Miscellaneous 5-limit temperaments: Difference between revisions

Below are listed some high-badness 5-limit temperaments (badness > 0.2). Most of these are temperaments which have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:  

== Absurdity ==

{{see also| Porwell temperaments #Absurdity }}

[[Comma]]: 10460353203/10240000000

[[Mapping]]: [{{Val| 7 0 -17 }}, {{Val| 0 1 3 }}]

[[POTE generator]]: ~10/9 = 185.901

{{Optimal ET sequence|legend=1| 7, 70, 77, 84, 329, 413b, 497b }}

[[Badness]]: 0.341202

== Archaeotherium ==

{{see also| Gamelismic clan #Archaeotherium }}

[[Comma]]: 597871125/536870912

[[Mapping]]: [{{Val| 1 1 5 }}, {{Val| 0 3 -14 }}]

[[POTE generator]]: ~1215/1024 = 230.351

{{Optimal ET sequence|legend=1| 21, 26, 73bc, 99bc }}

[[Badness]]: 1.434855

== Beatles ==

{{see also| Archytas clan #Beatles }}

[[Comma]]: 524288/492075

[[Mapping]]: [{{Val| 1 1 5 }}, {{Val| 0 2 -9 }}]

[[POTE generator]]: ~512/405 = 355.930

{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}

[[Badness]]: 0.358542

== Bohpier ==

{{see also| Sensamagic clan #Bohpier }}

[[Comma]]: 1220703125/1162261467

[[Mapping]]: [{{Val| 1 0 0 }}, {{Val| 0 13 19 }}]

[[POTE generator]]: ~27/25 = 146.476

{{Optimal ET sequence|legend=1| 8, 41, 131, 172, 213c }}

[[Badness]]: 0.860534

== Casablanca ==

{{see also| Starling temperaments #Casablanca }}

[[Comma]]: 20061226008576/19073486328125

[[Mapping]]: [{{Val| 1 -7 -14 }}, {{Val| 0 19 14 }}]

[[POTE generator]]: ~864/625 = 542.208

{{Optimal ET sequence|legend=1| 11b, 20b, 31, 73, 104c, 135c }}

[[Badness]]: 1.423736

== Chromo ==

{{see also| Keemic temperaments #Chromo }}

[[Comma]]: 1220703125/1146617856

[[Mapping]]: [{{Val| 1 1 2 }}, {{Val| 0 13 7 }}]

[[POTE generator]]: ~25/24 = 53.922

{{Optimal ET sequence|legend=1| 22, 45, 67c, 89c }}

[[Badness]]: 0.842835

== Comic ==

{{see also| Jubilismic clan #Comic }}

[[Comma]]: 5120000/4782969

[[Mapping]]: [{{Val| 2 1 -3 }}, {{Val| 0 2 7 }}]

[[POTE generator]]: ~81/80 = 55.382

[[Comma]]: {{Monzo| 80 -49 -1 }}

[[Mapping]]: [{{Val| 1 2 -18 }}, {{Val| 0 -1 49 }}]

[[POTE generator]]: ~3/2 = 702.315

{{Optimal ET sequence|legend=1| 41, 135c, 176, 217, 475, 1167, 1642, 2117b }}

[[Badness]]: 1.240078

== Counterhanson ==

{{See also| Ragismic microtemperaments #Counterkleismic }}

[[Comma]]: {{Monzo| -20 -24 25 }} = 298023223876953125/296148833645101056

[[Mapping]]: [{{Val| 1 -5 -4 }}, {{Val| 0 25 24 }}]

[[POTE generator]]: ~6/5 = 316.081

[[Comma]]: {{Monzo| 10 23 -20 }} = 96402615118848/95367431640625

[[Mapping]]: [{{Val| 1 10 12 }}, {{Val| 0 -20 -23 }}]

[[POTE generator]]: ~104976/78125 = 504.913

{{Optimal ET sequence|legend=1| 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c }}

[[Badness]]: 0.373477

== Countritonic ==

{{See also| Schismic–Mercator equivalence continuum #Countritonic }}

[[Comma]]: 16777216000000000/16677181699666569

[[Mapping]]: [{{Val| 1 6 19 }}, {{Val| 0 -9 -34 }}]

[[POTE generator]]: ~14348907/10240000 = 588.636

{{Optimal ET sequence|legend=1| 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b }}

[[Badness]]: 0.255594

== Cypress ==

{{see also| Starling temperaments #Cypress }}

[[Comma]]: 258280326/244140625

[[Mapping]]: [{{Val| 1 7 10 }}, {{Val| 0 -12 -17 }}]

[[POTE generator]]: ~4374/3125 = 541.726

{{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c, 381bcc }}

[[Badness]]: 0.816635

== Delorean ==

{{see also| Mint temperaments #Subklei }}

[[Comma]]: 17496/15625

[[Mapping]]: [{{Val| 1 3 4 }}, {{Val| 0 -6 -7 }}]

[[POTE generator]]: ~6/5 = 284.293

{{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }}

[[Badness]]: 0.355937

== Diesic ==

{{see also| Orwellismic temperaments #Diesic }}

[[Comma]]: 10460353203/9765625000

[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -13 -21 }}]

[[POTE generator]]: ~6561/6250 = 38.571

{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}

[[Badness]]: 1.344681

== Dodifo ==

{{see also| Porwell temperaments #Dodifo }}

[[Comma]]: {{Monzo| -67 -9 35 }}

[[Mapping]]: [{{Val| 1 12 5 }}, {{Val| 0 -35 -9 }}]

[[POTE generator]]: ~768/625 = 357.088

{{Optimal ET sequence|legend=1| 37, 84, 205, 289, 494, 783, 2060, 2843, 3626 }}

[[Badness]]: 0.213112

== Elvis ==

{{see also| Jubilismic clan #Elvis }}

[[Comma]]: 36905625/33554432

[[Mapping]]: [{{Val| 2 1 10 }}, {{Val| 0 2 -5 }}]

[[POTE generator]]: ~45/32 = 554.546

{{Optimal ET sequence|legend=1| 26, 80bc, 106bc, 132bc }}

[[Badness]]: 0.884000

== Emka ==

: ''See also: [[Hemimean clan #Emka]] and [[Horwell temperaments #Emkay]]''

[[Comma]]: {{monzo| -50 -8 27 }}

[[Mapping]]: [{{Val| 1 14 6 }}, {{Val| 0 -27 -8 }}]

[[POTE generator]]: ~9765625/7077888 = 551.784

{{Optimal ET sequence|legend=1| 37, 50, 87, 137, 224 }}

[[Badness]]: 0.544752

== Fervor ==

{{see also| Archytas clan #Fervor }}

[[Comma]]: 67108864/61509375

[[Mapping]]: [{{Val| 1 4 -2 }}, {{Val| 0 -5 9 }}]

[[POTE generator]]: ~64/45 = 577.705

{{Optimal ET sequence|legend=1| 2, 25, 27 }}

[[Badness]]: 0.852612

== Gamera ==

{{see also| Ragismic microtemperaments #Gamera }}

[[Comma]]: 12207031250000000000/12157665459056928801

[[Mapping]]: [{{Val| 1 6 10 }}, {{Val| 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

[[Comma]]: 2359296/1953125

[[Mapping]]: [{{Val| 1 0 2 }}, {{Val| 0 9 2 }}]

[[POTE generator]]: ~768/625 = 212.444

{{Optimal ET sequence|legend=1| 6b, 11b, 17c }}

[[Badness]]: 1.404977

== Gracecordial ==

: ''See also: [[Marvel temperaments #Gracecordial]]''

[[Comma]]: 17433922005/17179869184

[[Mapping]]: [{{Val| 1 0 34 }}, {{Val| 0 1 -20 }}]

[[POTE generator]]: ~3/2 = 700.734

{{Optimal ET sequence|legend=1| 12, 113, 125, 137 }}

[[Badness]]: 0.306809

== Hogzilla ==

[[Comma]]: 4428675/4194304

[[Mapping]]: [{{Val| 1 0 11 }}, {{Val| 0 2 -11 }}]

[[POTE generator]]: ~1215/1024 = 252.649

{{Optimal ET sequence|legend=1| 14, 19 }}

[[Badness]]: 0.424685

== Kangaroo ==

{{see also| Trienstonic clan #Parakangaroo }}

[[Comma]]: 64000/59049

[[Mapping]]: [{{Val| 1 0 -3 }}, {{Val| 0 3 10 }}]

[[POTE generator]]: ~27/20 = 561.195

{{Optimal ET sequence|legend=1| 15, 47b, 62b }}

[[Badness]]: 0.295767

== Kumonga ==

{{see also| Starling temperaments #Kumonga }}

[[Comma]]: 1289945088/1220703125

[[Mapping]]: [{{Val| 1 4 4 }}, {{Val| 0 -13 -9 }}]

[[POTE generator]]: ~144/125 = 222.912

{{Optimal ET sequence|legend=1| 16, 27, 43, 70, 183cc }}

[[Comma]]: 5629499534213120/5559060566555523

[[Mapping]]: [{{Val| 1 2 16 }}, {{Val| 0 -1 -33 }}]

[[POTE generator]]: ~3/2 = 702.630

{{Optimal ET sequence|legend=1| 41, 111, 152 }}

[[Badness]]: 0.636715

== Lafayette ==

{{see also| Mint temperaments #Progression }}

[[Comma]]: 3456/3125

[[Mapping]]: [{{Val| 1 1 2 }}, {{Val| 0 5 3 }}]

[[POTE generator]]: ~25/24 = 140.995

{{Optimal ET sequence|legend=1| 8, 9, 17c }}

: ''See also: [[Hemifamity temperaments #Leapday]] and [[Porwell temperaments #Polypyth]]''

[[Comma]]: 10737418240/10460353203

[[Mapping]]: [{{Val| 1 0 -31 }}, {{Val| 0 1 21 }}]

[[POTE generator]]: ~3/2 = 704.179

{{Optimal ET sequence|legend=1| 29, 46, 121, 167, 455bc, 622bbc }}

[[Badness]]: 0.523182

== Mabila ==

{{see also| Mabila family }}

[[Comma]]: 268435456/263671875

[[Mapping]]: [{{Val| 1 6 1 }}, {{Val| 0 -10 3 }}]

[[POTE generator]]: ~512/375 = 529.685

{{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }}

[[Badness]]: 0.232481

== Magus ==

: ''See also: [[Sensamagic clan #Magus]] and [[Starling temperaments #Amigo]]''

[[Comma]]: 50331648/48828125

[[Mapping]]: [{{Val| 1 -2 2 }}, {{Val| 0 11 1 }}]

[[POTE generator]]: ~5/4 = 391.225

{{Optimal ET sequence|legend=1| 3, 40, 43, 46, 181c, 227c, 273c, 319c }}

[[Badness]]: 0.360162

== Majvam ==

: ''See also: [[Subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]]''

[[Comma]]: 2404631929946112/2384185791015625

[[Mapping]]: [{{Val| 1 10 5 }}, {{Val| 0 -22 -7 }}]

[[POTE generator]]: ~125/96 = 458.995

{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }}

[[Badness]]: 0.356948

== Merman ==

{{see also| Marvel temperaments #Merman }}

[[Comma]]: 1121008359375/1099511627776

[[Mapping]]: [{{Val| 1 5 -5 }}, {{Val| 0 -7 15 }}]

[[POTE generator]]: ~45/32 = 585.634

{{Optimal ET sequence|legend=1| 41, 84, 125, 209, 334c, 543bc }}

[[Badness]]: 0.453848

== Mirkat ==

[[Comma]]: 4052555153018976267/4000000000000000000

[[Mapping]]: [{{Val| 3 2 1 }}, {{Val| 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]]: [{{Val| 1 3 1 }}, {{Val| 0 -15 14 }}]

[[POTE generator]]: ~16/15 = 113.240

{{Optimal ET sequence|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}

[[Badness]]: 0.609540

== Mowgli ==

{{see also| Hemimean clan #Mowglic }}

[[Comma]]: {{Monzo| 0 22 -15 }} = 31381059609/30517578125

[[Mapping]]: [{{Val| 1 0 0 }}, {{Val| 0 15 22 }}]

[[POTE generator]]: ~27/25 = 126.724

{{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161 }}

[[Badness]]: 0.653871

== Mynic ==

{{see also| Starling temperaments #Myna }}

[[Comma]]: 10077696/9765625

[[Mapping]]: [{{Val| 1 9 9 }}, {{Val| 0 -10 -9 }}]

[[POTE generator]]: ~6/5 = 310.140

{{Optimal ET sequence|legend=1| 27, 31, 58, 89, 325cc }}

[[Badness]]: 0.249965

== Nessafof ==

[[Comma]]: 481469424205824/476837158203125

[[Mapping]]: [{{Val| 3 2 5 }}, {{Val| 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 ==

{{See also| Breedsmic temperaments #Newt }}

[[Comma]]: {{Monzo| 95 -57 -2 }}

[[Mapping]]: [{{Val| 1 1 19 }}, {{Val| 0 2 -57 }}]

[[POTE generator]]: ~{{Monzo|47 -28 -1}} = 351.114

{{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 3592bc, 5523bbc }}

[[Badness]]: 1.528465

== Nusecond ==

{{see also| Starling temperaments #Nusecond }}

[[Comma]]: 51018336/48828125

[[Mapping]]: [{{Val| 1 3 4 }}, {{Val| 0 -11 -13 }}]

[[POTE generator]]: ~3125/2916 = 154.523

{{Optimal ET sequence|legend=1| 8, 23, 31, 70, 101, 132c, 233c, 365bcc }}

[[Badness]]: 0.466493

== Octacoid ==

[[Comma list]]: 8589934592/7688671875

{{Mapping|legend=1| 1 1 3 | 0 8 -9 }}

: mapping generators: ~2, ~16/15

[[Optimal tuning]]s:  

* [[CWE]]: ~2 = 1�, ~16/15 = 88.8168

{{Optimal ET sequence|legend=1| 13, 14, 27 }}

[[Badness]]: 1.75

== Oncle ==

{{see also| Gamelismic clan #Oncle }}

[[Comma]]: 145282683375/137438953472

[[Mapping]]: [{{Val| 1 1 6 }}, {{Val| 0 3 -19 }}]

[[POTE generator]]: ~4096/3645 = 232.521

{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}

[[Badness]]: 1.244699

== Oolong ==

{{see also| Starling temperaments #Oolong }}

[[Comma]]: 793437161472/762939453125

[[Mapping]]: [{{Val| 1 6 7 }}, {{Val| 0 -17 -18 }}]

[[POTE generator]]: ~6/5 = 311.694

{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }}

[[Badness]]: 0.942789

== Phillips ==

{{see also| Orwellismic temperaments #Phillips }}

[[Comma]]: 9685512225/8589934592

[[Mapping]]: [{{Val| 2 0 33 }}, {{Val| 0 1 -9 }}]

[[POTE generator]]: ~3/2 = 691.455

{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }}

[[Badness]]: 2.228904

== Progress ==

{{see also| Archytas clan #Progress }}

[[Comma]]: 32768/30375

[[Mapping]]: [{{Val| 1 0 5 }}, {{Val| 0 3 -5 }}]

[[POTE generator]]: ~64/45 = 561.264

{{Optimal ET sequence|legend=1| 2, 13, 15, 32c, 47bc, 62bc }}

[[Badness]]: 0.246073

== Quartemka ==

{{see also| Gamelismic clan #Quartemka }}

[[Comma]]: 1907348632812500/1853020188851841

[[Mapping]]: [{{Val| 1 4 6 }}, {{Val| 0 -21 -32 }}]

[[POTE generator]]: ~27/25 = 137.962

{{Optimal ET sequence|legend=1| 26, 61, 87, 287, 374, 461 }}

[[Badness]]: 1.381216

== Quasimoha ==

{{see also| Breedsmic temperaments #Quasimoha }}

[[Comma]]: 2353579470675/2199023255552

[[Mapping]]: [{{Val| 1 1 9 }}, {{Val| 0 2 -23 }}]

[[POTE generator]]: ~1048576/885735 = 348.600

{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}

[[Badness]]: 1.986675

 

 

 

 

[[Mapping]]: [{{Val| 1 31 0 }}, {{Val| 0 -38 3 }}]

 

 

 

[[Badness]] (Sintel): 30.581

== Quindromeda ==

{{see also| Quindromeda family }}

[[Comma]]: 72057594037927936/71489976421753125

[[POTE generator]]: ~4428675/4194304 = 99.526

[[Mapping]]: [{{Val| 1 2 0 }}, {{Val| 0 -5 28 }}]

{{Optimal ET sequence|legend=1| 12, 193, 205, 217, 422 }}

[[Badness]]: 0.399849

== Quintaleap ==

{{see also| Quintaleap family }}

[[Comma]]: 137438953472/134521003125

[[Mapping]]: [{{Val| 1 2 1 }}, {{Val| 0 -5 16 }}]

[[POTE generator]]: ~135/128 = 99.267

{{Optimal ET sequence|legend=1| 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]]: {{monzo| -57 17 13 }}

: mapping generators: ~16384/10125 = 869.392

[[Optimal tuning]] ([[CTE]]):  ~2 = 1\1, ~16384/10125 = 869.392

{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}

[[Category:Temperament collections]]

== Satin ==

{{see also| Canousmic temperaments #Satin }}

[[Comma]]: {{Monzo| 104 -70 3 }}

[[Mapping]]: [{{val| 1 2 12 }}, {{val| 0 -3 -70 }}]

[[POTE generator]]: ~{{monzo|-34 23 -1}} = 165.907

{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273 }}

[[Badness]]: 2.853049

== Semidimfourth ==

{{see also| Ragismic microtemperaments #Semidimfourth }}

[[Comma]]: {{monzo|7 41 -31}}

[[Mapping]]: [{{Val|1 21 28}}, {{Val|0 -31 -41}}]

[[POTE generator]]: ~162/125 = 448.449

{{Optimal ET sequence|legend=1| 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}

[[Badness]]: 0.233376

 

[[Comma]]: {{monzo|-12 -73 55}}

[[Mapping]]: [{{Val|1 36 48}}, {{Val|0 -55 -73}}]

[[POTE generator]]: ~162/125 = 449.127

{{Optimal ET sequence|legend=1| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}

[[Badness]]: 0.754866

== Semisept ==

{{see also| Hemimean clan #Semisept }}

[[Comma]]: 782757789696/762939453125

[[Mapping]]: [{{Val| 1 12 6 }}, {{Val| 0 -17 -6 }}]

[[POTE generator]]: ~192/125 = 735.146

{{Optimal ET sequence|legend=1| 18, 31, 80, 111 }}

[[Badness]]: 0.630576

== Sentinel ==

{{see also| Orwellismic temperaments #Sentinel }}

Subgroup: 2.3.5

[[Comma]]: 8968066875/8589934592

[[Mapping]]: [{{Val| 1 3 -3 }}, {{Val| 0 -4 15 }}]

[[POTE generator]]: ~512/405 = 425.474

{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bc }}