# Marvel family

(Redirected from Prodigy)

The marvel family is the set of temperaments that temper out the 7-limit marvel comma (225/224 = [-5 2 2 -1) which is also known as septimal kleisma. These temperaments hence equate 16/15 and 15/14, or equivalently they equate two 5/4's and one 14/9. The marvel comma is noteworthy in that it is tempered out by many common edos and rank-2 temperaments.

The marvel comma can also be viewed as a comma of the 2.9.25.7 subgroup. Hence it is tempered out by any subset edos of marvel-supporting edos that have this subgroup, such as 11edo and 17edo which are subsets of 22edo and 34edo (when using the 34b val) which temper out the marvel comma.

## Marvel

Main article: Marvel

The head of the marvel family is marvel, which tempers out 225/224. Marvel has a normal list basis of [2, 3, 5]; hence a 5-limit scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by 197edo.

Little is gained in tuning accuracy by not tempering out 4375/4374 as well as 225/224, leading to catakleismic temperament. Another temperament which does little damage to tuning accuracy is compton temperament, for which 240edo may be used. See marvel temperaments for some other rank-2 temperaments.

Subgroup: 2.3.5.7

Comma list: 225/224

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

mapping generators: ~2, ~3, ~5

Map to lattice: [0 0 -1 -2], 0 1 -1 0]]

Lattice basis:

secor length = 1.256, 3/2 length = 1.369
Angle (secor, 3/2) = 106.958 degrees

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.4075, ~5/4 = 383.6376

[[1 0 0 0, [5/4 1/2 -1/2 1/4, [5/4 -1/2 1/2 1/4, [0 0 0 1]
eigenmonzo (unchanged-interval) basis: 2.5/3.7
• 9-odd-limit: 3 1/6-comma flat, 5 1/3-comma flat, 7 just
[[1 0 0 0, [5/6 2/3 -1/3 1/6, [5/3 -2/3 1/3 1/3, [0 0 0 1]
eigenmonzo (unchanged-interval) basis: 2.9/5.7

Projection pairs: 7 225/32

Complexity spectrum: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9

Minkowski blocks

2.3.5 subgroup

• 8: 16/15, 250/243
• 9: 135/128, 128/125
• 10: 25/24, 2048/2025
• 11: 135/128, 2048/1875
• 12: 2048/2025, 128/125
• 15: 128/125, 32768/30375
• 17: 25/24, 2278125/2097152
• 19: 16875/16384, 81/80
• 21: 128/125, 273375/262144
• 22: 2048/2025, 3125/3072
• 29: 16875/16384, 32805/32768
• 31: 81/80, 34171875/33554432
• 41: 34171875/33554432, 3125/3072

### Overview to extensions

The second comma of the normal comma list defines which 11-limit family member we are looking at. 4125/4096 gives unidecimal marvel; 91125/90112 gives prodigy; 5632/5625 gives minerva. These and many others considered below use the same generators as marvel.

Temperaments discussed elsewhere include

## Undecimal marvel (unimarv)

Main article: Marvel

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384

Mapping[1 0 0 -5 12], 0 1 0 2 -1], 0 0 1 2 -3]]

Mapping to lattice: [0 -1 0 -2 1], 0 -1 1 0 -2]]

Lattice basis:

secor length = 1.0364, 5/4 length = 1.0759
Angle (secor, 5/4) = 104.028 degrees

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.3887, ~5/4 = 383.5403

[[1 0 0 0 0, [4/3 8/9 -1/3 0 -1/9, [8/3 -2/9 1/3 0 -2/9, [3 4/3 0 0 -2/3, [8/3 -2/9 -2/3 0 7/9]
eigenmonzo (unchanged-interval) basis: 2.9/5.11/9

Projection pairs: 7 225/32 11 4096/375

Complexity spectrum: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11

Scales: marvel22_11, unimarv19, unimarv22

Hobbit bases

2.3.5 subgroup

• 12: 128/125, 2048/2025
• 15: 128/125, 32768/30375
• 19: 16875/16384, 81/80
• 22: 2048/2025, 2109375/2097152
• 31: 2109375/2097152, 81/80
• 41: 3125/3072, 34171875/33554432

### 13-limit

Subgroup: 2.3.5.7.11.13

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

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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.7367, ~5/4 = 384.0613

Minimax tuning:

• 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/9
• 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.15/11.15/13

Complexity spectrum: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11

### Hecate

Subgroup: 2.3.5.7.11.13

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

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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.9779, ~5/4 = 383.1622

Minimax tuning:

• 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.7.13/5
• 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7.15/13

Projection pairs: 7 225/32 11 4096/375 13 324/25

Complexity spectrum: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11

#### 2.3.5.7.11.13.19 subgroup

Subgroup: 2.3.5.7.11.13.19

Comma list: 225/224, 325/324, 385/384, 400/399

Sval mapping: [1 0 0 -5 12 2 9], 0 1 0 2 -1 4 -3], 0 0 1 2 -3 -2 0]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.4245, ~5/4 = 383.0293

#### Apotropaia

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 325/324, 385/384, 595/594

Mapping: [1 0 0 -5 12 2 18], 0 1 0 2 -1 4 0], 0 0 1 2 -3 -2 -6]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.5860, ~5/4 = 382.7331

##### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

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

Mapping: [1 0 0 -5 12 2 18 9], 0 1 0 2 -1 4 0 -3], 0 0 1 2 -3 -2 -6 0]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.4435, ~5/4 = 382.7395

#### Enodia

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [1 0 0 -5 12 2 -13], 0 1 0 2 -1 4 2], 0 0 1 2 -3 -2 6]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.6270, ~5/4 = 383.3456

##### 19-limit

Subgroup: 2.3.5.7.11.13.17.19

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

Mapping: [1 0 0 -5 12 2 -13 9], 0 1 0 2 -1 4 2 -3], 0 0 1 2 -3 -2 6 0]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.4791, ~5/4 = 383.3795

### Marvell

Subgroup: 2.3.5.7.11.13

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

Mapping: [1 0 0 -5 12 -29], 0 1 0 2 -1 6], 0 0 1 2 -3 10]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.3937, ~5/4 = 383.5725

Minimax tuning:

• 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/5.11/9
• 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7.15/13

### Isis

Subgroup: 2.3.5.7.11.13

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

Mapping: [1 0 0 -5 12 17], 0 1 0 2 -1 4], 0 0 1 2 -3 -3]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.9156, ~5/4 = 383.2445

Projection pairs: 7 225/32 11 4096/375 13 131072/10125

### Deecee

Subgroup: 2.3.5.7.11.13

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

Mapping: [1 0 0 -5 12 27], 0 1 0 2 -1 -3], 0 0 1 2 -3 -8]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.4560, ~5/4 = 382.8177

Minimax tuning:

• 13-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.9/5.13/9
• 15-odd-limit eigenmonzo subgroup (unchanged-interval basis): 2.3.13/5

Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875

### Tripod

Subgroup: 2.3.5.7.11.13

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

Mapping: [1 0 0 -5 12 -8], 0 1 0 2 -1 3], 0 0 1 2 -3 3]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.2335, ~5/4 = 382.9775

Minimax tuning:

• 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/7.13/11
• 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.5/3.13/11

Projection pairs: 7 225/32 11 4096/375 13 3375/256

### Marvelcat

Subgroup: 2.3.5.7.11.13

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

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

mapping generators: ~2, ~26/15, ~5

Optimal tuning (POTE): ~2 = 1\1, ~15/13 = 249.7138, ~5/4 = 383.5816

## Minerva

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175

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

Map to lattice: [0 -1 0 -2 -2], 0 -1 1 0 2]]

Lattice basis:

16/15 length = 0.8997, 5/4 length = 1.0457
Angle (16/15, 5/4) = 98.6044 degrees

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.2593, ~5/4 = 386.5581

Projection pairs: 7 225/32 11 5625/512

Scales: minerva12, minerva22x

### Athene

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 176/175, 275/273

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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.2342, ~5/4 = 385.9594

Minimax tuning:

• 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/7
• 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/7

Projection pairs: 7 225/32 11 5625/512 13 625/48

## Apollo

Subgroup: 2.3.5.7.11

Comma list: 100/99, 225/224

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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.4846, ~5/4 = 381.6033

Projection pairs: 7 225/32 11 100/9

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 225/224, 275/273

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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.9984, ~5/4 = 381.5352

Minimax tuning: 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.11/9.13/9

Projection pairs: 7 225/32 11 100/9 13 3200/243

## Potassium

Subgroup: 2.3.5.7.11

Comma list: 45/44, 56/55

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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.1714, ~5/4 = 385.0500

Projection pairs: 7 225/32 11 45/4

### 13-limit

Subgroup: 2.3.5.7.11.13

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

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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 696.0103, ~5/4 = 384.6785

Minimax tuning:

• 13-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/7.13/9
• 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.9/7.13/9

Projection pairs: 7 225/32 11 45/4 13 3375/256

## Malcolm

"Malcolm" redirects here. For Alexander Malcolm's JI scale, see Malcolm (scale).

Subgroup: 2.3.5.7.11

Comma list: 225/224, 2200/2187

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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.8913, ~5/4 = 382.4083

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 275/273, 325/324

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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.8913, ~5/4 = 382.4083

Scales: malco

## Prodigy

Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to miracle. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.

Subgroup: 2.3.5.7.11

Comma list: 225/224, 441/440

Mapping[1 0 0 -5 -13], 0 1 0 2 6], 0 0 1 2 3]]

Map to lattice: [0 0 -1 -2 -3], 0 1 -1 0 3]]

Lattice basis:

secor length = 0.9111, 3/2 length = 0.9477
Angle (secor, 3/2) = 65.933

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.7981, ~5/4 = 383.5114

[[1 0 0 0 0, [13/12 1/2 -1/4 0 1/12, [13/6 -1 1/2 0 1/6, [3/2 -1 1/2 0 1/2, [0 0 0 0 1]
eigenmonzo (unchanged-interval) basis: 2.9/5.11

Projection pairs: 7 225/32 11 91125/8192

Scales: prodigy11, prodigy12, prodigy29

Hobbit bases

2.3.5 subgroup

• 31: 81/80, 34171875/33554432
• 41: 34171875/33554432, 32805/32768

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 196/195, 352/351

Mapping: [1 0 0 -5 -13 -8], 0 1 0 2 6 3], 0 0 1 2 3 3]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.4006, ~5/4 = 381.4025

### Prodigious

Subgroup: 2.3.5.7.11.13

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

Mapping: [1 0 0 -5 -13 -23], 0 1 0 2 6 11], 0 0 1 2 3 4]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.3407, ~5/4 = 383.2592

### Prodigal

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 351/350, 441/440

Mapping: [1 0 0 -5 -13 -4], 0 1 0 2 6 -1], 0 0 1 2 3 4]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.4864, ~5/4 = 384.0998

### Protannic

Subgroup: 2.3.5.7.11.13

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

Mapping: [1 0 0 -5 -13 21], 0 1 0 2 6 -8], 0 0 1 2 3 -2]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.5536, ~5/4 = 383.5696

#### 17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [1 0 0 -5 -13 21 12], 0 1 0 2 6 -8 -5], 0 0 1 2 3 -2 0]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.6262, ~5/4 = 383.4458

## Fantastic

Subgroup: 2.3.5.7.11

Comma list: 225/224, 4375/4356

Mapping[2 0 0 -10 -7], 0 1 0 2 0], 0 0 1 2 3]]

mapping generators: ~99/70, ~3, ~5

Optimal tuning (POTE): ~99/70 = 1\2, ~3/2 = 700.6242, ~5/4 = 383.2978

## Hestia

Subgroup: 2.3.5.7.11

Comma list: 225/224, 125000/124509

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

mapping generators: ~2, ~400/231, ~5

Optimal tuning (POTE): ~2 = 1\1, ~400/231 = 950.1474, ~5/4 = 383.6467

### 13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 1001/1000

Mapping: [1 0 0 -5 9 -1], 0 2 0 4 -7 3], 0 0 1 2 0 1]]

Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 950.2349, ~5/4 = 383.5558

## Morfil

Subgroup: 2.3.5.7.11

Comma list: 225/224, 1331/1323

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

mapping generators: ~2, ~3, ~84/55

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.8983, ~84/55 = 739.3812

## Catakleismoid

Subgroup: 2.3.5.7.11

Comma list: 225/224, 4375/4374

Mapping[1 0 1 -3 0], 0 6 5 22 0], 0 0 0 0 1]]

mapping generators: ~2, ~6/5, ~11

Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 316.7318, ~11/8 = 549.2528