Miscellaneous 5-limit temperaments: Difference between revisions

Below are listed some high-badness 5-limit temperaments (Smith [[TE logflat badness]] > 0.2, sorted by the same metric). 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:  

* [[Very high accuracy temperaments]]

{{see also| Mint temperaments #Progression }}

Subgroup: 2.3.5

[[Comma]]: 3456/3125

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

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

[[Badness]]: 0.200483

: ''See also: [[Sensamagic clan #Pycnic]] and [[Marvel temperaments #Triton]]''

Subgroup: 2.3.5

[[Comma]]: 273375/262144

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

[[POTE generator]]: ~64/45 = 631.737

{{Optimal ET sequence|legend=1| 17, 19 }}

[[Badness]]: 0.200600

{{see also| Porwell temperaments #Dodifo }}

Subgroup: 2.3.5

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

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

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

[[Badness]]: 0.213112

Subgroup: 2.3.5

[[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

== Semidimfourth ==

{{see also| Ragismic microtemperaments #Semidimfourth }}

Subgroup: 2.3.5

[[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

== Undim ==

{{see also| Undim family }}

Subgroup: 2.3.5

[[Comma]]: 2199023255552/2179240250625

[[Mapping]]: [{{Val| 4 6 11 }}, {{Val| 0 1 -5 }}]

[[POTE generator]]: ~3/2 = 702.605

{{Optimal ET sequence|legend=1| 12, 140, 152, 164, 1076bc, 1228bc }}

[[Badness]]: 0.241703

{{see also| Starling temperaments #Myna }}

Subgroup: 2.3.5

[[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

{{see also| Archytas clan #Progress }}

Subgroup: 2.3.5

[[Comma]]: 32768/30375

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

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

[[Badness]]: 0.246073

== Countritonic ==

:''For extensions, see [[Ragismic microtemperaments #Countritonic]] and [[Hemifamity temperaments #Countriton]].''

Subgroup: 2.3.5

[[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

== Tritriple ==

{{see also| Gamelismic clan #Tritriple }}

Subgroup: 2.3.5

[[Comma]]: {{monzo| 31 20 -27 }}

[[Mapping]]: [{{Val| 1 -11 -7 }}, {{Val| 0 27 20 }}]

[[POTE generator]]: ~864/625 = 559.332

{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }}

[[Badness]]: 0.283570

== Kangaroo ==

{{see also| Trienstonic clan #Parakangaroo }}

Subgroup: 2.3.5

[[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

== Tertiaseptal ==

{{see also| Breedsmic temperaments #Tertiaseptal }}

Subgroup: 2.3.5

[[Comma]]: 579357147216796875/576460752303423488

[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -22 5 }}]

[[POTE generator]]: ~17578125/16777216 = 77.191

{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}

[[Badness]]: 0.297544

== Gracecordial ==

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

Subgroup: 2.3.5

[[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

== Untriton ==

: ''See also: [[Marvel temperaments #Untriton]], [[Porwell temperaments #Aufo]] and [[Triwellismic temperaments #Interaufo]]''

Subgroup: 2.3.5

[[Comma]]: 2270041927734375/2251799813685248

[[Mapping]]: [{{Val| 1 6 -7 }}, {{Val| 0 -9 19 }}]

[[POTE generator]]: ~45/32 = 588.722

{{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}

[[Badness]]: 0.307073

{{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

{{Optimal ET sequence|legend=1| 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }}

[[Badness]]: 0.317551

{{See also| Keemic temperaments #Sevond }}

Subgroup: 2.3.5

[[Comma]]: 5000000/4782969

[[Mapping]]: [{{Val| 7 0 -6 }}, {{Val| 0 1 2 }}]

[[POTE generator]]: ~3/2 = 706.288

{{Optimal ET sequence|legend=1| 7, 42, 49, 56, 119 }}

[[Badness]]: 0.339335

{{see also| Porwell temperaments #Absurdity }}

Subgroup: 2.3.5

[[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

Subgroup: 2.3.5

[[Mapping]]: [{{Val| 6 0 -5 }}, {{Val| 0 1 2 }}]

[[POTE generator]]: ~3/2 = 695.040

{{Optimal ET sequence|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}

[[Badness]]: 0.341757

{{see also| Mint temperaments #Subklei }}

Subgroup: 2.3.5

[[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

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

Subgroup: 2.3.5

[[Comma]]: 2404631929946112/2384185791015625

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

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

[[Badness]]: 0.356948

{{see also| Archytas clan #Beatles }}

Subgroup: 2.3.5

[[Comma]]: 524288/492075

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

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

[[Badness]]: 0.358542

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

Subgroup: 2.3.5

[[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

 

 

 

 

 

 

 

Subgroup: 2.3.5

[[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

{{see also| Marvel temperaments #Tritonic }}

Subgroup: 2.3.5

[[Comma]]: 553584375/536870912

[[Mapping]]: [{{Val| 1 4 -3 }}, {{Val| 0 -5 11 }}]

[[POTE generator]]: ~45/32 = 580.219

[[Badness]]: 0.378527

{{see also| Marvel temperaments #Wizard }}

Subgroup: 2.3.5

[[Comma]]: 2197265625/2147483648

[[Mapping]]: [{{Val| 2 1 5 }}, {{Val| 0 6 -1 }}]

Mapping generators: ~42875/32768, ~9375/8192

[[POTE generator]]: ~5/4 = 383.212

{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}

[[Badness]]: 0.386367

== Quindromeda ==

{{see also| Quindromeda family }}

Subgroup: 2.3.5

[[Comma]]: 72057594037927936/71489976421753125

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

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

 

 

[[Badness]]: 0.399849

 

== Hogzilla ==

Subgroup: 2.3.5

 

[[Comma]]: 4428675/4194304

 

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

 

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

[[Badness]]: 0.424685

 

 

 

 

 

 

 

{{see also| Marvel temperaments #Merman }}

Subgroup: 2.3.5

[[Comma]]: 1121008359375/1099511627776

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

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

[[Badness]]: 0.453848

Subgroup: 2.3.5

[[Comma]]: 17578125/16777216

[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -9 2 }}]

[[POTE generator]]: ~2048/1875 = 189.049

[[Badness]]: 0.460168

{{see also| Starling temperaments #Nusecond }}

Subgroup: 2.3.5

[[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

{{see also| Jubilismic clan #Comic }}

Subgroup: 2.3.5

[[Comma]]: 5120000/4782969

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

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

[[Badness]]: 0.491181

{{see also| Ragismic microtemperaments #Sfourth }}

Subgroup: 2.3.5

[[Comma]]: 617673396283947/610351562500000

[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -19 -31 }}]

[[POTE generator]]: ~1594323/1562500 = 26.2342

{{Optimal ET sequence|legend=1| 45, 46, 91, 137, 183 }}

[[Badness]]: 0.504555

{{see also| Starling temperaments #Thuja }}

Subgroup: 2.3.5

[[Comma]]: 254803968/244140625

[[Mapping]]: [{{Val| 1 -4 0 }}, {{Val| 0 12 5 }}]

[[POTE generator]]: ~3125/2304 = 558.592

[[Badness]]: 0.511109

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

Subgroup: 2.3.5

[[Comma]]: 10737418240/10460353203

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

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

 

 

[[Badness]]: 0.523182

 

== Septendecic ==

Subgroup: 2.3.5

 

[[Comma]]: {{monzo| 27 -17 }} = 134217728/129140163

 

[[Mapping]]: [{{Val| 17 27 0 }}, {{Val| 0 0 1 }}]

 

Mapping generators: ~531441/524288, ~5

 

[[POTE generator]]: ~5/4 = 389.193

{{Optimal ET sequence|legend=1| 17c, 34 }}

[[Badness]]: 0.541384

{{see also| Starling temperaments #Vines }}

Subgroup: 2.3.5

[[Comma]]: 156728328192/152587890625

[[Mapping]]: [{{Val| 2 7 8 }}, {{Val| 0 -8 -7 }}]

[[POTE generator]]: ~6/5 = 312.713

{{Optimal ET sequence|legend=1| 4, 42, 46, 96, 142 }}

[[Badness]]: 0.541831

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

Subgroup: 2.3.5

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

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

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

[[Badness]]: 0.544752

{{see also| Marvel temperaments #Misneb }}

Subgroup: 2.3.5

[[Comma]]: 145964630126953125/144115188075855872

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

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

[[Badness]]: 0.609540

{{see also| Hemimean clan #Semisept }}

Subgroup: 2.3.5

[[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

== Kwai ==

{{see also| Mirkwai clan #Kwai }}

Subgroup: 2.3.5

[[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

== Mowgli ==

{{see also| Hemimean clan #Mowglic }}

Subgroup: 2.3.5

[[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

== Septimin ==

{{see also| Marvel temperaments #Septimin }}

Subgroup: 2.3.5

[[Comma]]: 35595703125/34359738368

[[Mapping]]: [{{Val| 1 4 1 }}, {{Val| 0 -11 6 }}]

[[POTE generator]]: ~75/64 = 263.658

{{Optimal ET sequence|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }}

[[Badness]]: 0.670947

== Slurpee ==

{{see also| Mint temperaments #Slurpee }}

Subgroup: 2.3.5

[[Comma]]: 177147/156250

[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -7 -11 }}]

[[POTE generator]]: ~27/25 = 72.742

{{Optimal ET sequence|legend=1| 16, 17c, 33 }}

[[Badness]]: 0.689274

== Pentadecal ==

{{see also| Cloudy clan #Pentadecal }}

Subgroup: 2.3.5

[[Comma]]: 30517578125/29386561536

[[Mapping]]: [{{Val| 15 0 11 }}, {{Val| 0 1 1 }}]

[[POTE generator]]: ~3/2 = 702.652

{{Optimal ET sequence|legend=1| 15, 45, 60, 75, 135, 210c, 345cc }}

[[Badness]]: 0.692042

== 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 }}

[[Badness]]: 0.723413

== Undeka ==

{{see also| Keemic temperaments #Undeka }}

Subgroup: 2.3.5

[[Comma]]: 48828125/45349632

[[Mapping]]: [{{Val| 11 0 8 }}, {{Val| 0 1 1 }}]

[[POTE generator]]: ~3/2 = 703.829

{{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }}

[[Badness]]: 0.727539

== Kumonga ==

{{see also| Starling temperaments #Kumonga }}

Subgroup: 2.3.5

[[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 }}

[[Badness]]: 0.729609

== Semidimi ==

{{see also| Ragismic microtemperaments #Semidimi }}

Subgroup: 2.3.5

[[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

{{see also| Keemic temperaments #Quasitemp }}

Subgroup: 2.3.5

[[Comma]]: 6103515625/5804752896

[[Mapping]]: [{{Val| 1 5 5 }}, {{Val| 0 -14 -11 }}]

[[POTE generator]]: ~3125/2592 = 292.702

{{Optimal ET sequence|legend=1| 4, 37, 41 }}

[[Badness]]: 0.767824

{{see also| Starling temperaments #Cypress }}

Subgroup: 2.3.5

[[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

{{see also| Keemic temperaments #Chromo }}

Subgroup: 2.3.5

[[Comma]]: 1220703125/1146617856

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

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

[[Badness]]: 0.842835

{{see also| Marvel temperaments #Tertiosec }}