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 blacksmith, cloudtone, pentacloud and sengasec.

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, named by Xenllium) 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:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [693.129, 702.512]
  • strict range: ~3/2 = [696.000, 700.000]

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:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [689.363, 702.512]
  • strict range: ~3/2 = [696.000, 700.000]

Vals: 10, 50, 160bcdd, 210bcddde, 260bbcddde, 310bbcdddde

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:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [689.363, 702.512]
  • strict range: ~3/2 = [696.000, 700.000]

Vals: 10, 50, 160bcdd, 210bcddde, 260bbcddde

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:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [689.363, 704.955]
  • strict range: ~3/2 = [696.000, 700.000]

Vals: 10, 50, 160bcddg, 210bcdddegg

Badness: 0.025064