# Marvel temperaments

(Redirected from Alphorn)

This page discusses miscellaneous rank-2 temperaments tempering out [-5 2 2 -1 = 225/224, the marvel comma or septimal kleisma.

Temperaments considered in families and clans are:

Considered below are negri, wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, submajor, alphorn, tertiosec, gwazy, and gracecordial.

Since (5/4)2 = 225/224 × 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.

The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.

Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4) = 64/45. Setting this equal to 10/7 gives (10/7)/(64/45) = 225/224.)

## Negri

Main article: 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]]

Wedgie⟨⟨4 -3 -14]]

POTE generator: ~16/15 = 125.7549

### 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 generator: ~15/14 = 125.608

#### Negra

This is the 2.3.5.7.13 extension of negri.

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]

POTE generator: ~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]]

POTE generator: ~15/14 = 126.474

Optimal GPV sequence: 9, 10, 19

#### 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]]

POTE generator: ~14/13 = 126.431

Optimal GPV sequence: 9, 10, 19

### 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]]

POTE generator: ~15/14 = 124.767

Optimal GPV sequence: 19, 29, 48d, 77cdd

#### 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]]

POTE generator: ~14/13 = 124.716

Optimal GPV sequence: 19, 29, 48df, 77cddf

### 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]]

POTE generator: ~15/14 = 127.039

Optimal GPV sequence: 9, 19e

#### 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]]

POTE generator: ~14/13 = 127.039

Optimal GPV sequence: 9, 19e

### 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]]

POTE generator: ~15/14 = 124.539

Optimal GPV sequence: 10, 19e, 29, 77cddee

#### 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]]

POTE generator: ~14/13 = 124.545

Optimal GPV sequence: 10, 19e, 29, 77cddeef

### 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]]

POTE generator: ~11/8 = 537.186

Optimal GPV sequence: 9, 20, 29, 38d, 67cdde

#### 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]]

POTE generator: ~11/8 = 537.208

Optimal GPV sequence: 9, 20, 29, 38df, 67cddef

#### 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]]

POTE generator: ~11/8 = 537.230

Optimal GPV sequence: 9, 20g, 29g, 38df, 67cddefg

#### 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]]

POTE generator: ~11/8 = 537.214

Optimal GPV sequence: 9, 20g, 29g, 38df, 67cddefgh

## Wizard

Main article: Wizard
For the 5-limit version of this temperament, see High badness temperaments #Wizard.

Subgroup: 2.3.5.7

Comma list: 225/224, 118098/117649

Mapping: [2 1 5 2], 0 6 -1 10]]

Mapping generators: ~1225/864, ~245/216

POTE generator: ~5/4 = 383.256

Wedgie⟨⟨12 -2 20 -31 -2 52]]

Scales: wizard22

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 4000/3993

Mapping: [2 1 5 2 8], 0 6 -1 10 -3]]

Mapping generators: ~99/70, ~25/22

POTE generator: ~5/4 = 383.232

Optimal GPV sequence: 22, 50, 72, 166, 238c, 310c

Scales: wizard22

#### Lizard

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 351/350, 364/363, 385/384

Mapping: [2 1 5 2 8 11], 0 6 -1 10 -3 -10]]

Mapping generators: ~99/70, ~25/22

POTE generator: ~5/4 = 383.389

Optimal GPV sequence: 22, 50, 72, 122, 194df

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 221/220, 273/272, 289/288, 351/350, 375/374

Mapping: [2 1 5 2 8 11 6], 0 6 -1 10 -3 -10 6]]

Mapping generators: ~17/12, ~17/15

POTE generator: ~5/4 = 383.381

Optimal GPV sequence: 22, 50, 72, 122g, 194dfg

##### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342

Mapping: [2 1 5 2 8 11 6 2], 0 6 -1 10 -3 -10 6 18]]

Mapping generators: ~17/12, ~17/15

POTE generator: ~5/4 = 383.477

Optimal GPV sequence: 22h, 50, 72, 122g, 194dfg

#### Gizzard

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 325/324, 385/384, 1573/1568

Mapping: [2 1 5 2 8 -2], 0 6 -1 10 -3 26]]

Mapping generators: ~99/70, ~25/22

POTE generator: ~5/4 = 383.170

Optimal GPV sequence: 72, 166, 238cf

##### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 289/288, 325/324, 375/374, 385/384

Mapping: [2 1 5 2 8 -2 6], 0 6 -1 10 -3 26 6]]

Mapping generators: ~17/12, ~17/15

POTE generator: ~5/4 = 383.175

Optimal GPV sequence: 72, 166g, 238cfg

##### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594

Mapping: [2 1 5 2 8 -2 6 15], 0 6 -1 10 -3 26 6 -18]]

Mapping generators: ~17/12, ~17/15

POTE generator: ~5/4 = 383.138

Optimal GPV sequence: 72, 94, 166g

### Mage

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 1331/1296

Mapping: [2 1 5 2 4], 0 6 -1 10 8]]

Mapping generators: ~77/54, ~55/48

POTE generator: ~5/4 = 383.124

Optimal GPV sequence: 22, 50e, 72ee, 94ee

## Tritonic

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

Subgroup: 2.3.5.7

Comma list: 225/224, 50421/50000

Mapping: [1 4 -3 -3], 0 -5 11 12]]

Wedgie⟨⟨5 -11 -12 -29 -33 3]]

POTE generator: ~7/5 = 580.286

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 441/440

Mapping: [1 4 -3 -3 2], 0 -5 11 12 3]]

POTE generator: ~7/5 = 580.267

Optimal GPV sequence: 29, 31, 60e

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 121/120, 196/195, 275/273

Mapping: [1 4 -3 -3 2 -5], 0 -5 11 12 3 18]]

POTE generator: ~7/5 = 580.108

Optimal GPV sequence: 29, 31, 60e, 151cde

### Tritoni

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 27783/27500

Mapping: [1 4 -3 -3 17], 0 -5 11 12 -28]]

POTE generator: ~7/5 = 580.389

Optimal GPV sequence: 31, 91, 122, 153d

## Septimin

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

Subgroup: 2.3.5.7

Comma list: 225/224, 84035/82944

Mapping: [1 4 1 5], 0 -11 6 -10]]

Wedgie⟨⟨11 -6 10 -35 -15 40]]

POTE generator: ~7/6 = 263.632

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 2401/2376

Mapping: [1 4 1 5 5], 0 -11 6 -10 -7]]

POTE generator: ~7/6 = 263.634

Optimal GPV sequence: 41, 91, 223cdef

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 196/195, 245/242

Mapping: [1 4 1 5 5 7], 0 -11 6 -10 -7 -15]]

POTE generator: ~7/6 = 263.700

Optimal GPV sequence: 41, 91

## Merman

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

Subgroup: 2.3.5.7

Comma list: 225/224, 2500000/2470629

Mapping: [1 5 -5 -5], 0 -7 15 16]]

Wedgie⟨⟨7 -15 -16 -40 -45 5]]

POTE generator: ~7/5 = 585.585

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 441/440, 1344/1331

Mapping: [1 5 -5 -5 2], 0 -7 15 16 3]]

POTE generator: ~7/5 = 585.606

Optimal GPV sequence: 41, 84, 125e

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 225/224, 364/363, 441/440

Mapping: [1 5 -5 -5 2 12], 0 -7 15 16 3 -17]]

POTE generator: ~7/5 = 585.657

Optimal GPV sequence: 41, 84, 125e, 209ef, 293ef

## Slender

Slender (31&32) tempers out the hewuermera comma in addition to the marvel comma, this has a generator 49/48, 3 of which equal marvel's 16/15 - 15/14, and 10 generators is 5/4.

Subgroup: 2.3.5.7

Comma list: 225/224, 589824/588245

Mapping: [1 2 2 3], 0 -13 10 -6]]

Wedgie⟨⟨13 -10 6 -46 -27 42]]

POTE generator: ~49/48 = 38.413

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 1331/1323

Mapping: [1 2 2 3 4], 0 -13 10 -6 -17]]

POTE generator: ~49/48 = 38.387

Optimal GPV sequence: 31, 63, 94, 125

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 275/273, 385/384, 1331/1323

Mapping: [1 2 2 3 4 3], 0 -13 10 -6 -17 22]]

POTE generator: ~49/48 = 38.314

Optimal GPV sequence: 31, 63, 94

## Triton

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

Subgroup: 2.3.5.7

Comma list: 225/224, 1029/1000

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

Wedgie⟨⟨3 -7 -8 -18 -21 1]]

POTE generator: ~7/5 = 568.865

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 56/55, 1029/1000

Mapping: [1 0 6 7 4], 0 3 -7 -8 -1]]

POTE generator: ~7/5 = 569.144

Optimal GPV sequence: 2, 17d, 19, 59bde, 78bde, 97bde

## Submajor

Subgroup: 2.3.5

Comma list: 69198046875/68719476736

Mapping: [1 4 -1], 0 -8 11]]

POTE generator: ~10125/8192 = 362.321

### 7-limit

Subgroup: 2.3.5.7

Comma list: 225/224, 51200/50421

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

Wedgie⟨⟨8 -11 -6 -36 -32 17]]

POTE generator: ~49/40 = 362.255

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 6655/6561

Mapping: [1 4 -1 1 11], 0 -8 11 6 -25]]

POTE generator: ~27/22 = 362.101

Optimal GPV sequence: 10, 43e, 53, 116, 169de, 285cde

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 275/273, 385/384

Mapping: [1 4 -1 1 11 4], 0 -8 11 6 -25 -1]]

POTE generator: ~16/13 = 362.105

Optimal GPV sequence: 10, 43e, 53, 116, 169de, 285cdef

### Interpental

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 51200/50421

POTE generator: ~49/40 = 362.418

Mapping: [1 4 -1 1 -5], 0 -8 11 6 28]]

POTE generator: ~49/40 = 362.418

Optimal GPV sequence: 43, 53, 96, 149d

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 169/168, 176/175, 640/637

POTE generator: ~16/13 = 362.402

Mapping: [1 4 -1 1 -5 4], 0 -8 11 6 28 -1]]

POTE generator: ~16/13 = 362.402

Optimal GPV sequence: 43, 53, 96, 149d

## Marvolo

Subgroup: 2.3.5.7

Comma list: 225/224, 156250000/155649627

Mapping: [1 2 1 1], 0 -6 19 26]]

Wedgie⟨⟨6 -19 -26 -44 -58 -7]]

POTE generator: ~21/20 = 83.348

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 441/440, 4000/3993

Mapping: [1 2 1 1 2], 0 -6 19 26 21]]

POTE generator: ~21/20 = 83.340

Optimal GPV sequence: 29, 43, 72

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 364/363, 441/440

Mapping: [1 2 1 1 2 3], 0 -6 19 26 21 10]]

POTE generator: ~21/20 = 83.330

Optimal GPV sequence: 29, 43, 72, 115f

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 169/168, 221/220, 225/224, 364/363, 441/440

Mapping: [1 2 1 1 2 3 2], 0 -6 19 26 21 10 30]]

POTE generator: ~21/20 = 83.330

Optimal GPV sequence: 29g, 43, 72

### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440

Mapping: [1 2 1 1 2 3 2 3], 0 -6 19 26 21 10 30 18]]

POTE generator: ~21/20 = 83.330

Optimal GPV sequence: 29g, 43, 72

## Enneaportent

Subgroup: 2.3.5.7

Comma list: 225/224, 40353607/40310784

Mapping: [9 0 28 11], 0 2 -1 2]]

Wedgie⟨⟨18 -9 18 -56 -22 67]]

POTE generator: ~5/4 = 383.165

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 12005/11979

Mapping: [9 0 28 11 24], 0 2 -1 2 1]]

POTE generator: ~5/4 = 383.146

Optimal GPV sequence: 9, 63, 72, 423cd, 495bcd

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 364/363, 1716/1715

Mapping: [9 0 28 11 24 19], 0 2 -1 2 1 2]]

POTE generator: ~5/4 = 383.047

Optimal GPV sequence: 9, 63, 72, 279cf

## Gracecordial

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

Subgroup: 2.3.5.7

Comma list: 225/224, 781250000/771895089

Mapping: [1 0 34 63], 0 1 -20 -38]]

Wedgie⟨⟨1 -20 -38 -34 -63 -32]]

POTE generator: ~3/2 = 700.824

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 236328125/234365481

Mapping: [1 0 34 63 -90], 0 1 -20 -38 59]]

POTE generator: ~3/2 = 700.834

Optimal GPV sequence: 12e, 101cde, 113, 125, 238c

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 325/324, 385/384, 831875/830466

Mapping: [1 0 34 63 -90 -66], 0 1 -20 -38 59 44]]

POTE generator: ~3/2 = 700.841

Optimal GPV sequence: 12e, 101cde, 113, 125f, 238cf

#### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913

Mapping: [1 0 34 63 -90 -66 -7], 0 1 -20 -38 59 44 7]]

POTE generator: ~3/2 = 700.841

Optimal GPV sequence: 12e, 101cde, 113, 125f, 238cf

#### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444

Mapping: [1 0 34 63 -90 -66 -7 9], 0 1 -20 -38 59 44 7 -3]]

POTE generator: ~3/2 = 700.842

Optimal GPV sequence: 12e, 101cde, 113, 125f, 238cf

#### 23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528

Mapping: [1 0 34 63 -90 -66 -7 9 -43], 0 1 -20 -38 59 44 7 -3 30]]

POTE generator: ~3/2 = 700.843

Optimal GPV sequence: 12e, 101cde, 113, 238cfi

#### 29-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29

Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493

Mapping: [1 0 34 63 -90 -66 -7 9 -43 -49], 0 1 -20 -38 59 44 7 -3 30 34]]

POTE generator: ~3/2 = 700.842

Optimal GPV sequence: 12e, 101cde, 113, 125f, 238cfi

#### 31-limit

Subgroup: 2.3.5.7.11.13.17.19.23.29.31

Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493

Mapping: [1 0 34 63 -90 -66 -7 9 -43 -49 -79], 0 1 -20 -38 59 44 7 -3 30 34 53]]

POTE generator: ~3/2 = 700.838

Optimal GPV sequence: 12e, 101cdek, 113, 125f, 238cfi

### Gracecord

Subgroup: 2.3.5.7.11

Comma list: 225/224, 441/440, 109375/107811

Mapping: [1 0 34 63 89], 0 1 -20 -38 -54]]

POTE generator: ~3/2 = 700.885

Optimal GPV sequence: 12, 101cd, 113

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 364/363, 441/440, 6125/6084

Mapping: [1 0 34 63 89 113], 0 1 -20 -38 -54 -69]]

POTE generator: ~3/2 = 700.890

Optimal GPV sequence: 12f, 101cdf, 113

#### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989

Mapping: [1 0 34 63 89 113 -7], 0 1 -20 -38 -54 -69 7]]

POTE generator: ~3/2 = 700.870

Optimal GPV sequence: 12f, 101cdf, 113

#### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663

Mapping: [1 0 34 63 89 113 -7 9], 0 1 -20 -38 -54 -69 7 -3]]

POTE generator: ~3/2 = 700.866

Optimal GPV sequence: 12f, 101cdf, 113

## Alphorn

Subgroup: 2.3.5.7

Comma list: 225/224, 5764801/5668704

Mapping: [1 9 0 13], 0 -16 5 -22]]

Wedgie⟨⟨16 -5 22 -45 -10 65]]

POTE generator: ~48/35 = 556.221

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 12250/11979

Mapping: [1 9 0 13 3], 0 -16 5 -22 1]]

POTE generator: ~11/8 = 556.144

Optimal GPV sequence: 28d, 41, 315cde

## Misneb

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

Subgroup: 2.3.5.7

Comma list: 225/224, 4194304/4117715

Mapping: [1 3 1 3], 0 -15 14 -2]]

Wedgie⟨⟨15 -14 2 -57 -39 44]]

POTE generator: ~16/15 = 113.235

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 1310720/1294139

Mapping: [1 3 1 3 1], 0 -15 14 -2 26]]

POTE generator: ~16/15 = 113.323

Optimal GPV sequence: 21, 32e, 53, 127, 180de

#### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 176/175, 640/637, 847/845

Mapping: [1 3 1 3 1 2], 0 -15 14 -2 26 18]]

POTE generator: ~16/15 = 113.323

Optimal GPV sequence: 21, 32e, 53, 127, 180de

### Musneb

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 66550/64827

Mapping: [1 3 1 3 6], 0 -15 14 -2 -27]]

POTE generator: ~16/15 = 113.142

Optimal GPV sequence: 32, 53, 191de, 244cddee, 297cddee

## Untriton

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

Subgroup: 2.3.5.7

Comma list: 225/224, 125000000/121060821

Mapping: [1 6 -7 -7], 0 -9 19 20]]

Wedgie⟨⟨9 -19 -20 -51 -57 7]]

POTE generator: ~7/5 = 588.641

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 22000/21609

Mapping: [1 6 -7 -7 1], 0 -9 19 20 5]]

POTE generator: ~7/5 = 588.626

Optimal GPV sequence: 51, 53

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 225/224, 275/273, 1040/1029

Mapping: [1 6 -7 -7 1 -12], 0 -9 19 20 5 32]]

POTE generator: ~7/5 = 588.654

Optimal GPV sequence: 51f, 53

## Quintannic

Subgroup: 2.3.5.7

Comma list: 225/224, 9805926501/9765625000

Mapping: [1 1 5 7], 0 5 -23 -36]]

Wedgie⟨⟨5 -23 -36 -48 -71 -19]]

POTE generator: ~10000/9261 = 139.838

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 441/440, 43923/43750

Mapping: [1 1 5 7 8], 0 5 -23 -36 -39]]

POTE generator: ~320/297 = 139.827

Optimal GPV sequence: 43, 60e, 103

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 441/440, 1001/1000, 1188/1183

Mapping: [1 1 5 7 8 3], 0 5 -23 -36 -39 6]]

POTE generator: ~13/12 = 139.812

Optimal GPV sequence: 43, 60e, 103

### 17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 273/272, 375/374, 441/440, 891/884

Mapping: [1 1 5 7 8 3 7], 0 5 -23 -36 -39 6 -25]]

POTE generator: ~13/12 = 139.815

Optimal GPV sequence: 43, 60e, 103

## Gwazy

Subgroup: 2.3.5.7

Comma list: 225/224, 5971968/5764801

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

Wedgie⟨⟨16 -10 12 -53 -26 56]]

POTE generator: ~35/32 = 162.658

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 65536/65219

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

POTE generator: ~11/10 = 162.592

Optimal GPV sequence: 22, 74, 96, 118d

## Tertiosec

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

Subgroup: 2.3.5.7

Comma list: 225/224, 14495514624/13841287201

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

Wedgie⟨⟨24 -21 6 -89 -58 73]]

POTE generator: ~15/14 = 112.283

### 11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 3840/3773, 12005/11979

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

POTE generator: ~15/14 = 112.171

Optimal GPV sequence: 21, 54, 75e