# Slendro clan

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The slendro clan tempers out the slendro diesis, 49/48, a triprime comma with factors of 2, 3 and 7.

## Semaphore

Subgroup: 2.3.7

Comma list: 49/48

Sval mapping[1 0 2], 0 2 1]]

sval mapping generators: ~2, ~7/4

Gencom mapping[1 2 0 3], 0 -2 0 -1]]

gencom: [2 7/6; 49/48]
• CTE: ~2 = 1\1, ~7/4 = 952.2948
• POTE: ~2 = 1\1, ~7/4 = 949.615

Scales: semaphore5, semaphore9, semaphore14

### Overview to extensions

The second comma of the comma list defines which 7-limit family member we are looking at.

Godzilla adds 81/80. Immunity adds 2240/2187. Superpelog adds 135/128. Beep adds 21/20. Baba adds 16/15. These all use the same nominal generator as semaphore, though some of them are of very low accuracy.

Decimal adds 25/24, splitting the octave in two. Negri adds 225/224, splitting the hemifourth in two. Triforce adds 128/125, splitting the octave in three. Keemun adds 126/125, splitting the hemitwelfth in three. Nautilus adds 250/243, splitting the hemifourth in three. Nuke is like nautilus, but adds 3584/3375 instead. Hemidim adds 648/625 with a 1/4-octave period. Blacksmith adds 28/27, splitting the octave in five. Spell adds 3125/3072, splitting the hemitwelfth in five. Hemiripple adds 6561/6250, splitting the hemifourth in five. Finally, mabila adds 28672/28125 and splits an interval of two octaves plus a hemifourth in five.

Discussed elsewhere are

Considered below are godzilla, superpelog, negri, nuke, mabila, and hemiripple.

## Godzilla

Godzilla tempers out 81/80, equating 9/8 and 10/9, so it finds the prime 5 at a stack of four fifths, as does any temperament in the meantone family. 19edo is close to being the optimal generator tuning; hence it can be more or less equated with taking 4\19 as a generator. Mos scales are of 5, 9, or 14 notes.

Subgroup: 2.3.5.7

Comma list: 49/48, 81/80

Mapping[1 0 -4 2], 0 2 8 1]]

mapping generators: ~2, ~7/4

Wedgie⟨⟨2 8 1 8 -4 -20]]

• CTE: ~2 = 1\1, ~7/4 = 948.7959
• POTE: ~2 = 1\1, ~7/4 = 947.365

Badness: 0.026747

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 49/48, 81/80

Mapping: [1 0 -4 2 -6], 0 2 8 1 12]]

Optimal tunings:

• CTE: ~2 = 1\1, ~7/4 = 947.4563
• POTE: ~2 = 1\1, ~7/4 = 945.973

Tuning ranges:

• 11-odd-limit diamond monotone: ~7/4 = [942.857, 947.368] (11\14 to 15\19)
• 11-odd-limit diamond tradeoff: ~7/4 = [933.129, 968.826]

Badness: 0.028947

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 49/48, 78/77, 81/80

Mapping: [1 0 -4 2 -6 -5], 0 2 8 1 12 11]]

Optimal tunings:

• CTE: ~2 = 1\1, ~7/4 = 947.8877
• POTE: ~2 = 1\1, ~7/4 = 946.397

Tuning ranges:

• 13- and 15-odd-limit diamond monotone: ~7/4 = 947.368 (15\19)
• 13- and 15-odd-limit diamond tradeoff: ~7/4 = [910.890, 968.826]

Badness: 0.022503

### Semafour

Subgroup: 2.3.5.7.11

Comma list: 33/32, 49/48, 55/54

Mapping: [1 0 -4 2 5], 0 2 8 1 -2]]

Optimal tunings:

• CTE: ~2 = 1\1, ~7/4 = 948.2089
• POTE: ~2 = 1\1, ~7/4 = 945.958

Badness: 0.028510

### Varan

Subgroup: 2.3.5.7.11

Comma list: 49/48, 77/75, 81/80

Mapping: [1 0 -4 2 -10], 0 2 8 1 17]]

Optimal tunings:

• CTE: ~2 = 1\1, ~7/4 = 949.6160
• POTE: ~2 = 1\1, ~7/4 = 948.921

Badness: 0.039647

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 66/65, 77/75, 81/80

Mapping: [1 0 -4 2 -10 -5], 0 2 8 1 17 11]]

Optimal tunings:

• CTE: ~2 = 1\1, ~7/4 = 949.5255
• POTE: ~2 = 1\1, ~7/4 = 948.835

Badness: 0.025676

### Baragon

Subgroup: 2.3.5.7.11

Comma list: 49/48, 56/55, 81/80

Mapping: [1 0 -4 2 9], 0 2 8 1 -7]]

Optimal tunings:

• CTE: ~2 = 1\1, ~7/4 = 949.0311
• POTE: ~2 = 1\1, ~7/4 = 948.827

Badness: 0.035673

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 56/55, 81/80, 91/90

Mapping: [1 0 -4 2 9 -5], 0 2 8 1 -7 11]]

Optimal tunings:

• CTE: ~2 = 1\1, ~7/4 = 949.0670
• POTE: ~2 = 1\1, ~7/4 = 948.802

Badness: 0.026703

## Helayo

For the 5-limit version of this temperament see High badness temperaments #Hogzilla.

Subgroup: 2.3.5.7

Comma list: 49/48, 3645/3584

Mapping[1 0 11 2], 0 2 -11 1]]

Wedgie⟨⟨2 -6 1 -14 -4 19]]

• CTE: ~2 = 1\1, ~7/4 = 947.0969

Badness: 0.0791

Music

## Superpelog

Subgroup: 2.3.5.7

Comma list: 49/48, 135/128

Mapping[1 0 7 2], 0 2 -6 1]]

Wedgie⟨⟨2 -6 1 -14 -4 19]]

• CTE: ~2 = 1\1, ~7/4 = 939.0297
• POTE: ~2 = 1\1, ~7/4 = 940.048

Badness: 0.058216

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 33/32, 45/44, 49/48

Mapping: [1 0 7 2 5], 0 2 -6 1 -2]]

Optimal tunings:

• CTE: ~2 = 1\1, ~7/4 = 938.4673
• POTE: ~2 = 1\1, ~7/4 = 940.041

Badness: 0.028535

Music
Mindaugas Rex Lithuaniae by Chris Vaisvil (blog) (superpelog[9] in 23edo tuning)

## Baba

Subgroup: 2.3.5.7

Comma list: 16/15, 49/45

Mapping[1 0 4 2], 0 2 -2 1]]

• POTE: ~2 = 1\1, ~7/4 = 973.296

Wedgie⟨⟨2 -2 1 -8 -4 8]]

Badness: 0.044321

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 16/15, 22/21, 49/45

Mapping: [1 0 4 2 1], 0 2 -2 1 3]]

Optimal tunings:

• POTE: ~2 = 1\1, ~7/4 = 978.164

Badness: 0.036538

## Negri

Negri tempers out the negri comma in the 5-limit, 49/48 and 225/224 in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding 91/90 to the comma list; this will be discussed below under the title of negra.

Subgroup: 2.3.5

Comma list: 16875/16384

Mapping[1 2 2], 0 -4 3]]

mapping generators: ~2, ~16/15

Wedgie⟨⟨4 -3 -14]]

• POTE: ~2 = 1\1, ~16/15 = 125.7549

Badness: 0.086856

### 7-limit

Subgroup: 2.3.5.7

Comma list: 49/48, 225/224

Mapping[1 2 2 3], 0 -4 3 -2]]

Wedgie⟨⟨4 -3 2 -14 -8 13]]

• POTE: ~2 = 1\1, ~15/14 = 125.608

Badness: 0.026483

#### 2.3.5.7.13 subgroup (negra)

Subgroup: 2.3.5.7.13

Comma list: 49/48, 65/64, 91/90

Sval mapping: [1 2 2 3 4], 0 -4 3 -2 -3]]

Gencom mapping: [1 2 2 3 0 4], 0 -4 3 -2 0 -3]]

gencom: [2 14/13; 49/48 65/64 91/90]

Optimal tunings:

• POTE: ~2 = 1\1, ~14/13 = 125.567

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 49/48, 56/55

Mapping: [1 2 2 3 4], 0 -4 3 -2 -5]]

Optimal tunings:

• POTE: ~2 = 1\1, ~15/14 = 126.474

Badness: 0.026190

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 49/48, 56/55, 78/77

Mapping: [1 2 2 3 4 4], 0 -4 3 -2 -5 -3]]

Optimal tunings:

• POTE: ~2 = 1\1, ~14/13 = 126.431

Badness: 0.017833

### Negril

Subgroup: 2.3.5.7.11

Comma list: 49/48, 100/99, 225/224

Mapping: [1 2 2 3 2], 0 -4 3 -2 14]]

Optimal tunings:

• POTE: ~2 = 1\1, ~15/14 = 124.767

Badness: 0.038679

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 65/64, 91/90, 875/858

Mapping: [1 2 2 3 2 4], 0 -4 3 -2 14 -3]]

Optimal tunings:

• POTE: ~2 = 1\1, ~14/13 = 124.716

Badness: 0.024383

### Negric

Subgroup: 2.3.5.7.11

Comma list: 33/32, 49/48, 77/75

Mapping: [1 2 2 3 3], 0 -4 3 -2 4]]

Optimal tunings:

• POTE: ~2 = 1\1, ~15/14 = 127.039

Badness: 0.030617

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 33/32, 49/48, 65/64, 91/90

Mapping: [1 2 2 3 3 4], 0 -4 3 -2 4 -3]]

Optimal tunings:

• POTE: ~2 = 1\1, ~14/13 = 127.039

Badness: 0.020205

### Negroni

Subgroup: 2.3.5.7.11

Comma list: 49/48, 55/54, 225/224

Mapping: [1 2 2 3 5], 0 -4 3 -2 -15]]

Optimal tunings:

• POTE: ~2 = 1\1, ~15/14 = 124.539

Badness: 0.035296

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 55/54, 65/64, 91/90

Mapping: [1 2 2 3 5 4], 0 -4 3 -2 -15 -3]]

Optimal tunings:

• POTE: ~2 = 1\1, ~14/13 = 124.545

Badness: 0.021559

### Wilsec

Subgroup: 2.3.5.7.11

Comma list: 49/48, 121/120, 225/224

Mapping: [1 6 -1 5 4], 0 -8 6 -4 -1]]

Optimal tunings:

• POTE: ~2 = 1\1, ~11/8 = 537.186

Badness: 0.041886

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 65/64, 91/90, 121/120

Mapping: [1 6 -1 5 4 7], 0 -8 6 -4 -1 -6]]

Optimal tunings:

• POTE: ~2 = 1\1, ~11/8 = 537.208

Badness: 0.025192

#### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 49/48, 65/64, 91/90, 121/120, 154/153

Mapping: [1 6 -1 5 4 7 -2], 0 -8 6 -4 -1 -6 11]]

Optimal tunings:

• POTE: ~2 = 1\1, ~11/8 = 537.230

Badness: 0.021778

#### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153

Mapping: [1 6 -1 5 4 7 -2 7], 0 -8 6 -4 -1 -6 11 -5]]

Optimal tunings:

• POTE: ~2 = 1\1, ~11/8 = 537.214

Badness: 0.016828

## Nuke

Subgroup: 2.3.5.7

Comma list: 49/48, 3584/3375

Mapping[1 2 2 3], 0 -6 5 -3]]

• POTE: ~2 = 1\1, ~16/15 = 80.9538

Badness: 0.129339

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 77/75, 512/495

Mapping: [1 2 2 3 3], 0 -6 5 -3 7]]

Optimal tunings:

• POTE: ~2 = 1\1, ~16/15 = 80.8171

Badness: 0.069398

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 66/65, 77/75, 448/429

Mapping: [1 2 2 3 3 4], 0 -6 5 -3 7 -4]]

Optimal tunings:

• POTE: ~2 = 1\1, ~16/15 = 81.0243

Badness: 0.048553

## Mabila

See also: Mabila family

Subgroup: 2.3.5.7

Comma list: 49/48, 28672/28125

Mapping: [1 6 1 5], 0 -10 3 -5]]

Wedgie⟨⟨10 -3 5 -28 -20 20]]

• POTE: ~2 = 1\1, ~75/56 = 529.667

Badness: 0.133638

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 56/55, 1350/1331

Mapping: [1 6 1 5 7], 0 -10 3 -5 -8]]

Optimal tunings:

• POTE: ~2 = 1\1, ~15/11 = 529.729

Badness: 0.061501

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 56/55, 91/90, 847/845

Mapping: [1 6 1 5 7 9], 0 -10 3 -5 -8 -12]]

Optimal tunings:

• POTE: ~2 = 1\1, ~15/11 = 529.763

Badness: 0.037270

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 49/48, 56/55, 91/90, 154/153, 375/374

Mapping: [1 6 1 5 7 9 1], 0 -10 3 -5 -8 -12 7]]

Optimal tunings:

• POTE: ~2 = 1\1, ~15/11 = 529.695

Badness: 0.031888

### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 49/48, 56/55, 76/75, 91/90, 154/153, 190/187

Mapping: [1 6 1 5 7 9 1 6], 0 -10 3 -5 -8 -12 7 -4]]

Optimal tunings:

• POTE: ~2 = 1\1, ~15/11 = 529.736

Badness: 0.026981

## Hemiripple

See also: Ripple family #Hemiripple

Subgroup: 2.3.5.7

Comma list: 49/48, 6561/6250

Mapping[1 2 3 3], 0 -10 -16 -5]]

Wedgie⟨⟨10 16 5 2 -20 -33]]

• POTE: ~2 = 1\1, ~36/35 = 50.826

Badness: 0.175113

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 121/120, 567/550

Mapping: [1 2 3 3 4], 0 -10 -16 -5 -13]]

Optimal tunings:

• POTE: ~2 = 1\1, ~36/35 = 50.826

Badness: 0.066834

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 66/65, 121/120, 351/350

Mapping: [1 2 3 3 4 4], 0 -10 -16 -5 -13 -7]]

Optimal tunings:

• POTE: ~2 = 1\1, ~36/35 = 50.635

Badness: 0.046588