# Cloudy clan

(Redirected from Cloudy)

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

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]]

Wedgie⟨⟨15 10 0 -19 -42 -28]]

• 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)

### 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

## 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

Wedgie⟨⟨10 -10 0 -39 -28 28]]

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

### 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)

#### 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)

#### 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)

### 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)

#### 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)

#### 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)

### 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)

#### 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)

#### 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)

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)

### 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)

#### 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)

### 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)

#### 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)

## 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)

### 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)

### 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)