# Gamelismic clan

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The 2.3.7 subgroup comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo [-10 1 0 3. For any member of the clan, for the rank-3 gamelismic temperament itself, and for the rank-2 2.3.7 temperament slendric, this means three ~8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)3 × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the harmonic seventh, or if they do not, the other of the pair must be flattened even more. 36edo is a good tuning for slendric, though if the full 7-limit is desired, 72edo, 77edo or 118edo might be preferred.

To the gamelisma itself we need to add the comma which appears next on the modified normal comma list for the full 7-limit. The second comma on the list for mothra is 81/80, for rodan 245/243, for guiron 32805/32768, for gorgo 36/35, and for gidorah 256/245. These all use ~8/7 as a generator, though in the case of gidorah that is the same as ~6/5.

Miracle adds 33075/32768 and uses the secor, half an ~8/7, as generator. Lemba adds 525/512 to the list, and has a half-octave period. Valentine adds 6144/6125 with a generator of ~21/20 and superkleismic adds 875/864 with a generator of ~6/5. Unidec adds 4375/4374, and has a generator of ~10/9 with a half-octave period. Hemithirds adds 65625/65536 with a generator half of a classical major third. Finally, tritikleismic adds 15625/15552 and has a generator of 6/5 with a 1/3-octave period.

Full 7-limit temperaments discussed elsewhere are:

The rest are considered below.

No-five subgroup extensions of slendric include radon, a 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, a 2.3.7.13.17 extension, considered below. Dicussed elsewhere is gigapyth in the 2.3.7.85 subgroup.

## Slendric

See also: No-fives subgroup temperaments #Slendric

Subgroup: 2.3.7

Comma list: 1029/1024

Sval mapping[1 1 3], 0 3 -1]]

sval mapping generators: ~2, ~8/7

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

gencom: [2 8/7; 1029/1024]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.688

### Radon

Subgroup: 2.3.7.11

Comma list: 896/891, 1029/1024

Sval mapping[1 1 3 6], 0 3 -1 -13]]

Gencom mapping[1 1 0 3 6], 0 3 0 -1 -13]]

gencom: [2 8/7; 896/891 1029/1024]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 234.381

### Baladic

Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. 36edo is an excellent baladic tuning.

Subgroup: 2.3.7.13.17

Comma list: 169/168, 273/272, 289/288

Sval mapping[2 2 6 7 7], 0 3 -1 1 3]]

sval mapping generators: ~17/12, ~8/7

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6155

## Rodan

Rodan tempers out 245/243 and can be described as the 41 & 46 temperament. This temperament extends neatly to the 13-limit, though the perfect fifth is sharper than ideal for slendric.

Subgroup: 2.3.5.7

Comma list: 245/243, 1029/1024

Mapping[1 1 -1 3], 0 3 17 -1]]

Wedgie⟨⟨3 17 -1 20 -10 -50]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 234.417

[[1 0 0 0, [5/3 0 1/6 -1/6, [25/9 0 17/18 -17/18, [25/9 0 -1/18 1/18]
Eigenmonzo (unchanged-interval) basis: 2.7/5

Algebraic generator: larger root of 20x2 - 36x + 15, or (9 + √6)/10.

Badness: 0.037112

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 245/243, 385/384, 441/440

Mapping: [1 1 -1 3 6], 0 3 17 -1 -13]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 234.459

Minimax tuning:

• 11-odd-limit: ~8/7 = [4/19 2/19 0 0 -1/19
[[1 0 0 0 0, [31/19 6/19 0 0 -3/19, [49/19 34/19 0 0 -17/19, [53/19 -2/19 0 0 1/19, [62/19 -26/19 0 0 13/19]
Eigenmonzo (unchanged-interval) basis: 2.11/9

Algebraic generator: positive root of x2 + 16x - 31, or √95 - 8.

Badness: 0.023093

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 245/243, 352/351, 364/363

Mapping: [1 1 -1 3 6 8], 0 3 17 -1 -13 -22]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 234.482

Minimax tuning:

• 13- and 15-odd-limit: ~8/7 = [3/14 1/14 0 0 0 -1/28
Eigenmonzos (unchanged-intervals): 2, 13/9

Algebraic generator: Gatetone, positive root of 4x6 - 7x - 1. Recurrence converges slowly.

Badness: 0.018448

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 154/153, 196/195, 245/243, 256/255, 273/272

Mapping: [1 1 -1 3 6 8 8], 0 3 17 -1 -13 -22 -20]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 234.524

Minimax tuning:

• 17-odd-limit: ~8/7 = [3/13 1/13 0 0 0 0 -1/26
Eigenmonzos (unchanged-intervals): 2, 18/17

Badness: 0.016743

#### Aerodactyl

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 245/243, 385/384, 441/440

Mapping: [1 1 -1 3 6 -1], 0 3 17 -1 -13 24]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 234.639

Badness: 0.033986

### Aerodino

Subgroup: 2.3.5.7.11

Comma list: 176/175, 245/243, 1029/1024

Mapping: [1 1 -1 3 -3], 0 3 17 -1 33]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 234.728

Badness: 0.054294

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 176/175, 245/243, 847/845

Mapping: [1 1 -1 3 -3 -1], 0 3 17 -1 33 24]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 234.782

Badness: 0.035836

### Varan

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/243, 1029/1024

Mapping: [1 1 -1 3 -2], 0 3 17 -1 28]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 234.145

Badness: 0.044937

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 105/104, 245/243, 352/351

Mapping: [1 1 -1 3 -2 0], 0 3 17 -1 28 19]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 234.089

Badness: 0.032284

## Guiron

Guiron tempers out the schisma, and finds the prime 5 at the diminished fourth as does any temperament in the schismatic family. It can be described as 36 & 41. It is more complex than rodan, but the optimal tuning is closer to optimal slendric.

Subgroup: 2.3.5.7

Comma list: 1029/1024, 10976/10935

Mapping[1 1 7 3], 0 3 -24 -1]]

mapping generators: ~2, ~8/7

Wedgie⟨⟨3 -24 -1 -45 -10 65]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.930

[[1 0 0 0, [15/8 0 -1/8 0, [0 0 1 0, [65/24 0 1/24 0]
Eigenmonzo (unchanged-interval) basis: 2.5

Badness: 0.047544

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 10976/10935

Mapping: [1 1 7 3 -2], 0 3 -24 -1 28]]

mapping generators: ~2, ~8/7

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.931

Minimax tuning:

• 11-odd-limit: ~8/7 = [7/24 0 -1/24
[[1 0 0 0 0, [15/8 0 -1/8 0 0, [0 0 1 0 0, [65/24 0 1/24 0 0, [37/6 0 -7/6 0 0]
Eigenmonzo (unchanged-interval) basis: 2.5

Badness: 0.026648

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 385/384, 729/728

Mapping: [1 1 7 3 -2 0], 0 3 -24 -1 28 19]]

mapping generators: ~2, ~8/7

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.890

Badness: 0.028444

## Mothra

Mothra tempers out 81/80 and finds the prime 5 at a stack of four fifths as does any temperament in the meantone family. It also tempers out 1728/1715, the orwellisma. It can be described as 26 & 31. Using 31edo with a generator of 6/31 is an excellent tuning choice. Once again something other than a mos should be used as a scale to get the most out of mothra.

Note that mothra is also called cynder in the 7-limit, which can be a little confusing sometimes.

Its S-expression-based comma list is {S6/S7, S7/S8(, S6/S8 = S9)}, taking advantage of the fact that 81/80 is a semiparticular.

Subgroup: 2.3.5.7

Comma list: 81/80, 1029/1024

Mapping[1 1 0 3], 0 3 12 -1]]

mapping generators: ~2, ~8/7

Wedgie⟨⟨3 12 -1 12 -10 -36]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.193

Algebraic generator: Rabrindanath, largest real root of x8 - 3x2 + 1, or 232.0774 cents.

[[1 0 0 0, [1 0 1/4 0, [0 0 1 0, [3 0 -1/12 0]
Eigenmonzo (unchanged-interval) basis: 2.5

Badness: 0.037146

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 81/80, 99/98, 385/384

Mapping: [1 1 0 3 5], 0 3 12 -1 -8]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.031

Badness: 0.025642

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 81/80, 99/98, 105/104, 144/143

Mapping: [1 1 0 3 5 1], 0 3 12 -1 -8 14]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 231.811

Badness: 0.023954

Music

### Cynder

Subgroup: 2.3.5.7.11

Comma list: 45/44, 81/80, 1029/1024

Mapping: [1 1 0 3 0], 0 3 12 -1 18]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 231.317

Badness: 0.055706

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 78/77, 81/80, 640/637

Mapping: [1 1 0 3 0 1], 0 3 12 -1 18 14]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 231.293

Badness: 0.034124

### Mosura

The S-expression-based comma list of mosura suggests it might be the most natural extension of 7-limit cynder to the 11-limit: {S6/S7, S7/S8, (S6/S8 = S9,) S8/S10}.

Subgroup: 2.3.5.7.11

Comma list: 81/80, 176/175, 540/539

Mapping: [1 1 0 3 -1], 0 3 12 -1 23]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.419

Badness: 0.031334

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 81/80, 144/143, 176/175, 196/195

Mapping: [1 1 0 3 -1 7], 0 3 12 -1 23 -17]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.640

Badness: 0.036857

## Gorgo

In the 5-limit, gorgo tempers out the laconic comma, 2187/2000, which is the difference between three 10/9's and a 3/2. Although a higher-error temperament, it does pop up enough in the low-numbered edos to be useful, most notably in 16edo and 21edo. The only 7-limit extension that makes any sense to use is to add the gamelisma to the comma list.

### 5-limit (laconic)

Subgroup: 2.3.5

Comma list: 2187/2000

Mapping[1 1 1], 0 3 7]]

Wedgie⟨⟨3 7 4]]

Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 227.426

Badness: 0.161799

### 7-limit

Subgroup: 2.3.5.7

Comma list: 36/35, 1029/1024

Mapping[1 1 1 3], 0 3 7 -1]]

Wedgie⟨⟨3 7 -1 4 -10 -22]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 228.334

Badness: 0.060663

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44, 1029/1024

Mapping: [1 1 1 3 1], 0 3 7 -1 13]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.373

Badness: 0.049500

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 36/35, 45/44, 507/500

Mapping: [1 1 1 3 1 2], 0 3 7 -1 13 9]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.230

Badness: 0.032664

### Spartan

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 1029/1024

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

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 229.535

Badness: 0.062683

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 36/35, 56/55, 507/500

Mapping: [1 1 1 3 5 2], 0 3 7 -1 -8 9]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 229.059

Badness: 0.047071

Music

## Gidorah

### 5-limit (university)

Subgroup: 2.3.5

Comma list: 144/125

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

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 235.4416

Optimal ET sequence5, 31cccc, 36…, 41…, 46…, 51

Badness: 0.101806

### 7-limit

Subgroup: 2.3.5.7

Comma list: 21/20, 144/125

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

Wedgie⟨⟨3 2 -1 -4 -10 -8]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 230.762

Badness: 0.062262

## Oncle

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

Subgroup: 2.3.5.7

Comma list: 1029/1024, 2430/2401

Mapping[1 1 6 3], 0 3 -19 -1]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 232.498

Badness: 0.088384

## Archaeotherium

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

Subgroup: 2.3.5.7

Comma list: 405/392, 1029/1024

Mapping[1 1 5 3], 0 3 -14 -1]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 230.258

Badness: 0.146306

## Clyndro

See also: Pelogic family

Subgroup: 2.3.5.7

Comma list: 135/128, 360/343

Mapping[1 1 4 3], 0 3 -9 -1]]

Wedgie⟨⟨3 -9 -1 -21 -10 23]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 226.469

Badness: 0.159179

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 33/32, 45/44, 352/343

Mapping: [1 1 4 3 4], 0 3 -9 -1 -3]]

Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 226.428

Badness: 0.069703

## Miracle

Subgroup: 2.3.5.7

Comma list: 225/224, 1029/1024

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

mapping generator: ~2, ~15/14

Wedgie⟨⟨6 -7 -2 -25 -20 15]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.675

[[1 0 0 0, [25/13 6/13 -6/13 0, [25/13 -7/13 7/13 0, [35/13 -2/13 2/13 0]
Eigenmonzo (unchanged-interval) basis: 2.5/3
[[1 0 0 0, [25/19 12/19 -6/19 0, [50/19 -14/19 7/19 0, [55/19 -4/19 2/19 0]
Eigenmonzo (unchanged-interval) basis: 2.9/5
• 7-odd-limit diamond monotone: ~15/14 = [114.286, 120.000] (2\21 to 1\10)
• 9-odd-limit diamond monotone: ~15/14 = [116.129, 120.000] (3\31 to 1\10)
• 7- and 9-odd-limit diamond tradeoff: ~15/14 = [115.587, 116.993]
• 7-odd-limit diamond monotone and tradeoff: ~15/14 = [115.587, 116.993]
• 9-odd-limit diamond monotone and tradeoff: ~15/14 = [116.129, 116.993]

Algebraic generator: Secor59, positive root of 15x6 - 8x4 - 12

Badness: 0.016742

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 243/242, 385/384

Mapping: [1 1 3 3 2], 0 6 -7 -2 15]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.633

Minimax tuning:

• 11-odd-limit: ~15/14 = [1/19 2/19 -1/19
[[1 0 0 0 0, [25/19 12/19 -6/19 0 0, [50/19 -14/19 7/19 0 0, [55/19 -4/19 2/19 0 0, [53/19 30/19 -15/19 0 0]
Eigenmonzo (unchanged-interval) basis: 2.9/5

Tuning ranges:

• 11-odd-limit diamond monotone: ~15/14 = [116.129, 117.073] (3\31 to 4\41)
• 11-odd-limit diamond tradeoff: ~15/14 = [115.587, 116.993]
• 11-odd-limit diamond monotone and tradeoff: ~15/14 = [116.129, 116.993]

Algebraic generator: Secor59

Badness: 0.010684

#### Miraculous

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 196/195, 243/242

Mapping: [1 1 3 3 2 4], 0 6 -7 -2 15 -3]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.747

Badness: 0.018669

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 105/104, 120/119, 144/143, 154/153, 170/169

Mapping: [1 1 3 3 2 4 4], 0 6 -7 -2 15 -3 1]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.769

Badness: 0.017084

#### Benediction

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 351/350, 385/384

Mapping: [1 1 3 3 2 7], 0 6 -7 -2 15 -34]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.574

Badness: 0.015715

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 351/350, 375/374

Mapping: [1 1 3 3 2 7 7], 0 6 -7 -2 15 -34 -30]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.585

Badness: 0.012537

#### Manna

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 325/324, 385/384

Mapping: [1 1 3 3 2 0], 0 6 -7 -2 15 38]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.739

Badness: 0.017012

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 325/324, 385/384

Mapping: [1 1 3 3 2 0 0], 0 6 -7 -2 15 38 42]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.727

Badness: 0.014680

#### Semimiracle

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 243/242, 385/384

Mapping: [2 2 6 6 4 7], 0 6 -7 -2 15 2]]

Optimal tuning (POTE): ~99/70 = 1\2, ~15/14 = 116.624

Badness: 0.024622

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 169/168, 221/220, 225/224, 243/242, 273/272

Mapping: [2 2 6 6 4 7 7], 0 6 -7 -2 15 2 6]]

Optimal tuning (POTE): ~2 = 17\12, ~15/14 = 116.628

Badness: 0.016130

#### Hemisecordite

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 385/384, 847/845

Mapping: [1 1 3 3 2 2], 0 12 -14 -4 30 35]]

Optimal tuning (POTE): ~2 = 1\1, ~27/26 = 58.288

Badness: 0.025589

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 385/384, 847/845

Mapping: [1 1 3 3 2 2 2], 0 12 -14 -4 30 35 43]]

Optimal tuning (POTE): ~2 = 1\1, ~27/26 = 58.261

Badness: 0.022535

##### Semihemisecordite

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 289/288, 385/384, 847/845

Mapping: [2 2 6 6 4 4 7], 0 12 -14 -4 30 35 12]]

Optimal tuning (POTE): ~17/12 = 1\2, ~27/26 = 58.288

Badness: 0.046958

###### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 209/208, 225/224, 243/242, 289/288, 361/360, 385/384

Mapping: [2 2 6 6 4 4 7 8], 0 12 -14 -4 30 35 12 5]]

Optimal tuning (POTE): ~17/12 = 1\2, ~27/26 = 58.283

Badness: 0.035057

###### 23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 209/208, 225/224, 243/242, 289/288, 323/322, 361/360, 385/384

Mapping: [2 2 6 6 4 4 7 8 7], 0 12 -14 -4 30 35 12 5 21]]

Optimal tuning (POTE): ~17/12 = 1\2, ~27/26 = 58.283

Badness: 0.026421

#### Phicordial

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 385/384, 2200/2197

Mapping: [1 7 -4 1 17 4], 0 -18 21 6 -45 -1]]

Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 361.121

Badness: 0.033198

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 441/440, 2200/2197

Mapping: [1 7 -4 1 17 4 8], 0 -18 21 6 -45 -1 -13]]

Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 361.123

Badness: 0.024705

### Revelation

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 1029/1024

Mapping: [1 1 3 3 5], 0 6 -7 -2 -16]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.277

Badness: 0.032946

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 99/98, 105/104, 512/507

Mapping: [1 1 3 3 5 4], 0 6 -7 -2 -16 -3]]

Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 116.268

Badness: 0.029452

### Hemimiracle

Subgroup: 2.3.5.7.11

Comma list: 225/224, 245/242, 1029/1024

Mapping: [1 1 3 3 4], 0 12 -14 -4 -11]]

Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 58.408

Badness: 0.059232

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 196/195, 245/242, 512/507

Mapping: [1 1 3 3 4 4], 0 12 -14 -4 -11 -6]]

Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 58.430

Badness: 0.043151

### Oracle

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 1029/1024

Mapping: [1 7 -4 1 3], 0 -12 14 4 1]]

Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 541.668

Badness: 0.042687

## Hemiseven

Subgroup: 2.3.5.7

Comma list: 1029/1024, 19683/19600

Mapping[1 4 14 2], 0 -6 -29 2]]

Wedgie⟨⟨6 29 -2 32 -20 -86]]

Optimal tuning (POTE): ~2 = 1\1, ~320/243 = 483.267

Badness: 0.056557

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 19683/19600

Mapping: [1 4 14 2 -5], 0 -6 -29 2 21]]

Optimal tuning (POTE): ~2 = 1\1, ~320/243 = 483.276

Badness: 0.028467

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 385/384, 441/440, 676/675

Mapping: [1 4 14 2 -5 19], 0 -6 -29 2 21 -38]]

Optimal tuning (POTE): ~2 = 1\1, ~120/91 = 483.256

Badness: 0.021900

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 351/350, 385/384, 441/440, 676/675

Mapping: [1 4 14 2 -5 19 21], 0 -6 -29 2 21 -38 -42]]

Optimal tuning (POTE): ~2 = 1\1, ~45/34 = 483.261

Badness: 0.015701

## Unidec

### 5-limit (unidecmic)

Subgroup: 2.3.5

Comma list: 31381059609/31250000000

Mapping[2 5 8], 0 -6 -11]]

mapping generators: ~177147/125000, ~10/9

Optimal tuning (POTE): ~177147/125000 = 1\2, ~10/9 = 183.047

Badness: 0.082423

### 7-limit

Subgroup: 2.3.5.7

Comma list: 1029/1024, 4375/4374

Mapping[2 5 8 5], 0 -6 -11 2]]

Wedgie⟨⟨12 22 -4 7 -40 -71]]

Optimal tuning (POTE): ~1225/864 = 1\2, ~10/9 = 183.161

[[1 0 0 0, [47/26 0 6/13 -6/13, [71/26 0 11/13 -11/13, [71/26 0 -2/13 2/13]
Eigenmonzo (unchanged-interval) basis: 2.7/5
[[1 0 0 0, [10/7 6/7 0 -3/7, [57/28 11/7 0 -11/14, [20/7 -2/7 0 1/7]
Eigenmonzo (unchanged-interval) basis: 2.9/7

Badness: 0.038393

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 4375/4374

Mapping: [2 5 8 5 6], 0 -6 -11 2 3]]

Minimax tuning:

[[1 0 0 0 0, [10/7 6/7 0 -3/7 0, [57/28 11/7 0 -11/14 0, [20/7 -2/7 0 1/7 0, [99/28 -3/7 0 3/14 0]
Eigenmonzo (unchanged-interval) basis: 2.9/7

Badness: 0.015479

#### Ekadash

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 441/440, 625/624, 729/728

Mapping: [2 5 8 5 6 19], 0 -6 -11 2 3 -38]]

Optimal tuning (POTE): ~99/70 = 1\2, ~10/9 = 183.187

Badness: 0.020381

#### Hendec

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 325/324, 364/363, 385/384

Mapping: [2 5 8 5 6 8], 0 -6 -11 2 3 -2]]

Optimal tuning (POTE): ~91/64 = 1\2, ~10/9 = 183.198

Badness: 0.017707

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 169/168, 221/220, 273/272, 325/324, 364/363

Mapping: [2 5 8 5 6 8 10], 0 -6 -11 2 3 -2 -6]]

Optimal tuning (POTE): ~17/12 = 1\2, ~10/9 = 183.196

Badness: 0.011676

## Superkleismic

See also: Shibboleth family #Superkleismic

Subgroup: 2.3.5.7

Comma list: 875/864, 1029/1024

Mapping[1 4 5 2], 0 -9 -10 3]]

Wedgie⟨⟨9 10 -3 -5 -30 -35]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.930

Badness: 0.047932

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/242, 385/384

Mapping: [1 4 5 2 4], 0 -9 -10 3 -2]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.847

Badness: 0.025659

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 105/104, 144/143, 245/243

Mapping: [1 4 5 2 4 8], 0 -9 -10 3 -2 -16]]

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 321.994

Badness: 0.021478

## Lagaca

Subgroup: 2.3.5.7

Comma list: 1029/1024, 11529602/11390625

Mapping[2 5 2 5], 0 -9 13 3]]

Wedgie⟨⟨18 -26 -6 -83 -60 59]]

Optimal tuning (POTE): ~3375/2401 = 1\2, ~15/14 = 122.027

Badness: 0.144345

## Necromanteion

Subgroup: 2.3.5.7

Comma list: 1029/1024, 5103/5000

Mapping[1 7 10 1], 0 -12 -17 4]]

Wedgie⟨⟨12 17 -4 -1 -40 -57]]

Optimal tuning (POTE): ~2 = 1\1, ~48/35 = 541.779

Badness: 0.117680

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 243/242, 1029/1024

Mapping: [1 7 10 1 17], 0 -12 -17 4 -30]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 541.729

Badness: 0.053459

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 176/175, 243/242, 343/338

Mapping: [1 7 10 1 17 1], 0 -12 -17 4 -30 6]]

Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 541.606

Badness: 0.047015

## Restles

Subgroup: 2.3.5.7

Comma list: 1029/1024, 153664/151875

Mapping[1 -2 8 4], 0 12 -19 -4]]

Wedgie⟨⟨12 -19 -4 -58 -40 44]]

Optimal tuning (POTE): ~2 = 1\1, ~315/256 = 358.5485

Badness: 0.108011

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 153664/151875

Mapping: [1 -2 8 4 -7], 0 12 -19 -4 35]]

Optimal tuning (POTE): ~2 = 1\1, ~27/22 = 358.5713

Badness: 0.054655

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 385/384, 676/675

Mapping: [1 -2 8 4 -7 4], 0 12 -19 -4 35 -1]]

Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 358.5739

Badness: 0.028187

## Quartemka

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

Subgroup: 2.3.5.7

Comma list: 1029/1024, 1250000/1240029

Mapping[1 4 6 2], 0 -21 -32 7]]

Wedgie⟨⟨21 32 -7 2 -70 -106]]

Optimal tuning (POTE): ~2 = 1\1, ~27/25 = 138.006

Badness: 0.152287

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 800000/793881

Mapping: [1 4 6 2 3], 0 -21 -32 7 4]]

Optimal tuning (POTE): ~2 = 1\1, ~27/25 = 137.990

Badness: 0.057307

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 364/363, 385/384, 2200/2197

Mapping: [1 4 6 2 3 6], 0 -21 -32 7 4 -20]]

Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 137.990

Badness: 0.028393

## Tritriple

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

Subgroup: 2.3.5.7

Comma list: 1029/1024, 1959552/1953125

Mapping[1 -11 -7 7], 0 27 20 -9]]

Wedgie⟨⟨27 20 -9 -31 -90 -77]]

Optimal tuning (POTE): ~2 = 1\1, ~864/625 = 559.295

Badness: 0.118640

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 43923/43750

Mapping: [1 -11 -7 7 -4], 0 27 20 -9 16]]

Optimal tuning (POTE): ~2 = 1\1, ~242/175 = 559.293

Badness: 0.035350

## Widefourth

Subgroup: 2.3.5.7

Comma list: 1029/1024, 48828125/48771072

Mapping[1 16 8 -2], 0 -33 -13 11]]

Wedgie⟨⟨33 13 -11 -56 -110 -62]]

Optimal tuning (POTE): ~2 = 1\1, ~3125/2304 = 524.210

Badness: 0.154117

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 234375/234256

Mapping: [1 16 8 -2 17], 0 -33 -13 11 -31]]

Optimal tuning (POTE): ~2 = 1\1, ~847/625 = 524.210

Badness: 0.040785

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 441/440, 625/624, 847/845

Mapping: [1 16 8 -2 17 12], 0 -33 -13 11 -31 -19]]

Optimal tuning (POTE): ~2 = 1\1, ~65/48 = 524.209

Badness: 0.021636