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 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.

Period: 1\1

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

EDO generators: (11, 6)\19, (18, 10)\31, (24, 13)\41

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

Associated temperament: catakleismic

Technical data

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

Minimax tuning:

• 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

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

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.

11-limit (unimarv)

Period: 1\1

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

EDO generators: (13, 7)\22, (18, 10)\31, (24, 13)\41

Scales (Scala files): marvel22_11, unimarv19, unimarv22

Associated temperament: catakleismic

Technical data

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

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

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

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

Period: 1\1

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

EDO generators: (18, 10)\31, (31, 17)\53, (42, 23)\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

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

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

Minimax tuning:

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

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

Period: 1\1

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

EDO generators: (24, 13)\41, (31, 17)\53, (42, 23)\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

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

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

Minimax tuning:

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

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

Period: 1\1

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

EDO generators: (13, 7)\22, (24, 13)\41, (42, 23)\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13.17

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

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

Badness: 0.869 × 10^-3

Enodia

Period: 1\1

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

EDO generators: (13, 7)\22, (31, 17)\53, (42, 23)\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13.17

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

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

Badness: 0.917 × 10^-3

Marvell

Period: 1\1

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

EDO generators: (5, 3)\9, (18, 10)\31, (42, 23)\72

Scales (Scala files):

Technical data

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]]

Minimax tuning:

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

Badness: 0.862 × 10^-3

Isis

Period: 1\1

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

EDO generators: (13, 7)\22, (18, 10)\31, (24, 13)\41

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

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

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

Badness: 0.866 × 10^-3

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

Deecee

Period: 1\1

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

EDO generators: (5, 3)\9, (24, 13)\41, (42, 23)\72

Scales (Scala files):

Technical data

Subgroup: 2.3.5.7.11.13

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

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

Minimax tuning:

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

Badness: 0.920 × 10^-3

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

Tripod

Period: 1\1

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

EDO generators: (5, 3)\9, (11, 6)\19, (18, 10)\31

Scales (Scala files):

Technical data

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]]

Minimax tuning:

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

Badness: 0.745 × 10^-3

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

Marvelcat

Period: 1\1

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

EDO generators: (5, 3)\9, (11, 6)\19, (31, 17)\53

Scales (Scala files):

Technical data

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

Badness: 0.9997 × 10^-3

Minerva

Period: 1\1

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

EDO generators: (7, 4)\12, (13, 7)\22, (18, 10)\31

Scales (Scala files): minerva12, minerva22x

Associated temperament: würschmidt

Technical data

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

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

Badness: 0.381 × 10^-3

Projection pairs: 7 225/32 11 5625/512

Athene

Period: 1\1

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

EDO generators: (7, 4)\12, (11, 6)\19, (13, 7)\22

Scales (Scala files):

Technical data

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]]

Minimax tuning:

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

Badness: 0.818 × 10^-3

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

Apollo

Period: 1\1

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

EDO generators: (7, 4)\12, (11, 6)\19, (13, 7)\22

Scales (Scala files):

Associated temperament: magic

Technical data

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]]

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

Projection pairs: 7 225/32 11 100/9

13-limit

Period: 1\1

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

EDO generators: (7, 4)\12, (13, 7)\22, (17, 9)\29

Scales (Scala files):

Technical data

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]]

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

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

Potassium

Period: 1\1

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

EDO generators: (4, 2)\7, (5, 3)\9, (7, 4)\12

Scales (Scala files):

Technical data

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]]

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

Badness: 0.464 × 10^-3

Projection pairs: 7 225/32 11 45/4

13-limit

Period: 1\1

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

EDO generators: (5, 3)\9, (6, 3)\10, (7, 4)\12

Scales (Scala files):

Technical data

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]]

Minimax tuning:

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

Badness: 0.733 × 10^-3

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

Malcolm

Period: 1\1

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

EDO generators: (11, 6)\19, (24, 13)\41, (31, 17)\53

Scales (Scala files):

Technical data

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]]

Badness: 1.250 × 10^-3

13-limit

Period: 1\1

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

EDO generators: (11, 6)\19, (24, 13)\41, (31, 17)\53

Scales (Scala files):

Technical data

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]]

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.

Period: 1\1

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

EDO generators: (7, 4)\12, (18, 10)\31, (24, 13)\41

Scales (Scala files): prodigy11, prodigy12, prodigy29

Associated temperament: miracle

Technical data

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

Minimax tuning:

• 11-odd-limit

[[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

Badness: 0.344 × 10^-3

Projection pairs: 7 225/32 11 91125/8192

Hobbit bases

{2, 3, 5} subgroup

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

13-limit

Period: 1\1

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

EDO generators: (6, 3)\10, (7, 4)\12, (11, 6)\19

Scales (Scala files):

Technical data

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]]

Badness: 0.736 × 10^-3

Prodigious

Period: 1\1

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

EDO generators: (7, 4)\12, (24, 13)\41, (42, 23)\72

Scales (Scala files):

Technical data

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]]

Badness: 0.900 × 10^-3

Prodigal

Period: 1\1

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

EDO generators: (11, 6)\19, (18, 10)\31, (42, 23)\72

Scales (Scala files):

Technical data

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]]

Badness: 0.889 × 10^-3

Fantastic

Period: 1\2

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

EDO generators: (7, 4)\12, (13, 7)\22, (42, 23)\72

Scales (Scala files):

Technical data

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

Badness: 0.743 × 10^-3

Spectacle

Period: 1\1

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

EDO generators: (9, 10)\31, (10, 11)\34, (12, 13)\41

Scales (Scala files): spectacle31

Associated temperament: marvo

Technical data

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

Minimax tuning:

• 11-odd-limit

[[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

Badness: 0.499 × 10^-3

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

13-limit

Period: 1\1

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

EDO generators: (9, 10)\31, (10, 11)\34, (21, 23)\72

Scales (Scala files):

Technical data

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

Badness: 1.009 × 10^-3

Hestia

Period: 1\1

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

EDO generators: (6, 9)\29, (11, 17)\53, (15, 23)\72

Scales (Scala files):

Technical data

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

Badness: 1.54 × 10^-3

13-limit

Period: 1\1

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

EDO generators: (4, 6)\19, (6, 9)\29, (11, 17)\53

Scales (Scala files):

Technical data

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

Badness: 1.062 × 10^-3

Artemis

Period: 1\1

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

EDO generators: (4, 2)\7, (13, 7)\22, (18, 10)\31

Scales (Scala files):

Technical data

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

13-limit

Period: 1\1

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

EDO generators: (5, 3)\9, (17, 9)\29, (18, 10)\31

Scales (Scala files):

Technical data

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

Diana

Period: 1\1

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

EDO generators: (13, 7)\22, (17, 9)\29, (18, 10)\31

Scales (Scala files):

Technical data

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

Catakleismoid

Period: 1\1

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

EDO generators: (5, 8)\19, (14, 24)\53, (19, 33)\72

Scales (Scala files):

Technical data

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

Badness: 1.275 × 10^-3

13-limit

Period: 1\1

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

EDO generators: (5, 8)\19, (14, 24)\53, (19, 33)\72

Scales (Scala files):

Technical data

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

Badness: 0.916 × 10^-3

Mirage

Period: 1\1

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

EDO generators: (3, 22)\31, (4, 29)\41, (7, 50)\22

Scales (Scala files):

Technical data

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

Badness: 0.738 × 10^-3