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Miscellaneous 5-limit temperaments: Difference between revisions

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This is actually backwards logic. subgroup temperaments are usually lower badness than 5-limit versions (like with 5-limit superpyth vs. 2.3.7 subgroup archy). Fractional octave and equivalence continua temperaments are not always high badness (diaschismic is one of the lowest 5-limit badnesses, in fact).
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* [[Very high accuracy temperaments]]
* [[Very high accuracy temperaments]]


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


Subgroup: 2.3.5
Subgroup: 2.3.5


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


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


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


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


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


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


Subgroup: 2.3.5
Subgroup: 2.3.5


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


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


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


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


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


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


Subgroup: 2.3.5
Subgroup: 2.3.5


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


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


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


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


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


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


Subgroup: 2.3.5
Subgroup: 2.3.5


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


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


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


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


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


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


Subgroup: 2.3.5
Subgroup: 2.3.5


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


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


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


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


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


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


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2199023255552/2179240250625
[[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 }}
 
Subgroup: 2.3.5


[[Mapping]]: [{{Val| 4 6 11 }}, {{Val| 0 1 -5 }}]
[[Comma]]: 5120000/4782969


[[POTE generator]]: ~3/2 = 702.605
[[Mapping]]: [{{Val| 2 1 -3 }}, {{Val| 0 2 7 }}]


{{Optimal ET sequence|legend=1| 12, 140, 152, 164, 1076bc, 1228bc }}
[[POTE generator]]: ~81/80 = 55.382


[[Badness]]: 0.241703
{{Optimal ET sequence|legend=1| 20c, 22, 86b, 108b, 130b }}


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


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


[[Comma]]: 32768/30375
[[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 }}
 
Subgroup: 2.3.5


[[Mapping]]: [{{Val| 1 0 5 }}, {{Val| 0 3 -5 }}]
[[Comma]]: {{Monzo| -20 -24 25 }} = 298023223876953125/296148833645101056


[[POTE generator]]: ~64/45 = 561.264
[[Mapping]]: [{{Val| 1 -5 -4 }}, {{Val| 0 25 24 }}]


{{Optimal ET sequence|legend=1| 2, 13, 15, 32c, 47bc, 62bc }}
[[POTE generator]]: ~6/5 = 316.081


[[Badness]]: 0.246073
{{Optimal ET sequence|legend=1| 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }}


== Mynic ==
[[Badness]]: 0.317551
{{see also| Starling temperaments #Myna }}


== Countermeantone ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 10077696/9765625
[[Comma]]: {{Monzo| 10 23 -20 }} = 96402615118848/95367431640625


[[Mapping]]: [{{Val| 1 9 9 }}, {{Val| 0 -10 -9 }}]
[[Mapping]]: [{{Val| 1 10 12 }}, {{Val| 0 -20 -23 }}]


[[POTE generator]]: ~6/5 = 310.140
[[POTE generator]]: ~104976/78125 = 504.913


{{Optimal ET sequence|legend=1| 27, 31, 58, 89, 325cc }}
{{Optimal ET sequence|legend=1| 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c }}


[[Badness]]: 0.249965
[[Badness]]: 0.373477


== Countritonic ==
== Countritonic ==
Line 139: Line 166:
[[Badness]]: 0.255594
[[Badness]]: 0.255594


== Tritriple ==
== Cypress ==
{{see also| Gamelismic clan #Tritriple }}
{{see also| Starling temperaments #Cypress }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{monzo| 31 20 -27 }}
[[Comma]]: 258280326/244140625


[[Mapping]]: [{{Val| 1 -11 -7 }}, {{Val| 0 27 20 }}]
[[Mapping]]: [{{Val| 1 7 10 }}, {{Val| 0 -12 -17 }}]


[[POTE generator]]: ~864/625 = 559.332
[[POTE generator]]: ~4374/3125 = 541.726


{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }}
{{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c, 381bcc }}


[[Badness]]: 0.283570
[[Badness]]: 0.816635


== Kangaroo ==
== Delorean ==
{{see also| Trienstonic clan #Kangaroo }}
{{see also| Mint temperaments #Subklei }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 64000/59049
[[Comma]]: 17496/15625


[[Mapping]]: [{{Val| 1 0 -3 }}, {{Val| 0 3 10 }}]
[[Mapping]]: [{{Val| 1 3 4 }}, {{Val| 0 -6 -7 }}]


[[POTE generator]]: ~27/20 = 561.195
[[POTE generator]]: ~6/5 = 284.293


{{Optimal ET sequence|legend=1| 15, 47b, 62b }}
{{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }}


[[Badness]]: 0.295767
[[Badness]]: 0.355937


== Tertiaseptal ==
== Diesic ==
{{see also| Breedsmic temperaments #Tertiaseptal }}
{{see also| Orwellismic temperaments #Diesic }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 579357147216796875/576460752303423488
[[Comma]]: 10460353203/9765625000


[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -22 5 }}]
[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -13 -21 }}]


[[POTE generator]]: ~17578125/16777216 = 77.191
[[POTE generator]]: ~6561/6250 = 38.571


{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}
{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}


[[Badness]]: 0.297544
[[Badness]]: 1.344681


== Gracecordial ==
== Dodifo ==
: ''See also: [[Marvel temperaments #Gracecordial]]''
{{see also| Porwell temperaments #Dodifo }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 17433922005/17179869184
[[Comma]]: {{Monzo| -67 -9 35 }}


[[Mapping]]: [{{Val| 1 0 34 }}, {{Val| 0 1 -20 }}]
[[Mapping]]: [{{Val| 1 12 5 }}, {{Val| 0 -35 -9 }}]


[[POTE generator]]: ~3/2 = 700.734
[[POTE generator]]: ~768/625 = 357.088


{{Optimal ET sequence|legend=1| 12, 113, 125, 137 }}
{{Optimal ET sequence|legend=1| 37, 84, 205, 289, 494, 783, 2060, 2843, 3626 }}


[[Badness]]: 0.306809
[[Badness]]: 0.213112


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


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2270041927734375/2251799813685248
[[Comma]]: 36905625/33554432


[[Mapping]]: [{{Val| 1 6 -7 }}, {{Val| 0 -9 19 }}]
[[Mapping]]: [{{Val| 2 1 10 }}, {{Val| 0 2 -5 }}]


[[POTE generator]]: ~45/32 = 588.722
[[POTE generator]]: ~45/32 = 554.546


{{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}
{{Optimal ET sequence|legend=1| 26, 80bc, 106bc, 132bc }}


[[Badness]]: 0.307073
[[Badness]]: 0.884000


== Counterhanson ==
== Emka ==
{{See also| Ragismic microtemperaments #Counterkleismic }}
: ''See also: [[Hemimean clan #Emka]] and [[Horwell temperaments #Emkay]]''


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| -20 -24 25 }} = 298023223876953125/296148833645101056
[[Comma]]: {{monzo| -50 -8 27 }}


[[Mapping]]: [{{Val| 1 -5 -4 }}, {{Val| 0 25 24 }}]
[[Mapping]]: [{{Val| 1 14 6 }}, {{Val| 0 -27 -8 }}]


[[POTE generator]]: ~6/5 = 316.081
[[POTE generator]]: ~9765625/7077888 = 551.784


{{Optimal ET sequence|legend=1| 19, 148, 167, 186, 205, 224, 429, 653, 1082, 1735c }}
{{Optimal ET sequence|legend=1| 37, 50, 87, 137, 224 }}


[[Badness]]: 0.317551
[[Badness]]: 0.544752


== Sevond ==
== Fervor ==
{{See also| Keemic temperaments #Sevond }}
{{see also| Archytas clan #Fervor }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 5000000/4782969
[[Comma]]: 67108864/61509375


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


[[POTE generator]]: ~3/2 = 706.288
[[POTE generator]]: ~64/45 = 577.705


{{Optimal ET sequence|legend=1| 7, 42, 49, 56, 119 }}
{{Optimal ET sequence|legend=1| 2, 25, 27 }}


[[Badness]]: 0.339335
[[Badness]]: 0.852612


== Absurdity ==
== Genocchi ==
{{see also| Porwell temperaments #Absurdity }}
Subgroup: 2.3.5


Subgroup: 2.3.5
[[Comma]]: 2359296/1953125


[[Comma]]: 10460353203/10240000000
[[Mapping]]: [{{Val| 1 0 2 }}, {{Val| 0 9 2 }}]


[[Mapping]]: [{{Val| 7 0 -17 }}, {{Val| 0 1 3 }}]
[[POTE generator]]: ~768/625 = 212.444


[[POTE generator]]: ~10/9 = 185.901
{{Optimal ET sequence|legend=1| 6b, 11b, 17c }}


{{Optimal ET sequence|legend=1| 7, 70, 77, 84, 329, 413b, 497b }}
[[Badness]]: 1.404977


[[Badness]]: 0.341202
== Gracecordial ==
: ''See also: [[Marvel temperaments #Gracecordial]]''


== Wronecki ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 531441/500000
[[Comma]]: 17433922005/17179869184


[[Mapping]]: [{{Val| 6 0 -5 }}, {{Val| 0 1 2 }}]
[[Mapping]]: [{{Val| 1 0 34 }}, {{Val| 0 1 -20 }}]


[[POTE generator]]: ~3/2 = 695.040
[[POTE generator]]: ~3/2 = 700.734


{{Optimal ET sequence|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}
{{Optimal ET sequence|legend=1| 12, 113, 125, 137 }}


[[Badness]]: 0.341757
[[Badness]]: 0.306809


== Delorean ==
== Hemififths ==
{{see also| Mint temperaments #Subklei }}
{{see also| Breedsmic temperaments #Hemififths }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 17496/15625
[[Comma]]: 858993459200/847288609443


[[Mapping]]: [{{Val| 1 3 4 }}, {{Val| 0 -6 -7 }}]
[[Mapping]]: [{{Val| 1 1 -5 }}, {{Val| 0 2 25 }}]


[[POTE generator]]: ~6/5 = 284.293
[[POTE generator]]: ~655360/531441 = 351.476


{{Optimal ET sequence|legend=1| 4, 17c, 21, 38c }}
{{Optimal ET sequence|legend=1| 41, 58, 99, 239, 338, 915b, 1253bc }}


[[Badness]]: 0.355937
[[Badness]]: 0.372848
 
== Majvam ==
: ''See also: [[Subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]]''


== Hogzilla ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2404631929946112/2384185791015625
[[Comma]]: 4428675/4194304


[[Mapping]]: [{{Val| 1 10 5 }}, {{Val| 0 -22 -7 }}]
[[Mapping]]: [{{Val| 1 0 11 }}, {{Val| 0 2 -11 }}]


[[POTE generator]]: ~125/96 = 458.995
[[POTE generator]]: ~1215/1024 = 252.649


{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }}
{{Optimal ET sequence|legend=1| 14, 19 }}


[[Badness]]: 0.356948
[[Badness]]: 0.424685


== Beatles ==
== Kangaroo ==
{{see also| Archytas clan #Beatles }}
{{see also| Trienstonic clan #Kangaroo }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 524288/492075
[[Comma]]: 64000/59049


[[Mapping]]: [{{Val| 1 1 5 }}, {{Val| 0 2 -9 }}]
[[Mapping]]: [{{Val| 1 0 -3 }}, {{Val| 0 3 10 }}]


[[POTE generator]]: ~512/405 = 355.930
[[POTE generator]]: ~27/20 = 561.195


{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}
{{Optimal ET sequence|legend=1| 15, 47b, 62b }}


[[Badness]]: 0.358542
[[Badness]]: 0.295767


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


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 50331648/48828125
[[Comma]]: 1289945088/1220703125


[[Mapping]]: [{{Val| 1 -2 2 }}, {{Val| 0 11 1 }}]
[[Mapping]]: [{{Val| 1 4 4 }}, {{Val| 0 -13 -9 }}]


[[POTE generator]]: ~5/4 = 391.225
[[POTE generator]]: ~144/125 = 222.912


{{Optimal ET sequence|legend=1| 3, 40, 43, 46, 181c, 227c, 273c, 319c }}
{{Optimal ET sequence|legend=1| 16, 27, 43, 70, 183cc }}


[[Badness]]: 0.360162
[[Badness]]: 0.729609


== Hemififths ==
== Kwai ==
{{see also| Breedsmic temperaments #Hemififths }}
{{see also| Mirkwai clan #Kwai }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 858993459200/847288609443
[[Comma]]: 5629499534213120/5559060566555523
 
[[Mapping]]: [{{Val| 1 2 16 }}, {{Val| 0 -1 -33 }}]


[[Mapping]]: [{{Val| 1 1 -5 }}, {{Val| 0 2 25 }}]
[[POTE generator]]: ~3/2 = 702.630


[[POTE generator]]: ~655360/531441 = 351.476
{{Optimal ET sequence|legend=1| 41, 111, 152 }}


{{Optimal ET sequence|legend=1| 41, 58, 99, 239, 338, 915b, 1253bc }}
[[Badness]]: 0.636715


[[Badness]]: 0.372848
== Lafayette ==
{{see also| Mint temperaments #Progression }}


== Countermeantone ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| 10 23 -20 }} = 96402615118848/95367431640625
[[Comma]]: 3456/3125


[[Mapping]]: [{{Val| 1 10 12 }}, {{Val| 0 -20 -23 }}]
[[Mapping]]: [{{Val| 1 1 2 }}, {{Val| 0 5 3 }}]


[[POTE generator]]: ~104976/78125 = 504.913
[[POTE generator]]: ~25/24 = 140.995


{{Optimal ET sequence|legend=1| 19, 126, 145, 164, 183, 713, 896c, 1079c, 1262c }}
{{Optimal ET sequence|legend=1| 8, 9, 17c }}


[[Badness]]: 0.373477
[[Badness]]: 0.200483


== Tritonic ==
== Leapday ==
{{see also| Marvel temperaments #Tritonic }}
: ''See also: [[Hemifamity temperaments #Leapday]] and [[Porwell temperaments #Polypyth]]''


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 553584375/536870912
[[Comma]]: 10737418240/10460353203


[[Mapping]]: [{{Val| 1 4 -3 }}, {{Val| 0 -5 11 }}]
[[Mapping]]: [{{Val| 1 0 -31 }}, {{Val| 0 1 21 }}]


[[POTE generator]]: ~45/32 = 580.219
[[POTE generator]]: ~3/2 = 704.179


{{Optimal ET sequence|legend=1| 29, 31, 60, 91 }}
{{Optimal ET sequence|legend=1| 29, 46, 121, 167, 455bc, 622bbc }}


[[Badness]]: 0.378527
[[Badness]]: 0.523182


== Wizard ==
== Mabila ==
{{see also| Marvel temperaments #Wizard }}
{{see also| Mabila family }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2197265625/2147483648
[[Comma]]: 268435456/263671875


[[Mapping]]: [{{Val| 2 1 5 }}, {{Val| 0 6 -1 }}]
[[Mapping]]: [{{Val| 1 6 1 }}, {{Val| 0 -10 3 }}]


Mapping generators: ~42875/32768, ~9375/8192
[[POTE generator]]: ~512/375 = 529.685


[[POTE generator]]: ~5/4 = 383.212
{{Optimal ET sequence|legend=1| 9, 25, 34, 77, 111, 145, 256c }}


{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}
[[Badness]]: 0.232481


[[Badness]]: 0.386367
== Magus ==
 
: ''See also: [[Sensamagic clan #Magus]] and [[Starling temperaments #Amigo]]''
Scales (Scala files): [[wizard22]]
 
== Quindromeda ==
{{see also| Quindromeda family }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 72057594037927936/71489976421753125
[[Comma]]: 50331648/48828125


[[POTE generator]]: ~4428675/4194304 = 99.526
[[Mapping]]: [{{Val| 1 -2 2 }}, {{Val| 0 11 1 }}]


[[Mapping]]: [{{Val| 1 2 0 }}, {{Val| 0 -5 28 }}]
[[POTE generator]]: ~5/4 = 391.225


{{Optimal ET sequence|legend=1| 12, 193, 205, 217, 422 }}
{{Optimal ET sequence|legend=1| 3, 40, 43, 46, 181c, 227c, 273c, 319c }}


[[Badness]]: 0.399849
[[Badness]]: 0.360162


== Hogzilla ==
== Majvam ==
Subgroup: 2.3.5
: ''See also: [[Subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]]''
 
[[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
 
== Quintaleap ==
{{see also| Quintaleap family }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 137438953472/134521003125
[[Comma]]: 2404631929946112/2384185791015625


[[Mapping]]: [{{Val| 1 2 1 }}, {{Val| 0 -5 16 }}]
[[Mapping]]: [{{Val| 1 10 5 }}, {{Val| 0 -22 -7 }}]


[[POTE generator]]: ~135/128 = 99.267
[[POTE generator]]: ~125/96 = 458.995


{{Optimal ET sequence|legend=1| 12, 109, 121, 133 }}
{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }}


[[Badness]]: 0.444506
[[Badness]]: 0.356948


== Merman ==
== Merman ==
Line 452: Line 462:
[[Badness]]: 0.453848
[[Badness]]: 0.453848


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


[[Comma]]: 17578125/16777216
[[Comma]]: 145964630126953125/144115188075855872


[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -9 2 }}]
[[Mapping]]: [{{Val| 1 3 1 }}, {{Val| 0 -15 14 }}]


[[POTE generator]]: ~2048/1875 = 189.049
[[POTE generator]]: ~16/15 = 113.240


{{Optimal ET sequence|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}
{{Optimal ET sequence|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}


[[Badness]]: 0.460168
[[Badness]]: 0.609540


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


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 51018336/48828125
[[Comma]]: {{Monzo| 0 22 -15 }} = 31381059609/30517578125


[[Mapping]]: [{{Val| 1 3 4 }}, {{Val| 0 -11 -13 }}]
[[Mapping]]: [{{Val| 1 0 0 }}, {{Val| 0 15 22 }}]


[[POTE generator]]: ~3125/2916 = 154.523
[[POTE generator]]: ~27/25 = 126.724


{{Optimal ET sequence|legend=1| 8, 23, 31, 70, 101, 132c, 233c, 365bcc }}
{{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161 }}


[[Badness]]: 0.466493
[[Badness]]: 0.653871


== 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| 2 1 -3 }}, {{Val| 0 2 7 }}]
[[Mapping]]: [{{Val| 1 9 9 }}, {{Val| 0 -10 -9 }}]


[[POTE generator]]: ~81/80 = 55.382
[[POTE generator]]: ~6/5 = 310.140


{{Optimal ET sequence|legend=1| 20c, 22, 86b, 108b, 130b }}
{{Optimal ET sequence|legend=1| 27, 31, 58, 89, 325cc }}


[[Badness]]: 0.491181
[[Badness]]: 0.249965


== Sfourth ==
== Newt ==
{{see also| Ragismic microtemperaments #Sfourth }}
{{See also| Breedsmic temperaments #Newt }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 617673396283947/610351562500000
[[Comma]]: {{Monzo| 95 -57 -2 }}


[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -19 -31 }}]
[[Mapping]]: [{{Val| 1 1 19 }}, {{Val| 0 2 -57 }}]


[[POTE generator]]: ~1594323/1562500 = 26.2342
[[POTE generator]]: ~{{Monzo|47 -28 -1}} = 351.114


{{Optimal ET sequence|legend=1| 45, 46, 91, 137, 183 }}
{{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 3592bc, 5523bbc }}


[[Badness]]: 0.504555
[[Badness]]: 1.528465


== Thuja ==
== Nusecond ==
{{see also| Starling temperaments #Thuja }}
{{see also| Starling temperaments #Nusecond }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 254803968/244140625
[[Comma]]: 51018336/48828125
 
[[Mapping]]: [{{Val| 1 3 4 }}, {{Val| 0 -11 -13 }}]


[[Mapping]]: [{{Val| 1 -4 0 }}, {{Val| 0 12 5 }}]
[[POTE generator]]: ~3125/2916 = 154.523


[[POTE generator]]: ~3125/2304 = 558.592
{{Optimal ET sequence|legend=1| 8, 23, 31, 70, 101, 132c, 233c, 365bcc }}


{{Optimal ET sequence|legend=1| 15, 43, 58 }}
[[Badness]]: 0.466493


[[Badness]]: 0.511109
== Octacoid ==
[[Subgroup]]: 2.3.5


== Leapday ==
[[Comma list]]: 8589934592/7688671875
: ''See also: [[Hemifamity temperaments #Leapday]] and [[Porwell temperaments #Polypyth]]''


Subgroup: 2.3.5
{{Mapping|legend=1| 1 1 3 | 0 8 -9 }}


[[Comma]]: 10737418240/10460353203
: mapping generators: ~2, ~16/15


[[Mapping]]: [{{Val| 1 0 -31 }}, {{Val| 0 1 21 }}]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1�, ~16/15 = 88.7331
* [[CWE]]: ~2 = 1�, ~16/15 = 88.8168


[[POTE generator]]: ~3/2 = 704.179
{{Optimal ET sequence|legend=1| 13, 14, 27 }}


{{Optimal ET sequence|legend=1| 29, 46, 121, 167, 455bc, 622bbc }}
[[Badness]]: 1.75


[[Badness]]: 0.523182
== 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
== Oolong ==
 
{{see also| Starling temperaments #Oolong }}
== Vines ==
{{see also| Starling temperaments #Vines }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 156728328192/152587890625
[[Comma]]: 793437161472/762939453125


[[Mapping]]: [{{Val| 2 7 8 }}, {{Val| 0 -8 -7 }}]
[[Mapping]]: [{{Val| 1 6 7 }}, {{Val| 0 -17 -18 }}]


[[POTE generator]]: ~6/5 = 312.713
[[POTE generator]]: ~6/5 = 311.694


{{Optimal ET sequence|legend=1| 4, 42, 46, 96, 142 }}
{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }}


[[Badness]]: 0.541831
[[Badness]]: 0.942789


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


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{monzo| -50 -8 27 }}
[[Comma]]: 30517578125/29386561536


[[Mapping]]: [{{Val| 1 14 6 }}, {{Val| 0 -27 -8 }}]
[[Mapping]]: [{{Val| 15 0 11 }}, {{Val| 0 1 1 }}]


[[POTE generator]]: ~9765625/7077888 = 551.784
[[POTE generator]]: ~3/2 = 702.652


{{Optimal ET sequence|legend=1| 37, 50, 87, 137, 224 }}
{{Optimal ET sequence|legend=1| 15, 45, 60, 75, 135, 210c, 345cc }}


[[Badness]]: 0.544752
[[Badness]]: 0.692042


== Misneb ==
== Phillips ==
{{see also| Marvel temperaments #Misneb }}
{{see also| Orwellismic temperaments #Phillips }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 145964630126953125/144115188075855872
[[Comma]]: 9685512225/8589934592


[[Mapping]]: [{{Val| 1 3 1 }}, {{Val| 0 -15 14 }}]
[[Mapping]]: [{{Val| 2 0 33 }}, {{Val| 0 1 -9 }}]


[[POTE generator]]: ~16/15 = 113.240
[[POTE generator]]: ~3/2 = 691.455


{{Optimal ET sequence|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }}


[[Badness]]: 0.609540
[[Badness]]: 2.228904


== Semisept ==
== Progress ==
{{see also| Hemimean clan #Semisept }}
{{see also| Archytas clan #Progress }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 782757789696/762939453125
[[Comma]]: 32768/30375


[[Mapping]]: [{{Val| 1 12 6 }}, {{Val| 0 -17 -6 }}]
[[Mapping]]: [{{Val| 1 0 5 }}, {{Val| 0 3 -5 }}]


[[POTE generator]]: ~192/125 = 735.146
[[POTE generator]]: ~64/45 = 561.264


{{Optimal ET sequence|legend=1| 18, 31, 80, 111 }}
{{Optimal ET sequence|legend=1| 2, 13, 15, 32c, 47bc, 62bc }}


[[Badness]]: 0.630576
[[Badness]]: 0.246073


== Kwai ==
== Quartemka ==
{{see also| Mirkwai clan #Kwai }}
{{see also| Gamelismic clan #Quartemka }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 5629499534213120/5559060566555523
[[Comma]]: 1907348632812500/1853020188851841


[[Mapping]]: [{{Val| 1 2 16 }}, {{Val| 0 -1 -33 }}]
[[Mapping]]: [{{Val| 1 4 6 }}, {{Val| 0 -21 -32 }}]


[[POTE generator]]: ~3/2 = 702.630
[[POTE generator]]: ~27/25 = 137.962


{{Optimal ET sequence|legend=1| 41, 111, 152 }}
{{Optimal ET sequence|legend=1| 26, 61, 87, 287, 374, 461 }}


[[Badness]]: 0.636715
[[Badness]]: 1.381216


== Mowgli ==
== Quasimoha ==
{{see also| Hemimean clan #Mowglic }}
{{see also| Breedsmic temperaments #Quasimoha }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| 0 22 -15 }} = 31381059609/30517578125
[[Comma]]: 2353579470675/2199023255552


[[Mapping]]: [{{Val| 1 0 0 }}, {{Val| 0 15 22 }}]
[[Mapping]]: [{{Val| 1 1 9 }}, {{Val| 0 2 -23 }}]


[[POTE generator]]: ~27/25 = 126.724
[[POTE generator]]: ~1048576/885735 = 348.600


{{Optimal ET sequence|legend=1| 19, 85c, 104c, 123, 142, 161 }}
{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}


[[Badness]]: 0.653871
[[Badness]]: 1.986675


== Septimin ==
== Quasitemp ==
{{see also| Marvel temperaments #Septimin }}
{{see also| Keemic temperaments #Quasitemp }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 35595703125/34359738368
[[Comma]]: 6103515625/5804752896


[[Mapping]]: [{{Val| 1 4 1 }}, {{Val| 0 -11 6 }}]
[[Mapping]]: [{{Val| 1 5 5 }}, {{Val| 0 -14 -11 }}]


[[POTE generator]]: ~75/64 = 263.658
[[POTE generator]]: ~3125/2592 = 292.702


{{Optimal ET sequence|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }}
{{Optimal ET sequence|legend=1| 4, 37, 41 }}


[[Badness]]: 0.670947
[[Badness]]: 0.767824


== Slurpee ==
== Quindromeda ==
{{see also| Mint temperaments #Slurpee }}
{{see also| Quindromeda family }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 177147/156250
[[Comma]]: 72057594037927936/71489976421753125


[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -7 -11 }}]
[[POTE generator]]: ~4428675/4194304 = 99.526


[[POTE generator]]: ~27/25 = 72.742
[[Mapping]]: [{{Val| 1 2 0 }}, {{Val| 0 -5 28 }}]


{{Optimal ET sequence|legend=1| 16, 17c, 33 }}
{{Optimal ET sequence|legend=1| 12, 193, 205, 217, 422 }}


[[Badness]]: 0.689274
[[Badness]]: 0.399849


== Pentadecal ==
== Quintaleap ==
{{see also| Cloudy clan #Pentadecal }}
{{see also| Quintaleap family }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 30517578125/29386561536
[[Comma]]: 137438953472/134521003125
 
[[Mapping]]: [{{Val| 1 2 1 }}, {{Val| 0 -5 16 }}]
 
[[POTE generator]]: ~135/128 = 99.267


[[Mapping]]: [{{Val| 15 0 11 }}, {{Val| 0 1 1 }}]
{{Optimal ET sequence|legend=1| 12, 109, 121, 133 }}


[[POTE generator]]: ~3/2 = 702.652
[[Badness]]: 0.444506


{{Optimal ET sequence|legend=1| 15, 45, 60, 75, 135, 210c, 345cc }}
== Rarity ==
{{See also| No-sevens subgroup temperaments #Rarity }}


[[Badness]]: 0.692042
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.


== Sentinel ==
[[Subgroup]]: 2.3.5
{{see also| Orwellismic temperaments #Sentinel }}


Subgroup: 2.3.5
[[Comma list]]: {{monzo| -57 17 13 }}


[[Comma]]: 8968066875/8589934592
{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}


[[Mapping]]: [{{Val| 1 3 -3 }}, {{Val| 0 -4 15 }}]
: mapping generators: ~16384/10125 = 869.392


[[POTE generator]]: ~512/405 = 425.474
[[Optimal tuning]] ([[CTE]]): ~2 = 1�, ~16384/10125 = 869.392


{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bc }}
{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}


[[Badness]]: 0.723413
[[Badness]]: 4.23


== Undeka ==
[[Category:Temperament collections]]
{{see also| Keemic temperaments #Undeka }}
== Satin ==
{{see also| Canousmic temperaments #Satin }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 48828125/45349632
[[Comma]]: {{Monzo| 104 -70 3 }}


[[Mapping]]: [{{Val| 11 0 8 }}, {{Val| 0 1 1 }}]
[[Mapping]]: [{{val| 1 2 12 }}, {{val| 0 -3 -70 }}]


[[POTE generator]]: ~3/2 = 703.829
[[POTE generator]]: ~{{monzo|-34 23 -1}} = 165.907


{{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }}
{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273 }}


[[Badness]]: 0.727539
[[Badness]]: 2.853049


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


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1289945088/1220703125
[[Comma]]: {{monzo|7 41 -31}}


[[Mapping]]: [{{Val| 1 4 4 }}, {{Val| 0 -13 -9 }}]
[[Mapping]]: [{{Val|1 21 28}}, {{Val|0 -31 -41}}]


[[POTE generator]]: ~144/125 = 222.912
[[POTE generator]]: ~162/125 = 448.449


{{Optimal ET sequence|legend=1| 16, 27, 43, 70, 183cc }}
{{Optimal ET sequence|legend=1| 8, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}


[[Badness]]: 0.729609
[[Badness]]: 0.233376


== Semidimi ==
== Semidimi ==
Line 750: Line 769:
[[Badness]]: 0.754866
[[Badness]]: 0.754866


== Quasitemp ==
== Semisept ==
{{see also| Keemic temperaments #Quasitemp }}
{{see also| Hemimean clan #Semisept }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 6103515625/5804752896
[[Comma]]: 782757789696/762939453125


[[Mapping]]: [{{Val| 1 5 5 }}, {{Val| 0 -14 -11 }}]
[[Mapping]]: [{{Val| 1 12 6 }}, {{Val| 0 -17 -6 }}]


[[POTE generator]]: ~3125/2592 = 292.702
[[POTE generator]]: ~192/125 = 735.146


{{Optimal ET sequence|legend=1| 4, 37, 41 }}
{{Optimal ET sequence|legend=1| 18, 31, 80, 111 }}


[[Badness]]: 0.767824
[[Badness]]: 0.630576


== Cypress ==
== Sentinel ==
{{see also| Starling temperaments #Cypress }}
{{see also| Orwellismic temperaments #Sentinel }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 258280326/244140625
[[Comma]]: 8968066875/8589934592


[[Mapping]]: [{{Val| 1 7 10 }}, {{Val| 0 -12 -17 }}]
[[Mapping]]: [{{Val| 1 3 -3 }}, {{Val| 0 -4 15 }}]


[[POTE generator]]: ~4374/3125 = 541.726
[[POTE generator]]: ~512/405 = 425.474


{{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c, 381bcc }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bc }}


[[Badness]]: 0.816635
[[Badness]]: 0.723413


== Chromo ==
== Septendecic ==
{{see also| Keemic temperaments #Chromo }}
Subgroup: 2.3.5


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


[[Comma]]: 1220703125/1146617856
[[Mapping]]: [{{Val| 17 27 0 }}, {{Val| 0 0 1 }}]


[[Mapping]]: [{{Val| 1 1 2 }}, {{Val| 0 13 7 }}]
Mapping generators: ~531441/524288, ~5


[[POTE generator]]: ~25/24 = 53.922
[[POTE generator]]: ~5/4 = 389.193


{{Optimal ET sequence|legend=1| 22, 45, 67c, 89c }}
{{Optimal ET sequence|legend=1| 17c, 34 }}


[[Badness]]: 0.842835
[[Badness]]: 0.541384


== Tertiosec ==
== Septimin ==
{{see also| Marvel temperaments #Tertiosec }}
{{see also| Marvel temperaments #Septimin }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{monzo| -89 21 24 }}
[[Comma]]: 35595703125/34359738368


[[Mapping]]: [{{Val| 3 7 5 }}, {{Val| 0 -8 7 }}]
[[Mapping]]: [{{Val| 1 4 1 }}, {{Val| 0 -11 6 }}]


[[POTE generator]]: ~16/15 = 112.281
[[POTE generator]]: ~75/64 = 263.658


{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171 }}
{{Optimal ET sequence|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bc }}


[[Badness]]: 0.851003
[[Badness]]: 0.670947


== Fervor ==
== Sevond ==
{{see also| Archytas clan #Fervor }}
{{See also| Keemic temperaments #Sevond }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 67108864/61509375
[[Comma]]: 5000000/4782969


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


[[POTE generator]]: ~64/45 = 577.705
[[POTE generator]]: ~3/2 = 706.288


{{Optimal ET sequence|legend=1| 2, 25, 27 }}
{{Optimal ET sequence|legend=1| 7, 42, 49, 56, 119 }}


[[Badness]]: 0.852612
[[Badness]]: 0.339335


== Bohpier ==
== Sfourth ==
{{see also| Sensamagic clan #Bohpier }}
{{see also| Ragismic microtemperaments #Sfourth }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1220703125/1162261467
[[Comma]]: 617673396283947/610351562500000


[[Mapping]]: [{{Val| 1 0 0 }}, {{Val| 0 13 19 }}]
[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -19 -31 }}]


[[POTE generator]]: ~27/25 = 146.476
[[POTE generator]]: ~1594323/1562500 = 26.2342


{{Optimal ET sequence|legend=1| 8, 41, 131, 172, 213c }}
{{Optimal ET sequence|legend=1| 45, 46, 91, 137, 183 }}


[[Badness]]: 0.860534
[[Badness]]: 0.504555


== Elvis ==
== Slurpee ==
{{see also| Jubilismic clan #Elvis }}
{{see also| Mint temperaments #Slurpee }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 36905625/33554432
[[Comma]]: 177147/156250
 
[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -7 -11 }}]


[[Mapping]]: [{{Val| 2 1 10 }}, {{Val| 0 2 -5 }}]
[[POTE generator]]: ~27/25 = 72.742


[[POTE generator]]: ~45/32 = 554.546
{{Optimal ET sequence|legend=1| 16, 17c, 33 }}


{{Optimal ET sequence|legend=1| 26, 80bc, 106bc, 132bc }}
[[Badness]]: 0.689274


[[Badness]]: 0.884000
== Stump ==
: ''See also: [[Sensamagic clan #Pycnic]] and [[Marvel temperaments #Triton]]''


== Vinegar ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 16000000/14348907
[[Comma]]: 273375/262144


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


[[POTE generator]]: ~10/9 = 156.861
[[POTE generator]]: ~64/45 = 631.737


{{Optimal ET sequence|legend=1| 15, 39c, 54, 69b, 84b }}
{{Optimal ET sequence|legend=1| 17, 19 }}


[[Badness]]: 0.903002
[[Badness]]: 0.200600


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


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 793437161472/762939453125
[[Comma]]: 579357147216796875/576460752303423488
 
[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -22 5 }}]


[[Mapping]]: [{{Val| 1 6 7 }}, {{Val| 0 -17 -18 }}]
[[POTE generator]]: ~17578125/16777216 = 77.191


[[POTE generator]]: ~6/5 = 311.694
{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}


{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }}
[[Badness]]: 0.297544


[[Badness]]: 0.942789
== Tertiosec ==
{{see also| Marvel temperaments #Tertiosec }}


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


[[Comma]]: {{Monzo| 80 -49 -1 }}
[[Comma]]: {{monzo| -89 21 24 }}


[[Mapping]]: [{{Val| 1 2 -18 }}, {{Val| 0 -1 49 }}]
[[Mapping]]: [{{Val| 3 7 5 }}, {{Val| 0 -8 7 }}]


[[POTE generator]]: ~3/2 = 702.315
[[POTE generator]]: ~16/15 = 112.281


{{Optimal ET sequence|legend=1| 41, 135c, 176, 217, 475, 1167, 1642, 2117b }}
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171 }}


[[Badness]]: 1.240078
[[Badness]]: 0.851003


== Oncle ==
== Thuja ==
{{see also| Gamelismic clan #Oncle }}
{{see also| Starling temperaments #Thuja }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 145282683375/137438953472
[[Comma]]: 254803968/244140625


[[Mapping]]: [{{Val| 1 1 6 }}, {{Val| 0 3 -19 }}]
[[Mapping]]: [{{Val| 1 -4 0 }}, {{Val| 0 12 5 }}]


[[POTE generator]]: ~4096/3645 = 232.521
[[POTE generator]]: ~3125/2304 = 558.592


{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}
{{Optimal ET sequence|legend=1| 15, 43, 58 }}


[[Badness]]: 1.244699
[[Badness]]: 0.511109


== Diesic ==
== Triskaidekic ==
{{see also| Orwellismic temperaments #Diesic }}
{{see also| Orwellismic temperaments #Triskaidekic }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 10460353203/9765625000
[[Comma]]: 1220703125/1073741824


[[Mapping]]: [{{Val| 1 2 3 }}, {{Val| 0 -13 -21 }}]
[[Mapping]]: [{{Val| 13 0 30 }}, {{Val| 0 1 0 }}]


[[POTE generator]]: ~6561/6250 = 38.571
[[POTE generator]]: ~3/2 = 696.142


{{Optimal ET sequence|legend=1| 31, 156c, 187c, 218bc, 249bc, 280bc }}
{{Optimal ET sequence|legend=1| 13, 26, 91c }}


[[Badness]]: 1.344681
[[Badness]]: 2.241568


== Quartemka ==
== Tritonic ==
{{see also| Gamelismic clan #Quartemka }}
{{see also| Marvel temperaments #Tritonic }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1907348632812500/1853020188851841
[[Comma]]: 553584375/536870912
 
[[Mapping]]: [{{Val| 1 4 -3 }}, {{Val| 0 -5 11 }}]


[[Mapping]]: [{{Val| 1 4 6 }}, {{Val| 0 -21 -32 }}]
[[POTE generator]]: ~45/32 = 580.219


[[POTE generator]]: ~27/25 = 137.962
{{Optimal ET sequence|legend=1| 29, 31, 60, 91 }}


{{Optimal ET sequence|legend=1| 26, 61, 87, 287, 374, 461 }}
[[Badness]]: 0.378527


[[Badness]]: 1.381216
== Tritriple ==
{{see also| Gamelismic clan #Tritriple }}


== Genocchi ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2359296/1953125
[[Comma]]: {{monzo| 31 20 -27 }}


[[Mapping]]: [{{Val| 1 0 2 }}, {{Val| 0 9 2 }}]
[[Mapping]]: [{{Val| 1 -11 -7 }}, {{Val| 0 27 20 }}]


[[POTE generator]]: ~768/625 = 212.444
[[POTE generator]]: ~864/625 = 559.332


{{Optimal ET sequence|legend=1| 6b, 11b, 17c }}
{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }}


[[Badness]]: 1.404977
[[Badness]]: 0.283570


== Casablanca ==
== Undeka ==
{{see also| Starling temperaments #Casablanca }}
{{see also| Keemic temperaments #Undeka }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 20061226008576/19073486328125
[[Comma]]: 48828125/45349632


[[Mapping]]: [{{Val| 1 -7 -14 }}, {{Val| 0 19 14 }}]
[[Mapping]]: [{{Val| 11 0 8 }}, {{Val| 0 1 1 }}]


[[POTE generator]]: ~864/625 = 542.208
[[POTE generator]]: ~3/2 = 703.829


{{Optimal ET sequence|legend=1| 11b, 20b, 31, 73, 104c, 135c }}
{{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }}


[[Badness]]: 1.423736
[[Badness]]: 0.727539


== Archaeotherium ==
== Undim ==
{{see also| Gamelismic clan #Archaeotherium }}
{{see also| Undim family }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 597871125/536870912
[[Comma]]: 2199023255552/2179240250625


[[Mapping]]: [{{Val| 1 1 5 }}, {{Val| 0 3 -14 }}]
[[Mapping]]: [{{Val| 4 6 11 }}, {{Val| 0 1 -5 }}]


[[POTE generator]]: ~1215/1024 = 230.351
[[POTE generator]]: ~3/2 = 702.605


{{Optimal ET sequence|legend=1| 21, 26, 73bc, 99bc }}
{{Optimal ET sequence|legend=1| 12, 140, 152, 164, 1076bc, 1228bc }}


[[Badness]]: 1.434855
[[Badness]]: 0.241703
 
== Newt ==
{{See also| Breedsmic temperaments #Newt }}


== Unsmate ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| 95 -57 -2 }}
[[Comma]]: 17578125/16777216


[[Mapping]]: [{{Val| 1 1 19 }}, {{Val| 0 2 -57 }}]
[[Mapping]]: [{{Val| 1 3 2 }}, {{Val| 0 -9 2 }}]


[[POTE generator]]: ~{{Monzo|47 -28 -1}} = 351.114
[[POTE generator]]: ~2048/1875 = 189.049


{{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 3592bc, 5523bbc }}
{{Optimal ET sequence|legend=1| 13, 19, 89c, 108c, 127c, 146cc }}


[[Badness]]: 1.528465
[[Badness]]: 0.460168


== Octacoid ==
== Untriton ==
[[Subgroup]]: 2.3.5
: ''See also: [[Marvel temperaments #Untriton]], [[Porwell temperaments #Aufo]] and [[Triwellismic temperaments #Interaufo]]''
 
[[Comma list]]: 8589934592/7688671875
 
{{Mapping|legend=1| 1 1 3 | 0 8 -9 }}
 
: mapping generators: ~2, ~16/15
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~16/15 = 88.7331
* [[CWE]]: ~2 = 1\1, ~16/15 = 88.8168
 
{{Optimal ET sequence|legend=1| 13, 14, 27 }}
 
[[Badness]]: 1.75
 
== Quasimoha ==
{{see also| Breedsmic temperaments #Quasimoha }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 2353579470675/2199023255552
[[Comma]]: 2270041927734375/2251799813685248


[[Mapping]]: [{{Val| 1 1 9 }}, {{Val| 0 2 -23 }}]
[[Mapping]]: [{{Val| 1 6 -7 }}, {{Val| 0 -9 19 }}]


[[POTE generator]]: ~1048576/885735 = 348.600
[[POTE generator]]: ~45/32 = 588.722


{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}
{{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}


[[Badness]]: 1.986675
[[Badness]]: 0.307073
 
== Phillips ==
{{see also| Orwellismic temperaments #Phillips }}


== Vinegar ==
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 9685512225/8589934592
[[Comma]]: 16000000/14348907


[[Mapping]]: [{{Val| 2 0 33 }}, {{Val| 0 1 -9 }}]
[[Mapping]]: [{{Val| 3 0 -5 }}, {{Val| 0 2 5 }}]


[[POTE generator]]: ~3/2 = 691.455
[[POTE generator]]: ~10/9 = 156.861


{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }}
{{Optimal ET sequence|legend=1| 15, 39c, 54, 69b, 84b }}


[[Badness]]: 2.228904
[[Badness]]: 0.903002


== Triskaidekic ==
== Vines ==
{{see also| Orwellismic temperaments #Triskaidekic }}
{{see also| Starling temperaments #Vines }}


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: 1220703125/1073741824
[[Comma]]: 156728328192/152587890625


[[Mapping]]: [{{Val| 13 0 30 }}, {{Val| 0 1 0 }}]
[[Mapping]]: [{{Val| 2 7 8 }}, {{Val| 0 -8 -7 }}]


[[POTE generator]]: ~3/2 = 696.142
[[POTE generator]]: ~6/5 = 312.713


{{Optimal ET sequence|legend=1| 13, 26, 91c }}
{{Optimal ET sequence|legend=1| 4, 42, 46, 96, 142 }}


[[Badness]]: 2.241568
[[Badness]]: 0.541831


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


Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma]]: {{Monzo| 104 -70 3 }}
[[Comma]]: 2197265625/2147483648


[[Mapping]]: [{{val| 1 2 12 }}, {{val| 0 -3 -70 }}]
[[Mapping]]: [{{Val| 2 1 5 }}, {{Val| 0 6 -1 }}]


[[POTE generator]]: ~{{monzo|-34 23 -1}} = 165.907
Mapping generators: ~42875/32768, ~9375/8192


{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273 }}
[[POTE generator]]: ~5/4 = 383.212


[[Badness]]: 2.853049
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}


== Rarity ==
[[Badness]]: 0.386367
{{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.
Scales (Scala files): [[wizard22]]


[[Subgroup]]: 2.3.5
== Wronecki ==
Subgroup: 2.3.5


[[Comma list]]: {{monzo| -57 17 13 }}
[[Comma]]: 531441/500000


{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}
[[Mapping]]: [{{Val| 6 0 -5 }}, {{Val| 0 1 2 }}]


: mapping generators: ~16384/10125 = 869.392
[[POTE generator]]: ~3/2 = 695.040


[[Optimal tuning]] ([[CTE]]):  ~2 = 1\1, ~16384/10125 = 869.392
{{Optimal ET sequence|legend=1| 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bbc }}


{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}
[[Badness]]: 0.341757
 
[[Badness]]: 4.23
 
[[Category:Temperament collections]]
Retrieved from "https://en.xen.wiki/w/Miscellaneous_5-limit_temperaments"