High badness temperaments

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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

See also: Porwell temperaments #Absurdity

Subgroup: 2.3.5

Comma: 10460353203/10240000000

Mapping: [7 0 -17], 0 1 3]]

POTE generator: ~10/9 = 185.901

Optimal ET sequence7, 70, 77, 84, 329, 413b, 497b

Badness: 0.341202

Archaeotherium

See also: Gamelismic clan #Archaeotherium

Subgroup: 2.3.5

Comma: 597871125/536870912

Mapping: [1 1 5], 0 3 -14]]

POTE generator: ~1215/1024 = 230.351

Optimal ET sequence21, 26, 73bc, 99bc

Badness: 1.434855

Beatles

See also: Archytas clan #Beatles

Subgroup: 2.3.5

Comma: 524288/492075

Mapping: [1 1 5], 0 2 -9]]

POTE generator: ~512/405 = 355.930

Optimal ET sequence10, 17c, 27, 64b, 91bc, 118bc

Badness: 0.358542

Bohpier

See also: Sensamagic clan #Bohpier

Subgroup: 2.3.5

Comma: 1220703125/1162261467

Mapping: [1 0 0], 0 13 19]]

POTE generator: ~27/25 = 146.476

Optimal ET sequence8, 41, 131, 172, 213c

Badness: 0.860534

Casablanca

See also: Starling temperaments #Casablanca

Subgroup: 2.3.5

Comma: 20061226008576/19073486328125

Mapping: [1 -7 -14], 0 19 14]]

POTE generator: ~864/625 = 542.208

Optimal ET sequence11b, 20b, 31, 73, 104c, 135c

Badness: 1.423736

Chromo

See also: Keemic temperaments #Chromo

Subgroup: 2.3.5

Comma: 1220703125/1146617856

Mapping: [1 1 2], 0 13 7]]

POTE generator: ~25/24 = 53.922

Optimal ET sequence22, 45, 67c, 89c

Badness: 0.842835

Comic

See also: Jubilismic clan #Comic

Subgroup: 2.3.5

Comma: 5120000/4782969

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

POTE generator: ~81/80 = 55.382

Optimal ET sequence20c, 22, 86b, 108b, 130b

Badness: 0.491181

Cotoneum

See also: Hemimage temperaments #Cotoneum

Subgroup: 2.3.5

Comma: [80 -49 -1

Mapping: [1 2 -18], 0 -1 49]]

POTE generator: ~3/2 = 702.315

Optimal ET sequence41, 135c, 176, 217, 475, 1167, 1642, 2117b

Badness: 1.240078

Counterhanson

See also: Ragismic microtemperaments #Counterkleismic

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 sequence19, 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 sequence19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c

Badness: 0.373477

Countritonic

See also: Schismic-Mercator equivalence continuum #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 sequence53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b

Badness: 0.255594

Cypress

See also: Starling temperaments #Cypress

Subgroup: 2.3.5

Comma: 258280326/244140625

Mapping: [1 7 10], 0 -12 -17]]

POTE generator: ~4374/3125 = 541.726

Optimal ET sequence11c, 20c, 31, 113c, 144c, 175c, 381bcc

Badness: 0.816635

Delorean

See also: Mint temperaments #Subklei

Subgroup: 2.3.5

Comma: 17496/15625

Mapping: [1 3 4], 0 -6 -7]]

POTE generator: ~6/5 = 284.293

Optimal ET sequence4, 17c, 21, 38c

Badness: 0.355937

Diesic

See also: Orwellismic temperaments #Diesic

Subgroup: 2.3.5

Comma: 10460353203/9765625000

Mapping: [1 2 3], 0 -13 -21]]

POTE generator: ~6561/6250 = 38.571

Optimal ET sequence31, 156c, 187c, 218bc, 249bc, 280bc

Badness: 1.344681

Dodifo

See also: Porwell temperaments #Dodifo

Subgroup: 2.3.5

Comma: [-67 -9 35

Mapping: [1 12 5], 0 -35 -9]]

POTE generator: ~768/625 = 357.088

Optimal ET sequence37, 84, 205, 289, 494, 783, 2060, 2843, 3626

Badness: 0.213112

Elvis

See also: Jubilismic clan #Elvis

Subgroup: 2.3.5

Comma: 36905625/33554432

Mapping: [2 1 10], 0 2 -5]]

POTE generator: ~45/32 = 554.546

Optimal ET sequence26, 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 sequence37, 50, 87, 137, 224

Badness: 0.544752

Fervor

See also: Archytas clan #Fervor

Subgroup: 2.3.5

Comma: 67108864/61509375

Mapping: [1 4 -2], 0 -5 9]]

POTE generator: ~64/45 = 577.705

Optimal ET sequence2, 25, 27

Badness: 0.852612

Genocchi

Subgroup: 2.3.5

Comma: 2359296/1953125

Mapping: [1 0 2], 0 9 2]]

POTE generator: ~768/625 = 212.444

Optimal ET sequence6b, 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 sequence12, 113, 125, 137

Badness: 0.306809

Hemififths

See also: Breedsmic temperaments #Hemififths

Subgroup: 2.3.5

Comma: 858993459200/847288609443

Mapping: [1 1 -5], 0 2 25]]

POTE generator: ~655360/531441 = 351.476

Optimal ET sequence41, 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

Optimal ET sequence14, 19

Badness: 0.424685

Kangaroo

See also: Trienstonic clan #Parakangaroo

Subgroup: 2.3.5

Comma: 64000/59049

Mapping: [1 0 -3], 0 3 10]]

POTE generator: ~27/20 = 561.195

Optimal ET sequence15, 47b, 62b

Badness: 0.295767

Kumonga

See also: Starling temperaments #Kumonga

Subgroup: 2.3.5

Comma: 1289945088/1220703125

Mapping: [1 4 4], 0 -13 -9]]

POTE generator: ~144/125 = 222.912

Optimal ET sequence16, 27, 43, 70, 183cc

Badness: 0.729609

Kwai

See also: Mirkwai clan #Kwai

Subgroup: 2.3.5

Comma: 5629499534213120/5559060566555523

Mapping: [1 2 16], 0 -1 -33]]

POTE generator: ~3/2 = 702.630

Optimal ET sequence41, 111, 152

Badness: 0.636715

Lafayette

See also: Mint temperaments #Progression

Subgroup: 2.3.5

Comma: 3456/3125

Mapping: [1 1 2], 0 5 3]]

POTE generator: ~25/24 = 140.995

Optimal ET sequence8, 9, 17c

Badness: 0.200483

Leapday

See also: Hemifamity temperaments #Leapday and Porwell temperaments #Polypyth

Subgroup: 2.3.5

Comma: 10737418240/10460353203

Mapping: [1 0 -31], 0 1 21]]

POTE generator: ~3/2 = 704.179

Optimal ET sequence29, 46, 121, 167, 455bc, 622bbc

Badness: 0.523182

Mabila

See also: Mabila family

Subgroup: 2.3.5

Comma: 268435456/263671875

Mapping: [1 6 1], 0 -10 3]]

POTE generator: ~512/375 = 529.685

Optimal ET sequence9, 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 sequence3, 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 sequence34, 115, 149, 183, 217, 400, 617

Badness: 0.356948

Merman

See also: Marvel temperaments #Merman

Subgroup: 2.3.5

Comma: 1121008359375/1099511627776

Mapping: [1 5 -5], 0 -7 15]]

POTE generator: ~45/32 = 585.634

Optimal ET sequence41, 84, 125, 209, 334c, 543bc

Badness: 0.453848

Misneb

See also: Marvel temperaments #Misneb

Subgroup: 2.3.5

Comma: 145964630126953125/144115188075855872

Mapping: [1 3 1], 0 -15 14]]

POTE generator: ~16/15 = 113.240

Optimal ET sequence21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc

Badness: 0.609540

Mowgli

See also: Hemimean clan #Mowglic

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 sequence19, 85c, 104c, 123, 142, 161

Badness: 0.653871

Mynic

See also: Starling temperaments #Myna

Subgroup: 2.3.5

Comma: 10077696/9765625

Mapping: [1 9 9], 0 -10 -9]]

POTE generator: ~6/5 = 310.140

Optimal ET sequence27, 31, 58, 89, 325cc

Badness: 0.249965

Newt

See also: Breedsmic temperaments #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 sequence41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 3592bc, 5523bbc

Badness: 1.528465

Nusecond

See also: Starling temperaments #Nusecond

Subgroup: 2.3.5

Comma: 51018336/48828125

Mapping: [1 3 4], 0 -11 -13]]

POTE generator: ~3125/2916 = 154.523

Optimal ET sequence8, 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 tunings:

  • CTE: ~2 = 1�, ~16/15 = 88.7331
  • CWE: ~2 = 1�, ~16/15 = 88.8168

Optimal ET sequence13, 14, 27

Badness: 1.75

Oncle

See also: Gamelismic clan #Oncle

Subgroup: 2.3.5

Comma: 145282683375/137438953472

Mapping: [1 1 6], 0 3 -19]]

POTE generator: ~4096/3645 = 232.521

Optimal ET sequence31, 98c, 129c, 160bc, 289bbcc

Badness: 1.244699

Oolong

See also: Starling temperaments #Oolong

Subgroup: 2.3.5

Comma: 793437161472/762939453125

Mapping: [1 6 7], 0 -17 -18]]

POTE generator: ~6/5 = 311.694

Optimal ET sequence23, 27, 50, 77

Badness: 0.942789

Pentadecal

See also: Cloudy clan #Pentadecal

Subgroup: 2.3.5

Comma: 30517578125/29386561536

Mapping: [15 0 11], 0 1 1]]

POTE generator: ~3/2 = 702.652

Optimal ET sequence15, 45, 60, 75, 135, 210c, 345cc

Badness: 0.692042

Phillips

See also: Orwellismic temperaments #Phillips

Subgroup: 2.3.5

Comma: 9685512225/8589934592

Mapping: [2 0 33], 0 1 -9]]

POTE generator: ~3/2 = 691.455

Optimal ET sequence14, 26, 66b, 92bc, 118bbc

Badness: 2.228904

Progress

See also: Archytas clan #Progress

Subgroup: 2.3.5

Comma: 32768/30375

Mapping: [1 0 5], 0 3 -5]]

POTE generator: ~64/45 = 561.264

Optimal ET sequence2, 13, 15, 32c, 47bc, 62bc

Badness: 0.246073

Quartemka

See also: Gamelismic clan #Quartemka

Subgroup: 2.3.5

Comma: 1907348632812500/1853020188851841

Mapping: [1 4 6], 0 -21 -32]]

POTE generator: ~27/25 = 137.962

Optimal ET sequence26, 61, 87, 287, 374, 461

Badness: 1.381216

Quasimoha

See also: Breedsmic temperaments #Quasimoha

Subgroup: 2.3.5

Comma: 2353579470675/2199023255552

Mapping: [1 1 9], 0 2 -23]]

POTE generator: ~1048576/885735 = 348.600

Optimal ET sequence31, 117c, 148bc, 179bc

Badness: 1.986675

Quasitemp

See also: Keemic temperaments #Quasitemp

Subgroup: 2.3.5

Comma: 6103515625/5804752896

Mapping: [1 5 5], 0 -14 -11]]

POTE generator: ~3125/2592 = 292.702

Optimal ET sequence4, 37, 41

Badness: 0.767824

Quindromeda

See also: Quindromeda family

Subgroup: 2.3.5

Comma: 72057594037927936/71489976421753125

POTE generator: ~4428675/4194304 = 99.526

Mapping: [1 2 0], 0 -5 28]]

Optimal ET sequence12, 193, 205, 217, 422

Badness: 0.399849

Quintaleap

See also: Quintaleap family

Subgroup: 2.3.5

Comma: 137438953472/134521003125

Mapping: [1 2 1], 0 -5 16]]

POTE generator: ~135/128 = 99.267

Optimal ET sequence12, 109, 121, 133

Badness: 0.444506

Rarity

See also: No-sevens subgroup temperaments #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�, ~16384/10125 = 869.392

Optimal ET sequence11, 29, 69, 98c

Badness: 4.23

Satin

See also: Canousmic temperaments #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 sequence94, 217, 528, 745, 1273

Badness: 2.853049

Semidimfourth

See also: Ragismic microtemperaments #Semidimfourth

Subgroup: 2.3.5

Comma: [7 41 -31

Mapping: [1 21 28], 0 -31 -41]]

POTE generator: ~162/125 = 448.449

Optimal ET sequence8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc

Badness: 0.233376

Semidimi

See also: Ragismic microtemperaments #Semidimi

Subgroup: 2.3.5

Comma: [-12 -73 55

Mapping: [1 36 48], 0 -55 -73]]

POTE generator: ~162/125 = 449.127

Optimal ET sequence8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419

Badness: 0.754866

Semisept

See also: Hemimean clan #Semisept

Subgroup: 2.3.5

Comma: 782757789696/762939453125

Mapping: [1 12 6], 0 -17 -6]]

POTE generator: ~192/125 = 735.146

Optimal ET sequence18, 31, 80, 111

Badness: 0.630576

Sentinel

See also: Orwellismic temperaments #Sentinel

Subgroup: 2.3.5

Comma: 8968066875/8589934592

Mapping: [1 3 -3], 0 -4 15]]

POTE generator: ~512/405 = 425.474

Optimal ET sequence14, 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

Optimal ET sequence17c, 34

Badness: 0.541384

Septimin

See also: Marvel temperaments #Septimin

Subgroup: 2.3.5

Comma: 35595703125/34359738368

Mapping: [1 4 1], 0 -11 6]]

POTE generator: ~75/64 = 263.658

Optimal ET sequence9, 23b, 32, 41, 91, 132, 223c, 355bc

Badness: 0.670947

Sevond

See also: Keemic temperaments #Sevond

Subgroup: 2.3.5

Comma: 5000000/4782969

Mapping: [7 0 -6], 0 1 2]]

POTE generator: ~3/2 = 706.288

Optimal ET sequence7, 42, 49, 56, 119

Badness: 0.339335

Sfourth

See also: Ragismic microtemperaments #Sfourth

Subgroup: 2.3.5

Comma: 617673396283947/610351562500000

Mapping: [1 2 3], 0 -19 -31]]

POTE generator: ~1594323/1562500 = 26.2342

Optimal ET sequence45, 46, 91, 137, 183

Badness: 0.504555

Slurpee

See also: Mint temperaments #Slurpee

Subgroup: 2.3.5

Comma: 177147/156250

Mapping: [1 2 3], 0 -7 -11]]

POTE generator: ~27/25 = 72.742

Optimal ET sequence16, 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

Optimal ET sequence17, 19

Badness: 0.200600

Tertiaseptal

See also: Breedsmic temperaments #Tertiaseptal

Subgroup: 2.3.5

Comma: 579357147216796875/576460752303423488

Mapping: [1 3 2], 0 -22 5]]

POTE generator: ~17578125/16777216 = 77.191

Optimal ET sequence31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c

Badness: 0.297544

Tertiosec

See also: Marvel temperaments #Tertiosec

Subgroup: 2.3.5

Comma: [-89 21 24

Mapping: [3 7 5], 0 -8 7]]

POTE generator: ~16/15 = 112.281

Optimal ET sequence21, 54, 75, 96, 171

Badness: 0.851003

Thuja

See also: Starling temperaments #Thuja

Subgroup: 2.3.5

Comma: 254803968/244140625

Mapping: [1 -4 0], 0 12 5]]

POTE generator: ~3125/2304 = 558.592

Optimal ET sequence15, 43, 58

Badness: 0.511109

Triskaidekic

See also: Orwellismic temperaments #Triskaidekic

Subgroup: 2.3.5

Comma: 1220703125/1073741824

Mapping: [13 0 30], 0 1 0]]

POTE generator: ~3/2 = 696.142

Optimal ET sequence13, 26, 91c

Badness: 2.241568

Tritonic

See also: Marvel temperaments #Tritonic

Subgroup: 2.3.5

Comma: 553584375/536870912

Mapping: [1 4 -3], 0 -5 11]]

POTE generator: ~45/32 = 580.219

Optimal ET sequence29, 31, 60, 91

Badness: 0.378527

Tritriple

See also: Gamelismic clan #Tritriple

Subgroup: 2.3.5

Comma: [31 20 -27

Mapping: [1 -11 -7], 0 27 20]]

POTE generator: ~864/625 = 559.332

Optimal ET sequence15, 88, 103, 118, 959, 1077

Badness: 0.283570

Undeka

See also: Keemic temperaments #Undeka

Subgroup: 2.3.5

Comma: 48828125/45349632

Mapping: [11 0 8], 0 1 1]]

POTE generator: ~3/2 = 703.829

Optimal ET sequence22, 77c, 99c, 121c

Badness: 0.727539

Undim

See also: Undim family

Subgroup: 2.3.5

Comma: 2199023255552/2179240250625

Mapping: [4 6 11], 0 1 -5]]

POTE generator: ~3/2 = 702.605

Optimal ET sequence12, 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 sequence13, 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 sequence51, 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 sequence15, 39c, 54, 69b, 84b

Badness: 0.903002

Vines

See also: Starling temperaments #Vines

Subgroup: 2.3.5

Comma: 156728328192/152587890625

Mapping: [2 7 8], 0 -8 -7]]

POTE generator: ~6/5 = 312.713

Optimal ET sequence4, 42, 46, 96, 142

Badness: 0.541831

Wizard

See also: Marvel temperaments #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 sequence22, 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 sequence12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc

Badness: 0.341757