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 1 7 14], 0 3 2 0]]

Wedgie⟨⟨15 10 0 -19 -42 -28]]

POTE generator: ~21/20 = 73.044

Vals15, 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 1 7 14 15], 0 3 2 0 1]]

POTE generator: ~21/20 = 73.264

Vals: 15, 35, 50, 65, 115d

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

Tuning ranges:

  • 7-odd-limit diamond monotone: ~3/2 = [680.000, 720.000] (34\60 to 6\10)
  • 9-odd-limit diamond monotone: ~3/2 = [696.000, 720.000] (29\50 to 6\10)
  • 7- and 9-odd-limit diamond tradeoff: ~3/2 = [693.129, 702.512]
  • 7-odd-limit diamond monotone and tradeoff: ~3/2 = [693.129, 702.512]
  • 9-odd-limit diamond monotone and tradeoff: ~3/2 = [696.000, 702.512]

Vals10, 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

Tuning ranges:

  • 11-odd-limit diamond monotone: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • 11-odd-limit diamond tradeoff: ~3/2 = [689.363, 702.512]
  • 11-odd-limit diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]

Vals: 10, 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

Tuning ranges:

  • 13- and 15-odd-limit diamond monotone: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • 13- and 15-odd-limit diamond tradeoff: ~3/2 = [689.363, 702.512]
  • 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]

Vals: 10, 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

Tuning ranges:

  • 17-odd-limit diamond monotone: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • 17-odd-limit diamond tradeoff: ~3/2 = [689.363, 704.955]
  • 17-odd-limit diamond monotone and tradeoff: ~3/2 = [696.000, 700.000]

Vals: 10, 50

Badness: 0.025064

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

Comma list: 30517578125/29386561536

Mapping: [15 0 11], 0 1 1]]

POTE generator: ~3/2 = 702.652

Vals15, 45, 60, 75, 135, 210c, 345cc

Badness: 0.692042

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

Vals15, 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals15, 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

Vals: 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

Vals: 15, 40, 55

Badness: 0.048440