High badness temperaments
Below are listed some high-badness temperaments (badness > 0.2). Most of these are 5-limit temperaments which have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. You may find other high-badness temperaments in:
Absurdity
Subgroup: 2.3.5
Comma: 10460353203/10240000000
Mapping: [⟨7 0 -17], ⟨0 1 3]]
POTE generator: ~10/9 = 185.901
Optimal ET sequence: 7, 70, 77, 84, 329, 413b, 497b
Badness: 0.341202
Archaeotherium
Subgroup: 2.3.5
Comma: 597871125/536870912
Mapping: [⟨1 1 5], ⟨0 3 -14]]
POTE generator: ~1215/1024 = 230.351
Optimal ET sequence: 21, 26, 73bc, 99bc
Badness: 1.434855
Beatles
Subgroup: 2.3.5
Comma: 524288/492075
Mapping: [⟨1 1 5], ⟨0 2 -9]]
POTE generator: ~512/405 = 355.930
Optimal ET sequence: 10, 17c, 27, 64b, 91bc, 118bc
Badness: 0.358542
Bohpier
Subgroup: 2.3.5
Comma: 1220703125/1162261467
Mapping: [⟨1 0 0], ⟨0 13 19]]
POTE generator: ~27/25 = 146.476
Optimal ET sequence: 8, 41, 131, 172, 213c
Badness: 0.860534
Casablanca
Subgroup: 2.3.5
Comma: 20061226008576/19073486328125
Mapping: [⟨1 -7 -14], ⟨0 19 14]]
POTE generator: ~864/625 = 542.208
Optimal ET sequence: 11b, 20b, 31, 73, 104c, 135c
Badness: 1.423736
Chromo
Subgroup: 2.3.5
Comma: 1220703125/1146617856
Mapping: [⟨1 1 2], ⟨0 13 7]]
POTE generator: ~25/24 = 53.922
Optimal ET sequence: 22, 45, 67c, 89c
Badness: 0.842835
Comic
Subgroup: 2.3.5
Comma: 5120000/4782969
Mapping: [⟨2 1 -3], ⟨0 2 7]]
POTE generator: ~81/80 = 55.382
Optimal ET sequence: 20c, 22, 86b, 108b, 130b
Badness: 0.491181
Cotoneum
Subgroup: 2.3.5
Comma: [80 -49 -1⟩
Mapping: [⟨1 2 -18], ⟨0 -1 49]]
POTE generator: ~3/2 = 702.315
Optimal ET sequence: 41, 135c, 176, 217, 475, 1167, 1642, 2117b
Badness: 1.240078
Counterhanson
Subgroup: 2.3.5
Comma: [-20 -24 25⟩ = 298023223876953125/296148833645101056
Mapping: [⟨1 -5 -4], ⟨0 25 24]]
POTE generator: ~6/5 = 316.081
Optimal ET sequence: 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c
Badness: 0.317551
Countermeantone
Subgroup: 2.3.5
Comma: [10 23 -20⟩ = 96402615118848/95367431640625
Mapping: [⟨1 10 12], ⟨0 -20 -23]]
POTE generator: ~104976/78125 = 504.913
Optimal ET sequence: 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c
Badness: 0.373477
Countritonic
- For extensions, see Ragismic microtemperaments #Countritonic and Hemifamity temperaments #Countriton.
Subgroup: 2.3.5
Comma: 16777216000000000/16677181699666569
Mapping: [⟨1 6 19], ⟨0 -9 -34]]
POTE generator: ~14348907/10240000 = 588.636
Optimal ET sequence: 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b
Badness: 0.255594
Cypress
Subgroup: 2.3.5
Comma: 258280326/244140625
Mapping: [⟨1 7 10], ⟨0 -12 -17]]
POTE generator: ~4374/3125 = 541.726
Optimal ET sequence: 11c, 20c, 31, 113c, 144c, 175c, 381bcc
Badness: 0.816635
Delorean
Subgroup: 2.3.5
Comma: 17496/15625
Mapping: [⟨1 3 4], ⟨0 -6 -7]]
POTE generator: ~6/5 = 284.293
Optimal ET sequence: 4, 17c, 21, 38c
Badness: 0.355937
Diesic
Subgroup: 2.3.5
Comma: 10460353203/9765625000
Mapping: [⟨1 2 3], ⟨0 -13 -21]]
POTE generator: ~6561/6250 = 38.571
Optimal ET sequence: 31, 156c, 187c, 218bc, 249bc, 280bc
Badness: 1.344681
Dodifo
Subgroup: 2.3.5
Comma: [-67 -9 35⟩
Mapping: [⟨1 12 5], ⟨0 -35 -9]]
POTE generator: ~768/625 = 357.088
Optimal ET sequence: 37, 84, 205, 289, 494, 783, 2060, 2843, 3626
Badness: 0.213112
Elvis
Subgroup: 2.3.5
Comma: 36905625/33554432
Mapping: [⟨2 1 10], ⟨0 2 -5]]
POTE generator: ~45/32 = 554.546
Optimal ET sequence: 26, 80bc, 106bc, 132bc
Badness: 0.884000
Emka
- See also: Hemimean clan #Emka and Horwell temperaments #Emkay
Subgroup: 2.3.5
Comma: [-50 -8 27⟩
Mapping: [⟨1 14 6], ⟨0 -27 -8]]
POTE generator: ~9765625/7077888 = 551.784
Optimal ET sequence: 37, 50, 87, 137, 224
Badness: 0.544752
Fervor
Subgroup: 2.3.5
Comma: 67108864/61509375
Mapping: [⟨1 4 -2], ⟨0 -5 9]]
POTE generator: ~64/45 = 577.705
Optimal ET sequence: 2, 25, 27
Badness: 0.852612
Gamera
Subgroup: 2.3.5
Comma: 12207031250000000000/12157665459056928801
Mapping: [⟨1 6 10], ⟨0 -23 -40]]
Optimal tuning (CWE): ~2 = 1\1, ~2500/2187 = 230.345
Supporting ETs: 99, 323, 224, 26, 125, 547, 5bccc, 422, 73, 870, 21bcc, 47bc, 771, 349
Badness (Sintel): 6.394
Genocchi
Subgroup: 2.3.5
Comma: 2359296/1953125
Mapping: [⟨1 0 2], ⟨0 9 2]]
POTE generator: ~768/625 = 212.444
Optimal ET sequence: 6b, 11b, 17c
Badness: 1.404977
Gracecordial
- See also: Marvel temperaments #Gracecordial
Subgroup: 2.3.5
Comma: 17433922005/17179869184
Mapping: [⟨1 0 34], ⟨0 1 -20]]
POTE generator: ~3/2 = 700.734
Optimal ET sequence: 12, 113, 125, 137
Badness: 0.306809
Hemififths
Subgroup: 2.3.5
Comma: 858993459200/847288609443
Mapping: [⟨1 1 -5], ⟨0 2 25]]
POTE generator: ~655360/531441 = 351.476
Optimal ET sequence: 41, 58, 99, 239, 338, 915b, 1253bc
Badness: 0.372848
Hogzilla
Subgroup: 2.3.5
Comma: 4428675/4194304
Mapping: [⟨1 0 11], ⟨0 2 -11]]
POTE generator: ~1215/1024 = 252.649
Badness: 0.424685
Kangaroo
Subgroup: 2.3.5
Comma: 64000/59049
Mapping: [⟨1 0 -3], ⟨0 3 10]]
POTE generator: ~27/20 = 561.195
Optimal ET sequence: 15, 47b, 62b
Badness: 0.295767
Kumonga
Subgroup: 2.3.5
Comma: 1289945088/1220703125
Mapping: [⟨1 4 4], ⟨0 -13 -9]]
POTE generator: ~144/125 = 222.912
Optimal ET sequence: 16, 27, 43, 70, 183cc
Badness: 0.729609
Kwai
Subgroup: 2.3.5
Comma: 5629499534213120/5559060566555523
Mapping: [⟨1 2 16], ⟨0 -1 -33]]
POTE generator: ~3/2 = 702.630
Optimal ET sequence: 41, 111, 152
Badness: 0.636715
Lafayette
Subgroup: 2.3.5
Comma: 3456/3125
Mapping: [⟨1 1 2], ⟨0 5 3]]
POTE generator: ~25/24 = 140.995
Optimal ET sequence: 8, 9, 17c
Badness: 0.200483
Leapday
Subgroup: 2.3.5
Comma: 10737418240/10460353203
Mapping: [⟨1 0 -31], ⟨0 1 21]]
POTE generator: ~3/2 = 704.179
Optimal ET sequence: 29, 46, 121, 167, 455bc, 622bbc
Badness: 0.523182
Mabila
Subgroup: 2.3.5
Comma: 268435456/263671875
Mapping: [⟨1 6 1], ⟨0 -10 3]]
POTE generator: ~512/375 = 529.685
Optimal ET sequence: 9, 25, 34, 77, 111, 145, 256c
Badness: 0.232481
Magus
- See also: Sensamagic clan #Magus and Starling temperaments #Amigo
Subgroup: 2.3.5
Comma: 50331648/48828125
Mapping: [⟨1 -2 2], ⟨0 11 1]]
POTE generator: ~5/4 = 391.225
Optimal ET sequence: 3, 40, 43, 46, 181c, 227c, 273c, 319c
Badness: 0.360162
Majvam
- See also: Subgroup temperaments #Majvam, Cataharry temperaments #Majvamoid, and Parkleiness temperaments #Majvamic
Subgroup: 2.3.5
Comma: 2404631929946112/2384185791015625
Mapping: [⟨1 10 5], ⟨0 -22 -7]]
POTE generator: ~125/96 = 458.995
Optimal ET sequence: 34, 115, 149, 183, 217, 400, 617
Badness: 0.356948
Merman
Subgroup: 2.3.5
Comma: 1121008359375/1099511627776
Mapping: [⟨1 5 -5], ⟨0 -7 15]]
POTE generator: ~45/32 = 585.634
Optimal ET sequence: 41, 84, 125, 209, 334c, 543bc
Badness: 0.453848
Mirkat
Subgroup: 2.3.5
Comma: 4052555153018976267/4000000000000000000
Mapping: [⟨3 2 1], ⟨0 6 13]]
Optimal tuning (CWE): ~2000000/1594323 = 1\3, ~10/9 = 183.585
Supporting ETs: 72, 183, 6cc, 39, 111, 33c, 255, 294, 438, 327, 105c, 150c, 45bccc, 477
Badness (Sintel): 17.631
Misneb
Subgroup: 2.3.5
Comma: 145964630126953125/144115188075855872
Mapping: [⟨1 3 1], ⟨0 -15 14]]
POTE generator: ~16/15 = 113.240
Optimal ET sequence: 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc
Badness: 0.609540
Mowgli
Subgroup: 2.3.5
Comma: [0 22 -15⟩ = 31381059609/30517578125
Mapping: [⟨1 0 0], ⟨0 15 22]]
POTE generator: ~27/25 = 126.724
Optimal ET sequence: 19, 85c, 104c, 123, 142, 161
Badness: 0.653871
Mynic
Subgroup: 2.3.5
Comma: 10077696/9765625
Mapping: [⟨1 9 9], ⟨0 -10 -9]]
POTE generator: ~6/5 = 310.140
Optimal ET sequence: 27, 31, 58, 89, 325cc
Badness: 0.249965
Nessafof
Subgroup: 2.3.5
Comma: 481469424205824/476837158203125
Mapping: [⟨3 2 5], ⟨0 7 5]]
Optimal tuning (CWE): ~78125/62208 = 1\3, ~9765625/8957952 = 157.409
Supporting ETs: 15, 99, 84, 183, 282, 69, 114, 9bbc, 267, 54b, 381, 24bbc, 39bc, 465
Badness (Sintel): 7.807
Newt
Subgroup: 2.3.5
Comma: [95 -57 -2⟩
Mapping: [⟨1 1 19], ⟨0 2 -57]]
POTE generator: ~[47 -28 -1⟩ = 351.114
Optimal ET sequence: 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 3592bc, 5523bbc
Badness: 1.528465
Nusecond
Subgroup: 2.3.5
Comma: 51018336/48828125
Mapping: [⟨1 3 4], ⟨0 -11 -13]]
POTE generator: ~3125/2916 = 154.523
Optimal ET sequence: 8, 23, 31, 70, 101, 132c, 233c, 365bcc
Badness: 0.466493
Octacoid
Subgroup: 2.3.5
Comma list: 8589934592/7688671875
Mapping: [⟨1 1 3], ⟨0 8 -9]]
- mapping generators: ~2, ~16/15
Optimal ET sequence: 13, 14, 27
Badness: 1.75
Oncle
Subgroup: 2.3.5
Comma: 145282683375/137438953472
Mapping: [⟨1 1 6], ⟨0 3 -19]]
POTE generator: ~4096/3645 = 232.521
Optimal ET sequence: 31, 98c, 129c, 160bc, 289bbcc
Badness: 1.244699
Oolong
Subgroup: 2.3.5
Comma: 793437161472/762939453125
Mapping: [⟨1 6 7], ⟨0 -17 -18]]
POTE generator: ~6/5 = 311.694
Optimal ET sequence: 23, 27, 50, 77
Badness: 0.942789
Pentadecal
Subgroup: 2.3.5
Comma: 30517578125/29386561536
Mapping: [⟨15 0 11], ⟨0 1 1]]
POTE generator: ~3/2 = 702.652
Optimal ET sequence: 15, 45, 60, 75, 135, 210c, 345cc
Badness: 0.692042
Phillips
Subgroup: 2.3.5
Comma: 9685512225/8589934592
Mapping: [⟨2 0 33], ⟨0 1 -9]]
POTE generator: ~3/2 = 691.455
Optimal ET sequence: 14, 26, 66b, 92bc, 118bbc
Badness: 2.228904
Progress
Subgroup: 2.3.5
Comma: 32768/30375
Mapping: [⟨1 0 5], ⟨0 3 -5]]
POTE generator: ~64/45 = 561.264
Optimal ET sequence: 2, 13, 15, 32c, 47bc, 62bc
Badness: 0.246073
Quartemka
Subgroup: 2.3.5
Comma: 1907348632812500/1853020188851841
Mapping: [⟨1 4 6], ⟨0 -21 -32]]
POTE generator: ~27/25 = 137.962
Optimal ET sequence: 26, 61, 87, 287, 374, 461
Badness: 1.381216
Quasimoha
Subgroup: 2.3.5
Comma: 2353579470675/2199023255552
Mapping: [⟨1 1 9], ⟨0 2 -23]]
POTE generator: ~1048576/885735 = 348.600
Optimal ET sequence: 31, 117c, 148bc, 179bc
Badness: 1.986675
Quasiorwell
Subgroup: 2.3.5
Comma: 9903520314283042199192993792/9822542779147624969482421875
Mapping: [⟨1 31 0], ⟨0 -38 3]]
Optimal tuning (CWE): ~2 = 1\1, ~3662109375/2147483648 = 928.893
Supporting ETs: 31, 270, 301, 239, 571, 208, 841, 332, 509, 177, 1111, 146b, 872, 363
Badness (Sintel): 30.581
Quasitemp
Subgroup: 2.3.5
Comma: 6103515625/5804752896
Mapping: [⟨1 5 5], ⟨0 -14 -11]]
POTE generator: ~3125/2592 = 292.702
Optimal ET sequence: 4, 37, 41
Badness: 0.767824
Quindromeda
Subgroup: 2.3.5
Comma: 72057594037927936/71489976421753125
POTE generator: ~4428675/4194304 = 99.526
Mapping: [⟨1 2 0], ⟨0 -5 28]]
Optimal ET sequence: 12, 193, 205, 217, 422
Badness: 0.399849
Quintaleap
Subgroup: 2.3.5
Comma: 137438953472/134521003125
Mapping: [⟨1 2 1], ⟨0 -5 16]]
POTE generator: ~135/128 = 99.267
Optimal ET sequence: 12, 109, 121, 133
Badness: 0.444506
Rarity
The rarity temperament is notable due to the fact that it offers a 7L 4s scale of reasonable hardness, in the 5-limit and among relatively small edos.
Subgroup: 2.3.5
Comma list: [-57 17 13⟩
Mapping: [⟨1 11 -10], ⟨0 -13 17]]
- mapping generators: ~16384/10125 = 869.392
Optimal tuning (CTE): ~2 = 1\1, ~16384/10125 = 869.392
Optimal ET sequence: 11, 29, 69, 98c
Badness: 4.23
Satin
Subgroup: 2.3.5
Comma: [104 -70 3⟩
Mapping: [⟨1 2 12], ⟨0 -3 -70]]
POTE generator: ~[-34 23 -1⟩ = 165.907
Optimal ET sequence: 94, 217, 528, 745, 1273
Badness: 2.853049
Semidimfourth
Subgroup: 2.3.5
Comma: [7 41 -31⟩
Mapping: [⟨1 21 28], ⟨0 -31 -41]]
POTE generator: ~162/125 = 448.449
Optimal ET sequence: 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc
Badness: 0.233376
Semidimi
Subgroup: 2.3.5
Comma: [-12 -73 55⟩
Mapping: [⟨1 36 48], ⟨0 -55 -73]]
POTE generator: ~162/125 = 449.127
Optimal ET sequence: 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419
Badness: 0.754866
Semisept
Subgroup: 2.3.5
Comma: 782757789696/762939453125
Mapping: [⟨1 12 6], ⟨0 -17 -6]]
POTE generator: ~192/125 = 735.146
Optimal ET sequence: 18, 31, 80, 111
Badness: 0.630576
Sentinel
Subgroup: 2.3.5
Comma: 8968066875/8589934592
Mapping: [⟨1 3 -3], ⟨0 -4 15]]
POTE generator: ~512/405 = 425.474
Optimal ET sequence: 14, 17, 31, 79, 110, 361bc
Badness: 0.723413
Septendecic
Subgroup: 2.3.5
Comma: [27 -17⟩ = 134217728/129140163
Mapping: [⟨17 27 0], ⟨0 0 1]]
Mapping generators: ~531441/524288, ~5
POTE generator: ~5/4 = 389.193
Badness: 0.541384
Septimin
Subgroup: 2.3.5
Comma: 35595703125/34359738368
Mapping: [⟨1 4 1], ⟨0 -11 6]]
POTE generator: ~75/64 = 263.658
Optimal ET sequence: 9, 23b, 32, 41, 91, 132, 223c, 355bc
Badness: 0.670947
Sevond
Subgroup: 2.3.5
Comma: 5000000/4782969
Mapping: [⟨7 0 -6], ⟨0 1 2]]
POTE generator: ~3/2 = 706.288
Optimal ET sequence: 7, 42, 49, 56, 119
Badness: 0.339335
Sfourth
Subgroup: 2.3.5
Comma: 617673396283947/610351562500000
Mapping: [⟨1 2 3], ⟨0 -19 -31]]
POTE generator: ~1594323/1562500 = 26.2342
Optimal ET sequence: 45, 46, 91, 137, 183
Badness: 0.504555
Slender
Subgroup: 2.3.5
Comma: 72081298828125/70368744177664
Mapping: [⟨1 2 2], ⟨0 -13 10]]
Optimal tuning (CWE): ~2 = 1\1, ~16875/16384 = 38.400
Supporting ETs: 31, 125, 94, 63, 32, 156, 30b, 219c, 187, 281, 157c, 218b, 95c, 344c
Badness (Sintel): 17.842
Slurpee
Subgroup: 2.3.5
Comma: 177147/156250
Mapping: [⟨1 2 3], ⟨0 -7 -11]]
POTE generator: ~27/25 = 72.742
Optimal ET sequence: 16, 17c, 33
Badness: 0.689274
Stump
- See also: Sensamagic clan #Pycnic and Marvel temperaments #Triton
Subgroup: 2.3.5
Comma: 273375/262144
Mapping: [⟨1 0 6], ⟨0 3 -7]]
POTE generator: ~64/45 = 631.737
Badness: 0.200600
Tertiaseptal
Subgroup: 2.3.5
Comma: 579357147216796875/576460752303423488
Mapping: [⟨1 3 2], ⟨0 -22 5]]
POTE generator: ~17578125/16777216 = 77.191
Optimal ET sequence: 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c
Badness: 0.297544
Tertiosec
Subgroup: 2.3.5
Comma: [-89 21 24⟩
Mapping: [⟨3 7 5], ⟨0 -8 7]]
POTE generator: ~16/15 = 112.281
Optimal ET sequence: 21, 54, 75, 96, 171
Badness: 0.851003
Thuja
Subgroup: 2.3.5
Comma: 254803968/244140625
Mapping: [⟨1 -4 0], ⟨0 12 5]]
POTE generator: ~3125/2304 = 558.592
Optimal ET sequence: 15, 43, 58
Badness: 0.511109
Triskaidekic
Subgroup: 2.3.5
Comma: 1220703125/1073741824
Mapping: [⟨13 0 30], ⟨0 1 0]]
POTE generator: ~3/2 = 696.142
Optimal ET sequence: 13, 26, 91c
Badness: 2.241568
Tritonic
Subgroup: 2.3.5
Comma: 553584375/536870912
Mapping: [⟨1 4 -3], ⟨0 -5 11]]
POTE generator: ~45/32 = 580.219
Optimal ET sequence: 29, 31, 60, 91
Badness: 0.378527
Tritriple
Subgroup: 2.3.5
Comma: [31 20 -27⟩
Mapping: [⟨1 -11 -7], ⟨0 27 20]]
POTE generator: ~864/625 = 559.332
Optimal ET sequence: 15, 88, 103, 118, 959, 1077
Badness: 0.283570
Undeka
Subgroup: 2.3.5
Comma: 48828125/45349632
Mapping: [⟨11 0 8], ⟨0 1 1]]
POTE generator: ~3/2 = 703.829
Optimal ET sequence: 22, 77c, 99c, 121c
Badness: 0.727539
Undim
Subgroup: 2.3.5
Comma: 2199023255552/2179240250625
Mapping: [⟨4 6 11], ⟨0 1 -5]]
POTE generator: ~3/2 = 702.605
Optimal ET sequence: 12, 140, 152, 164, 1076bc, 1228bc
Badness: 0.241703
Unsmate
Subgroup: 2.3.5
Comma: 17578125/16777216
Mapping: [⟨1 3 2], ⟨0 -9 2]]
POTE generator: ~2048/1875 = 189.049
Optimal ET sequence: 13, 19, 89c, 108c, 127c, 146cc
Badness: 0.460168
Untriton
- See also: Marvel temperaments #Untriton, Porwell temperaments #Aufo and Triwellismic temperaments #Interaufo
Subgroup: 2.3.5
Comma: 2270041927734375/2251799813685248
Mapping: [⟨1 6 -7], ⟨0 -9 19]]
POTE generator: ~45/32 = 588.722
Optimal ET sequence: 51, 53, 267, 320, 373, 426, 479, 532, 2607bc
Badness: 0.307073
Vinegar
Subgroup: 2.3.5
Comma: 16000000/14348907
Mapping: [⟨3 0 -5], ⟨0 2 5]]
POTE generator: ~10/9 = 156.861
Optimal ET sequence: 15, 39c, 54, 69b, 84b
Badness: 0.903002
Vines
Subgroup: 2.3.5
Comma: 156728328192/152587890625
Mapping: [⟨2 7 8], ⟨0 -8 -7]]
POTE generator: ~6/5 = 312.713
Optimal ET sequence: 4, 42, 46, 96, 142
Badness: 0.541831
Wizard
Subgroup: 2.3.5
Comma: 2197265625/2147483648
Mapping: [⟨2 1 5], ⟨0 6 -1]]
Mapping generators: ~42875/32768, ~9375/8192
POTE generator: ~5/4 = 383.212
Optimal ET sequence: 22, 50, 72, 166, 238c, 310c, 548bc
Badness: 0.386367
Scales (Scala files): wizard22
Wronecki
Subgroup: 2.3.5
Comma: 531441/500000
Mapping: [⟨6 0 -5], ⟨0 1 2]]
POTE generator: ~3/2 = 695.040
Optimal ET sequence: 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc
Badness: 0.341757