Marvel family
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
- 7-odd-limit: 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-odd-limit: 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
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
{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
- 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
{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
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
- [[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
{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
- [[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
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
* 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
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