Cloudy clan

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This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

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

In addition to the cloudy comma, the coblack temperament tempers out the starling comma (126/125). Coblack was named by Petr Pařízek in 2011, who considered it a counterpart of blacksmith[1].

Subgroup: 2.3.5.7

Comma list: 126/125, 16807/16384

Mapping: [⟨5 1 7 14], ⟨0 3 2 0]]

Optimal tunings:

  • CTE: ~8/7 = 1\5, ~48/35 = 553.8429 (~21/20 = 73.8429)
  • POTE: ~8/7 = 1\5, ~48/35 = 553.044 (~21/20 = 73.044)

Optimal ET sequence: 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: [⟨5 1 7 14 15], ⟨0 3 2 0 1]]

Optimal tunings:

  • CTE: ~8/7 = 1\5, ~11/8 = 553.7951 (~21/20 = 73.7951)
  • POTE: ~8/7 = 1\5, ~11/8 = 553.264 (~21/20 = 73.264)

Optimal ET 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 60edo, 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

Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 698.696 (~49/48 = 21.304)

Optimal ET sequence: 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: [⟨10 0 39 28 3], ⟨0 1 -1 0 2]]

mapping generators: ~15/14, ~3

Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 696.791 (~56/55 = 23.209)

Optimal ET 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

Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 696.993 (~78/77 = 23.007)

Optimal ET 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

Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 697.085 (~78/77 = 22.915)

Optimal ET 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 temperament of the fantastic rank-3 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]]

Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 698.518 (~99/98 = 21.482)

Optimal ET 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]]

Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 698.365 (~91/90 = 21.635)

Optimal ET 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]]

Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 698.375 (~91/90 = 21.625)

Optimal ET 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 temperament of the prodigy rank-3 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]]

Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 700.210 (~55/54 = 19.790)

Optimal ET 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]]

Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 700.503 (~91/90 = 19.497)

Optimal ET 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]]

Optimal tuning (POTE): ~15/14 = 1\10, ~3/2 = 700.474 (~91/90 = 19.526)

Optimal ET 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

Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 700.223 (~126/125 = 19.777)

Optimal ET sequence: 15, 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

Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 702.733 (~56/55 = 17.267)

Optimal ET 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

Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 701.715 (~91/90 = 18.285)

Optimal ET 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

Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 700.318 (~126/125 = 19.682)

Optimal ET 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

Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 701.647 (~65/64 = 18.353)

Optimal ET 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]]

Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 393.439 (~25/24 = 86.561)

Optimal ET sequence: 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: [⟨5 9 12 14 18], ⟨0 -3 -1 0 -2]]

Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 393.438 (~22/21 = 86.562)

Optimal ET 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]]

Optimal tuning (POTE): ~8/7 = 1\5, ~5/4 = 392.798 (~22/21 = 87.202)

Optimal ET sequence: 15, 40, 55

Badness: 0.048440

Notes

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
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