Miscellaneous 5-limit temperaments: Difference between revisions

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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:  
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:  
* Individual [[temperament families and clans]]
* Individual [[temperament families and clans]]
* Individual [[equivalence continuum|equivalence continua]]
* Individual [[equivalence continuum|equivalence continua]]
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* [[Very high accuracy temperaments]]
* [[Very high accuracy temperaments]]


== Absurdity ==
== Lafayette ==
{{see also| Porwell temperaments #Absurdity }}
{{see also| Mint temperaments #Progression }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 10460353203/10240000000
[[Comma]]: 3456/3125


[[Mapping]]: [{{Val| 7 0 -17 }}, {{Val| 0 1 3 }}]
[[Mapping]]: [{{Val| 1 1 2 }}, {{Val| 0 5 3 }}]


[[POTE generator]]: ~10/9 = 185.901
[[POTE generator]]: ~25/24 = 140.995


{{Optimal ET sequence|legend=1| 7, 70, 77, 84, 329, 413b, 497b }}
{{Optimal ET sequence|legend=1| 8, 9, 17c }}


[[Badness]]: 0.341202
[[Badness]]: 0.200483


== Archaeotherium ==
== Stump ==
{{see also| Gamelismic clan #Archaeotherium }}
: ''See also: [[Sensamagic clan #Pycnic]] and [[Marvel temperaments #Triton]]''


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 597871125/536870912
[[Comma]]: 273375/262144


[[Mapping]]: [{{Val| 1 1 5 }}, {{Val| 0 3 -14 }}]
[[Mapping]]: [{{Val| 1 0 6 }}, {{Val| 0 3 -7 }}]


[[POTE generator]]: ~1215/1024 = 230.351
[[POTE generator]]: ~64/45 = 631.737


{{Optimal ET sequence|legend=1| 21, 26, 73bc, 99bc }}
{{Optimal ET sequence|legend=1| 17, 19 }}


[[Badness]]: 1.434855
[[Badness]]: 0.200600


== Beatles ==
== Dodifo ==
{{see also| Archytas clan #Beatles }}
{{see also| Porwell temperaments #Dodifo }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 524288/492075
[[Comma]]: {{Monzo| -67 -9 35 }}


[[Mapping]]: [{{Val| 1 1 5 }}, {{Val| 0 2 -9 }}]
[[Mapping]]: [{{Val| 1 12 5 }}, {{Val| 0 -35 -9 }}]


[[POTE generator]]: ~512/405 = 355.930
[[POTE generator]]: ~768/625 = 357.088


{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}
{{Optimal ET sequence|legend=1| 37, 84, 205, 289, 494, 783, 2060, 2843, 3626 }}


[[Badness]]: 0.358542
[[Badness]]: 0.213112


== Bohpier ==
== Mabila ==
{{see also| Sensamagic clan #Bohpier }}
{{see also| Mabila family }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1220703125/1162261467
[[Comma]]: 268435456/263671875


[[Mapping]]: [{{Val| 1 0 0 }}, {{Val| 0 13 19 }}]
[[Mapping]]: [{{Val| 1 6 1 }}, {{Val| 0 -10 3 }}]


[[POTE generator]]: ~27/25 = 146.476
[[POTE generator]]: ~512/375 = 529.685


{{Optimal ET sequence|legend=1| 8, 41, 131, 172, 213c }}
{{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }}


[[Badness]]: 0.860534
[[Badness]]: 0.232481


== Casablanca ==
== Semidimfourth ==
{{see also| Starling temperaments #Casablanca }}
{{see also| Ragismic microtemperaments #Semidimfourth }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 20061226008576/19073486328125
[[Comma]]: {{monzo|7 41 -31}}


[[Mapping]]: [{{Val| 1 -7 -14 }}, {{Val| 0 19 14 }}]
[[Mapping]]: [{{Val|1 21 28}}, {{Val|0 -31 -41}}]


[[POTE generator]]: ~864/625 = 542.208
[[POTE generator]]: ~162/125 = 448.449


{{Optimal ET sequence|legend=1| 11b, 20b, 31, 73, 104c, 135c }}
{{Optimal ET sequence|legend=1| 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}


[[Badness]]: 1.423736
[[Badness]]: 0.233376


== Chromo ==
== Undim ==
{{see also| Keemic temperaments #Chromo }}
{{see also| Undim family }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1220703125/1146617856
[[Comma]]: 2199023255552/2179240250625


[[Mapping]]: [{{Val| 1 1 2 }}, {{Val| 0 13 7 }}]
[[Mapping]]: [{{Val| 4 6 11 }}, {{Val| 0 1 -5 }}]


[[POTE generator]]: ~25/24 = 53.922
[[POTE generator]]: ~3/2 = 702.605


{{Optimal ET sequence|legend=1| 22, 45, 67c, 89c }}
{{Optimal ET sequence|legend=1| 12, 140, 152, 164, 1076bc, 1228bc }}


[[Badness]]: 0.842835
[[Badness]]: 0.241703


== Comic ==
== Mynic ==
{{see also| Jubilismic clan #Comic }}
{{see also| Starling temperaments #Myna }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 5120000/4782969
[[Comma]]: 10077696/9765625
 
[[Mapping]]: [{{Val| 1 9 9 }}, {{Val| 0 -10 -9 }}]


[[Mapping]]: [{{Val| 2 1 -3 }}, {{Val| 0 2 7 }}]
[[POTE generator]]: ~6/5 = 310.140


[[POTE generator]]: ~81/80 = 55.382
{{Optimal ET sequence|legend=1| 27, 31, 58, 89, 325cc }}


{{Optimal ET sequence|legend=1| 20c, 22, 86b, 108b, 130b }}
[[Badness]]: 0.249965


[[Badness]]: 0.491181
== Progress ==
{{see also| Archytas clan #Progress }}


== Cotoneum ==
{{See also| Hemimage temperaments #Cotoneum }}
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| 80 -49 -1 }}
[[Comma]]: 32768/30375


[[Mapping]]: [{{Val| 1 2 -18 }}, {{Val| 0 -1 49 }}]
[[Mapping]]: [{{Val| 1 0 5 }}, {{Val| 0 3 -5 }}]


[[POTE generator]]: ~3/2 = 702.315
[[POTE generator]]: ~64/45 = 561.264


{{Optimal ET sequence|legend=1| 41, 135c, 176, 217, 475, 1167, 1642, 2117b }}
{{Optimal ET sequence|legend=1| 2, 13, 15, 32c, 47bc, 62bc }}


[[Badness]]: 1.240078
[[Badness]]: 0.246073


== Counterhanson ==
== Countritonic ==
{{See also| Ragismic microtemperaments #Counterkleismic }}
{{See also| Schismic–Mercator equivalence continuum #Countritonic }}
:''For extensions, see [[Ragismic microtemperaments #Countritonic]] and [[Hemifamity temperaments #Countriton]].''


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| -20 -24 25 }} = 298023223876953125/296148833645101056
[[Comma]]: 16777216000000000/16677181699666569
 
[[Mapping]]: [{{Val| 1 6 19 }}, {{Val| 0 -9 -34 }}]


[[Mapping]]: [{{Val| 1 -5 -4 }}, {{Val| 0 25 24 }}]
[[POTE generator]]: ~14348907/10240000 = 588.636


[[POTE generator]]: ~6/5 = 316.081
{{Optimal ET sequence|legend=1| 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b }}


{{Optimal ET sequence|legend=1| 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }}
[[Badness]]: 0.255594


[[Badness]]: 0.317551
== Tritriple ==
{{see also| Gamelismic clan #Tritriple }}


== Countermeantone ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| 10 23 -20 }} = 96402615118848/95367431640625
[[Comma]]: {{monzo| 31 20 -27 }}


[[Mapping]]: [{{Val| 1 10 12 }}, {{Val| 0 -20 -23 }}]
[[Mapping]]: [{{Val| 1 -11 -7 }}, {{Val| 0 27 20 }}]


[[POTE generator]]: ~104976/78125 = 504.913
[[POTE generator]]: ~864/625 = 559.332


{{Optimal ET sequence|legend=1| 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c }}
{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }}


[[Badness]]: 0.373477
[[Badness]]: 0.283570


== Countritonic ==
== Kangaroo ==
{{See also| Schismic–Mercator equivalence continuum #Countritonic }}
{{see also| Trienstonic clan #Parakangaroo }}
:''For extensions, see [[Ragismic microtemperaments #Countritonic]] and [[Hemifamity temperaments #Countriton]].''


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 16777216000000000/16677181699666569
[[Comma]]: 64000/59049


[[Mapping]]: [{{Val| 1 6 19 }}, {{Val| 0 -9 -34 }}]
[[Mapping]]: [{{Val| 1 0 -3 }}, {{Val| 0 3 10 }}]


[[POTE generator]]: ~14348907/10240000 = 588.636
[[POTE generator]]: ~27/20 = 561.195


{{Optimal ET sequence|legend=1| 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b }}
{{Optimal ET sequence|legend=1| 15, 47b, 62b }}


[[Badness]]: 0.255594
[[Badness]]: 0.295767


== Cypress ==
== Tertiaseptal ==
{{see also| Starling temperaments #Cypress }}
{{see also| Breedsmic temperaments #Tertiaseptal }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 258280326/244140625
[[Comma]]: 579357147216796875/576460752303423488


[[Mapping]]: [{{Val| 1 7 10 }}, {{Val| 0 -12 -17 }}]
[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -22 5 }}]


[[POTE generator]]: ~4374/3125 = 541.726
[[POTE generator]]: ~17578125/16777216 = 77.191


{{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c, 381bcc }}
{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}


[[Badness]]: 0.816635
[[Badness]]: 0.297544


== Delorean ==
== Gracecordial ==
{{see also| Mint temperaments #Subklei }}
: ''See also: [[Marvel temperaments #Gracecordial]]''


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 17496/15625
[[Comma]]: 17433922005/17179869184


[[Mapping]]: [{{Val| 1 3 4 }}, {{Val| 0 -6 -7 }}]
[[Mapping]]: [{{Val| 1 0 34 }}, {{Val| 0 1 -20 }}]


[[POTE generator]]: ~6/5 = 284.293
[[POTE generator]]: ~3/2 = 700.734


{{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }}
{{Optimal ET sequence|legend=1| 12, 113, 125, 137 }}


[[Badness]]: 0.355937
[[Badness]]: 0.306809


== Diesic ==
== Untriton ==
{{see also| Orwellismic temperaments #Diesic }}
: ''See also: [[Marvel temperaments #Untriton]], [[Porwell temperaments #Aufo]] and [[Triwellismic temperaments #Interaufo]]''


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 10460353203/9765625000
[[Comma]]: 2270041927734375/2251799813685248


[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -13 -21 }}]
[[Mapping]]: [{{Val| 1 6 -7 }}, {{Val| 0 -9 19 }}]


[[POTE generator]]: ~6561/6250 = 38.571
[[POTE generator]]: ~45/32 = 588.722


{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
{{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}


[[Badness]]: 1.344681
[[Badness]]: 0.307073


== Dodifo ==
== Counterhanson ==
{{see also| Porwell temperaments #Dodifo }}
{{See also| Ragismic microtemperaments #Counterkleismic }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| -67 -9 35 }}
[[Comma]]: {{Monzo| -20 -24 25 }} = 298023223876953125/296148833645101056


[[Mapping]]: [{{Val| 1 12 5 }}, {{Val| 0 -35 -9 }}]
[[Mapping]]: [{{Val| 1 -5 -4 }}, {{Val| 0 25 24 }}]


[[POTE generator]]: ~768/625 = 357.088
[[POTE generator]]: ~6/5 = 316.081


{{Optimal ET sequence|legend=1| 37, 84, 205, 289, 494, 783, 2060, 2843, 3626 }}
{{Optimal ET sequence|legend=1| 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }}


[[Badness]]: 0.213112
[[Badness]]: 0.317551


== Elvis ==
== Sevond ==
{{see also| Jubilismic clan #Elvis }}
{{See also| Keemic temperaments #Sevond }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 36905625/33554432
[[Comma]]: 5000000/4782969


[[Mapping]]: [{{Val| 2 1 10 }}, {{Val| 0 2 -5 }}]
[[Mapping]]: [{{Val| 7 0 -6 }}, {{Val| 0 1 2 }}]


[[POTE generator]]: ~45/32 = 554.546
[[POTE generator]]: ~3/2 = 706.288


{{Optimal ET sequence|legend=1| 26, 80bc, 106bc, 132bc }}
{{Optimal ET sequence|legend=1| 7, 42, 49, 56, 119 }}


[[Badness]]: 0.884000
[[Badness]]: 0.339335


== Emka ==
== Absurdity ==
: ''See also: [[Hemimean clan #Emka]] and [[Horwell temperaments #Emkay]]''
{{see also| Porwell temperaments #Absurdity }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{monzo| -50 -8 27 }}
[[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
 
== Wronecki ==
Subgroup: 2.3.5
 
[[Comma]]: 531441/500000


[[Mapping]]: [{{Val| 1 14 6 }}, {{Val| 0 -27 -8 }}]
[[Mapping]]: [{{Val| 6 0 -5 }}, {{Val| 0 1 2 }}]


[[POTE generator]]: ~9765625/7077888 = 551.784
[[POTE generator]]: ~3/2 = 695.040


{{Optimal ET sequence|legend=1| 37, 50, 87, 137, 224 }}
{{Optimal ET sequence|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}


[[Badness]]: 0.544752
[[Badness]]: 0.341757


== Fervor ==
== Delorean ==
{{see also| Archytas clan #Fervor }}
{{see also| Mint temperaments #Subklei }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 67108864/61509375
[[Comma]]: 17496/15625


[[Mapping]]: [{{Val| 1 4 -2 }}, {{Val| 0 -5 9 }}]
[[Mapping]]: [{{Val| 1 3 4 }}, {{Val| 0 -6 -7 }}]


[[POTE generator]]: ~64/45 = 577.705
[[POTE generator]]: ~6/5 = 284.293


{{Optimal ET sequence|legend=1| 2, 25, 27 }}
{{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }}


[[Badness]]: 0.852612
[[Badness]]: 0.355937


== Gamera ==
== Majvam ==
{{see also| Ragismic microtemperaments #Gamera }}
: ''See also: [[Subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]]''


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 12207031250000000000/12157665459056928801
[[Comma]]: 2404631929946112/2384185791015625
 
[[Mapping]]: [{{Val| 1 10 5 }}, {{Val| 0 -22 -7 }}]


[[Mapping]]: [{{Val| 1 6 10 }}, {{Val| 0 -23 -40 }}]
[[POTE generator]]: ~125/96 = 458.995


Optimal tuning ([[CWE]]): ~2 = 1\1, ~2500/2187 = 230.345
{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }}


Supporting ETs: 99, 323, 224, 26, 125, 547, 5bccc, 422, 73, 870, 21bcc, 47bc, 771, 349
[[Badness]]: 0.356948


[[Badness]] (Sintel): 6.394
== Beatles ==
{{see also| Archytas clan #Beatles }}


== Genocchi ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2359296/1953125
[[Comma]]: 524288/492075


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


[[POTE generator]]: ~768/625 = 212.444
[[POTE generator]]: ~512/405 = 355.930


{{Optimal ET sequence|legend=1| 6b, 11b, 17c }}
{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}


[[Badness]]: 1.404977
[[Badness]]: 0.358542


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


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 17433922005/17179869184
[[Comma]]: 50331648/48828125


[[Mapping]]: [{{Val| 1 0 34 }}, {{Val| 0 1 -20 }}]
[[Mapping]]: [{{Val| 1 -2 2 }}, {{Val| 0 11 1 }}]


[[POTE generator]]: ~3/2 = 700.734
[[POTE generator]]: ~5/4 = 391.225


{{Optimal ET sequence|legend=1| 12, 113, 125, 137 }}
{{Optimal ET sequence|legend=1| 3, 40, 43, 46, 181c, 227c, 273c, 319c }}


[[Badness]]: 0.306809
[[Badness]]: 0.360162


== Hemififths ==
== Hemififths ==
Line 332: Line 350:
[[Badness]]: 0.372848
[[Badness]]: 0.372848


== Hogzilla ==
== Countermeantone ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 4428675/4194304
[[Comma]]: {{Monzo| 10 23 -20 }} = 96402615118848/95367431640625


[[Mapping]]: [{{Val| 1 0 11 }}, {{Val| 0 2 -11 }}]
[[Mapping]]: [{{Val| 1 10 12 }}, {{Val| 0 -20 -23 }}]


[[POTE generator]]: ~1215/1024 = 252.649
[[POTE generator]]: ~104976/78125 = 504.913


{{Optimal ET sequence|legend=1| 14, 19 }}
{{Optimal ET sequence|legend=1| 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c }}


[[Badness]]: 0.424685
[[Badness]]: 0.373477


== Kangaroo ==
== Tritonic ==
{{see also| Trienstonic clan #Parakangaroo }}
{{see also| Marvel temperaments #Tritonic }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 64000/59049
[[Comma]]: 553584375/536870912


[[Mapping]]: [{{Val| 1 0 -3 }}, {{Val| 0 3 10 }}]
[[Mapping]]: [{{Val| 1 4 -3 }}, {{Val| 0 -5 11 }}]


[[POTE generator]]: ~27/20 = 561.195
[[POTE generator]]: ~45/32 = 580.219


{{Optimal ET sequence|legend=1| 15, 47b, 62b }}
{{Optimal ET sequence|legend=1| 29, 31, 60, 91 }}


[[Badness]]: 0.295767
[[Badness]]: 0.378527


== Kumonga ==
== Wizard ==
{{see also| Starling temperaments #Kumonga }}
{{see also| Marvel temperaments #Wizard }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1289945088/1220703125
[[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
 
Scales (Scala files): [[wizard22]]
 
== Quindromeda ==
{{see also| Quindromeda family }}
 
Subgroup: 2.3.5


[[Mapping]]: [{{Val| 1 4 4 }}, {{Val| 0 -13 -9 }}]
[[Comma]]: 72057594037927936/71489976421753125


[[POTE generator]]: ~144/125 = 222.912
[[POTE generator]]: ~4428675/4194304 = 99.526


{{Optimal ET sequence|legend=1| 16, 27, 43, 70, 183cc }}
[[Mapping]]: [{{Val| 1 2 0 }}, {{Val| 0 -5 28 }}]


[[Badness]]: 0.729609
{{Optimal ET sequence|legend=1| 12, 193, 205, 217, 422 }}


== Kwai ==
[[Badness]]: 0.399849
{{see also| Mirkwai clan #Kwai }}


== Hogzilla ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 5629499534213120/5559060566555523
[[Comma]]: 4428675/4194304


[[Mapping]]: [{{Val| 1 2 16 }}, {{Val| 0 -1 -33 }}]
[[Mapping]]: [{{Val| 1 0 11 }}, {{Val| 0 2 -11 }}]


[[POTE generator]]: ~3/2 = 702.630
[[POTE generator]]: ~1215/1024 = 252.649


{{Optimal ET sequence|legend=1| 41, 111, 152 }}
{{Optimal ET sequence|legend=1| 14, 19 }}


[[Badness]]: 0.636715
[[Badness]]: 0.424685


== Lafayette ==
== Quintaleap ==
{{see also| Mint temperaments #Progression }}
{{see also| Quintaleap family }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 3456/3125
[[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
 
== Merman ==
{{see also| Marvel temperaments #Merman }}
 
Subgroup: 2.3.5


[[Mapping]]: [{{Val| 1 1 2 }}, {{Val| 0 5 3 }}]
[[Comma]]: 1121008359375/1099511627776


[[POTE generator]]: ~25/24 = 140.995
[[Mapping]]: [{{Val| 1 5 -5 }}, {{Val| 0 -7 15 }}]


{{Optimal ET sequence|legend=1| 8, 9, 17c }}
[[POTE generator]]: ~45/32 = 585.634


[[Badness]]: 0.200483
{{Optimal ET sequence|legend=1| 41, 84, 125, 209, 334c, 543bc }}


== Leapday ==
[[Badness]]: 0.453848
: ''See also: [[Hemifamity temperaments #Leapday]] and [[Porwell temperaments #Polypyth]]''


== Unsmate ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 10737418240/10460353203
[[Comma]]: 17578125/16777216


[[Mapping]]: [{{Val| 1 0 -31 }}, {{Val| 0 1 21 }}]
[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -9 2 }}]


[[POTE generator]]: ~3/2 = 704.179
[[POTE generator]]: ~2048/1875 = 189.049


{{Optimal ET sequence|legend=1| 29, 46, 121, 167, 455bc, 622bbc }}
{{Optimal ET sequence|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}


[[Badness]]: 0.523182
[[Badness]]: 0.460168


== Mabila ==
== Nusecond ==
{{see also| Mabila family }}
{{see also| Starling temperaments #Nusecond }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 268435456/263671875
[[Comma]]: 51018336/48828125


[[Mapping]]: [{{Val| 1 6 1 }}, {{Val| 0 -10 3 }}]
[[Mapping]]: [{{Val| 1 3 4 }}, {{Val| 0 -11 -13 }}]


[[POTE generator]]: ~512/375 = 529.685
[[POTE generator]]: ~3125/2916 = 154.523


{{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }}
{{Optimal ET sequence|legend=1| 8, 23, 31, 70, 101, 132c, 233c, 365bcc }}


[[Badness]]: 0.232481
[[Badness]]: 0.466493


== Magus ==
== Comic ==
: ''See also: [[Sensamagic clan #Magus]] and [[Starling temperaments #Amigo]]''
{{see also| Jubilismic clan #Comic }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 50331648/48828125
[[Comma]]: 5120000/4782969


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


[[POTE generator]]: ~5/4 = 391.225
[[POTE generator]]: ~81/80 = 55.382


{{Optimal ET sequence|legend=1| 3, 40, 43, 46, 181c, 227c, 273c, 319c }}
{{Optimal ET sequence|legend=1| 20c, 22, 86b, 108b, 130b }}


[[Badness]]: 0.360162
[[Badness]]: 0.491181


== Majvam ==
== Sfourth ==
: ''See also: [[Subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]]''
{{see also| Ragismic microtemperaments #Sfourth }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2404631929946112/2384185791015625
[[Comma]]: 617673396283947/610351562500000


[[Mapping]]: [{{Val| 1 10 5 }}, {{Val| 0 -22 -7 }}]
[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -19 -31 }}]


[[POTE generator]]: ~125/96 = 458.995
[[POTE generator]]: ~1594323/1562500 = 26.2342


{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }}
{{Optimal ET sequence|legend=1| 45, 46, 91, 137, 183 }}


[[Badness]]: 0.356948
[[Badness]]: 0.504555


== Merman ==
== Thuja ==
{{see also| Marvel temperaments #Merman }}
{{see also| Starling temperaments #Thuja }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1121008359375/1099511627776
[[Comma]]: 254803968/244140625


[[Mapping]]: [{{Val| 1 5 -5 }}, {{Val| 0 -7 15 }}]
[[Mapping]]: [{{Val| 1 -4 0 }}, {{Val| 0 12 5 }}]


[[POTE generator]]: ~45/32 = 585.634
[[POTE generator]]: ~3125/2304 = 558.592


{{Optimal ET sequence|legend=1| 41, 84, 125, 209, 334c, 543bc }}
{{Optimal ET sequence|legend=1| 15, 43, 58 }}


[[Badness]]: 0.453848
[[Badness]]: 0.511109


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


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 4052555153018976267/4000000000000000000
[[Comma]]: 10737418240/10460353203


[[Mapping]]: [{{Val| 3 2 1 }}, {{Val| 0 6 13 }}]
[[Mapping]]: [{{Val| 1 0 -31 }}, {{Val| 0 1 21 }}]


Optimal tuning ([[CWE]]): ~2000000/1594323 = 1\3, ~10/9 = 183.585
[[POTE generator]]: ~3/2 = 704.179


Supporting ETs: 72, 183, 6cc, 39, 111, 33c, 255, 294, 438, 327, 105c, 150c, 45bccc, 477
{{Optimal ET sequence|legend=1| 29, 46, 121, 167, 455bc, 622bbc }}


[[Badness]] (Sintel): 17.631
[[Badness]]: 0.523182


== Misneb ==
== Septendecic ==
{{see also| Marvel temperaments #Misneb }}
Subgroup: 2.3.5


Subgroup: 2.3.5
[[Comma]]: {{monzo| 27 -17 }} = 134217728/129140163


[[Comma]]: 145964630126953125/144115188075855872
[[Mapping]]: [{{Val| 17 27 0 }}, {{Val| 0 0 1 }}]


[[Mapping]]: [{{Val| 1 3 1 }}, {{Val| 0 -15 14 }}]
Mapping generators: ~531441/524288, ~5


[[POTE generator]]: ~16/15 = 113.240
[[POTE generator]]: ~5/4 = 389.193


{{Optimal ET sequence|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}
{{Optimal ET sequence|legend=1| 17c, 34 }}


[[Badness]]: 0.609540
[[Badness]]: 0.541384


== Mowgli ==
== Vines ==
{{see also| Hemimean clan #Mowglic }}
{{see also| Starling temperaments #Vines }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| 0 22 -15 }} = 31381059609/30517578125
[[Comma]]: 156728328192/152587890625


[[Mapping]]: [{{Val| 1 0 0 }}, {{Val| 0 15 22 }}]
[[Mapping]]: [{{Val| 2 7 8 }}, {{Val| 0 -8 -7 }}]


[[POTE generator]]: ~27/25 = 126.724
[[POTE generator]]: ~6/5 = 312.713


{{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161 }}
{{Optimal ET sequence|legend=1| 4, 42, 46, 96, 142 }}


[[Badness]]: 0.653871
[[Badness]]: 0.541831


== Mynic ==
== Emka ==
{{see also| Starling temperaments #Myna }}
: ''See also: [[Hemimean clan #Emka]] and [[Horwell temperaments #Emkay]]''


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 10077696/9765625
[[Comma]]: {{monzo| -50 -8 27 }}


[[Mapping]]: [{{Val| 1 9 9 }}, {{Val| 0 -10 -9 }}]
[[Mapping]]: [{{Val| 1 14 6 }}, {{Val| 0 -27 -8 }}]


[[POTE generator]]: ~6/5 = 310.140
[[POTE generator]]: ~9765625/7077888 = 551.784


{{Optimal ET sequence|legend=1| 27, 31, 58, 89, 325cc }}
{{Optimal ET sequence|legend=1| 37, 50, 87, 137, 224 }}


[[Badness]]: 0.249965
[[Badness]]: 0.544752


== Nessafof ==
== Misneb ==
{{see also| Marvel temperaments #Misneb }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 481469424205824/476837158203125
[[Comma]]: 145964630126953125/144115188075855872


[[Mapping]]: [{{Val| 3 2 5 }}, {{Val| 0 7 5 }}]
[[Mapping]]: [{{Val| 1 3 1 }}, {{Val| 0 -15 14 }}]


Optimal tuning ([[CWE]]): ~78125/62208 = 1\3, ~9765625/8957952 = 157.409
[[POTE generator]]: ~16/15 = 113.240


Supporting ETs: 15, 99, 84, 183, 282, 69, 114, 9bbc, 267, 54b, 381, 24bbc, 39bc, 465
{{Optimal ET sequence|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}


[[Badness]] (Sintel): 7.807
[[Badness]]: 0.609540


== Newt ==
== Semisept ==
{{See also| Breedsmic temperaments #Newt }}
{{see also| Hemimean clan #Semisept }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| 95 -57 -2 }}
[[Comma]]: 782757789696/762939453125


[[Mapping]]: [{{Val| 1 1 19 }}, {{Val| 0 2 -57 }}]
[[Mapping]]: [{{Val| 1 12 6 }}, {{Val| 0 -17 -6 }}]


[[POTE generator]]: ~{{Monzo|47 -28 -1}} = 351.114
[[POTE generator]]: ~192/125 = 735.146


{{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 3592bc, 5523bbc }}
{{Optimal ET sequence|legend=1| 18, 31, 80, 111 }}


[[Badness]]: 1.528465
[[Badness]]: 0.630576


== Nusecond ==
== Kwai ==
{{see also| Starling temperaments #Nusecond }}
{{see also| Mirkwai clan #Kwai }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 51018336/48828125
[[Comma]]: 5629499534213120/5559060566555523


[[Mapping]]: [{{Val| 1 3 4 }}, {{Val| 0 -11 -13 }}]
[[Mapping]]: [{{Val| 1 2 16 }}, {{Val| 0 -1 -33 }}]


[[POTE generator]]: ~3125/2916 = 154.523
[[POTE generator]]: ~3/2 = 702.630


{{Optimal ET sequence|legend=1| 8, 23, 31, 70, 101, 132c, 233c, 365bcc }}
{{Optimal ET sequence|legend=1| 41, 111, 152 }}


[[Badness]]: 0.466493
[[Badness]]: 0.636715


== Octacoid ==
== Mowgli ==
[[Subgroup]]: 2.3.5
{{see also| Hemimean clan #Mowglic }}


[[Comma list]]: 8589934592/7688671875
Subgroup: 2.3.5


{{Mapping|legend=1| 1 1 3 | 0 8 -9 }}
[[Comma]]: {{Monzo| 0 22 -15 }} = 31381059609/30517578125


: mapping generators: ~2, ~16/15
[[Mapping]]: [{{Val| 1 0 0 }}, {{Val| 0 15 22 }}]


[[Optimal tuning]]s:  
[[POTE generator]]: ~27/25 = 126.724
* [[CTE]]: ~2 = 1�, ~16/15 = 88.7331
* [[CWE]]: ~2 = 1�, ~16/15 = 88.8168


{{Optimal ET sequence|legend=1| 13, 14, 27 }}
{{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161 }}


[[Badness]]: 1.75
[[Badness]]: 0.653871


== Oncle ==
== Septimin ==
{{see also| Gamelismic clan #Oncle }}
{{see also| Marvel temperaments #Septimin }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 145282683375/137438953472
[[Comma]]: 35595703125/34359738368


[[Mapping]]: [{{Val| 1 1 6 }}, {{Val| 0 3 -19 }}]
[[Mapping]]: [{{Val| 1 4 1 }}, {{Val| 0 -11 6 }}]


[[POTE generator]]: ~4096/3645 = 232.521
[[POTE generator]]: ~75/64 = 263.658


{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}
{{Optimal ET sequence|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }}


[[Badness]]: 1.244699
[[Badness]]: 0.670947


== Oolong ==
== Slurpee ==
{{see also| Starling temperaments #Oolong }}
{{see also| Mint temperaments #Slurpee }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 793437161472/762939453125
[[Comma]]: 177147/156250


[[Mapping]]: [{{Val| 1 6 7 }}, {{Val| 0 -17 -18 }}]
[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -7 -11 }}]


[[POTE generator]]: ~6/5 = 311.694
[[POTE generator]]: ~27/25 = 72.742


{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }}
{{Optimal ET sequence|legend=1| 16, 17c, 33 }}


[[Badness]]: 0.942789
[[Badness]]: 0.689274


== Pentadecal ==
== Pentadecal ==
Line 645: Line 693:
[[Badness]]: 0.692042
[[Badness]]: 0.692042


== Phillips ==
== Sentinel ==
{{see also| Orwellismic temperaments #Phillips }}
{{see also| Orwellismic temperaments #Sentinel }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 9685512225/8589934592
[[Comma]]: 8968066875/8589934592


[[Mapping]]: [{{Val| 2 0 33 }}, {{Val| 0 1 -9 }}]
[[Mapping]]: [{{Val| 1 3 -3 }}, {{Val| 0 -4 15 }}]


[[POTE generator]]: ~3/2 = 691.455
[[POTE generator]]: ~512/405 = 425.474


{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bc }}


[[Badness]]: 2.228904
[[Badness]]: 0.723413


== Progress ==
== Undeka ==
{{see also| Archytas clan #Progress }}
{{see also| Keemic temperaments #Undeka }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 32768/30375
[[Comma]]: 48828125/45349632


[[Mapping]]: [{{Val| 1 0 5 }}, {{Val| 0 3 -5 }}]
[[Mapping]]: [{{Val| 11 0 8 }}, {{Val| 0 1 1 }}]


[[POTE generator]]: ~64/45 = 561.264
[[POTE generator]]: ~3/2 = 703.829


{{Optimal ET sequence|legend=1| 2, 13, 15, 32c, 47bc, 62bc }}
{{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }}


[[Badness]]: 0.246073
[[Badness]]: 0.727539


== Quartemka ==
== Kumonga ==
{{see also| Gamelismic clan #Quartemka }}
{{see also| Starling temperaments #Kumonga }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1907348632812500/1853020188851841
[[Comma]]: 1289945088/1220703125


[[Mapping]]: [{{Val| 1 4 6 }}, {{Val| 0 -21 -32 }}]
[[Mapping]]: [{{Val| 1 4 4 }}, {{Val| 0 -13 -9 }}]


[[POTE generator]]: ~27/25 = 137.962
[[POTE generator]]: ~144/125 = 222.912


{{Optimal ET sequence|legend=1| 26, 61, 87, 287, 374, 461 }}
{{Optimal ET sequence|legend=1| 16, 27, 43, 70, 183cc }}


[[Badness]]: 1.381216
[[Badness]]: 0.729609


== Quasimoha ==
== Semidimi ==
{{see also| Breedsmic temperaments #Quasimoha }}
{{see also| Ragismic microtemperaments #Semidimi }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2353579470675/2199023255552
[[Comma]]: {{monzo|-12 -73 55}}


[[Mapping]]: [{{Val| 1 1 9 }}, {{Val| 0 2 -23 }}]
[[Mapping]]: [{{Val|1 36 48}}, {{Val|0 -55 -73}}]


[[POTE generator]]: ~1048576/885735 = 348.600
[[POTE generator]]: ~162/125 = 449.127


{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}
{{Optimal ET sequence|legend=1| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}


[[Badness]]: 1.986675
[[Badness]]: 0.754866
 
== Quasiorwell ==
 
Subgroup: 2.3.5
 
[[Comma]]: 9903520314283042199192993792/9822542779147624969482421875
 
[[Mapping]]: [{{Val| 1 31 0 }}, {{Val| 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 ==
== Quasitemp ==
Line 734: Line 768:
[[Badness]]: 0.767824
[[Badness]]: 0.767824


== Quindromeda ==
== Cypress ==
{{see also| Quindromeda family }}
{{see also| Starling temperaments #Cypress }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 72057594037927936/71489976421753125
[[Comma]]: 258280326/244140625


[[POTE generator]]: ~4428675/4194304 = 99.526
[[Mapping]]: [{{Val| 1 7 10 }}, {{Val| 0 -12 -17 }}]


[[Mapping]]: [{{Val| 1 2 0 }}, {{Val| 0 -5 28 }}]
[[POTE generator]]: ~4374/3125 = 541.726


{{Optimal ET sequence|legend=1| 12, 193, 205, 217, 422 }}
{{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c, 381bcc }}


[[Badness]]: 0.399849
[[Badness]]: 0.816635


== Quintaleap ==
== Chromo ==
{{see also| Quintaleap family }}
{{see also| Keemic temperaments #Chromo }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 137438953472/134521003125
[[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


[[Mapping]]: [{{Val| 1 2 1 }}, {{Val| 0 -5 16 }}]
== Tertiosec ==
{{see also| Marvel temperaments #Tertiosec }}


[[POTE generator]]: ~135/128 = 99.267
Subgroup: 2.3.5


{{Optimal ET sequence|legend=1| 12, 109, 121, 133 }}
[[Comma]]: {{monzo| -89 21 24 }}


[[Badness]]: 0.444506
[[Mapping]]: [{{Val| 3 7 5 }}, {{Val| 0 -8 7 }}]


== Rarity ==
[[POTE generator]]: ~16/15 = 112.281
{{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.
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171 }}


[[Subgroup]]: 2.3.5
[[Badness]]: 0.851003


[[Comma list]]: {{monzo| -57 17 13 }}
== Fervor ==
{{see also| Archytas clan #Fervor }}


{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}
Subgroup: 2.3.5


: mapping generators: ~16384/10125 = 869.392
[[Comma]]: 67108864/61509375


[[Optimal tuning]] ([[CTE]]):  ~2 = 1\1, ~16384/10125 = 869.392
[[Mapping]]: [{{Val| 1 4 -2 }}, {{Val| 0 -5 9 }}]


{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}
[[POTE generator]]: ~64/45 = 577.705


[[Badness]]: 4.23
{{Optimal ET sequence|legend=1| 2, 25, 27 }}


[[Category:Temperament collections]]
[[Badness]]: 0.852612


== Satin ==
== Bohpier ==
{{see also| Canousmic temperaments #Satin }}
{{see also| Sensamagic clan #Bohpier }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| 104 -70 3 }}
[[Comma]]: 1220703125/1162261467


[[Mapping]]: [{{val| 1 2 12 }}, {{val| 0 -3 -70 }}]
[[Mapping]]: [{{Val| 1 0 0 }}, {{Val| 0 13 19 }}]


[[POTE generator]]: ~{{monzo|-34 23 -1}} = 165.907
[[POTE generator]]: ~27/25 = 146.476


{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273 }}
{{Optimal ET sequence|legend=1| 8, 41, 131, 172, 213c }}


[[Badness]]: 2.853049
[[Badness]]: 0.860534


== Semidimfourth ==
== Elvis ==
{{see also| Ragismic microtemperaments #Semidimfourth }}
{{see also| Jubilismic clan #Elvis }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{monzo|7 41 -31}}
[[Comma]]: 36905625/33554432


[[Mapping]]: [{{Val|1 21 28}}, {{Val|0 -31 -41}}]
[[Mapping]]: [{{Val| 2 1 10 }}, {{Val| 0 2 -5 }}]


[[POTE generator]]: ~162/125 = 448.449
[[POTE generator]]: ~45/32 = 554.546


{{Optimal ET sequence|legend=1| 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}
{{Optimal ET sequence|legend=1| 26, 80bc, 106bc, 132bc }}


[[Badness]]: 0.233376
[[Badness]]: 0.884000
 
== Semidimi ==
{{see also| Ragismic microtemperaments #Semidimi }}


== Vinegar ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{monzo|-12 -73 55}}
[[Comma]]: 16000000/14348907


[[Mapping]]: [{{Val|1 36 48}}, {{Val|0 -55 -73}}]
[[Mapping]]: [{{Val| 3 0 -5 }}, {{Val| 0 2 5 }}]


[[POTE generator]]: ~162/125 = 449.127
[[POTE generator]]: ~10/9 = 156.861


{{Optimal ET sequence|legend=1| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}
{{Optimal ET sequence|legend=1| 15, 39c, 54, 69b, 84b }}


[[Badness]]: 0.754866
[[Badness]]: 0.903002


== Semisept ==
== Oolong ==
{{see also| Hemimean clan #Semisept }}
{{see also| Starling temperaments #Oolong }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 782757789696/762939453125
[[Comma]]: 793437161472/762939453125


[[Mapping]]: [{{Val| 1 12 6 }}, {{Val| 0 -17 -6 }}]
[[Mapping]]: [{{Val| 1 6 7 }}, {{Val| 0 -17 -18 }}]


[[POTE generator]]: ~192/125 = 735.146
[[POTE generator]]: ~6/5 = 311.694


{{Optimal ET sequence|legend=1| 18, 31, 80, 111 }}
{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }}


[[Badness]]: 0.630576
[[Badness]]: 0.942789


== Sentinel ==
== Cotoneum ==
{{see also| Orwellismic temperaments #Sentinel }}
{{See also| Hemimage temperaments #Cotoneum }}
Subgroup: 2.3.5


Subgroup: 2.3.5
[[Comma]]: {{Monzo| 80 -49 -1 }}


[[Comma]]: 8968066875/8589934592
[[Mapping]]: [{{Val| 1 2 -18 }}, {{Val| 0 -1 49 }}]


[[Mapping]]: [{{Val| 1 3 -3 }}, {{Val| 0 -4 15 }}]
[[POTE generator]]: ~3/2 = 702.315


[[POTE generator]]: ~512/405 = 425.474
{{Optimal ET sequence|legend=1| 41, 135c, 176, 217, 475, 1167, 1642, 2117b }}


{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bc }}
[[Badness]]: 1.240078


[[Badness]]: 0.723413
== Oncle ==
{{see also| Gamelismic clan #Oncle }}


== Septendecic ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{monzo| 27 -17 }} = 134217728/129140163
[[Comma]]: 145282683375/137438953472


[[Mapping]]: [{{Val| 17 27 0 }}, {{Val| 0 0 1 }}]
[[Mapping]]: [{{Val| 1 1 6 }}, {{Val| 0 3 -19 }}]


Mapping generators: ~531441/524288, ~5
[[POTE generator]]: ~4096/3645 = 232.521


[[POTE generator]]: ~5/4 = 389.193
{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}


{{Optimal ET sequence|legend=1| 17c, 34 }}
[[Badness]]: 1.244699


[[Badness]]: 0.541384
== Diesic ==
 
{{see also| Orwellismic temperaments #Diesic }}
== Septimin ==
{{see also| Marvel temperaments #Septimin }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 35595703125/34359738368
[[Comma]]: 10460353203/9765625000


[[Mapping]]: [{{Val| 1 4 1 }}, {{Val| 0 -11 6 }}]
[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -13 -21 }}]


[[POTE generator]]: ~75/64 = 263.658
[[POTE generator]]: ~6561/6250 = 38.571


{{Optimal ET sequence|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }}
{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}


[[Badness]]: 0.670947
[[Badness]]: 1.344681


== Sevond ==
== Quartemka ==
{{See also| Keemic temperaments #Sevond }}
{{see also| Gamelismic clan #Quartemka }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 5000000/4782969
[[Comma]]: 1907348632812500/1853020188851841


[[Mapping]]: [{{Val| 7 0 -6 }}, {{Val| 0 1 2 }}]
[[Mapping]]: [{{Val| 1 4 6 }}, {{Val| 0 -21 -32 }}]


[[POTE generator]]: ~3/2 = 706.288
[[POTE generator]]: ~27/25 = 137.962


{{Optimal ET sequence|legend=1| 7, 42, 49, 56, 119 }}
{{Optimal ET sequence|legend=1| 26, 61, 87, 287, 374, 461 }}


[[Badness]]: 0.339335
[[Badness]]: 1.381216
 
== Sfourth ==
{{see also| Ragismic microtemperaments #Sfourth }}


== Genocchi ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 617673396283947/610351562500000
[[Comma]]: 2359296/1953125


[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -19 -31 }}]
[[Mapping]]: [{{Val| 1 0 2 }}, {{Val| 0 9 2 }}]


[[POTE generator]]: ~1594323/1562500 = 26.2342
[[POTE generator]]: ~768/625 = 212.444


{{Optimal ET sequence|legend=1| 45, 46, 91, 137, 183 }}
{{Optimal ET sequence|legend=1| 6b, 11b, 17c }}


[[Badness]]: 0.504555
[[Badness]]: 1.404977


== Slender ==
== Casablanca ==
{{see also| Starling temperaments #Casablanca }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 72081298828125/70368744177664
[[Comma]]: 20061226008576/19073486328125


[[Mapping]]: [{{Val| 1 2 2 }}, {{Val| 0 -13 10 }}]
[[Mapping]]: [{{Val| 1 -7 -14 }}, {{Val| 0 19 14 }}]


Optimal tuning ([[CWE]]): ~2 = 1\1, ~16875/16384 = 38.400
[[POTE generator]]: ~864/625 = 542.208


Supporting ETs: 31, 125, 94, 63, 32, 156, 30b, 219c, 187, 281, 157c, 218b, 95c, 344c
{{Optimal ET sequence|legend=1| 11b, 20b, 31, 73, 104c, 135c }}


[[Badness]] (Sintel): 17.842
[[Badness]]: 1.423736


== Slurpee ==
== Archaeotherium ==
{{see also| Mint temperaments #Slurpee }}
{{see also| Gamelismic clan #Archaeotherium }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 177147/156250
[[Comma]]: 597871125/536870912


[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -7 -11 }}]
[[Mapping]]: [{{Val| 1 1 5 }}, {{Val| 0 3 -14 }}]


[[POTE generator]]: ~27/25 = 72.742
[[POTE generator]]: ~1215/1024 = 230.351


{{Optimal ET sequence|legend=1| 16, 17c, 33 }}
{{Optimal ET sequence|legend=1| 21, 26, 73bc, 99bc }}


[[Badness]]: 0.689274
[[Badness]]: 1.434855


== Stump ==
== Newt ==
: ''See also: [[Sensamagic clan #Pycnic]] and [[Marvel temperaments #Triton]]''
{{See also| Breedsmic temperaments #Newt }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 273375/262144
[[Comma]]: {{Monzo| 95 -57 -2 }}


[[Mapping]]: [{{Val| 1 0 6 }}, {{Val| 0 3 -7 }}]
[[Mapping]]: [{{Val| 1 1 19 }}, {{Val| 0 2 -57 }}]


[[POTE generator]]: ~64/45 = 631.737
[[POTE generator]]: ~{{Monzo|47 -28 -1}} = 351.114


{{Optimal ET sequence|legend=1| 17, 19 }}
{{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 3592bc, 5523bbc }}


[[Badness]]: 0.200600
[[Badness]]: 1.528465


== Tertiaseptal ==
== Octacoid ==
{{see also| Breedsmic temperaments #Tertiaseptal }}
[[Subgroup]]: 2.3.5


Subgroup: 2.3.5
[[Comma list]]: 8589934592/7688671875


[[Comma]]: 579357147216796875/576460752303423488
{{Mapping|legend=1| 1 1 3 | 0 8 -9 }}


[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -22 5 }}]
: mapping generators: ~2, ~16/15


[[POTE generator]]: ~17578125/16777216 = 77.191
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1�, ~16/15 = 88.7331
* [[CWE]]: ~2 = 1�, ~16/15 = 88.8168


{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}
{{Optimal ET sequence|legend=1| 13, 14, 27 }}


[[Badness]]: 0.297544
[[Badness]]: 1.75


== Tertiosec ==
== Quasimoha ==
{{see also| Marvel temperaments #Tertiosec }}
{{see also| Breedsmic temperaments #Quasimoha }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{monzo| -89 21 24 }}
[[Comma]]: 2353579470675/2199023255552


[[Mapping]]: [{{Val| 3 7 5 }}, {{Val| 0 -8 7 }}]
[[Mapping]]: [{{Val| 1 1 9 }}, {{Val| 0 2 -23 }}]


[[POTE generator]]: ~16/15 = 112.281
[[POTE generator]]: ~1048576/885735 = 348.600


{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171 }}
{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}


[[Badness]]: 0.851003
[[Badness]]: 1.986675


== Thuja ==
== Phillips ==
{{see also| Starling temperaments #Thuja }}
{{see also| Orwellismic temperaments #Phillips }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 254803968/244140625
[[Comma]]: 9685512225/8589934592


[[Mapping]]: [{{Val| 1 -4 0 }}, {{Val| 0 12 5 }}]
[[Mapping]]: [{{Val| 2 0 33 }}, {{Val| 0 1 -9 }}]


[[POTE generator]]: ~3125/2304 = 558.592
[[POTE generator]]: ~3/2 = 691.455


{{Optimal ET sequence|legend=1| 15, 43, 58 }}
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }}


[[Badness]]: 0.511109
[[Badness]]: 2.228904


== Triskaidekic ==
== Triskaidekic ==
Line 1,024: Line 1,065:
[[Badness]]: 2.241568
[[Badness]]: 2.241568


== Tritonic ==
== Satin ==
{{see also| Marvel temperaments #Tritonic }}
{{see also| Canousmic temperaments #Satin }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 553584375/536870912
[[Comma]]: {{Monzo| 104 -70 3 }}


[[Mapping]]: [{{Val| 1 4 -3 }}, {{Val| 0 -5 11 }}]
[[Mapping]]: [{{val| 1 2 12 }}, {{val| 0 -3 -70 }}]


[[POTE generator]]: ~45/32 = 580.219
[[POTE generator]]: ~{{monzo|-34 23 -1}} = 165.907


{{Optimal ET sequence|legend=1| 29, 31, 60, 91 }}
{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273 }}


[[Badness]]: 0.378527
[[Badness]]: 2.853049


== Tritriple ==
== Rarity ==
{{see also| Gamelismic clan #Tritriple }}
{{See also| No-sevens subgroup temperaments #Rarity }}


Subgroup: 2.3.5
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.


[[Comma]]: {{monzo| 31 20 -27 }}
[[Subgroup]]: 2.3.5


[[Mapping]]: [{{Val| 1 -11 -7 }}, {{Val| 0 27 20 }}]
[[Comma list]]: {{monzo| -57 17 13 }}


[[POTE generator]]: ~864/625 = 559.332
{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}


{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }}
: mapping generators: ~16384/10125 = 869.392


[[Badness]]: 0.283570
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~16384/10125 = 869.392


== Undeka ==
{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}
{{see also| Keemic temperaments #Undeka }}


Subgroup: 2.3.5
[[Badness]]: 4.23


[[Comma]]: 48828125/45349632
== Gamera ==
{{see also| Ragismic microtemperaments #Gamera }}


[[Mapping]]: [{{Val| 11 0 8 }}, {{Val| 0 1 1 }}]
Subgroup: 2.3.5


[[POTE generator]]: ~3/2 = 703.829
[[Comma]]: 12207031250000000000/12157665459056928801


{{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }}
[[Mapping]]: [{{Val| 1 6 10 }}, {{Val| 0 -23 -40 }}]


[[Badness]]: 0.727539
Optimal tuning ([[CWE]]): ~2 = 1\1, ~2500/2187 = 230.345


== Undim ==
Supporting ETs: 99, 323, 224, 26, 125, 547, 5bccc, 422, 73, 870, 21bcc, 47bc, 771, 349
{{see also| Undim family }}


Subgroup: 2.3.5
[[Badness]] (Sintel): 6.394


[[Comma]]: 2199023255552/2179240250625
== Nessafof ==
 
[[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
== Unsmate ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 17578125/16777216
[[Comma]]: 481469424205824/476837158203125


[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -9 2 }}]
[[Mapping]]: [{{Val| 3 2 5 }}, {{Val| 0 7 5 }}]


[[POTE generator]]: ~2048/1875 = 189.049
Optimal tuning ([[CWE]]): ~78125/62208 = 1\3, ~9765625/8957952 = 157.409


{{Optimal ET sequence|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}
Supporting ETs: 15, 99, 84, 183, 282, 69, 114, 9bbc, 267, 54b, 381, 24bbc, 39bc, 465


[[Badness]]: 0.460168
[[Badness]] (Sintel): 7.807


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


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2270041927734375/2251799813685248
[[Comma]]: 4052555153018976267/4000000000000000000


[[Mapping]]: [{{Val| 1 6 -7 }}, {{Val| 0 -9 19 }}]
[[Mapping]]: [{{Val| 3 2 1 }}, {{Val| 0 6 13 }}]


[[POTE generator]]: ~45/32 = 588.722
Optimal tuning ([[CWE]]): ~2000000/1594323 = 1\3, ~10/9 = 183.585


{{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}
Supporting ETs: 72, 183, 6cc, 39, 111, 33c, 255, 294, 438, 327, 105c, 150c, 45bccc, 477


[[Badness]]: 0.307073
[[Badness]] (Sintel): 17.631


== Vinegar ==
== Slender ==
Subgroup: 2.3.5
 
[[Comma]]: 16000000/14348907
 
[[Mapping]]: [{{Val| 3 0 -5 }}, {{Val| 0 2 5 }}]
 
[[POTE generator]]: ~10/9 = 156.861
 
{{Optimal ET sequence|legend=1| 15, 39c, 54, 69b, 84b }}
 
[[Badness]]: 0.903002
 
== Vines ==
{{see also| Starling temperaments #Vines }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 156728328192/152587890625
[[Comma]]: 72081298828125/70368744177664


[[Mapping]]: [{{Val| 2 7 8 }}, {{Val| 0 -8 -7 }}]
[[Mapping]]: [{{Val| 1 2 2 }}, {{Val| 0 -13 10 }}]


[[POTE generator]]: ~6/5 = 312.713
Optimal tuning ([[CWE]]): ~2 = 1\1, ~16875/16384 = 38.400


{{Optimal ET sequence|legend=1| 4, 42, 46, 96, 142 }}
Supporting ETs: 31, 125, 94, 63, 32, 156, 30b, 219c, 187, 281, 157c, 218b, 95c, 344c


[[Badness]]: 0.541831
[[Badness]] (Sintel): 17.842


== Wizard ==
== Quasiorwell ==
{{see also| Marvel temperaments #Wizard }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2197265625/2147483648
[[Comma]]: 9903520314283042199192993792/9822542779147624969482421875


[[Mapping]]: [{{Val| 2 1 5 }}, {{Val| 0 6 -1 }}]
[[Mapping]]: [{{Val| 1 31 0 }}, {{Val| 0 -38 3 }}]


Mapping generators: ~42875/32768, ~9375/8192
Optimal tuning ([[CWE]]): ~2 = 1\1, ~3662109375/2147483648 = 928.893


[[POTE generator]]: ~5/4 = 383.212
Supporting ETs: 31, 270, 301, 239, 571, 208, 841, 332, 509, 177, 1111, 146b, 872, 363


{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}
[[Badness]] (Sintel): 30.581


[[Badness]]: 0.386367
[[Category:Temperament collections]]
 
Scales (Scala files): [[wizard22]]
 
== Wronecki ==
Subgroup: 2.3.5
 
[[Comma]]: 531441/500000
 
[[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

Revision as of 10:04, 22 December 2024

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:

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 sequence: 8, 9, 17c

Badness: 0.200483

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 sequence: 17, 19

Badness: 0.200600

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 sequence: 37, 84, 205, 289, 494, 783, 2060, 2843, 3626

Badness: 0.213112

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 sequence: 9, 25, 34, 77, 111, 145, 256c

Badness: 0.232481

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 sequence: 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: [⟨4 6 11], ⟨0 1 -5]]

POTE generator: ~3/2 = 702.605

Optimal ET sequence: 12, 140, 152, 164, 1076bc, 1228bc

Badness: 0.241703

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 sequence: 27, 31, 58, 89, 325cc

Badness: 0.249965

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 sequence: 2, 13, 15, 32c, 47bc, 62bc

Badness: 0.246073

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 sequence: 53, 263, 316, 369, 422, 475, 528, 2587b, 3115b, 3643b

Badness: 0.255594

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 sequence: 15, 88, 103, 118, 959, 1077

Badness: 0.283570

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 sequence: 15, 47b, 62b

Badness: 0.295767

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 sequence: 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: [⟨1 0 34], ⟨0 1 -20]]

POTE generator: ~3/2 = 700.734

Optimal ET sequence: 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: [⟨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

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 sequence: 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c

Badness: 0.317551

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 sequence: 7, 42, 49, 56, 119

Badness: 0.339335

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 sequence: 7, 70, 77, 84, 329, 413b, 497b

Badness: 0.341202

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

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 sequence: 4, 17c, 21, 38c

Badness: 0.355937

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

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 sequence: 10, 17c, 27, 64b, 91bc, 118bc

Badness: 0.358542

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

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 sequence: 41, 58, 99, 239, 338, 915b, 1253bc

Badness: 0.372848

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

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 sequence: 29, 31, 60, 91

Badness: 0.378527

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 sequence: 22, 50, 72, 166, 238c, 310c, 548bc

Badness: 0.386367

Scales (Scala files): wizard22

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 sequence: 12, 193, 205, 217, 422

Badness: 0.399849

Hogzilla

Subgroup: 2.3.5

Comma: 4428675/4194304

Mapping: [⟨1 0 11], ⟨0 2 -11]]

POTE generator: ~1215/1024 = 252.649

Optimal ET sequence: 14, 19

Badness: 0.424685

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 sequence: 12, 109, 121, 133

Badness: 0.444506

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 sequence: 41, 84, 125, 209, 334c, 543bc

Badness: 0.453848

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

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 sequence: 8, 23, 31, 70, 101, 132c, 233c, 365bcc

Badness: 0.466493

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 sequence: 20c, 22, 86b, 108b, 130b

Badness: 0.491181

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 sequence: 45, 46, 91, 137, 183

Badness: 0.504555

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 sequence: 15, 43, 58

Badness: 0.511109

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 sequence: 29, 46, 121, 167, 455bc, 622bbc

Badness: 0.523182

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 sequence: 17c, 34

Badness: 0.541384

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 sequence: 4, 42, 46, 96, 142

Badness: 0.541831

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

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 sequence: 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc

Badness: 0.609540

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 sequence: 18, 31, 80, 111

Badness: 0.630576

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 sequence: 41, 111, 152

Badness: 0.636715

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 sequence: 19, 85c, 104c, 123, 142, 161

Badness: 0.653871

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 sequence: 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: [⟨1 2 3], ⟨0 -7 -11]]

POTE generator: ~27/25 = 72.742

Optimal ET sequence: 16, 17c, 33

Badness: 0.689274

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 sequence: 15, 45, 60, 75, 135, 210c, 345cc

Badness: 0.692042

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 sequence: 14, 17, 31, 79, 110, 361bc

Badness: 0.723413

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 sequence: 22, 77c, 99c, 121c

Badness: 0.727539

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 sequence: 16, 27, 43, 70, 183cc

Badness: 0.729609

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 sequence: 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419

Badness: 0.754866

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 sequence: 4, 37, 41

Badness: 0.767824

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 sequence: 11c, 20c, 31, 113c, 144c, 175c, 381bcc

Badness: 0.816635

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 sequence: 22, 45, 67c, 89c

Badness: 0.842835

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 sequence: 21, 54, 75, 96, 171

Badness: 0.851003

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 sequence: 2, 25, 27

Badness: 0.852612

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 sequence: 8, 41, 131, 172, 213c

Badness: 0.860534

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 sequence: 26, 80bc, 106bc, 132bc

Badness: 0.884000

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

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 sequence: 23, 27, 50, 77

Badness: 0.942789

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 sequence: 41, 135c, 176, 217, 475, 1167, 1642, 2117b

Badness: 1.240078

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 sequence: 31, 98c, 129c, 160bc, 289bbcc

Badness: 1.244699

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 sequence: 31, 156c, 187c, 218bc, 249bc, 280bc

Badness: 1.344681

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 sequence: 26, 61, 87, 287, 374, 461

Badness: 1.381216

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

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 sequence: 11b, 20b, 31, 73, 104c, 135c

Badness: 1.423736

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 sequence: 21, 26, 73bc, 99bc

Badness: 1.434855

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 sequence: 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 3592bc, 5523bbc

Badness: 1.528465

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 sequence: 13, 14, 27

Badness: 1.75

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 sequence: 31, 117c, 148bc, 179bc

Badness: 1.986675

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 sequence: 14, 26, 66b, 92bc, 118bbc

Badness: 2.228904

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 sequence: 13, 26, 91c

Badness: 2.241568

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 sequence: 94, 217, 528, 745, 1273

Badness: 2.853049

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\1, ~16384/10125 = 869.392

Optimal ET sequence: 11, 29, 69, 98c

Badness: 4.23

Gamera

See also: Ragismic microtemperaments § 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

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

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

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

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

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