# Marvel family

(Redirected from Isis)

The marvel family is the set of temperaments that temper out the 7-limit comma 225/224 = [-5 2 2 -1, the septimal kleisma or marvel comma. 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 which temper out the marvel comma.

# 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.

## Vital statistics

Comma c = 225/224

Related linear temperament: catakleismic temperament

7-limit minimax: 3 and 5 1/4c flat, 7 just

[|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 subgroup: 2.5/3.7

9-limit minimax: 3 1/6c flat, 5 1/3c 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 subgroup: 2.9/5.7

Lattice basis: secor length 1.256, 3/2 length 1.369

Angle(secor, 3/2) = 106.958 degrees

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

Map: [<1 0 0 -5|, <0 1 0 2|, <0 0 1 2|]

Generators: 2, 3, 5

EDOs: 10, 12, 19, 22, 31, 41,72, 197, 269c

Projection pairs: 7 225/32

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

## 11-limit (Unimarv)

Commas: 225/224, 385/384

Related linear temperament: catakleismic temperament

[|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 subgroup: 2.9/5.11/9

Lattice basis: secor length 1.0364 5/4 length 1.0759

Angle(secor, 5/4) = 104.028 degrees

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

Map: [<1 0 0 -5 12|, <0 1 0 2 -1|, <0 0 1 2 -3|]

Generators: 2, 3, 5

Edos: 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 269ce, 341ce

Projection pairs: 7 225/32 11 4096/375

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

Commas: 225/224, 385/384, 351/350

13-limit eigenmonzo subgroup: 2.11/9.13/9

15-limit eigenmonzo subgroup: 2.15/11.15/13

Map: [<1 0 0 -5 12 -4|, <0 1 0 2 -1 -1|, <0 0 1 2 -3 4|]

EDOs: 19, 22, 31, 50, 53, 72, 103, 175f, 300cef, 403bcef

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

Commas: 225/224, 385/384, 325/324

13-limit eigenmonzo subgroup: 2.7.13/5

15-limit eigenmonzo subgroup: 2.7.15/13

Map: [<1 0 0 -5 12 2|, <0 1 0 2 -1 4|, <0 0 1 2 -3 -2|]

EDOs: 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef

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

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

## 17-limit

Commas: 225/224, 385/384, 325/324, 595/594

Map: [<1 0 0 -5 12 2 18|, <0 1 0 2 -1 4 0|, <0 0 1 2 -3 -2 -6|]

EDOs: 19, 41, 53g, 72, 113, 166g, 238cfg, 351cfg, 404cefg

## Enodia

Commas: 225/224, 385/384, 325/324, 375/374

Map: [<1 0 0 -5 12 2 18|, <0 1 0 2 -1 4 0|, <0 0 1 2 -3 -2 6|]

EDOs: 41g, 53, 72, 125f, 166g, 238cfg, 363cefg, 404cefg

# Marvelcat

Commas: 169/168, 225/224, 385/384

Map: [<1 0 0 -5 12 -|, <0 2 0 4 -2 3|, <0 0 1 2 -3 1|]

EDOs: 9, 10, 19, 44, 53, 72, 125f, 197ef, 269cef

# Marvell

Commas: 225/224, 385/384, 1573/1568

13-limit eigenmonzo subgroup: 2.9/5.11/9

15-limit eigenmonzo subgroup: 2.7.15/13

Map: [<1 0 0 -5 12 -29|, <0 1 0 2 -1 6|, <0 0 1 2 -3 10|]

EDOs: 9, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcef, 610bcef

# Isis

Commas: 225/224, 385/384, 275/273

Map: [<1 0 0 -5 12 17|, <0 1 0 2 -1 4|, <0 0 1 2 -3 -3|]

EDOs: 10, 22, 31, 41, 53, 94

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

# Deecee

Commas: 225/224, 385/384, 364/363

13-limit eigenmonzo subgroup: 2.9/5.13/9

15-limit eigenmonzo subgroup: 2.3.13/5

Map: [<1 0 0 -5 12 27|, <0 1 0 2 -1 -3|, <0 0 1 2 -3 -8|]

EDOs: 9, 22, 41, 63, 72, 185cf, 257cf

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

# Mirage

Commas: 225/224, 243/242, 385/384

Map: [<1 1 3 3 2 0|, <0 6 -7 -2 15 0|, <0 0 0 0 0 1|]

EDOs: 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef

# Minerva

Commas: 99/98, 176/175

Related linear temperament: orwell

Eigenmonzo subgroup: 2.7/5.11/9

Lattice basis: 16/15 length 0.8997 5/4 length 1.0457

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

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

Map: [<1 0 0 -5 -9|, <0 1 0 2 2|, <0 0 1 2 4|]

Generators: 2, 3, 5

EDOs: 9, 12, 21, 22, 31, 43, 53, 74, 75, 96, 127

Projection pairs: 7 225/32 11 5625/512

Scales: minerva12, minerva22x

## Athene

Commas: 99/98, 176/175, 275/273

13-limit eigenmonzo subgroup: 2.11/9.13/7

15-limit eigenmonzo subgroup: 2.11/9.13/7

Map: [<1 0 0 -5 -9 -4|, <0 1 0 2 2 -1|, <0 0 1 2 4 4|]

EDOs: 22, 31, 53, 84e, 118d, 149df, 171de, 202def

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

## Other eleven limit marvel children

The second comma of the normal comma list defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.

# Spectacle

Commas: 225/224, 243/242

Related linear temperament: marvo

[|1 0 0 0 0>, |1/5 0 0 0 2/5>, |2/5 -2 1 0 4/5>, |-19/5 -4 2 0 12/5>, |0 0 0 0 1>]

Eigenmonzo subgroup: 2.9/5.11

Map: [<1 1 0 -3 2|, <0 2 0 4 5|, <0 0 1 2 0|]

Generators: 2, 11/9, 5

EDOs: 10, 31, 41, 72, 240, 259b, 269ce, 310c, 331bc, 353c, 497bc, 569bc

Projection pairs: 3 242/81 7 366025/52488 11 644204/59049 to 2.5.11/9

Scales: spectacle31

## 13-limit

Commas: 225/224, 243/242, 351/350

Map: [<1 1 0 -3 2 -5|, <0 2 0 4 5 -2|, <0 0 1 2 0 4|]

EDOs: 31, 72, 103, 175f, 209, 240

# Apollo

Commas: 100/99, 225/224

Related linear temperament: Magic

Eigenmonzo subgroup: 2.7/5.11/9

Map: [<1 0 0 -5 2|, <0 1 0 2 -2|, <0 0 1 2 2|]

EDOs: 12, 19, 22, 41, 104edo, 157ce, 198ce, 220ce, 261ce

Projection pairs: 7 225/32 11 100/9

## 13-limit

Commas: 100/99, 225/224, 245/243

Eigenmonzo subgroup: 2.11/9.13/9

Map: [<1 0 0 -5 2 7|, <0 1 0 2 -2 -5|, <0 0 1 2 2 2|]

EDOs: 22, 29, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef

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

# Potassium

Commas: 45/44, 56/55

Eigenmonzo subgroup: 2.9/7.11

Map: [<1 0 0 -5 -2|, <0 1 0 2 2|, <0 0 1 2 1|]

EDOs: 9, 10, 12, 19, 31e, 50e

Projection pairs: 7 225/32 11 45/4

## 13-limit

Commas: 45/44, 56/55, 78/77

13-limit eigenmonzo subgroup: 2.9/7.13/9

15-limit eigenmonzo subgroup: 2.9/7.13/9

Map: [<1 0 0 -5 -2 -8|, <0 1 0 2 2 3|, <0 0 1 2 1 3|]

EDOs: 9, 10, 19, 31e, 50e

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

# Fantastic

Commas: 225/224, 4375/4356

Map: [<2 0 0 -10 -7|, <0 1 0 2 0|, <0 0 1 2 3|]

EDOs: 12, 22, 50, 72, 166, 238c, 310c

# Catakleismoid

Commas: 225/224, 4375/4374

Map: [<1 0 1 -3 0|, <0 6 5 22 0|, <0 0 0 0 1|]

EDOs: 19, 53, 72, 197e, 269ce

## 13-limit

Commas: 169/168, 225/224, 325/324

Map: [<1 0 1 -3 0 0|, <0 6 5 22 0 14|, <0 0 0 0 1 0|]

EDOs: 19, 53, 72, 125f, 197ef, 269cef

# Hestia

Commas: 225/224, 125000/124509

Map: [<1 0 0 -5 9|, <0 2 0 4 -7|, <0 0 1 2 0|]

EDOs: 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce

## 13-limit

Commas: 169/168, 225/224, 1001/1000

Map: [<1 0 0 -5 9 -1|, <0 2 0 4 -7 3|, <0 0 1 2 0 1|]

EDOs: 19, 29, 43, 53, 72, 125f, 197ef, 269cef

# Malcolm

Commas: 225/224, 2200/2187

Map: [<1 0 0 -5 -3|, <0 1 0 2 7|, <0 0 1 2 -2|]

EDOs: 41, 53, 94, 229c, 248ce, 289ce, 342ce, 383ce

## 13-limit

commas: 225/224, 275/273, 325/324

Map: [<1 0 0 -5 -3 2|, <0 1 0 2 7 4|, <0 0 1 2 -2 -2|]

EDOs: 41, 53, 94, 429cdef, 523cdef

# Tripod

Commas: 105/104, 144/143, 196/195

13-limit eigenmonzo subgroup: 2.9/7.13/11

15-limit eigenmonzo subgroup: 2.5/3.13/11

Map: [<1 0 0 -5 12 -8|, <0 1 0 2 -1 3|, <0 0 1 2 -3 3|]

EDOs: 9, 10, 19, 31, 41, 72f, 81, 91, 122f, 163df

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

# 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 temperament. 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.

Commas: 225/224, 441/440

Related linear temperament: miracle

[|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 subgroup: 2.9/5.11

Lattice basis: secor length 0.9111, 3/2 length 0.9477

Angle(secor, 3/2) = 65.933

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

Map: [<1 0 0 -5 -13|, <0 1 0 2 6|, <0 0 1 2 3|]

Generators: 2, 3, 5

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

Commas: 105/104, 196/195, 352/351

Map: [<1 0 0 -5 -13 -8|, <0 1 0 2 6 3|, <0 0 1 2 3 3|]

EDOs: 10, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233cdef, 274cdef, 305cdef

## Prodigious

Commas: 225/224, 441/440, 364/363

Map: [<1 0 0 -5 -13 -23|, <0 1 0 2 6 11|, <0 0 1 2 3 4|]

EDOs: 29, 41, 72, 113, 185cf, 341cf, 413bcf, 526bcdf