Marvel family

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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 named 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: c = 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

POTE generators: ~3/2 = 700.4075, ~5/4 = 383.6376

Minimax tuning:

[[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
[[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

Optimal GPV sequence: 9, 10, 12, 19, 31, 41, 53, 72, 197, 269c

Badness: 0.0365 × 10-3

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

Associated temperament: catakleismic

Scales: marvel9, marvel10, marvel11, marvel12, marvel19, marvel22, pump12_1, pump12_2, pump13, pump14, pump15, pump16, pump17, pump18

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

Eleven-limit 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, and
  • 243/242 gives spectacle.

Undecimal marvel (unimarv)

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]]

Map 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

POTE generators: ~3/2 = 700.3887, ~5/4 = 383.5403

Minimax tuning:

  • 11-odd-limit
[[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

Optimal GPV sequence: 9, 10, 12e, 19, 22, 31, 41, 53, 72, 166, 197e, 238c, 269ce, 341ce

Badness: 0.255 × 10-3

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

Associated temperament: catakleismic

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]]

POTE generators: ~3/2 = 699.7367, ~5/4 = 384.0613

Minimax tuning:

  • 13-odd-limit eigenmonzo subgroup: 2.11/9.13/9
  • 15-odd-limit eigenmonzo subgroup: 2.15/11.15/13

Vals: 19, 22, 31, 50, 53, 72, 103, 175f, 300ceff, 403bceeff, 578bbccdeeefff

Badness: 0.690 × 10-3

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]]

POTE generators: ~3/2 = 700.9779, ~5/4 = 383.1622

Minimax tuning:

  • 13-odd-limit eigenmonzo subgroup: 2.7.13/5
  • 15-odd-limit eigenmonzo subgroup: 2.7.15/13

Vals: 19, 22f, 31f, 41, 53, 72, 125f, 166, 238cf

Badness: 0.721 × 10-3

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

17-limit

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]]

POTE generators: ~3/2 = 700.9619, ~5/4 = 383.0310

Vals: 19, 22f, 31fg, 41, 53g, 72, 166g, 238cfg, 404ccefgg

Badness: 0.869 × 10-3

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 18], ⟨0 1 0 2 -1 4 0], ⟨0 0 1 2 -3 -2 6]]

POTE generators: ~3/2 = 700.9658, ~5/4 = 383.3063

Vals: 19g, 22f, 31f, 41g, 53, 72, 166g, 238cfg, 404ccefgg

Badness: 0.917 × 10-3

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]]

POTE generators: ~3/2 = 700.3937, ~5/4 = 383.5725

Minimax tuning:

  • 13-odd-limit eigenmonzo subgroup: 2.9/5.11/9
  • 15-odd-limit eigenmonzo subgroup: 2.7.15/13

Vals: 9, 22f, 31, 63, 72, 103, 166, 238cf, 269ce, 507bcceff, 610bcceeff

Badness: 0.862 × 10-3

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]]

POTE generators: ~3/2 = 701.9156, ~5/4 = 383.2445

Vals: 10, 19f, 22, 31, 41, 53, 94

Badness: 0.866 × 10-3

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]]

POTE generators: ~3/2 = 700.4560, ~5/4 = 382.8177

Minimax tuning:

  • 13-odd-limit eigenmonzo subgroup: 2.9/5.13/9
  • 15-odd-limit eigenmonzo subgroup: 2.3.13/5

Vals: 9, 19f, 22, 31f, 41, 63, 72, 185cf, 257cff

Badness: 0.920 × 10-3

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]]

POTE generators: ~3/2 = 699.2335, ~5/4 = 382.9775

Minimax tuning:

  • 13-odd-limit eigenmonzo subgroup: 2.9/7.13/11
  • 15-odd-limit eigenmonzo subgroup: 2.5/3.13/11

Vals: 9, 10, 19, 22f, 31, 41, 72f, 91, 122f, 163df

Badness: 0.745 × 10-3

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

POTE generators: ~15/13 = 249.7138, ~5/4 = 383.5816

Vals: 9, 10, 19, 44, 53, 72, 125f, 197ef, 269ceff

Badness: 0.9997 × 10-3

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

POTE generators: ~3/2 = 700.2593, ~5/4 = 386.5581

Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.7/5.11/9

Optimal GPV sequence: 9, 12, 19e, 22, 31, 53, 84e, 96, 127

Badness: 0.381 × 10-3

Projection pairs: 7 225/32 11 5625/512

Scales (Scala files): minerva12, minerva22x

Associated temperament: würschmidt

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]]

POTE generators: ~3/2 = 701.2342, ~5/4 = 385.9594

Minimax tuning:

  • 13-odd-limit eigenmonzo subgroup: 2.11/9.13/7
  • 15-odd-limit eigenmonzo subgroup: 2.11/9.13/7

Vals: 12f, 19e, 22, 31, 53, 84e, 118d, 171de, 202def

Badness: 0.818 × 10-3

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]]

POTE generators: ~3/2 = 703.4846, ~5/4 = 381.6033

Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.7/5.11/9

Optimal GPV sequence: 12, 19, 22, 34d, 41, 104, 157ce, 198ce, 220ce, 261ce

Projection pairs: 7 225/32 11 100/9

Associated temperament: magic

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]]

POTE generators: ~3/2 = 703.9984, ~5/4 = 381.5352

Minimax tuning: 13-odd-limit eigenmonzo subgroup: 2.11/9.13/9

Vals: 12f, 19f, 22, 29, 34d, 41, 63, 104, 179cef, 242cde, 283def, 346bcdef

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]]

POTE generators: ~3/2 = 696.1714, ~5/4 = 385.0500

Minimax tuning: 11-odd-limit eigenmonzo subgroup: 2.9/7.11

Optimal GPV sequence: 7d, 9, 10, 12, 19, 31e, 50e

Badness: 0.464 × 10-3

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]]

POTE generators: ~3/2 = 696.0103, ~5/4 = 384.6785

Minimax tuning:

  • 13-odd-limit eigenmonzo subgroup: 2.9/7.13/9
  • 15-odd-limit eigenmonzo subgroup: 2.9/7.13/9

Vals: 9, 10, 12f, 19, 31e, 50e

Badness: 0.733 × 10-3

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

Malcolm

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]]

POTE generators: ~3/2 = 701.8913, ~5/4 = 382.4083

Optimal GPV sequence: 12e, 19e, 34d, 41, 53, 60e, 94, 229c, 248ce, 289cce, 342ccee, 383cce

Badness: 1.250 × 10-3

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]]

POTE generators: ~3/2 = 701.8913, ~5/4 = 382.4083

Vals: 12e, 19e, 34d, 41, 53, 94, 429ccdeef, 523ccdeef

Badness: 1.075 × 10-3

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.

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

POTE generators: ~3/2 = 699.7981, ~5/4 = 383.5114

Minimax tuning:

[[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

Optimal GPV sequence: 10, 12, 19e, 29, 31, 41, 60e, 72, 247c, 319bcde, 391bcde, 463bccde

Badness: 0.344 × 10-3

Projection pairs: 7 225/32 11 91125/8192

Scales: prodigy11, prodigy12, prodigy29

Associated temperament: miracle

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]]

POTE generators: ~3/2 = 700.4006, ~5/4 = 381.4025

Vals: 10, 12f, 19e, 29, 31, 41, 60e, 72f, 91e, 101cd, 132def, 233ccddeef, 274ccddeff, 305ccddeeff

Badness: 0.736 × 10-3

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]]

POTE generators: ~3/2 = 700.3407, ~5/4 = 383.2592

Vals: 12f, 29, 31f, 41, 72, 185cf, 341cf, 413bcff, 526bccdff

Badness: 0.900 × 10-3

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]]

POTE generators: ~3/2 = 699.4864, ~5/4 = 384.0998

Vals: 12f, 19e, 31, 53e, 60eff, 72, 103, 175f

Badness: 0.889 × 10-3

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]]

POTE generators: ~3/2 = 699.5536, ~5/4 = 383.5696

Vals: 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff

Badness: 0.953 × 10-3

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]]

POTE generators: ~3/2 = 699.6262, ~5/4 = 383.4458

Vals: 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg

Badness: 0.772 × 10-3

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

POTE generators: ~3/2 = 700.6242, ~5/4 = 383.2978

Optimal GPV sequence: 12, 22, 34d, 50, 60e, 72, 166, 238c, 310c

Badness: 0.743 × 10-3

Spectacle

Subgroup: 2.3.5.7.11

Comma list: 225/224, 243/242

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

Mapping generators: ~2, ~11/9, ~5

POTE generators: ~11/9 = 350.0570, ~5/4 = 383.9323

Minimax tuning:

[[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

Optimal GPV sequence: 31, 41, 72, 247c, 281, 353c, 425bc, 497bc

Badness: 0.499 × 10-3

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

Scales (Scala files): spectacle31

Associated temperament: marvo

13-limit

Subgroup: 2.3.5.7.11.13

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

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

Mapping generators: ~2, ~11/9, ~5

POTE generators: ~11/9 = 349.9247, ~5/4 = 384.3505

Vals: 31, 72, 103, 175f *

* optimal patent val: 240

Badness: 1.009 × 10-3

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

POTE generators: ~231/200 = 249.8526, ~5/4 = 383.6467

Optimal GPV sequence: 19, 29, 43, 53, 72, 197e, 269ce, 341ce, 610bce

Badness: 1.54 × 10-3

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]]

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

POTE generators: ~15/13 = 249.7651, ~5/4 = 383.5558

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

Badness: 1.062 × 10-3

Artemis

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224

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

Mapping generators: ~2, ~3, ~11/10

POTE generators: ~3/2 = 699.8719, ~11/10 = 158.3232

Optimal GPV sequence: 9, 15d, 16d, 20, 22, 31, 53, 82e, 84e, 113e, 144ee

13-limit

Subgroup: 2.3.5.7.11.13

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

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

Mapping generators: ~2, ~3, ~11/10

POTE generators: ~3/2 = 698.7090, ~11/10 = 158.7117

Vals: 9, 20, 22f, 29, 31

Diana

Subgroup: 2.3.5.7.11.13

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

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

Mapping generators: ~2, ~3, ~11/10

POTE generators: ~3/2 = 700.9789, ~11/10 = 159.0048

Vals: 22, 29, 31, 53, 82e, 84e, 113e, 166ee

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

POTE generators: ~3/2 = 700.8983, ~84/55 = 739.3812

Optimal GPV sequence: 29, 31, 60e, 91e, 94, 125

Badness: 1.152 × 10-3

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

POTE generators: ~6/5 = 316.7318, ~11/8 = 549.2528

Optimal GPV sequence: 19, 34d, 53, 72, 197e, 269ce

Badness: 1.275 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 325/324

Mapping: [⟨1 0 1 -3 0 0], ⟨0 6 5 22 0 14], ⟨0 0 0 0 1 0]]

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

POTE generators: ~6/5 = 316.7410, ~11/8 = 548.6028

Vals: 19, 34d, 53, 72, 125f, 197ef, 269cef

Badness: 0.916 × 10-3

Mirage

Subgroup: 2.3.5.7.11.13

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

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

Mapping generators: ~2, ~15/14, ~13

POTE generators: ~15/14 = 116.6327, ~13/8 = 837.7040

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

Badness: 0.738 × 10-3

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