
| * [[Pental]], {245/243, 16807/16384} → [[Pental family #Pentacloud|Pental family]]
| |
| * [[Sengasec]], {686/675, 16807/16384} → [[Qintosec family #Sengasec|Qintosec family]]
| |
| * [[Warlock]], {3125/3072, 16807/16384} → [[Magic family #Warlock|Magic family]]
| |
| | |
| == Coblack ==
| |
| {{See also| Trisedodge family #Coblack }}
| |
| | |
| Subgroup: 2.3.5.7
| |
| | |
| [[Comma list]]: 126/125, 16807/16384
| |
| | |
| [[Mapping]]: [{{val| 5 7 11 14 }}, {{val| 0 3 2 0 }}]
| |
| | |
| {{Multival|legend=1| 15 10 0 -19 -42 -28 }}
| |
| | |
| [[POTE generator]]: ~21/20 = 73.044
| |
| | |
| {{Val list|legend=1| 15, 35, 50, 65, 115d }}
| |
| | |
| [[Badness]]: 0.107282
| |
| | |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 126/125, 245/242, 385/384
| |
| | |
| Mapping: [{{val| 5 7 11 14 17 }}, {{val| 0 3 2 0 1 }}]
| |
| | |
| POTE generator: ~21/20 = 73.264
| |
| | |
| Optimal GPV sequence: {{Val list| 15, 35, 50, 65, 115d }}
| |
| | |
| Badness: 0.045070
| |
| | |
| == Decic ==
| |
| {{main| Decic }}
| |
| | |
| The ''decic'' temperament (10&50) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit, as well as the [[15/14ths equal temperament|linus comma]], {{monzo|11 -10 -10 10}}. This temperament is supported by [[10edo|10]], [[50edo|50]], and [[60edo|60]] EDOs, and 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]]: [{{val| 10 0 39 28 }}, {{val| 0 1 -1 0 }}]
| |
| | |
| Mapping generators: ~15/14, ~3
| |
| | |
| {{Multival|legend=1| 10 -10 0 -39 -28 28 }}
| |
| | |
| [[POTE generator]]: ~3/2 = 698.696
| |
| | |
| {{Val list|legend=1| 10, 30b, 40, 50, 60, 110d, 170cdd }}
| |
| | |
| [[Badness]]: 0.089135
| |
| | |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 225/224, 385/384, 3087/3025
| |
| | |
| Mapping: [{{val| 10 0 39 28 3 }}, {{val| 0 1 -1 0 2 }}]
| |
| | |
| Mapping generators: ~15/14, ~3
| |
| | |
| POTE generator: ~3/2 = 696.791
| |
| | |
| Optimal GPV sequence: {{Val list| 10, 30be, 40, 50 }}
| |
| | |
| Badness: 0.063900
| |
| | |
| ==== 13-limit ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 105/104, 144/143, 196/195, 2200/2197
| |
| | |
| Mapping: [{{val| 10 0 39 28 3 37 }}, {{val| 0 1 -1 0 2 0 }}]
| |
| | |
| Mapping generators: ~14/13, ~3
| |
| | |
| POTE generator: ~3/2 = 696.993
| |
| | |
| Optimal GPV sequence: {{Val list| 10, 30be, 40, 50 }}
| |
| | |
| Badness: 0.036880
| |
| | |
| ==== 17-limit ====
| |
| Subgroup: 2.3.5.7.11.13.17
| |
| | |
| Comma list: 105/104, 144/143, 170/169, 196/195, 221/220
| |
| | |
| Mapping: [{{val| 10 0 39 28 3 37 25 }}, {{val| 0 1 -1 0 2 0 1 }}]
| |
| | |
| Mapping generators: ~14/13, ~3
| |
| | |
| POTE generator: ~3/2 = 697.085
| |
| | |
| Optimal GPV sequence: {{Val list| 10, 30beg, 40, 50 }}
| |
| | |
| Badness: 0.025064
| |
| | |
| === Splendecic ===
| |
| ''Splendecic'' (10e&50) is an alternative extension of decic, tempering out 1617/1600, 2401/2376 and 4375/4356 in the 11-limit. As a subset of the [[Marvel family #Fantastic|fantastic rank-three temperament]], its name is a portmanteau of "[[wiktionary:splendid|splendid]]" (synonym of "[[wiktionary:fantastic|fantastic]]") and "decic".
| |
| | |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 225/224, 1617/1600, 2401/2376
| |
| | |
| Mapping: [{{val| 10 0 39 28 82 }}, {{val| 0 1 -1 0 -3 }}]
| |
| | |
| POTE generator: ~3/2 = 698.518
| |
| | |
| Optimal GPV sequence: {{Val list| 10e, 30bee, 40e, 50, 60e, 110de }}
| |
| | |
| Badness: 0.059802
| |
| | |
| ==== 13-limit ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 105/104, 196/195, 1001/1000, 1188/1183
| |
| | |
| Mapping: [{{val| 10 0 39 28 82 37 }}, {{val| 0 1 -1 0 -3 0 }}]
| |
| | |
| POTE generator: ~3/2 = 698.365
| |
| | |
| Optimal GPV sequence: {{Val list| 10e, 30bee, 40e, 50, 60e, 110de }}
| |
| | |
| Badness: 0.037989
| |
| | |
| ==== 17-limit ====
| |
| Subgroup: 2.3.5.7.11.13.17
| |
| | |
| Comma list: 105/104, 170/169, 196/195, 289/288, 375/374
| |
| | |
| Mapping: [{{val| 10 0 39 28 82 37 25 }}, {{val| 0 1 -1 0 -3 0 1 }}]
| |
| | |
| POTE generator: ~3/2 = 698.375
| |
| | |
| Optimal GPV sequence: {{Val list| 10e, 30beeg, 40e, 50, 60e, 110deg }}
| |
| | |
| Badness: 0.026050
| |
| | |
| === Prodecic ===
| |
| ''Prodecic'' (10&50e) is an alternative extension of decic, tempering out 441/440, 1375/1372 and 4375/4356 in the 11-limit. As a subset of the [[Marvel family #Prodigy|prodigy rank-three temperament]], its name is a portmanteau of "[[wiktionary:prodigy|prodigy]]" and "decic".
| |
| | |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 225/224, 441/440, 5929/5832
| |
| | |
| Mapping: [{{val| 10 0 39 28 -13 }}, {{val| 0 1 -1 0 3 }}]
| |
| | |
| POTE generator: ~3/2 = 700.210
| |
| | |
| Optimal GPV sequence: {{Val list| 10, 40ee, 50e, 60e }}
| |
| | |
| Badness: 0.066600
| |
| | |
| ==== 13-limit ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 105/104, 196/195, 275/273, 5929/5832
| |
| | |
| Mapping: [{{val| 10 0 39 28 -13 37 }}, {{val| 0 1 -1 0 3 0 }}]
| |
| | |
| POTE generator: ~3/2 = 700.503
| |
| | |
| Optimal GPV sequence: {{Val list| 10, 40ee, 50e, 60e }}
| |
| | |
| Badness: 0.041788
| |
| | |
| ==== 17-limit ====
| |
| Subgroup: 2.3.5.7.11.13.17
| |
| | |
| Comma list: 105/104, 154/153, 170/169, 196/195, 289/288
| |
| | |
| Mapping: [{{val| 10 0 39 28 -13 37 25 }}, {{val| 0 1 -1 0 3 0 1 }}]
| |
| | |
| POTE generator: ~3/2 = 700.474
| |
| | |
| Optimal GPV sequence: {{Val list| 10, 40ee, 50e, 60e }}
| |
| | |
| Badness: 0.027590
| |
| | |
| == Pentadecal ==
| |
| : ''For the 5-limit version of this temperament, see [[High badness temperaments #Pentadecal]].''
| |
| | |
| The ''pentadecal'' temperament tempers out the 15-5/3-comma (Quintriyo, pentadecatonic minor thirds comma), {{monzo|-11 -15 15}}. This temperament can be described as 15&60 temperament, tempering out the [[cloudy comma]], 16807/16384 and the [[875/864|keema]], 875/864 in the 7-limit.
| |
| | |
| Subgroup: 2.3.5.7
| |
| | |
| [[Comma list]]: 875/864, 16807/16384
| |
| | |
| [[Mapping]]: [{{val|15 0 11 42}}, {{val|0 1 1 0}}]
| |
| | |
| Mapping generators: ~21/20, ~3
| |
| | |
| [[POTE generator]]: ~3/2 = 700.223
| |
| | |
| {{Val list|legend=1| 15, 45, 60 }}
| |
| | |
| [[Badness]]: 0.114833
| |
| | |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 100/99, 385/384, 1372/1331
| |
| | |
| Mapping: [{{val|15 0 11 42 52}}, {{val|0 1 1 0 0}}]
| |
| | |
| Mapping generators: ~21/20, ~3
| |
| | |
| POTE generator: ~3/2 = 702.733
| |
| | |
| Optimal GPV sequence: {{Val list| 15, 45, 60, 75de, 135de }}
| |
| | |
| Badness: 0.077420
| |
| | |
| ==== 13-limit ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 100/99, 105/104, 144/143, 1372/1331
| |
| | |
| Mapping: [{{val|15 0 11 42 52 8}}, {{val|0 1 1 0 0 2}}]
| |
| | |
| Mapping generators: ~21/20, ~3
| |
| | |
| POTE generator: ~3/2 = 701.715
| |
| | |
| Optimal GPV sequence: {{Val list| 15, 45f, 60, 135de, 195cddee }}
| |
| | |
| Badness: 0.051740
| |
| | |
| === Quindecal ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 121/120, 441/440, 875/864
| |
| | |
| Mapping: [{{val|15 0 11 42 28}}, {{val|0 1 1 0 1}}]
| |
| | |
| Mapping generators: ~21/20, ~3
| |
| | |
| POTE generator: ~3/2 = 700.318
| |
| | |
| Optimal GPV sequence: {{Val list| 15, 45e, 60e }}
| |
| | |
| Badness: 0.044405
| |
| | |
| ==== 13-limit ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 121/120, 196/195, 352/351, 875/864
| |
| | |
| Mapping: [{{val|15 0 11 42 28 103}}, {{val|0 1 1 0 1 -2}}]
| |
| | |
| Mapping generators: ~21/20, ~3
| |
| | |
| POTE generator: ~3/2 = 701.647
| |
| | |
| Optimal GPV sequence: {{Val list| 15f, 45e, 60e }}
| |
| | |
| Badness: 0.055361
| |
| | |
| == Quinkee ==
| |
| The ''quinkee'' temperament (15&40) has a period of 1/5 octave and tempers out the keega (1029/1000), and from this it derives its name.
| |
| | |
| Subgroup: 2.3.5.7
| |
| | |
| [[Comma list]]: 1029/1000, 6144/6125
| |
| | |
| [[Mapping]]: [{{val|5 9 12 14}}, {{val|0 -3 -1 0}}]
| |
| | |
| [[POTE generator]]: ~5/4 = 393.439
| |
| | |
| {{Val list|legend=1| 15, 40, 55, 125cd, 180ccdd }}
| |
| | |
| [[Badness]]: 0.184222
| |
| | |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 121/120, 176/175, 1029/1000
| |
| | |
| Mapping: [{{val|5 9 12 14 18}}, {{val|0 -3 -1 0 -2}}]
| |
| | |
| POTE generator: ~5/4 = 393.438
| |
| | |
| Optimal GPV sequence: {{Val list| 15, 40, 55, 125cd, 180ccdde }}
| |
| | |
| Badness: 0.065192
| |
| | |
| === 13-limit ===
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 66/65, 105/104, 121/120, 637/625
| |
| | |
| Mapping: [{{val|5 9 12 14 18 20}}, {{val|0 -3 -1 0 -2 -4}}]
| |
| | |
| POTE generator: ~5/4 = 392.798
| |
| | |
| Optimal GPV sequence: {{Val list| 15, 40, 55 }}
| |
| | |
| Badness: 0.048440
| |
| | |
| [[Category:Regular temperament theory]]
| |
| [[Category:Temperament clans]]
| |
| [[Category:Cloudy]]
| |
| [[Category:Rank 2]]
| |