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Miscellaneous 5-limit temperaments: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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:  
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-17 15:34:41 UTC</tt>.<br>
* Individual [[temperament families and clans]]
: The original revision id was <tt>336767284</tt>.<br>
* Individual [[equivalence continuum|equivalence continua]]
: The revision comment was: <tt></tt><br>
* [[Very low accuracy temperaments]]
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
* [[Very high accuracy temperaments]]
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc]]


=Hogzilla=
== Unidecmic ==
Comma: 4428675/4194304
: ''For extensions, see [[Gamelismic clan #Unidec]].''


POTE generator: ~1215/1024 = 252.649
[[Subgroup]]: 2.3.5


Map: [&lt;1 0 11|, &lt;0 2 -11|]
[[Comma list]]: 31381059609/31250000000
EDOs: 14, 19
Badness: 0.4247


=Archaeotherium=
{{Mapping|legend=1| 2 -1 -3 | 0 6 11 }}
Comma: 597871125/536870912
: mapping generators: ~177147/125000, ~25000/19683


POTE generator: ~1215/1024 = 230.351
[[Optimal tuning]]s:  
* [[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 }}


Map: [&lt;1 1 5|, &lt;0 3 -14|]
{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 2524, 2642, 2760 }}
EDOs: 21, 26, 73bc, 99bc
Badness: 1.4349


=Stump=
[[Badness]] (Sintel): 1.93
Comma: 273375/262144


POTE generator: ~64/45 = 631.737
== Quasithird ==
: ''For extensions, see [[Ragismic microtemperaments #Quasithird]].''


Map: [&lt;1 0 6|, &lt;0 3 -7|]
[[Subgroup]]: 2.3.5
EDOs: 17, 19
Badness: 0.2006
==[[Sensamagic clan#Pycnic|Pycnic]]==
==[[Marvel temperaments#Triton|Triton]]==


=Unsmate=
[[Comma list]]: {{monzo| 55 -64 20 }}
Comma: 17578125/16777216


POTE generator: ~2048/1875 = 189.049
{{Mapping|legend=1| 4 0 -11 | 0 5 16 }}
: mapping generators: ~51200000/43046721, ~1594323/1280000


Map: [&lt;1 3 2|, &lt;0 -9 2|]
[[Optimal tuning]]s:  
EDOs: 13, 19, 89c, 108c, 127c, 146c
* [[WE]]: ~51200000/43046721 = 299.9990{{c}}, ~1594323/1280000 = 380.3934{{c}}
Badness: 0.4602
: [[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 }}


=Chromo=
{{Optimal ET sequence|legend=1| 60, 104c, 164, 224, 388, 612, 1612, 2224, 2836, 6284, 9120, 15404 }}
Comma: 1220703125/1146617856


POTE generator: ~25/24 = 53.922
[[Badness]] (Sintel): 2.33


Map: [&lt;1 1 2|, &lt;0 13 7|]
== Supersharp ==
EDOs: 22, 45, 67c, 89c
: ''For extensions, see [[Trienstonic clan #Octokaidecal]].''
Badness: 0.8428


=Wizard=
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: 2197265625/2147483648


POTE generator: ~5/4 = 383.212
[[Subgroup]]: 2.3.5


Map: [&lt;2 1 5|, &lt;0 6 -1|]
[[Comma list]]: 800/729
EDOs: 22, 50, 72, 166, 238c, 310c, 548bc
Badness: 0.3864
[[Marvel temperaments#Wizard|Wizard]]


=Undeka=
{{Mapping|legend=1| 2 0 -5 | 0 1 3 }}
Comma: 48828125/45349632
: mapping generators: ~27/20, ~3


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


Map: [&lt;11 0 8|, &lt;0 1 1|]
{{Optimal ET sequence|legend=1| 8, 10, 18, 28b }}
EDOs: 22, 77c, 99c, 121c
Badness: 0.7275


==7-limit==
[[Badness]] (Sintel): 2.88
Commas: 875/864, 3200/3087


POTE generator: ~3/2 = 708.792
== Avila ==
: ''For extensions, see [[Septisemi temperaments #Avila]].''


Map: [&lt;11 0 8 31|, &lt;0 1 1 0|]
[[Subgroup]]: 2.3.5
Wedgie: &lt;&lt;11 11 0 -8 -31 -31||
EDOs: 22
Badness: 0.1418


==11-limit==
[[Comma list]]: 729/640
Commas: 100/99, 352/343, 385/384


POTE generator: ~3/2 = 706.768
{{Mapping|legend=1| 1 0 -7 | 0 1 6 }}
: mapping generators: ~2, ~3


Map: [&lt;11 0 8 31 38|, &lt;0 1 1 0 0|]
[[Optimal tuning]]s:  
EDOs: 22
* [[WE]]: ~2 = 1210.600{{c}}, ~3/2 = 667.437{{c}}
Badness: 0.0687
: [[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 }}


==13-limit==
{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20b, 29b }}
Commas: 65/63, 100/99, 169/165, 352/343


POTE generator: ~3/2 = 707.764
[[Badness]] (Sintel): 4.27


Map: [&lt;11 0 8 31 38 23|, &lt;0 1 1 0 0 1|]
== Lafa ==
EDOs: 22
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.  
Badness: 0.0565


=Triskaidekic=
[[Subgroup]]: 2.3.5
Comma: 1220703125/1073741824


POTE generator: ~3/2 = 696.142
[[Comma list]]: {{monzo| 77 -31 -12 }}


Map: [&lt;13 0 30|, &lt;0 1 0|]
{{Mapping|legend=1| 1 -1 9 | 0 12 -31 }}
EDOs: 13, 26, 91c
: mapping generators: ~2, ~{{monzo| -32 13 5 }}
Badness: 2.2416


==7-limit==
[[Optimal tuning]]s:
Commas: 1728/1715, 1875/1792
* [[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 }}


POTE generator: ~3/2 = 694.143
{{Optimal ET sequence|legend=1| 65, 246, 311, 376, 441, 2711, 3152, 3593, 4034, 4475, 4916, 5357, 10273bc, 15630bbcc }}


Map: [&lt;13 0 30 16|, &lt;0 1 0 1|]
[[Badness]] (Sintel): 4.33
Wedgie: &lt;&lt;13 0 13 -30 -16 30||
EDOs: 26
Badness: 0.2190


==11-limit==
== Lafayette ==
Commas: 99/98, 125/121, 385/384
: ''For extensions, see [[Mint temperaments #Progression]].''


POTE generator: ~3/2 = 696.296
[[Subgroup]]: 2.3.5


Map: [&lt;13 0 30 16 45|, &lt;0 1 0 1 0|]
[[Comma list]]: 3456/3125
EDOs: 26, 91cd
Badness: 0.0988


==13-limit==
{{Mapping|legend=1| 1 1 2 | 0 5 3 }}
Commas: 78/77, 99/98, 125/121, 1200/1183


POTE generator: ~3/2 = 695.879
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~25/24 = 138.722{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~25/24 = 140.995{{c}}


Map: [&lt;13 0 30 16 45 48|, &lt;0 1 0 1 0 0|]
{{Optimal ET sequence|legend=1| 8, 9, 17c }}
EDOs: 26, 91cdf
Badness: 0.0592


=Phillips=
[[Badness]] (Sintel): 4.70
Comma: 9685512225/8589934592


POTE generator: ~3/2 = 691.455
== Dodifo ==
: ''For extensions, see [[Porwell temperaments #Dodifo]].''


Map: [&lt;2 0 33|, &lt;0 1 -9|]
[[Subgroup]]: 2.3.5
EDOs: 14, 26, 66b, 92bc, 118bc
Badness: 2.2289


=Oncle=
[[Comma list]]: {{monzo| -67 -9 35 }}
Comma: 145282683375/137438953472


POTE generator: ~4096/3645 = 232.521
{{Mapping|legend=1| 1 12 5 | 0 -35 -9 }}


Map: [&lt;1 1 6|, &lt;0 3 -19|]
[[Optimal tuning]]s:  
EDOs: 31, 98c, 129c, 160bc, 289bc
* [[CTE]]: ~2 = 1200.000{{c}}, ~768/625 = 357.087{{c}}
Badness: 1.2447
* [[POTE]]: ~2 = 1200.000{{c}}, ~768/625 = 357.088{{c}}


=Quasimoha=
{{Optimal ET sequence|legend=1| 37, 84, 205, 289, 494, 783, 2060, 2843, 3626 }}
Comma: 2353579470675/2199023255552


POTE generator: ~1048576/885735 = 348.600
[[Badness]] (Sintel): 5.00


Map: [&lt;1 1 9|, &lt;0 2 -23|]
== Doublewide ==
EDOs: 31, 117c, 148bc, 179bc
: ''For extensions, see [[Jubilismic clan #Doublewide]].''
Badness: 1.9867


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


POTE generator: ~768/625 = 212.444
[[Comma list]]: 390625/373248


Map: [&lt;1 0 2|, &lt;0 9 2|]
{{Mapping|legend=1| 2 1 3 | 0 4 3 }}
EDOs: 17c
: mapping generators: ~625/432, ~6/5
Badness: 1.4050


=Misneb=
[[Optimal tuning]]s:
Commas: 145964630126953125/144115188075855872
* [[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 }}


POTE generator: ~16/15 = 113.240
{{Optimal ET sequence|legend=1| 4, 14b, 18, 22, 48, 70c, 118c }}


Map: [&lt;1 3 1|, &lt;0 -15 14|]
[[Badness]] (Sintel): 5.32
EDOs: 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bc
Badness: 0.6095


==7-limit==
== Shibboleth ==
Commas: 225/224, 4194304/4117715
: ''For extensions, see [[Gamelismic clan #Superkleismic]], [[Starling temperaments #Gilead]], and [[Sensamagic clan #Superthird]].''


POTE generator: ~16/15 = 113.235
[[Subgroup]]: 2.3.5


Map: [&lt;1 3 1 3|, &lt;0 -15 14 -2|]
[[Comma list]]: 1953125/1889568
Wedgie: &lt;&lt;15 -14 2 -57 -39 44||
EDOs: 21, 32, 53
Badness: 0.1410


==11-limit==
{{Mapping|legend=1| 1 4 5 | 0 -9 -10 }}
Commas: 99/98, 176/175, 1310720/1294139


POTE generator: ~16/15 = 113.323
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 321.773{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 321.852{{c}}


Map: [&lt;1 3 1 3 1|, &lt;0 -15 14 -2 26|]
{{Optimal ET sequence|legend=1| 15, 26, 41, 179c }}
EDOS: 21, 53, 127, 180de
Badness: 0.0854


==13-limit==
[[Badness]] (Sintel): 5.34
Commas: 99/98, 176/175, 640/637 847/845


POTE generator: ~16/15 = 113.323
== Semidimfourth ==
: ''For extensions, see [[Ragismic microtemperaments #Semidimfourth]].''


Map: [&lt;1 3 1 3 1 2|, &lt;0 -15 14 -2 26 18|]
[[Subgroup]]: 2.3.5
EDOs: 21, 53, 127, 189de
Badness: 0.0456


==Musneb==
[[Comma list]]: {{monzo| 7 41 -31 }}
Commas: 225/224, 385/384, 66550/64827


POTE generator: ~16/15 = 113.142
{{Mapping|legend=1| 1 21 28 | 0 -31 -41 }}


Map: [&lt;1 3 1 3 6|, &lt;0 -15 14 -2 -27|]
[[Optimal tuning]]s:  
EDOS: 32, 53, 191de, 244cde, 297cde
* [[CTE]]: ~2 = 1200.000{{c}}, ~162/125 = 448.449{{c}}
Badness: 0.0873
* [[POTE]]: ~2 = 1200.000{{c}}, ~162/125 = 448.449{{c}}


=Aufo=
{{Optimal ET sequence|legend=1| 8, …, 91, 99, 190, 289, 388, 677, 3674, 4351, 5028, 5705, 6382, 13441c, 19823bcc }}
Comma: 2270041927734375/2251799813685248


POTE generator: ~45/32 = 588.722
[[Badness]] (Sintel): 5.47


Map: [&lt;1 6 -7|, &lt;0 -9 19|]
== Mynic ==
EDOs: 51, 53, 267, 320, 373, 426, 479, 532, 2607bc
: ''For extensions, see [[Starling temperaments #Myna]].''
Badness: 0.3071


=Untriton=
[[Subgroup]]: 2.3.5
Commas: 225/224, 125000000/121060821


POTE generator: ~7/5 = 588.641
[[Comma list]]: 10077696/9765625


Map: [&lt;1 6 -7 -7|, &lt;0 -9 19 20|]
{{Mapping|legend=1| 1 9 9 | 0 -10 -9 }}
Wedgie: &lt;&lt;9 -19 -20 -51 -57 7||
EDOs: 51, 53, 316cd, 369cd, 422cd
Badness: 0.1440


==11-limit==
[[Optimal tuning]]s:
Commas: 121/120, 225/224, 22000/21609
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 310.030{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 310.140{{c}}


POTE generator: ~7/5 = 588.626
{{Optimal ET sequence|legend=1| 27, 31, 58, 89 }}


Map: [&lt;1 6 -7 -7 1|, &lt;0 -9 19 20 5|]
[[Badness]] (Sintel): 5.86
EDOs: 51, 53
Badness: 0.0743


==13-limit==
== Progress ==
Commas: 121/120, 225/224, 275/273, 1040/1029
: ''For extensions, see [[Archytas clan #Progress]].''


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]]: 32768/30375
EDOs: 53
Badness: 0.0474


=Vinegar=
{{Mapping|legend=1| 1 0 5 | 0 3 -5 }}
Comma: 16000000/14348907


POTE generator: ~10/9 = 156.861
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 638.922{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 638.736{{c}}


Map: [&lt;3 0 -5|, &lt;0 2 5|]
{{Optimal ET sequence|legend=1| 2, 13, 15, 32c, 47bc, 62bc }}
EDOs: 15, 39c, 54, 69b, 84b
Badness: 0.9030


=Wronecki=
[[Badness]] (Sintel): 5.77
Comma: 531441/500000


POTE generator: ~3/2 = 695.040
== Abigail ==
: ''For extensions, see [[Ragismic microtemperaments #Abigail]].''


Map: [&lt;6 0 -5|, &lt;0 1 2|]
[[Subgroup]]: 2.3.5
EDOs: 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bc
Badness: 0.3418


</pre></div>
[[Comma list]]: {{monzo| 25 -48 22 }}
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;High badness temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:62:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hogzilla"&gt;Hogzilla&lt;/a&gt;&lt;/div&gt;
{{Mapping|legend=1| 2 7 13 | 0 -11 -24 }}
&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Archaeotherium"&gt;Archaeotherium&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Stump"&gt;Stump&lt;/a&gt;&lt;/div&gt;
[[Optimal tuning]]s:  
&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Stump-Pycnic"&gt;Pycnic&lt;/a&gt;&lt;/div&gt;
* [[CTE]]: ~{{monzo| -12 24 -11 }} = 600.000{{c}}, ~200000/177147 = 208.907{{c}}
&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Stump-Triton"&gt;Triton&lt;/a&gt;&lt;/div&gt;
* [[CWE]]: ~{{monzo| -12 24 -11 }} = 600.000{{c}}, ~200000/177147 = 208.906{{c}}
&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Unsmate"&gt;Unsmate&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Chromo"&gt;Chromo&lt;/a&gt;&lt;/div&gt;
{{Optimal ET sequence|legend=1| 46, 132, 178, 224, 270, 494, 1752, 2246, 2740, 4986, 7726b }}
&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Wizard"&gt;Wizard&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Undeka"&gt;Undeka&lt;/a&gt;&lt;/div&gt;
[[Badness]] (Sintel): 5.97
&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Undeka-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Undeka-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
== Supermajor ==
&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Undeka-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
: ''For extensions, see [[Ragismic microtemperaments #Supermajor]].''
&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Triskaidekic"&gt;Triskaidekic&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triskaidekic-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
[[Subgroup]]: 2.3.5
&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triskaidekic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triskaidekic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
[[Comma list]]: {{monzo| -13 -46 37 }}
&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Phillips"&gt;Phillips&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Oncle"&gt;Oncle&lt;/a&gt;&lt;/div&gt;
{{Mapping|legend=1| 1 15 19 | 0 -37 -46 }}
&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quasimoha"&gt;Quasimoha&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Genocchi"&gt;Genocchi&lt;/a&gt;&lt;/div&gt;
[[Optimal tuning]]s:  
&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Misneb"&gt;Misneb&lt;/a&gt;&lt;/div&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~625/486 = 435.081{{c}}
&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Misneb-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
* [[CWE]]: ~2 = 1200.000{{c}}, ~625/486 = 435.081{{c}}
&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Misneb-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Misneb-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
{{Optimal ET sequence|legend=1| 80, 171, 593, 764, 935, 1106, 3489, 4595, 5701 }}
&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Misneb-Musneb"&gt;Musneb&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Aufo"&gt;Aufo&lt;/a&gt;&lt;/div&gt;
[[Badness]] (Sintel): 6.19
&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Untriton"&gt;Untriton&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Untriton-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
== Gamera ==
&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Untriton-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
: ''For extensions, see [[Ragismic microtemperaments #Gamera]].''
&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Vinegar"&gt;Vinegar&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Wronecki"&gt;Wronecki&lt;/a&gt;&lt;/div&gt;
[[Subgroup]]: 2.3.5
&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;br /&gt;
[[Comma list]]: {{monzo| 10 -40 23 }}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Hogzilla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Hogzilla&lt;/h1&gt;
 
Comma: 4428675/4194304&lt;br /&gt;
{{Mapping|legend=1| 1 6 10 | 0 -23 -40 }}
&lt;br /&gt;
 
POTE generator: ~1215/1024 = 252.649&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~2500/2187 = 230.345{{c}}
Map: [&amp;lt;1 0 11|, &amp;lt;0 2 -11|]&lt;br /&gt;
* [[CWE]]: ~2 = 1200.000{{c}}, ~2500/2187 = 230.345{{c}}
EDOs: 14, 19&lt;br /&gt;
 
Badness: 0.4247&lt;br /&gt;
{{Optimal ET sequence|legend=1| 26, 73, 99, 224, 323, 547, 870 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Archaeotherium"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Archaeotherium&lt;/h1&gt;
[[Badness]] (Sintel): 6.39
Comma: 597871125/536870912&lt;br /&gt;
 
&lt;br /&gt;
== Tritriple ==
POTE generator: ~1215/1024 = 230.351&lt;br /&gt;
: ''For extensions, see [[Gamelismic clan #Tritriple]].''
&lt;br /&gt;
 
Map: [&amp;lt;1 1 5|, &amp;lt;0 3 -14|]&lt;br /&gt;
[[Subgroup]]: 2.3.5
EDOs: 21, 26, 73bc, 99bc&lt;br /&gt;
 
Badness: 1.4349&lt;br /&gt;
[[Comma list]]: {{monzo| 31 20 -27 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Stump"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Stump&lt;/h1&gt;
{{Mapping|legend=1| 1 -11 -7 | 0 27 20 }}
Comma: 273375/262144&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
POTE generator: ~64/45 = 631.737&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~864/625 = 559.328{{c}}
&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~864/625 = 559.332{{c}}
Map: [&amp;lt;1 0 6|, &amp;lt;0 3 -7|]&lt;br /&gt;
 
EDOs: 17, 19&lt;br /&gt;
{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }}
Badness: 0.2006&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Stump-Pycnic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;a class="wiki_link" href="/Sensamagic%20clan#Pycnic"&gt;Pycnic&lt;/a&gt;&lt;/h2&gt;
[[Badness]] (Sintel): 6.65
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Stump-Triton"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;a class="wiki_link" href="/Marvel%20temperaments#Triton"&gt;Triton&lt;/a&gt;&lt;/h2&gt;
 
&lt;br /&gt;
== Kangaroo ==
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Unsmate"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Unsmate&lt;/h1&gt;
: ''For extensions, see [[Trienstonic clan #Parakangaroo]].''
Comma: 17578125/16777216&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
POTE generator: ~2048/1875 = 189.049&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 64000/59049
Map: [&amp;lt;1 3 2|, &amp;lt;0 -9 2|]&lt;br /&gt;
 
EDOs: 13, 19, 89c, 108c, 127c, 146c&lt;br /&gt;
{{Mapping|legend=1| 1 0 -3 | 0 3 10 }}
Badness: 0.4602&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Chromo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Chromo&lt;/h1&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~40/27 = 637.879{{c}}
Comma: 1220703125/1146617856&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~40/27 = 638.805{{c}}
&lt;br /&gt;
 
POTE generator: ~25/24 = 53.922&lt;br /&gt;
{{Optimal ET sequence|legend=1| 15, 47b, 62b }}
&lt;br /&gt;
 
Map: [&amp;lt;1 1 2|, &amp;lt;0 13 7|]&lt;br /&gt;
[[Badness]] (Sintel): 6.94
EDOs: 22, 45, 67c, 89c&lt;br /&gt;
 
Badness: 0.8428&lt;br /&gt;
== Tertiaseptal ==
&lt;br /&gt;
: ''For extensions, see [[Breedsmic temperaments #Tertiaseptal]].''
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Wizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Wizard&lt;/h1&gt;
 
Comma: 2197265625/2147483648&lt;br /&gt;
[[Subgroup]]: 2.3.5
&lt;br /&gt;
 
POTE generator: ~5/4 = 383.212&lt;br /&gt;
[[Comma list]]: {{monzo| -59 5 22 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 1 5|, &amp;lt;0 6 -1|]&lt;br /&gt;
{{Mapping|legend=1| 1 3 2 | 0 -22 5 }}
EDOs: 22, 50, 72, 166, 238c, 310c, 548bc&lt;br /&gt;
 
Badness: 0.3864&lt;br /&gt;
[[Optimal tuning]]s:
&lt;a class="wiki_link" href="/Marvel%20temperaments#Wizard"&gt;Wizard&lt;/a&gt;&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~17578125/16777216 = 77.186{{c}}
&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~17578125/16777216 = 77.191{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Undeka"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Undeka&lt;/h1&gt;
 
Comma: 48828125/45349632&lt;br /&gt;
{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}
&lt;br /&gt;
 
POTE generator: ~3/2 = 703.829&lt;br /&gt;
[[Badness]] (Sintel): 6.98
&lt;br /&gt;
 
Map: [&amp;lt;11 0 8|, &amp;lt;0 1 1|]&lt;br /&gt;
== Untriton ==
EDOs: 22, 77c, 99c, 121c&lt;br /&gt;
: ''For extensions, see [[Marvel temperaments #Untriton]], [[Porwell temperaments #Aufo]] and [[Triwellismic temperaments #Interaufo]].''
Badness: 0.7275&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Undeka-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;7-limit&lt;/h2&gt;
 
Commas: 875/864, 3200/3087&lt;br /&gt;
[[Comma list]]: {{monzo| -51 19 9 }}
&lt;br /&gt;
 
POTE generator: ~3/2 = 708.792&lt;br /&gt;
{{Mapping|legend=1| 1 6 -7 | 0 -9 19 }}
&lt;br /&gt;
 
Map: [&amp;lt;11 0 8 31|, &amp;lt;0 1 1 0|]&lt;br /&gt;
[[Optimal tuning]]s:  
Wedgie: &amp;lt;&amp;lt;11 11 0 -8 -31 -31||&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 588.727{{c}}
EDOs: 22&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 588.722{{c}}
Badness: 0.1418&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Undeka-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;11-limit&lt;/h2&gt;
 
Commas: 100/99, 352/343, 385/384&lt;br /&gt;
[[Badness]] (Sintel): 7.20
&lt;br /&gt;
 
POTE generator: ~3/2 = 706.768&lt;br /&gt;
== Nessafof ==
&lt;br /&gt;
: ''For extensions, see [[Porwell temperaments #Nessafof]].''
Map: [&amp;lt;11 0 8 31 38|, &amp;lt;0 1 1 0 0|]&lt;br /&gt;
 
EDOs: 22&lt;br /&gt;
[[Subgroup]]: 2.3.5
Badness: 0.0687&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: {{monzo| 25 15 -21 }}
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Undeka-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;13-limit&lt;/h2&gt;
 
Commas: 65/63, 100/99, 169/165, 352/343&lt;br /&gt;
{{Mapping|legend=1| 3 2 5 | 0 7 5 }}
&lt;br /&gt;
 
POTE generator: ~3/2 = 707.764&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~78125/62208 = 400.000{{c}}, ~9765625/8957952 = 157.392{{c}}
Map: [&amp;lt;11 0 8 31 38 23|, &amp;lt;0 1 1 0 0 1|]&lt;br /&gt;
* [[CWE]]: ~78125/62208 = 400.000{{c}}, ~9765625/8957952 = 157.409{{c}}
EDOs: 22&lt;br /&gt;
 
Badness: 0.0565&lt;br /&gt;
{{Optimal ET sequence|legend=1| 15, 54b, 69, 84, 99, 183, 282, 465, 1212c, 1677cc }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Triskaidekic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Triskaidekic&lt;/h1&gt;
[[Badness]] (Sintel): 7.81
Comma: 1220703125/1073741824&lt;br /&gt;
 
&lt;br /&gt;
== Lemba ==
POTE generator: ~3/2 = 696.142&lt;br /&gt;
: ''For extensions, see [[Jubilismic clan #Lemba]].''
&lt;br /&gt;
 
Map: [&amp;lt;13 0 30|, &amp;lt;0 1 0|]&lt;br /&gt;
[[Subgroup]]: 2.3.5
EDOs: 13, 26, 91c&lt;br /&gt;
 
Badness: 2.2416&lt;br /&gt;
[[Comma list]]: 140625/131072
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Triskaidekic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;7-limit&lt;/h2&gt;
{{Mapping|legend=1| 2 2 5 | 0 3 -1 }}
Commas: 1728/1715, 1875/1792&lt;br /&gt;
: Mapping generators: ~375/256, ~75/64
&lt;br /&gt;
 
POTE generator: ~3/2 = 694.143&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~375/256 = 600.000{{c}}, ~75/64 = 232.986{{c}}
Map: [&amp;lt;13 0 30 16|, &amp;lt;0 1 0 1|]&lt;br /&gt;
: [[error map]]: {{val| 0.000 -2.998 -19.300 }}
Wedgie: &amp;lt;&amp;lt;13 0 13 -30 -16 30||&lt;br /&gt;
* [[CWE]]: ~375/256 = 600.000{{c}}, ~75/64 = 231.832{{c}}
EDOs: 26&lt;br /&gt;
: error map: {{val| 0.000 -6.458 -18.146 }}
Badness: 0.2190&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 10, 16, 26, 88cc }}
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Triskaidekic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h2&gt;
 
Commas: 99/98, 125/121, 385/384&lt;br /&gt;
[[Badness]] (Sintel): 7.85
&lt;br /&gt;
 
POTE generator: ~3/2 = 696.296&lt;br /&gt;
== Delorean ==
&lt;br /&gt;
: ''For extensions, see [[Mint temperaments #Subklei]].''
Map: [&amp;lt;13 0 30 16 45|, &amp;lt;0 1 0 1 0|]&lt;br /&gt;
 
EDOs: 26, 91cd&lt;br /&gt;
[[Subgroup]]: 2.3.5
Badness: 0.0988&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 17496/15625
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Triskaidekic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;13-limit&lt;/h2&gt;
 
Commas: 78/77, 99/98, 125/121, 1200/1183&lt;br /&gt;
{{Mapping|legend=1| 1 3 4 | 0 -6 -7 }}
&lt;br /&gt;
 
POTE generator: ~3/2 = 695.879&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 284.817{{c}}
Map: [&amp;lt;13 0 30 16 45 48|, &amp;lt;0 1 0 1 0 0|]&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 284.293{{c}}
EDOs: 26, 91cdf&lt;br /&gt;
 
Badness: 0.0592&lt;br /&gt;
{{Optimal ET sequence|legend=1| 4, 13c, 17c, 21, 38c }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Phillips"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Phillips&lt;/h1&gt;
[[Badness]] (Sintel): 8.35
Comma: 9685512225/8589934592&lt;br /&gt;
 
&lt;br /&gt;
== Majvam ==
POTE generator: ~3/2 = 691.455&lt;br /&gt;
: ''For extensions, see [[No-sevens subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]].''
&lt;br /&gt;
 
Map: [&amp;lt;2 0 33|, &amp;lt;0 1 -9|]&lt;br /&gt;
[[Subgroup]]: 2.3.5
EDOs: 14, 26, 66b, 92bc, 118bc&lt;br /&gt;
 
Badness: 2.2289&lt;br /&gt;
[[Comma list]]: 2404631929946112/2384185791015625
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Oncle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Oncle&lt;/h1&gt;
{{Mapping|legend=1| 1 10 5 | 0 -22 -7 }}
Comma: 145282683375/137438953472&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:
POTE generator: ~4096/3645 = 232.521&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~125/96 = 459.006{{c}}
&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~125/96 = 458.995{{c}}
Map: [&amp;lt;1 1 6|, &amp;lt;0 3 -19|]&lt;br /&gt;
 
EDOs: 31, 98c, 129c, 160bc, 289bc&lt;br /&gt;
{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }}
Badness: 1.2447&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 8.37
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Quasimoha"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Quasimoha&lt;/h1&gt;
 
Comma: 2353579470675/2199023255552&lt;br /&gt;
== Beatles ==
&lt;br /&gt;
: ''For extensions, see [[Archytas clan #Beatles]].''
POTE generator: ~1048576/885735 = 348.600&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
Map: [&amp;lt;1 1 9|, &amp;lt;0 2 -23|]&lt;br /&gt;
 
EDOs: 31, 117c, 148bc, 179bc&lt;br /&gt;
[[Comma list]]: 524288/492075
Badness: 1.9867&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 1 5 | 0 2 -9 }}
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Genocchi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Genocchi&lt;/h1&gt;
 
Comma: 2359296/1953125&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~512/405 = 356.492{{c}}
POTE generator: ~768/625 = 212.444&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~512/405 = 355.930{{c}}
&lt;br /&gt;
 
Map: [&amp;lt;1 0 2|, &amp;lt;0 9 2|]&lt;br /&gt;
{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}
EDOs: 17c&lt;br /&gt;
 
Badness: 1.4050&lt;br /&gt;
[[Badness]] (Sintel): 8.41
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Misneb"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Misneb&lt;/h1&gt;
== Magus ==
Commas: 145964630126953125/144115188075855872&lt;br /&gt;
: ''For extensions, see [[Sensamagic clan #Magus]] and [[Starling temperaments #Amigo]].''
&lt;br /&gt;
 
POTE generator: ~16/15 = 113.240&lt;br /&gt;
[[Subgroup]]: 2.3.5
&lt;br /&gt;
 
Map: [&amp;lt;1 3 1|, &amp;lt;0 -15 14|]&lt;br /&gt;
[[Comma list]]: 50331648/48828125
EDOs: 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bc&lt;br /&gt;
 
Badness: 0.6095&lt;br /&gt;
{{Mapping|legend=1| 1 -2 2 | 0 11 1 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Misneb-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;7-limit&lt;/h2&gt;
[[Optimal tuning]]s:
Commas: 225/224, 4194304/4117715 &lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 391.068{{c}}
&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 391.225{{c}}
POTE generator: ~16/15 = 113.235&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 3, …, 40, 43, 46, 181c, 227c, 273c, 319c }}
Map: [&amp;lt;1 3 1 3|, &amp;lt;0 -15 14 -2|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;15 -14 2 -57 -39 44||&lt;br /&gt;
[[Badness]] (Sintel): 8.45
EDOs: 21, 32, 53&lt;br /&gt;
 
Badness: 0.1410&lt;br /&gt;
== Tritonic ==
&lt;br /&gt;
: ''For extensions, see [[Marvel temperaments #Tritonic]].''
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Misneb-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;11-limit&lt;/h2&gt;
 
Commas: 99/98, 176/175, 1310720/1294139&lt;br /&gt;
[[Subgroup]]: 2.3.5
&lt;br /&gt;
 
POTE generator: ~16/15 = 113.323&lt;br /&gt;
[[Comma list]]: 553584375/536870912
&lt;br /&gt;
 
Map: [&amp;lt;1 3 1 3 1|, &amp;lt;0 -15 14 -2 26|]&lt;br /&gt;
{{Mapping|legend=1| 1 4 -3 | 0 -5 11 }}
EDOS: 21, 53, 127, 180de&lt;br /&gt;
 
Badness: 0.0854&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 580.278{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Misneb-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;13-limit&lt;/h2&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 580.219{{c}}
Commas: 99/98, 176/175, 640/637 847/845&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 29, 31, 60, 91 }}
POTE generator: ~16/15 = 113.323&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 8.88
Map: [&amp;lt;1 3 1 3 1 2|, &amp;lt;0 -15 14 -2 26 18|]&lt;br /&gt;
 
EDOs: 21, 53, 127, 189de&lt;br /&gt;
== Wizard ==
Badness: 0.0456&lt;br /&gt;
: ''For extensions, see [[Marvel temperaments #Wizard]].''
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Misneb-Musneb"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Musneb&lt;/h2&gt;
[[Subgroup]]: 2.3.5
Commas: 225/224, 385/384, 66550/64827&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 2197265625/2147483648
POTE generator: ~16/15 = 113.142&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 2 1 5 | 0 6 -1 }}
Map: [&amp;lt;1 3 1 3 6|, &amp;lt;0 -15 14 -2 -27|]&lt;br /&gt;
: mapping generators: ~42875/32768, ~9375/8192
EDOS: 32, 53, 191de, 244cde, 297cde&lt;br /&gt;
 
Badness: 0.0873&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~42875/32768 = 600.000{{c}}, ~9375/8192 = 216.950{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Aufo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Aufo&lt;/h1&gt;
* [[POTE]]: ~42875/32768 = 600.000{{c}}, ~9375/8192 = 216.788{{c}}
Comma: 2270041927734375/2251799813685248&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bcc }}
POTE generator: ~45/32 = 588.722&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 9.06
Map: [&amp;lt;1 6 -7|, &amp;lt;0 -9 19|]&lt;br /&gt;
 
EDOs: 51, 53, 267, 320, 373, 426, 479, 532, 2607bc&lt;br /&gt;
Scales (Scala files): [[wizard22]]
Badness: 0.3071&lt;br /&gt;
 
&lt;br /&gt;
== Merman ==
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc26"&gt;&lt;a name="Untriton"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Untriton&lt;/h1&gt;
: ''For extensions, see [[Marvel temperaments #Merman]].''
Commas: 225/224, 125000000/121060821&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
POTE generator: ~7/5 = 588.641&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: {{monzo| -40 15 7 }}
Map: [&amp;lt;1 6 -7 -7|, &amp;lt;0 -9 19 20|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;9 -19 -20 -51 -57 7||&lt;br /&gt;
{{Mapping|legend=1| 1 5 -5 | 0 -7 15 }}
EDOs: 51, 53, 316cd, 369cd, 422cd&lt;br /&gt;
 
Badness: 0.1440&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 585.653{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Untriton-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;11-limit&lt;/h2&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 585.634{{c}}
Commas: 121/120, 225/224, 22000/21609&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 41, 84, 125, 209, 334c, 543bc }}
POTE generator: ~7/5 = 588.626&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 10.6
Map: [&amp;lt;1 6 -7 -7 1|, &amp;lt;0 -9 19 20 5|]&lt;br /&gt;
 
EDOs: 51, 53&lt;br /&gt;
== Nusecond ==
Badness: 0.0743&lt;br /&gt;
: ''For extensions, see [[Starling temperaments #Nusecond]].''
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Untriton-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;13-limit&lt;/h2&gt;
[[Subgroup]]: 2.3.5
Commas: 121/120, 225/224, 275/273, 1040/1029&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 51018336/48828125
POTE generator: ~7/5 = 588.654&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 3 4 | 0 -11 -13 }}
Map: [&amp;lt;1 6 -7 -7 1 -12|, &amp;lt;0 -9 19 20 5 32|]&lt;br /&gt;
 
EDOs: 53&lt;br /&gt;
[[Optimal tuning]]s:
Badness: 0.0474&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~3125/2916 = 154.577{{c}}
&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~3125/2916 = 154.523{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Vinegar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Vinegar&lt;/h1&gt;
 
Comma: 16000000/14348907&lt;br /&gt;
{{Optimal ET sequence|legend=1| 8, 23, 31, 70, 101, 132c }}
&lt;br /&gt;
 
POTE generator: ~10/9 = 156.861&lt;br /&gt;
[[Badness]] (Sintel): 10.9
&lt;br /&gt;
 
Map: [&amp;lt;3 0 -5|, &amp;lt;0 2 5|]&lt;br /&gt;
== Comic ==
EDOs: 15, 39c, 54, 69b, 84b&lt;br /&gt;
: ''For extensions, see [[Jubilismic clan #Comic]].''
Badness: 0.9030&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc30"&gt;&lt;a name="Wronecki"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Wronecki&lt;/h1&gt;
 
Comma: 531441/500000&lt;br /&gt;
[[Comma list]]: 5120000/4782969
&lt;br /&gt;
 
POTE generator: ~3/2 = 695.040&lt;br /&gt;
{{Mapping|legend=1| 2 1 -3 | 0 2 7 }}
&lt;br /&gt;
 
Map: [&amp;lt;6 0 -5|, &amp;lt;0 1 2|]&lt;br /&gt;
: mapping generators: ~2187/1600, ~40/27
EDOs: 12, 66b, 78b, 90b, 102b, 114b, 126b, 240bc&lt;br /&gt;
 
Badness: 0.3418&lt;/body&gt;&lt;/html&gt;</pre></div>
[[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]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 20 -39 18 }}
 
{{Mapping|legend=1| 3 2 1 | 0 6 13 }}
 
[[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}}
 
{{Optimal ET sequence|legend=1| 33c, 39, 72, 111, 183, 438, 621, 1425b }}
 
[[Badness]] (Sintel): 17.6
 
== Semidimi ==
: ''For extensions, see [[Ragismic microtemperaments #Semidimi]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -12 -73 55 }}
 
{{Mapping|legend=1| 1 36 48 | 0 -55 -73 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~162/125 = 449.127{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~162/125 = 449.127{{c}}
 
{{Optimal ET sequence|legend=1| 8, …, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}
 
[[Badness]] (Sintel): 17.7
 
== Slender ==
: ''For extensions, see [[Marvel temperaments #Slender]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -46 10 13 }}
 
{{Mapping|legend=1| 1 2 2 | 0 -13 10 }}
 
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~16875/16384 = 38.380{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~16875/16384 = 38.400{{c}}
 
{{Optimal ET sequence|legend=1| 31, 94, 125, 781bcc }}
 
[[Badness]] (Sintel): 17.8
 
== Quasitemp ==
: ''For extensions, see [[Keemic temperaments #Quasitemp]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 6103515625/5804752896
 
{{Mapping|legend=1| 1 5 5 | 0 -14 -11 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~3125/2592 = 292.591{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3125/2592 = 292.702{{c}}
 
{{Optimal ET sequence|legend=1| 4, …, 37, 41 }}
 
[[Badness]] (Sintel): 18.0
 
== Cypress ==
: ''For extensions, see [[Starling temperaments #Cypress]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 258280326/244140625
 
{{Mapping|legend=1| 1 7 10 | 0 -12 -17 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~4374/3125 = 541.735{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~4374/3125 = 541.726{{c}}
 
{{Optimal ET sequence|legend=1| 11c, 20c, 31, 113c, 144c, 175c }}
 
[[Badness]] (Sintel): 19.2
 
== Chromo ==
: ''For extensions, see [[Keemic temperaments #Chromo]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 1220703125/1146617856
 
{{Mapping|legend=1| 1 1 2 | 0 13 7 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~25/24 = 54.138{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~25/24 = 53.922{{c}}
 
{{Optimal ET sequence|legend=1| 22, 45, 67c, 89c }}
 
[[Badness]] (Sintel): 19.8
 
== Tertiosec ==
: ''For extensions, see [[Marvel temperaments #Tertiosec]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -89 21 24 }}
 
{{Mapping|legend=1| 3 7 5 | 0 -8 7 }}
 
[[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}}
 
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171 }}
 
[[Badness]] (Sintel): 20.0
 
== Fervor ==
: ''For extensions, see [[Archytas clan #Fervor]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 67108864/61509375
 
{{Mapping|legend=1| 1 4 -2 | 0 -5 9 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~64/45 = 577.593{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~64/45 = 577.705{{c}}
 
{{Optimal ET sequence|legend=1| 2, …, 25, 27 }}
 
[[Badness]] (Sintel): 20.0
 
== Bohpier ==
: ''For extensions, see [[Sensamagic clan #Bohpier]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 1220703125/1162261467
 
{{Mapping|legend=1| 1 0 0 | 0 13 19 }}
 
[[Optimal tuning]]s:
* [[CTE]] and [[POTE]]: ~2 = 1200.000{{c}}, ~27/25 = 146.476{{c}}
 
{{Optimal ET sequence|legend=1| 8, …, 41, 131, 172, 213c }}
 
[[Badness]] (Sintel): 20.2
 
== Elvis ==
: ''For extensions, see [[Jubilismic clan #Elvis]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 36905625/33554432
 
{{Mapping|legend=1| 2 1 10 | 0 2 -5 }}
 
[[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}}
 
{{Optimal ET sequence|legend=1| 26, 80bc, 106bbcc, 132bbcc }}
 
[[Badness]] (Sintel): 20.7
 
== Enneadecacot ==
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 79 -22 -19 }}
 
{{Mapping|legend=1| 1 1 3 | 0 19 -22 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.0000{{c}}, ~34171875/33554432 = 36.9607{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~34171875/33554432 = 36.9622{{c}}
 
{{Optimal ET sequence|legend=1| 32, 65, 292, 357, 422, 487, 1396c }}
 
[[Badness]] (Sintel): 20.9
 
== Vinegar ==
: ''For extensions, see [[Starling temperaments #Vinegar]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 16000000/14348907
 
{{Mapping|legend=1| 3 0 -5 | 0 2 5 }}
 
[[Optimal tuning]]s:
* [[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}})
 
{{Optimal ET sequence|legend=1| 15, 39c, 54, 69b }}
 
[[Badness]] (Sintel): 21.2
 
== Oolong ==
: ''For extensions, see [[Starling temperaments #Oolong]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 793437161472/762939453125
 
{{Mapping|legend=1| 1 6 7 | 0 -17 -18 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 311.726{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 311.694{{c}}
 
{{Optimal ET sequence|legend=1| 23, 27, 50, 77 }}
 
[[Badness]] (Sintel): 22.1
 
== Oncle ==
: ''For extensions, see [[Gamelismic clan #Oncle]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 145282683375/137438953472
 
{{Mapping|legend=1| 1 1 6 | 0 3 -19 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~4096/3645 = 232.385{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~4096/3645 = 232.521{{c}}
 
{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc, 289bbcc }}
 
[[Badness]] (Sintel): 29.2
 
== Quasiorwell ==
: ''For extensions, see [[Breedsmic temperaments #Quasiorwell]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| -93 3 38 }}
 
{{Mapping|legend=1| 1 31 0 | 0 -38 3 }}
 
[[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}}
 
{{Optimal ET sequence|legend=1| 31, …, 177, 208, 239, 270, 841, 1111, 1381, 2492c }}
 
[[Badness]] (Sintel): 30.6
 
== Diesic ==
: ''For extensions, see [[Orwellismic temperaments #Diesic]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 10460353203/9765625000
 
{{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 }}
 
{{Optimal ET sequence|legend=1| 94, 217, 528, 745, 1273, 2018b }}
 
[[Badness]] (Sintel): 66.9
 
== Lockerbie ==
: ''For extensions, see [[Breedsmic temperaments #Lockerbie]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 91 51 -74 }}
 
{{Mapping|legend=1| 1 -25 -16 | 0 74 51 }}
: mapping generators: ~2, ~{{monzo| 36 20 -29 }}
 
[[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 }}
 
{{Optimal ET sequence|legend=1| 103, 167, 270, 643, 913, 1183, 2636, 3819c, 5002c }}
 
[[Badness]] (Sintel): 72.4
 
== Rarity ==
: ''For extensions, see [[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]]: {{monzo| -57 17 13 }}
 
{{Mapping|legend=1| 1 11 -10 | 0 -13 17 }}
: Mapping generators: ~2, ~16384/10125
 
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.392{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~16384/10125 = 869.402{{c}}
 
{{Optimal ET sequence|legend=1| 11, 29, 69, 98c }}
 
[[Badness]] (Sintel): 99.2
 
== Jorgensen ==
: ''For extensions, see [[Hemifamity temperaments #Jorgensen]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo| 111 -70 }}
 
{{Mapping|legend=1| 70 111 0 | 0 0 1 }}
: mapping generators: ~{{monzo| 46 -29 }}, ~5
 
[[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 }}
 
{{Optimal ET sequence|legend=1| 70, 140, 350, 490 }}
 
[[Badness]] (Sintel): 203
 
== References ==
 
[[Category:Temperament collections]]
Retrieved from "https://en.xen.wiki/w/Miscellaneous_5-limit_temperaments"