Cloudy clan
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:
- Blacksmith, {28/27, 49/48} → Limmic temperaments
- Cloudtone, {81/80, 16807/16384} → Meantone family
- Pental, {245/243, 16807/16384} → Pental family
- Sengasec, {686/675, 16807/16384} → Qintosec family
- Warlock, {3125/3072, 16807/16384} → Magic family
Coblack
Subgroup: 2.3.5.7
Comma list: 126/125, 16807/16384
Mapping: [⟨5 7 11 14], ⟨0 3 2 0]]
Wedgie: ⟨⟨ 15 10 0 -19 -42 -28 ]]
POTE generator: ~21/20 = 73.044
Badness: 0.107282
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/242, 385/384
Mapping: [⟨5 7 11 14 17], ⟨0 3 2 0 1]]
POTE generator: ~21/20 = 73.264
Optimal GPV sequence: Template:Val list
Badness: 0.045070
Decic
The decic temperament (10&50) tempers out the cloudy comma, 16807/16384 and the marvel comma, 225/224 in the 7-limit, as well as the linus comma, [11 -10 -10 10⟩. This temperament is supported by 10, 50, and 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: [⟨10 0 39 28], ⟨0 1 -1 0]]
Mapping generators: ~15/14, ~3
Wedgie: ⟨⟨ 10 -10 0 -39 -28 28 ]]
POTE generator: ~3/2 = 698.696
Badness: 0.089135
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 3087/3025
Mapping: [⟨10 0 39 28 3], ⟨0 1 -1 0 2]]
Mapping generators: ~15/14, ~3
POTE generator: ~3/2 = 696.791
Optimal GPV sequence: Template:Val list
Badness: 0.063900
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 196/195, 2200/2197
Mapping: [⟨10 0 39 28 3 37], ⟨0 1 -1 0 2 0]]
Mapping generators: ~14/13, ~3
POTE generator: ~3/2 = 696.993
Optimal GPV sequence: Template:Val list
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: [⟨10 0 39 28 3 37 25], ⟨0 1 -1 0 2 0 1]]
Mapping generators: ~14/13, ~3
POTE generator: ~3/2 = 697.085
Optimal GPV sequence: Template:Val list
Badness: 0.025064
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), [-11 -15 15⟩. This temperament can be described as 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: [⟨15 0 11 42], ⟨0 1 1 0]]
Mapping generators: ~21/20, ~3
POTE generator: ~3/2 = 700.223
Badness: 0.114833
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 1372/1331
Mapping: [⟨15 0 11 42 52], ⟨0 1 1 0 0]]
Mapping generators: ~21/20, ~3
POTE generator: ~3/2 = 702.733
Optimal GPV sequence: Template:Val list
Badness: 0.077420
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 144/143, 1372/1331
Mapping: [⟨15 0 11 42 52 8], ⟨0 1 1 0 0 2]]
Mapping generators: ~21/20, ~3
POTE generator: ~3/2 = 701.715
Optimal GPV sequence: Template:Val list
Badness: 0.051740
Quindecal
Subgroup: 2.3.5.7.11
Comma list: 121/120, 441/440, 875/864
Mapping: [⟨15 0 11 42 28], ⟨0 1 1 0 1]]
Mapping generators: ~21/20, ~3
POTE generator: ~3/2 = 700.318
Optimal GPV sequence: Template:Val list
Badness: 0.044405
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 196/195, 352/351, 875/864
Mapping: [⟨15 0 11 42 28 103], ⟨0 1 1 0 1 -2]]
Mapping generators: ~21/20, ~3
POTE generator: ~3/2 = 701.647
Optimal GPV sequence: Template:Val list
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: [⟨5 9 12 14], ⟨0 -3 -1 0]]
POTE generator: ~5/4 = 393.439
Badness: 0.184222
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 1029/1000
Mapping: [⟨5 9 12 14 18], ⟨0 -3 -1 0 -2]]
POTE generator: ~5/4 = 393.438
Optimal GPV sequence: Template:Val list
Badness: 0.065192
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 105/104, 121/120, 637/625
Mapping: [⟨5 9 12 14 18 20], ⟨0 -3 -1 0 -2 -4]]
POTE generator: ~5/4 = 392.798
Optimal GPV sequence: Template:Val list
Badness: 0.048440