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Miscellaneous 5-limit temperaments: Difference between revisions

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= Hogzilla =
{{Technical data page}}
Comma: 4428675/4194304
Below are listed some [[5-limit]] [[regular temperament|temperament]]s that do not belong to some other temperament collection, the majority of which are [[restriction]]s to the 5-limit of temperaments that emerge more fully in higher [[prime limit|limits]] or [[subgroup]]s; they are sorted by [[TE logflat badness]], of which most have Sintel's > 4.7 (Smith's > 0.20). Most of these temperaments 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 [[equivalence continuum|equivalence continua]]
* [[Very low accuracy temperaments]]
* [[Very high accuracy temperaments]]


POTE generator: ~1215/1024 = 252.649
== Unidecmic ==
: ''For extensions, see [[Gamelismic clan #Unidec]].''


Map: [<1 0 11|, <0 2 -11|]
[[Subgroup]]: 2.3.5


EDOs: 14, 19
[[Comma list]]: 31381059609/31250000000


Badness: 0.4247
{{Mapping|legend=1| 2 -1 -3 | 0 6 11 }}
: mapping generators: ~177147/125000, ~25000/19683


= Archaeotherium =
[[Optimal tuning]]s:
Comma: 597871125/536870912
* [[WE]]: ~177147/125000 = 600.0124{{c}}, ~25000/19683 = 416.9619{{c}}
: [[error map]]: {{val| +0.025 -0.196 +0.235 }}
* [[CWE]]: ~177147/125000 = 600.0000{{c}}, ~25000/19683 = 416.9561{{c}}
: error map: {{val| 0.000 -0.236 +0.172 }}


POTE generator: ~1215/1024 = 230.351
{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 2524, 2642, 2760 }}


Map: [<1 1 5|, <0 3 -14|]
[[Badness]] (Sintel): 1.93


EDOs: 21, 26, 73bc, 99bc
== Quasithird ==
: ''For extensions, see [[Ragismic microtemperaments #Quasithird]].''


Badness: 1.4349
[[Subgroup]]: 2.3.5


= Stump =
[[Comma list]]: {{monzo| 55 -64 20 }}
{{see also| Sensamagic clan #Pycnic }}
{{see also| Marvel temperaments #Triton }}


Comma: 273375/262144
{{Mapping|legend=1| 4 0 -11 | 0 5 16 }}
: mapping generators: ~51200000/43046721, ~1594323/1280000


POTE generator: ~64/45 = 631.737
[[Optimal tuning]]s:  
* [[WE]]: ~51200000/43046721 = 299.9990{{c}}, ~1594323/1280000 = 380.3934{{c}}
: [[error map]]: {{val| -0.004 +0.012 -0.008 }}
* [[CWE]]: ~51200000/43046721 = 300.0000{{c}}, ~1594323/1280000 = 380.3944{{c}}
: error map: {{val| 0.000 +0.017 -0.004 }}


Map: [<1 0 6|, <0 3 -7|]
{{Optimal ET sequence|legend=1| 60, 104c, 164, 224, 388, 612, 1612, 2224, 2836, 6284, 9120, 15404 }}


EDOs: 17, 19
[[Badness]] (Sintel): 2.33


Badness: 0.2006
== Supersharp ==
: ''For extensions, see [[Trienstonic clan #Octokaidecal]].''


= Unsmate =
Supersharp tempers out [[800/729]], the difference between the [[27/20]] wolf fourth and the [[40/27]] wolf fifth, splitting the octave into two 27/20~40/27 semioctaves. It generally requires a very sharp fifth, even sharper than 3\5, as a generator. This means that five steps from the [[generator sequence #JI scales obtained from guided generator sequences|Zarlino generator sequence]] starting with 6/5 are tempered to one and a half octaves. The only reasonable 7-limit extension adds 28/27 and 50/49 to the comma list, taking advantage of the existing semioctave.
Comma: 17578125/16777216


POTE generator: ~2048/1875 = 189.049
[[Subgroup]]: 2.3.5


Map: [<1 3 2|, <0 -9 2|]
[[Comma list]]: 800/729


EDOs: 13, 19, 89c, 108c, 127c, 146c
{{Mapping|legend=1| 2 0 -5 | 0 1 3 }}
: mapping generators: ~27/20, ~3


Badness: 0.4602
[[Optimal tuning]]s:
* [[WE]]: ~27/20 = 596.986{{c}}, ~3/2 = 725.434{{c}} (~10/9 = 128.448{{c}})
: [[error map]]: {{val| -6.029 +17.450 -13.027 }}
* [[CWE]]: ~27/20 = 600.000{{c}}, ~3/2 = 726.548{{c}} (~10/9 = 126.548{{c}})
: error map: {{val| 0.000 +24.593 -6.670 }}


= Chromo =
{{Optimal ET sequence|legend=1| 8, 10, 18, 28b }}
Comma: 1220703125/1146617856


POTE generator: ~25/24 = 53.922
[[Badness]] (Sintel): 2.88


Map: [<1 1 2|, <0 13 7|]
== Avila ==
: ''For extensions, see [[Septisemi temperaments #Avila]].''


EDOs: 22, 45, 67c, 89c
[[Subgroup]]: 2.3.5


Badness: 0.8428
[[Comma list]]: 729/640


= Wizard =
{{Mapping|legend=1| 1 0 -7 | 0 1 6 }}
: mapping generators: ~2, ~3


{{see also| Marvel temperaments #Wizard }}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1210.600{{c}}, ~3/2 = 667.437{{c}}
: [[error map]]: {{val| +10.600 -23.917 +7.711 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 663.474{{c}}
: error map: {{val| 0.000 -38.481 -5.472 }}


Period: 1\2
{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20b, 29b }}


Optimal ([[POTE]]) generator: ~5/4 = 383.212
[[Badness]] (Sintel): 4.27


EDO generators: [[22edo|7\22]], [[50edo|16\50]], [[72edo|23\72]], [[94edo|30\94]]
== Lafa ==
This temperament was named by [[Petr Pařízek]] in 2011, referring to the characteristic that stacking 12 generators makes 6/1 – "l" for 12, "f" for 6<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. Its ploidacot is therefore beta-dodecacot.
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 77 -31 -12 }}
 
{{Mapping|legend=1| 1 -1 9 | 0 12 -31 }}
: mapping generators: ~2, ~{{monzo| -32 13 5 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9693{{c}}, ~{{monzo| -32 13 5 }} = 258.4963{{c}}
: [[error map]]: {{val| -0.031 +0.031 +0.026 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -32 13 5 }} = 258.5031{{c}}
: error map: {{val| 0.000 +0.082 +0.091 }}
 
{{Optimal ET sequence|legend=1| 65, 246, 311, 376, 441, 2711, 3152, 3593, 4034, 4475, 4916, 5357, 10273bc, 15630bbcc }}
 
[[Badness]] (Sintel): 4.33
 
== Lafayette ==
: ''For extensions, see [[Mint temperaments #Progression]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 3456/3125
 
{{Mapping|legend=1| 1 1 2 | 0 5 3 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~25/24 = 138.722{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~25/24 = 140.995{{c}}
 
{{Optimal ET sequence|legend=1| 8, 9, 17c }}
 
[[Badness]] (Sintel): 4.70
 
== Dodifo ==
: ''For extensions, see [[Porwell temperaments #Dodifo]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -67 -9 35 }}
 
{{Mapping|legend=1| 1 12 5 | 0 -35 -9 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~768/625 = 357.087{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~768/625 = 357.088{{c}}
 
{{Optimal ET sequence|legend=1| 37, 84, 205, 289, 494, 783, 2060, 2843, 3626 }}
 
[[Badness]] (Sintel): 5.00
 
== Doublewide ==
: ''For extensions, see [[Jubilismic clan #Doublewide]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 390625/373248
 
{{Mapping|legend=1| 2 1 3 | 0 4 3 }}
: mapping generators: ~625/432, ~6/5
 
[[Optimal tuning]]s:
* [[WE]]: ~625/432 = 600.6814{{c}}, ~6/5 = 325.8892{{c}} (~144/125 = 274.7921{{c}})
: [[error map]]: {{val| +1.363 +2.283 -6.602 }}
* [[CWE]]: ~625/432 = 600.0000{{c}}, ~6/5 = 325.8147{{c}} (~144/125 = 274.185{{c}})
: error map: {{val| 0.000 +1.304 -8.869 }}
 
{{Optimal ET sequence|legend=1| 4, 14b, 18, 22, 48, 70c, 118c }}
 
[[Badness]] (Sintel): 5.32
 
== Shibboleth ==
: ''For extensions, see [[Gamelismic clan #Superkleismic]], [[Starling temperaments #Gilead]], and [[Sensamagic clan #Superthird]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 1953125/1889568
 
{{Mapping|legend=1| 1 4 5 | 0 -9 -10 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 321.773{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 321.852{{c}}
 
{{Optimal ET sequence|legend=1| 15, 26, 41, 179c }}
 
[[Badness]] (Sintel): 5.34
 
== Semidimfourth ==
: ''For extensions, see [[Ragismic microtemperaments #Semidimfourth]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 7 41 -31 }}
 
{{Mapping|legend=1| 1 21 28 | 0 -31 -41 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~162/125 = 448.449{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~162/125 = 448.449{{c}}
 
{{Optimal ET sequence|legend=1| 8, …, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}
 
[[Badness]] (Sintel): 5.47
 
== Mynic ==
: ''For extensions, see [[Starling temperaments #Myna]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 10077696/9765625
 
{{Mapping|legend=1| 1 9 9 | 0 -10 -9 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 310.030{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 310.140{{c}}
 
{{Optimal ET sequence|legend=1| 27, 31, 58, 89 }}
 
[[Badness]] (Sintel): 5.86
 
== Progress ==
: ''For extensions, see [[Archytas clan #Progress]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 32768/30375
 
{{Mapping|legend=1| 1 0 5 | 0 3 -5 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 638.922{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 638.736{{c}}
 
{{Optimal ET sequence|legend=1| 2, 13, 15, 32c, 47bc, 62bc }}
 
[[Badness]] (Sintel): 5.77
 
== Abigail ==
: ''For extensions, see [[Ragismic microtemperaments #Abigail]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 25 -48 22 }}
 
{{Mapping|legend=1| 2 7 13 | 0 -11 -24 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~{{monzo| -12 24 -11 }} = 600.000{{c}}, ~200000/177147 = 208.907{{c}}
* [[CWE]]: ~{{monzo| -12 24 -11 }} = 600.000{{c}}, ~200000/177147 = 208.906{{c}}
 
{{Optimal ET sequence|legend=1| 46, 132, 178, 224, 270, 494, 1752, 2246, 2740, 4986, 7726b }}
 
[[Badness]] (Sintel): 5.97
 
== Supermajor ==
: ''For extensions, see [[Ragismic microtemperaments #Supermajor]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -13 -46 37 }}
 
{{Mapping|legend=1| 1 15 19 | 0 -37 -46 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~625/486 = 435.081{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~625/486 = 435.081{{c}}
 
{{Optimal ET sequence|legend=1| 80, 171, 593, 764, 935, 1106, 3489, 4595, 5701 }}
 
[[Badness]] (Sintel): 6.19
 
== Gamera ==
: ''For extensions, see [[Ragismic microtemperaments #Gamera]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 10 -40 23 }}
 
{{Mapping|legend=1| 1 6 10 | 0 -23 -40 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~2500/2187 = 230.345{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~2500/2187 = 230.345{{c}}
 
{{Optimal ET sequence|legend=1| 26, 73, 99, 224, 323, 547, 870 }}
 
[[Badness]] (Sintel): 6.39
 
== Tritriple ==
: ''For extensions, see [[Gamelismic clan #Tritriple]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 31 20 -27 }}
 
{{Mapping|legend=1| 1 -11 -7 | 0 27 20 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~864/625 = 559.328{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~864/625 = 559.332{{c}}
 
{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }}
 
[[Badness]] (Sintel): 6.65
 
== Kangaroo ==
: ''For extensions, see [[Trienstonic clan #Parakangaroo]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 64000/59049
 
{{Mapping|legend=1| 1 0 -3 | 0 3 10 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~40/27 = 637.879{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~40/27 = 638.805{{c}}
 
{{Optimal ET sequence|legend=1| 15, 47b, 62b }}
 
[[Badness]] (Sintel): 6.94
 
== Tertiaseptal ==
: ''For extensions, see [[Breedsmic temperaments #Tertiaseptal]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -59 5 22 }}
 
{{Mapping|legend=1| 1 3 2 | 0 -22 5 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~17578125/16777216 = 77.186{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~17578125/16777216 = 77.191{{c}}
 
{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}
 
[[Badness]] (Sintel): 6.98
 
== Untriton ==
: ''For extensions, see [[Marvel temperaments #Untriton]], [[Porwell temperaments #Aufo]] and [[Triwellismic temperaments #Interaufo]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -51 19 9 }}
 
{{Mapping|legend=1| 1 6 -7 | 0 -9 19 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 588.727{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 588.722{{c}}
 
{{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}
 
[[Badness]] (Sintel): 7.20
 
== Nessafof ==
: ''For extensions, see [[Porwell temperaments #Nessafof]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 25 15 -21 }}
 
{{Mapping|legend=1| 3 2 5 | 0 7 5 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~78125/62208 = 400.000{{c}}, ~9765625/8957952 = 157.392{{c}}
* [[CWE]]: ~78125/62208 = 400.000{{c}}, ~9765625/8957952 = 157.409{{c}}
 
{{Optimal ET sequence|legend=1| 15, 54b, 69, 84, 99, 183, 282, 465, 1212c, 1677cc }}
 
[[Badness]] (Sintel): 7.81
 
== Lemba ==
: ''For extensions, see [[Jubilismic clan #Lemba]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 140625/131072
 
{{Mapping|legend=1| 2 2 5 | 0 3 -1 }}
: Mapping generators: ~375/256, ~75/64
 
[[Optimal tuning]]s:
* [[CTE]]: ~375/256 = 600.000{{c}}, ~75/64 = 232.986{{c}}
: [[error map]]: {{val| 0.000 -2.998 -19.300 }}
* [[CWE]]: ~375/256 = 600.000{{c}}, ~75/64 = 231.832{{c}}
: error map: {{val| 0.000 -6.458 -18.146 }}
 
{{Optimal ET sequence|legend=1| 10, 16, 26, 88cc }}
 
[[Badness]] (Sintel): 7.85
 
== Delorean ==
: ''For extensions, see [[Mint temperaments #Subklei]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 17496/15625
 
{{Mapping|legend=1| 1 3 4 | 0 -6 -7 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 284.817{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 284.293{{c}}
 
{{Optimal ET sequence|legend=1| 4, 13c, 17c, 21, 38c }}
 
[[Badness]] (Sintel): 8.35
 
== Majvam ==
: ''For extensions, see [[No-sevens subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 2404631929946112/2384185791015625
 
{{Mapping|legend=1| 1 10 5 | 0 -22 -7 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~125/96 = 459.006{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~125/96 = 458.995{{c}}
 
{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }}
 
[[Badness]] (Sintel): 8.37
 
== Beatles ==
: ''For extensions, see [[Archytas clan #Beatles]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 524288/492075
 
{{Mapping|legend=1| 1 1 5 | 0 2 -9 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~512/405 = 356.492{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~512/405 = 355.930{{c}}
 
{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}
 
[[Badness]] (Sintel): 8.41
 
== Magus ==
: ''For extensions, see [[Sensamagic clan #Magus]] and [[Starling temperaments #Amigo]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 50331648/48828125
 
{{Mapping|legend=1| 1 -2 2 | 0 11 1 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 391.068{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 391.225{{c}}
 
{{Optimal ET sequence|legend=1| 3, …, 40, 43, 46, 181c, 227c, 273c, 319c }}
 
[[Badness]] (Sintel): 8.45
 
== Tritonic ==
: ''For extensions, see [[Marvel temperaments #Tritonic]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 553584375/536870912
 
{{Mapping|legend=1| 1 4 -3 | 0 -5 11 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 580.278{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 580.219{{c}}
 
{{Optimal ET sequence|legend=1| 29, 31, 60, 91 }}
 
[[Badness]] (Sintel): 8.88
 
== Wizard ==
: ''For extensions, see [[Marvel temperaments #Wizard]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 2197265625/2147483648
 
{{Mapping|legend=1| 2 1 5 | 0 6 -1 }}
: mapping generators: ~42875/32768, ~9375/8192
 
[[Optimal tuning]]s:
* [[CTE]]: ~42875/32768 = 600.000{{c}}, ~9375/8192 = 216.950{{c}}
* [[POTE]]: ~42875/32768 = 600.000{{c}}, ~9375/8192 = 216.788{{c}}
 
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bcc }}
 
[[Badness]] (Sintel): 9.06


Scales (Scala files): [[wizard22]]
Scales (Scala files): [[wizard22]]


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
== Merman ==
<div style="line-height:1.6;">Technical data</div>
: ''For extensions, see [[Marvel temperaments #Merman]].''
<div class="mw-collapsible-content">
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -40 15 7 }}
 
{{Mapping|legend=1| 1 5 -5 | 0 -7 15 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 585.653{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 585.634{{c}}
 
{{Optimal ET sequence|legend=1| 41, 84, 125, 209, 334c, 543bc }}
 
[[Badness]] (Sintel): 10.6
 
== Nusecond ==
: ''For extensions, see [[Starling temperaments #Nusecond]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 51018336/48828125
 
{{Mapping|legend=1| 1 3 4 | 0 -11 -13 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~3125/2916 = 154.577{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3125/2916 = 154.523{{c}}
 
{{Optimal ET sequence|legend=1| 8, 23, 31, 70, 101, 132c }}
 
[[Badness]] (Sintel): 10.9
 
== Comic ==
: ''For extensions, see [[Jubilismic clan #Comic]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 5120000/4782969
 
{{Mapping|legend=1| 2 1 -3 | 0 2 7 }}
 
: mapping generators: ~2187/1600, ~40/27
 
[[Optimal tuning]]s:
* [[WE]]: ~2187/1600 = 598.9674{{c}}, ~40/27 = 654.2542{{c}} (~81/80 = 55.2868{{c}})
: [[error map]]: {{val| -2.065 +5.521 -3.436 }}
* [[CWE]]: ~2187/1600 = 600.0000{{c}}, ~40/27 = 655.0201{{c}} (~81/80 = 55.0201{{c}})
: error map: {{val| 0.000 +8.085 -1.173 }}
 
{{Optimal ET sequence|legend=1| 20c, 22, 86b, 108b, 130b }}
 
[[Badness]] (Sintel): 11.5
 
== Sfourth ==
: ''For extensions, see [[Ragismic microtemperaments #Sfourth]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -5 31 -19 }}
 
{{Mapping|legend=1| 1 2 3 | 0 -19 -31 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000{{c}}, ~1594323/1562500 = 26.2323{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~1594323/1562500 = 26.2342{{c}}
 
{{Optimal ET sequence|legend=1| 45, 46, 91, 137, 183, 869, 1052, 1235, 1418c }}
 
[[Badness]] (Sintel): 11.8
 
== Thuja ==
: ''For extensions, see [[Buzzardsmic clan #Thuja]].''
{{See also| Hypovishnuzma }}
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 254803968/244140625
 
{{Mapping|legend=1| 1 -4 0 | 0 12 5 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~3125/2304 = 558.404{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3125/2304 = 558.592{{c}}
 
{{Optimal ET sequence|legend=1| 15, 43, 58 }}
 
[[Badness]] (Sintel): 12.0
 
== Leapday ==
: ''For extensions, see [[Hemifamity temperaments #Leapday]] and [[Porwell temperaments #Polypyth]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 10737418240/10460353203
 
{{Mapping|legend=1| 1 0 -31 | 0 1 21 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 704.100{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 704.179{{c}}
 
{{Optimal ET sequence|legend=1| 17c, 29, 46, 121, 167, 455bc, 622bbc }}
 
[[Badness]] (Sintel): 12.3
 
== Vines ==
: ''For extensions, see [[Starling temperaments #Vines]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 156728328192/152587890625
 
{{Mapping|legend=1| 2 7 8 | 0 -8 -7 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~390625/279936 = 600.000{{c}}, ~6/5 = 312.636{{c}}
* [[POTE]]: ~390625/279936 = 600.000{{c}}, ~6/5 = 312.713{{c}}
 
{{Optimal ET sequence|legend=1| 4, …, 42, 46, 96, 142, 330c, 472cc }}
 
[[Badness]] (Sintel): 12.7
 
== Emka ==
: ''For extensions, see [[Hemimean clan #Emka]] and [[Horwell temperaments #Emkay]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -50 -8 27 }}
 
{{Mapping|legend=1| 1 14 6 | 0 -27 -8 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~9765625/7077888 = 551.777{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~9765625/7077888 = 551.784{{c}}
 
{{Optimal ET sequence|legend=1| 37, 50, 87, 137, 224 }}
 
[[Badness]] (Sintel): 12.8
 
== Misneb ==
: ''For extensions, see [[Marvel temperaments #Misneb]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -57 14 15 }}
 
{{Mapping|legend=1| 1 3 1 | 0 -15 14 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~16/15 = 113.233{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~16/15 = 113.240{{c}}
 
{{Optimal ET sequence|legend=1| 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bcc }}
 
[[Badness]] (Sintel): 14.3
 
== Semisept ==
: ''For extensions, see [[Hemimean clan #Semisept]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 782757789696/762939453125
 
{{Mapping|legend=1| 1 12 6 | 0 -17 -6 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~192/125 = 735.203{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~192/125 = 735.146{{c}}
 
{{Optimal ET sequence|legend=1| 18, 31, 80, 111, 586cc, 697ccc }}
 
[[Badness]] (Sintel): 14.8
 
== Septimin ==
: ''For extensions, see [[Marvel temperaments #Septimin]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 35595703125/34359738368
 
{{Mapping|legend=1| 1 4 1 | 0 -11 6 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~75/64 = 263.571{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~75/64 = 263.658{{c}}
 
{{Optimal ET sequence|legend=1| 9, 23b, 32, 41, 91, 132, 223c, 355bcc }}
 
[[Badness]] (Sintel): 15.7
 
== Slurpee ==
: ''For extensions, see [[Mint temperaments #Slurpee]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 177147/156250
 
{{Mapping|legend=1| 1 2 3 | 0 -7 -11 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~27/25 = 72.659{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~27/25 = 72.742{{c}}
 
{{Optimal ET sequence|legend=1| 16, 17c, 33 }}
 
[[Badness]] (Sintel): 16.2
 
== Pentadecal ==
: ''For extensions, see [[Cloudy clan #Pentadecal]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 30517578125/29386561536
 
{{Mapping|legend=1| 15 0 11 | 0 1 1 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~648/625 = 80.000{{c}}, ~3/2 = 703.340{{c}}
* [[POTE]]: ~648/625 = 80.000{{c}}, ~3/2 = 702.652{{c}}
 
{{Optimal ET sequence|legend=1| 15, 45, 60, 75, 135, 210c }}
 
[[Badness]] (Sintel): 16.2
 
== Anthoine ==
: ''For extensions, see [[Buzzardsmic clan #Anthoine]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 286102294921875/281474976710656
 
{{Mapping|legend=1| 1 8 2 | 0 -20 1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.303{{c}}, ~5/4 = 385.024{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 384.920{{c}}
 
{{Optimal ET sequence|legend=1| 25, 28, 53 }}
 
[[Badness]] (Sintel): 16.5
 
== Sentinel ==
: ''For extensions, see [[Orwellismic temperaments #Sentinel]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 8968066875/8589934592
 
{{Mapping|legend=1| 1 3 -3 | 0 -4 15 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~512/405 = 425.590{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~512/405 = 425.474{{c}}
 
{{Optimal ET sequence|legend=1| 14, 17, 31, 79, 110, 361bbcc }}
 
[[Badness]] (Sintel): 17.0
 
== Kumonga ==
: ''For extensions, see [[Starling temperaments #Kumonga]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 1289945088/1220703125
 
{{Mapping|legend=1| 1 4 4 | 0 -13 -9 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~144/125 = 223.076{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~144/125 = 222.912{{c}}
 
{{Optimal ET sequence|legend=1| 16, 27, 43, 70, 183cc }}
 
[[Badness]] (Sintel): 17.1
 
== Mirkat ==
: ''For extensions, see [[Mirkwai clan #Mirkat]].''


Comma list: 2197265625/2147483648
[[Subgroup]]: 2.3.5


Mapping: [{{val| 2 1 5 }}, {{val| 0 6 -1 }}]
[[Comma list]]: {{monzo| 20 -39 18 }}


Mapping generators: ~42875/32768, ~9375/8192
{{Mapping|legend=1| 3 2 1 | 0 6 13 }}


{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 548bc }}
[[Optimal tuning]]s:
* [[CTE]]: ~2000000/1594323 = 400.000{{c}}, ~10/9 = 183.593{{c}}
* [[CWE]]: ~2000000/1594323 = 400.000{{c}}, ~10/9 = 183.585{{c}}


Badness: 0.3864
{{Optimal ET sequence|legend=1| 33c, 39, 72, 111, 183, 438, 621, 1425b }}


</div></div>
[[Badness]] (Sintel): 17.6


= Undeka =
== Semidimi ==
Comma: 48828125/45349632
: ''For extensions, see [[Ragismic microtemperaments #Semidimi]].''


POTE generator: ~3/2 = 703.829
[[Subgroup]]: 2.3.5


Map: [&lt;11 0 8|, &lt;0 1 1|]
[[Comma list]]: {{monzo| -12 -73 55 }}


EDOs: 22, 77c, 99c, 121c
{{Mapping|legend=1| 1 36 48 | 0 -55 -73 }}


Badness: 0.7275
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~162/125 = 449.127{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~162/125 = 449.127{{c}}


== 7-limit ==
{{Optimal ET sequence|legend=1| 8, …, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}
Commas: 875/864, 3200/3087


POTE generator: ~3/2 = 708.792
[[Badness]] (Sintel): 17.7


Map: [&lt;11 0 8 31|, &lt;0 1 1 0|]
== Slender ==
: ''For extensions, see [[Marvel temperaments #Slender]].''


Wedgie: &lt;&lt;11 11 0 -8 -31 -31||
[[Subgroup]]: 2.3.5


EDOs: 22
[[Comma list]]: {{monzo| -46 10 13 }}


Badness: 0.1418
{{Mapping|legend=1| 1 2 2 | 0 -13 10 }}


== 11-limit ==
[[Optimal tuning]]s:
Commas: 100/99, 352/343, 385/384
* [[CTE]]: ~2 = 1200.000{{c}}, ~16875/16384 = 38.380{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~16875/16384 = 38.400{{c}}


POTE generator: ~3/2 = 706.768
{{Optimal ET sequence|legend=1| 31, 94, 125, 781bcc }}


Map: [&lt;11 0 8 31 38|, &lt;0 1 1 0 0|]
[[Badness]] (Sintel): 17.8


EDOs: 22
== Quasitemp ==
: ''For extensions, see [[Keemic temperaments #Quasitemp]].''


Badness: 0.0687
[[Subgroup]]: 2.3.5


== 13-limit ==
[[Comma list]]: 6103515625/5804752896
Commas: 65/63, 100/99, 169/165, 352/343


POTE generator: ~3/2 = 707.764
{{Mapping|legend=1| 1 5 5 | 0 -14 -11 }}


Map: [&lt;11 0 8 31 38 23|, &lt;0 1 1 0 0 1|]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~3125/2592 = 292.591{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3125/2592 = 292.702{{c}}


EDOs: 22
{{Optimal ET sequence|legend=1| 4, …, 37, 41 }}


Badness: 0.0565
[[Badness]] (Sintel): 18.0


= Triskaidekic =
== Cypress ==
Comma: 1220703125/1073741824
: ''For extensions, see [[Starling temperaments #Cypress]].''


POTE generator: ~3/2 = 696.142
[[Subgroup]]: 2.3.5


Map: [&lt;13 0 30|, &lt;0 1 0|]
[[Comma list]]: 258280326/244140625


EDOs: 13, 26, 91c
{{Mapping|legend=1| 1 7 10 | 0 -12 -17 }}


Badness: 2.2416
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~4374/3125 = 541.735{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~4374/3125 = 541.726{{c}}


== 7-limit ==
{{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c }}
Commas: 1728/1715, 1875/1792


POTE generator: ~3/2 = 694.143
[[Badness]] (Sintel): 19.2


Map: [&lt;13 0 30 16|, &lt;0 1 0 1|]
== Chromo ==
: ''For extensions, see [[Keemic temperaments #Chromo]].''


Wedgie: &lt;&lt;13 0 13 -30 -16 30||
[[Subgroup]]: 2.3.5


EDOs: 26
[[Comma list]]: 1220703125/1146617856


Badness: 0.2190
{{Mapping|legend=1| 1 1 2 | 0 13 7 }}


== 11-limit ==
[[Optimal tuning]]s:
Commas: 99/98, 125/121, 385/384
* [[CTE]]: ~2 = 1200.000{{c}}, ~25/24 = 54.138{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~25/24 = 53.922{{c}}


POTE generator: ~3/2 = 696.296
{{Optimal ET sequence|legend=1| 22, 45, 67c, 89c }}


Map: [&lt;13 0 30 16 45|, &lt;0 1 0 1 0|]
[[Badness]] (Sintel): 19.8


EDOs: 26, 91cd
== Tertiosec ==
: ''For extensions, see [[Marvel temperaments #Tertiosec]].''


Badness: 0.0988
[[Subgroup]]: 2.3.5


== 13-limit ==
[[Comma list]]: {{monzo| -89 21 24 }}
Commas: 78/77, 99/98, 125/121, 1200/1183


POTE generator: ~3/2 = 695.879
{{Mapping|legend=1| 3 7 5 | 0 -8 7 }}


Map: [&lt;13 0 30 16 45 48|, &lt;0 1 0 1 0 0|]
[[Optimal tuning]]s:  
* [[CTE]]: ~{{monzo| 30 -7 -8 }} = 400.000{{c}}, ~16/15 = 112.275{{c}}
* [[POTE]]: ~{{monzo| 30 -7 -8 }} = 400.000{{c}}, ~16/15 = 112.281{{c}}


EDOs: 26, 91cdf
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171 }}


Badness: 0.0592
[[Badness]] (Sintel): 20.0


= Phillips =
== Fervor ==
Comma: 9685512225/8589934592
: ''For extensions, see [[Archytas clan #Fervor]].''


POTE generator: ~3/2 = 691.455
[[Subgroup]]: 2.3.5


Map: [&lt;2 0 33|, &lt;0 1 -9|]
[[Comma list]]: 67108864/61509375


EDOs: 14, 26, 66b, 92bc, 118bc
{{Mapping|legend=1| 1 4 -2 | 0 -5 9 }}


Badness: 2.2289
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~64/45 = 577.593{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~64/45 = 577.705{{c}}


= Oncle =
{{Optimal ET sequence|legend=1| 2, …, 25, 27 }}
Comma: 145282683375/137438953472


POTE generator: ~4096/3645 = 232.521
[[Badness]] (Sintel): 20.0


Map: [&lt;1 1 6|, &lt;0 3 -19|]
== Bohpier ==
: ''For extensions, see [[Sensamagic clan #Bohpier]].''


EDOs: 31, 98c, 129c, 160bc, 289bc
[[Subgroup]]: 2.3.5


Badness: 1.2447
[[Comma list]]: 1220703125/1162261467


= Quasimoha =
{{Mapping|legend=1| 1 0 0 | 0 13 19 }}
Comma: 2353579470675/2199023255552


POTE generator: ~1048576/885735 = 348.600
[[Optimal tuning]]s:
* [[CTE]] and [[POTE]]: ~2 = 1200.000{{c}}, ~27/25 = 146.476{{c}}


Map: [&lt;1 1 9|, &lt;0 2 -23|]
{{Optimal ET sequence|legend=1| 8, …, 41, 131, 172, 213c }}


EDOs: 31, 117c, 148bc, 179bc
[[Badness]] (Sintel): 20.2


Badness: 1.9867
== Elvis ==
: ''For extensions, see [[Jubilismic clan #Elvis]].''


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


POTE generator: ~768/625 = 212.444
[[Comma list]]: 36905625/33554432


Map: [&lt;1 0 2|, &lt;0 9 2|]
{{Mapping|legend=1| 2 1 10 | 0 2 -5 }}


EDOs: 17c
[[Optimal tuning]]s:  
* [[CTE]]: ~6075/4096 = 600.000{{c}}, ~64/45 = 644.844{{c}}
* [[POTE]]: ~6075/4096 = 600.000{{c}}, ~64/45 = 645.454{{c}}


Badness: 1.4050
{{Optimal ET sequence|legend=1| 26, 80bc, 106bbcc, 132bbcc }}


= Misneb =
[[Badness]] (Sintel): 20.7
Commas: 145964630126953125/144115188075855872


POTE generator: ~16/15 = 113.240
== Enneadecacot ==
[[Subgroup]]: 2.3.5


Map: [&lt;1 3 1|, &lt;0 -15 14|]
[[Comma list]]: {{monzo| 79 -22 -19 }}


EDOs: 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bc
{{Mapping|legend=1| 1 1 3 | 0 19 -22 }}


Badness: 0.6095
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000{{c}}, ~34171875/33554432 = 36.9607{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~34171875/33554432 = 36.9622{{c}}


== 7-limit ==
{{Optimal ET sequence|legend=1| 32, 65, 292, 357, 422, 487, 1396c }}
Commas: 225/224, 4194304/4117715


POTE generator: ~16/15 = 113.235
[[Badness]] (Sintel): 20.9


Map: [&lt;1 3 1 3|, &lt;0 -15 14 -2|]
== Vinegar ==
: ''For extensions, see [[Starling temperaments #Vinegar]].''


Wedgie: &lt;&lt;15 -14 2 -57 -39 44||
[[Subgroup]]: 2.3.5


EDOs: 21, 32, 53
[[Comma list]]: 16000000/14348907


Badness: 0.1410
{{Mapping|legend=1| 3 0 -5 | 0 2 5 }}


== 11-limit ==
[[Optimal tuning]]s:
Commas: 99/98, 176/175, 1310720/1294139
* [[CTE]]: ~243/200 = 400.000{{c}}, ~4000/2187 = 955.656{{c}} (~10/9 = 155.656{{c}})
* [[POTE]]: ~243/200 = 400.000{{c}}, ~4000/2187 = 956.861{{c}} (~10/9 = 156.861{{c}})


POTE generator: ~16/15 = 113.323
{{Optimal ET sequence|legend=1| 15, 39c, 54, 69b }}


Map: [&lt;1 3 1 3 1|, &lt;0 -15 14 -2 26|]
[[Badness]] (Sintel): 21.2


EDOS: 21, 53, 127, 180de
== Oolong ==
: ''For extensions, see [[Starling temperaments #Oolong]].''


Badness: 0.0854
[[Subgroup]]: 2.3.5


=== 13-limit ===
[[Comma list]]: 793437161472/762939453125
Commas: 99/98, 176/175, 640/637 847/845


POTE generator: ~16/15 = 113.323
{{Mapping|legend=1| 1 6 7 | 0 -17 -18 }}


Map: [&lt;1 3 1 3 1 2|, &lt;0 -15 14 -2 26 18|]
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 311.726{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 311.694{{c}}


EDOs: 21, 53, 127, 189de
{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }}


Badness: 0.0456
[[Badness]] (Sintel): 22.1


== Musneb ==
== Oncle ==
Commas: 225/224, 385/384, 66550/64827
: ''For extensions, see [[Gamelismic clan #Oncle]].''


POTE generator: ~16/15 = 113.142
[[Subgroup]]: 2.3.5


Map: [&lt;1 3 1 3 6|, &lt;0 -15 14 -2 -27|]
[[Comma list]]: 145282683375/137438953472


EDOS: 32, 53, 191de, 244cde, 297cde
{{Mapping|legend=1| 1 1 6 | 0 3 -19 }}


Badness: 0.0873
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~4096/3645 = 232.385{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~4096/3645 = 232.521{{c}}


= Aufo =
{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}
Comma: 2270041927734375/2251799813685248


POTE generator: ~45/32 = 588.722
[[Badness]] (Sintel): 29.2


Map: [&lt;1 6 -7|, &lt;0 -9 19|]
== Quasiorwell ==
: ''For extensions, see [[Breedsmic temperaments #Quasiorwell]].''


EDOs: 51, 53, 267, 320, 373, 426, 479, 532, 2607bc
[[Subgroup]]: 2.3.5


Badness: 0.3071
[[Comma list]]: {{monzo| -93 3 38 }}


== 7-limit ==
{{Mapping|legend=1| 1 31 0 | 0 -38 3 }}
Commas: 6144/6125, 177147/175616


POTE generator: ~45/32 = 588.782
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~{{monzo| -31 1 13 }} = 928.896{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~{{monzo| -31 1 13 }} = 928.893{{c}}


Map: [&lt;1 6 -7 19|, &lt;0 -9 19 -33|]
{{Optimal ET sequence|legend=1| 31, …, 177, 208, 239, 270, 841, 1111, 1381, 2492c }}


Wedgie: &lt;&lt;9 -19 33 -51 27 130||
[[Badness]] (Sintel): 30.6


EDOs: 53, 55, 108, 161, 214, 267
== Diesic ==
: ''For extensions, see [[Orwellismic temperaments #Diesic]].''


Badness: 0.1214
[[Subgroup]]: 2.3.5


== Untriton ==
[[Comma list]]: 10460353203/9765625000
Commas: 225/224, 125000000/121060821
 
{{Mapping|legend=1| 1 2 3 | 0 -13 -21 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~6561/6250 = 38.550{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6561/6250 = 38.571{{c}}
 
{{Optimal ET sequence|legend=1| 31, 156c }}
 
[[Badness]] (Sintel): 31.5
 
== Quartemka ==
: ''For extensions, see [[Gamelismic clan #Quartemka]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 2 -32 21 }}
 
{{Mapping|legend=1| 1 4 6 | 0 -21 -32 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~27/25 = 137.963{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~27/25 = 137.962{{c}}
 
{{Optimal ET sequence|legend=1| 26, 61, 87, 287, 374, 461 }}
 
[[Badness]] (Sintel): 32.4
 
== Genocchi ==
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 2359296/1953125
 
{{Mapping|legend=1| 1 0 2 | 0 9 2 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~768/625 = 210.920{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~768/625 = 212.444{{c}}
 
{{Optimal ET sequence|legend=1| 6b, 11b, 17c }}
 
[[Badness]] (Sintel): 33.0
 
== Casablanca ==
: ''For extensions, see [[Starling temperaments #Casablanca]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 22 14 -19 }}
 
{{Mapping|legend=1| 1 -7 -14 | 0 19 14 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~864/625 = 542.142{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~864/625 = 542.208{{c}}
 
{{Optimal ET sequence|legend=1| 11b, 20b, 31, 73, 104c, 135c }}
 
[[Badness]] (Sintel): 33.4
 
== Archaeotherium ==
: ''For extensions, see [[Gamelismic clan #Archaeotherium]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 597871125/536870912
 
{{Mapping|legend=1| 1 1 5 | 0 3 -14 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~1215/1024 = 229.947{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~1215/1024 = 230.351{{c}}
 
{{Optimal ET sequence|legend=1| 21, 26, 73bc, 99bc }}
 
[[Badness]] (Sintel): 33.7
 
== Octacoid ==
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 8589934592/7688671875
 
{{Mapping|legend=1| 1 1 3 | 0 8 -9 }}
 
: Mapping generators: ~2, ~16/15
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000{{c}}, ~16/15 = 88.7331{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 88.8168{{c}}
 
{{Optimal ET sequence|legend=1| 13, 14, 27 }}
 
[[Badness]] (Sintel): 41.1
 
== Quasimoha ==
: ''For extensions, see [[Breedsmic temperaments #Quasimoha]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -41 23 2 }}
 
{{Mapping|legend=1| 1 1 9 | 0 2 -23 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~1048576/885735 = 348.462{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~1048576/885735 = 348.600{{c}}
 
{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}
 
[[Badness]] (Sintel): 46.6
 
== Phillips ==
: ''For extensions, see [[Orwellismic temperaments #Phillips]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 9685512225/8589934592
 
{{Mapping|legend=1| 2 0 33 | 0 1 -9 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~98415/65536 = 600.000{{c}}, ~3/2 = 690.708{{c}}
* [[POTE]]: ~98415/65536 = 600.000{{c}}, ~3/2 = 691.455{{c}}
 
{{Optimal ET sequence|legend=1| 14, 26, 66b, 92bc, 118bbc }}
 
[[Badness]] (Sintel): 52.3
 
== Satin ==
: ''For extensions, see [[Garischismic clan #Satin]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 104 -70 3 }}
 
{{Mapping|legend=1| 1 2 12 | 0 -3 -70 }}
: mapping generators: ~2, ~{{monzo| -34 23 -1 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9008{{c}}, ~{{monzo| -34 23 -1 }} = 165.8930{{c}}
: [[error map]]: {{val| -0.099 +0.168 -0.015 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -34 23 -1 }} = 165.9079{{c}}
: error map: {{val| 0.000 +0.321 +0.130 }}


POTE generator: ~7/5 = 588.641
{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273, 2018b }}


Map: [&lt;1 6 -7 -7|, &lt;0 -9 19 20|]
[[Badness]] (Sintel): 66.9


Wedgie: &lt;&lt;9 -19 -20 -51 -57 7||
== Lockerbie ==
: ''For extensions, see [[Breedsmic temperaments #Lockerbie]].''


EDOs: 51, 53, 316cd, 369cd, 422cd
[[Subgroup]]: 2.3.5


Badness: 0.1440
[[Comma list]]: {{monzo| 91 51 -74 }}


=== 11-limit ===
{{Mapping|legend=1| 1 -25 -16 | 0 74 51 }}
Commas: 121/120, 225/224, 22000/21609
: mapping generators: ~2, ~{{monzo| 36 20 -29 }}


POTE generator: ~7/5 = 588.626
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000{{c}}, ~{{monzo| 36 20 -29 }} = 431.1069{{c}}
: [[error map]]: {{val| 0.0000 -0.0444 +0.1382 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| 36 20 -29 }} = 431.1073{{c}}
: error map: {{val| 0.0000 -0.0174 +0.1568 }}


Map: [&lt;1 6 -7 -7 1|, &lt;0 -9 19 20 5|]
{{Optimal ET sequence|legend=1| 103, 167, 270, 643, 913, 1183, 2636, 3819c, 5002c }}


EDOs: 51, 53
[[Badness]] (Sintel): 72.4


Badness: 0.0743
== Rarity ==
: ''For extensions, see [[No-sevens subgroup temperaments #Rarity]].''


=== 13-limit ===
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.
Commas: 121/120, 225/224, 275/273, 1040/1029


POTE generator: ~7/5 = 588.654
[[Subgroup]]: 2.3.5


Map: [&lt;1 6 -7 -7 1 -12|, &lt;0 -9 19 20 5 32|]
[[Comma list]]: {{monzo| -57 17 13 }}


EDOs: 53
{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}
: Mapping generators: ~2, ~16384/10125


Badness: 0.0474
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.392{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.402{{c}}


= Vinegar =
{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}
Comma: 16000000/14348907


POTE generator: ~10/9 = 156.861
[[Badness]] (Sintel): 99.2


Map: [&lt;3 0 -5|, &lt;0 2 5|]
== Jorgensen ==
: ''For extensions, see [[Hemifamity temperaments #Jorgensen]].''


EDOs: 15, 39c, 54, 69b, 84b
[[Subgroup]]: 2.3.5


Badness: 0.9030
[[Comma list]]: {{monzo| 111 -70 }}


= Wronecki =
{{Mapping|legend=1| 70 111 0 | 0 0 1 }}
Comma: 531441/500000
: mapping generators: ~{{monzo| 46 -29 }}, ~5


POTE generator: ~3/2 = 695.040
[[Optimal tuning]]s:
* [[WE]]: ~{{monzo| 46 -29 }} = 17.1388{{c}}, ~5/4 = 386.8829{{c}}
: [[error map]]: {{val| -0.285 +0.451 -0.000 }}
* [[CWE]]: ~{{monzo| 46 -29 }} = 17.1429{{c}}, ~5/4 = 386.7543{{c}}
: error map: {{val| 0.000 +0.902 +0.441 }}


Map: [&lt;6 0 -5|, &lt;0 1 2|]
{{Optimal ET sequence|legend=1| 70, 140, 350, 490 }}


EDOs: 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bc
[[Badness]] (Sintel): 203


Badness: 0.3418
== References ==


[[Category:Theory]]
[[Category:Temperament collections]]
[[Category:Temperament]]
Retrieved from "https://en.xen.wiki/w/Miscellaneous_5-limit_temperaments"