Cloudy clan

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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:

Coblack

See also: Trisedodge 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

Optimal GPV sequence15, 35, 50, 65, 115d

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: 15, 35, 50, 65, 115d

Badness: 0.045070

Decic

Main article: 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

Optimal GPV sequence10, 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: [10 0 39 28 3], 0 1 -1 0 2]]

Mapping generators: ~15/14, ~3

POTE generator: ~3/2 = 696.791

Optimal GPV sequence: 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: [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: 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: [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: 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 fantastic rank-three temperament, its name is a portmanteau of "splendid" (synonym of "fantastic") and "decic".

Subgroup: 2.3.5.7.11

Comma list: 225/224, 1617/1600, 2401/2376

Mapping: [10 0 39 28 82], 0 1 -1 0 -3]]

POTE generator: ~3/2 = 698.518

Optimal GPV sequence: 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: [10 0 39 28 82 37], 0 1 -1 0 -3 0]]

POTE generator: ~3/2 = 698.365

Optimal GPV sequence: 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: [10 0 39 28 82 37 25], 0 1 -1 0 -3 0 1]]

POTE generator: ~3/2 = 698.375

Optimal GPV sequence: 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 prodigy rank-three 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: [10 0 39 28 -13], 0 1 -1 0 3]]

POTE generator: ~3/2 = 700.210

Optimal GPV sequence: 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: [10 0 39 28 -13 37], 0 1 -1 0 3 0]]

POTE generator: ~3/2 = 700.503

Optimal GPV sequence: 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: [10 0 39 28 -13 37 25], 0 1 -1 0 3 0 1]]

POTE generator: ~3/2 = 700.474

Optimal GPV sequence: 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), [-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

Optimal GPV sequence15, 45, 60

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: 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: [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: 15, 45f, 60, 135de, 195cddee

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: 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: [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: 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: [5 9 12 14], 0 -3 -1 0]]

POTE generator: ~5/4 = 393.439

Optimal GPV sequence15, 40, 55, 125cd, 180ccdd

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: 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: [5 9 12 14 18 20], 0 -3 -1 0 -2 -4]]

POTE generator: ~5/4 = 392.798

Optimal GPV sequence: 15, 40, 55

Badness: 0.048440