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>2012-05-06 16:08:56 UTC</tt>.<br>
* Individual [[temperament families and clans]]
: The original revision id was <tt>330758246</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</pre></div>
[[Badness]] (Sintel): 5.77
<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:60:&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:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hogzilla"&gt;Hogzilla&lt;/a&gt;&lt;/div&gt;
== Abigail ==
&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Archaeotherium"&gt;Archaeotherium&lt;/a&gt;&lt;/div&gt;
: ''For extensions, see [[Ragismic microtemperaments #Abigail]].''
&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Stump"&gt;Stump&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Stump-Pycnic"&gt;Pycnic&lt;/a&gt;&lt;/div&gt;
[[Subgroup]]: 2.3.5
&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Stump-Triton"&gt;Triton&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Unsmate"&gt;Unsmate&lt;/a&gt;&lt;/div&gt;
[[Comma list]]: {{monzo| 25 -48 22 }}
&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Chromo"&gt;Chromo&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Wizard"&gt;Wizard&lt;/a&gt;&lt;/div&gt;
{{Mapping|legend=1| 2 7 13 | 0 -11 -24 }}
&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Undeka"&gt;Undeka&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Undeka-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
[[Optimal tuning]]s:  
&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Undeka-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
* [[CTE]]: ~{{monzo| -12 24 -11 }} = 600.000{{c}}, ~200000/177147 = 208.907{{c}}
&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Undeka-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
* [[CWE]]: ~{{monzo| -12 24 -11 }} = 600.000{{c}}, ~200000/177147 = 208.906{{c}}
&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Triskaidekic"&gt;Triskaidekic&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triskaidekic-7-limit"&gt;7-limit&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:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&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:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triskaidekic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
[[Badness]] (Sintel): 5.97
&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Phillips"&gt;Phillips&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Oncle"&gt;Oncle&lt;/a&gt;&lt;/div&gt;
== Supermajor ==
&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Quasimoha"&gt;Quasimoha&lt;/a&gt;&lt;/div&gt;
: ''For extensions, see [[Ragismic microtemperaments #Supermajor]].''
&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Genocchi"&gt;Genocchi&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Misneb"&gt;Misneb&lt;/a&gt;&lt;/div&gt;
[[Subgroup]]: 2.3.5
&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Misneb-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Misneb-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
[[Comma list]]: {{monzo| -13 -46 37 }}
&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Misneb-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Misneb-Musneb"&gt;Musneb&lt;/a&gt;&lt;/div&gt;
{{Mapping|legend=1| 1 15 19 | 0 -37 -46 }}
&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Aufo"&gt;Aufo&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Untriton"&gt;Untriton&lt;/a&gt;&lt;/div&gt;
[[Optimal tuning]]s:  
&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Untriton-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~625/486 = 435.081{{c}}
&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Untriton-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
* [[CWE]]: ~2 = 1200.000{{c}}, ~625/486 = 435.081{{c}}
&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Vinegar"&gt;Vinegar&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;/div&gt;
{{Optimal ET sequence|legend=1| 80, 171, 593, 764, 935, 1106, 3489, 4595, 5701 }}
&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;br /&gt;
 
&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;
[[Badness]] (Sintel): 6.19
Comma: 4428675/4194304&lt;br /&gt;
 
&lt;br /&gt;
== Gamera ==
POTE generator: ~1215/1024 = 252.649&lt;br /&gt;
: ''For extensions, see [[Ragismic microtemperaments #Gamera]].''
&lt;br /&gt;
 
Map: [&amp;lt;1 0 11|, &amp;lt;0 2 -11|]&lt;br /&gt;
[[Subgroup]]: 2.3.5
EDOs: 14, 19&lt;br /&gt;
 
Badness: 0.4247&lt;br /&gt;
[[Comma list]]: {{monzo| 10 -40 23 }}
&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;
{{Mapping|legend=1| 1 6 10 | 0 -23 -40 }}
Comma: 597871125/536870912&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
POTE generator: ~1215/1024 = 230.351&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~2500/2187 = 230.345{{c}}
&lt;br /&gt;
* [[CWE]]: ~2 = 1200.000{{c}}, ~2500/2187 = 230.345{{c}}
Map: [&amp;lt;1 1 5|, &amp;lt;0 3 -14|]&lt;br /&gt;
 
EDOs: 21, 26, 73bc, 99bc&lt;br /&gt;
{{Optimal ET sequence|legend=1| 26, 73, 99, 224, 323, 547, 870 }}
Badness: 1.4349&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 6.39
&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;
 
Comma: 273375/262144&lt;br /&gt;
== Tritriple ==
&lt;br /&gt;
: ''For extensions, see [[Gamelismic clan #Tritriple]].''
POTE generator: ~64/45 = 631.737&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
Map: [&amp;lt;1 0 6|, &amp;lt;0 3 -7|]&lt;br /&gt;
 
EDOs: 17, 19&lt;br /&gt;
[[Comma list]]: {{monzo| 31 20 -27 }}
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;
{{Mapping|legend=1| 1 -11 -7 | 0 27 20 }}
&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;
[[Optimal tuning]]s:  
&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;
* [[CTE]]: ~2 = 1200.000{{c}}, ~864/625 = 559.328{{c}}
Comma: 17578125/16777216&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~864/625 = 559.332{{c}}
&lt;br /&gt;
 
POTE generator: ~2048/1875 = 189.049&lt;br /&gt;
{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 959, 1077 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 3 2|, &amp;lt;0 -9 2|]&lt;br /&gt;
[[Badness]] (Sintel): 6.65
EDOs: 13, 19, 89c, 108c, 127c, 146c&lt;br /&gt;
 
Badness: 0.4602&lt;br /&gt;
== Kangaroo ==
&lt;br /&gt;
: ''For extensions, see [[Trienstonic clan #Parakangaroo]].''
&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;
 
Comma: 1220703125/1146617856&lt;br /&gt;
[[Subgroup]]: 2.3.5
&lt;br /&gt;
 
POTE generator: ~25/24 = 53.922&lt;br /&gt;
[[Comma list]]: 64000/59049
&lt;br /&gt;
 
Map: [&amp;lt;1 1 2|, &amp;lt;0 13 7|]&lt;br /&gt;
{{Mapping|legend=1| 1 0 -3 | 0 3 10 }}
EDOs: 22, 45, 67c, 89c&lt;br /&gt;
 
Badness: 0.8428&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~40/27 = 637.879{{c}}
&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;
* [[POTE]]: ~2 = 1200.000{{c}}, ~40/27 = 638.805{{c}}
Comma: 2197265625/2147483648&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 15, 47b, 62b }}
POTE generator: ~5/4 = 383.212&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 6.94
Map: [&amp;lt;2 1 5|, &amp;lt;0 6 -1|]&lt;br /&gt;
 
EDOs: 22, 50, 72, 166, 238c, 310c, 548bc&lt;br /&gt;
== Tertiaseptal ==
Badness: 0.3864&lt;br /&gt;
: ''For extensions, see [[Breedsmic temperaments #Tertiaseptal]].''
&lt;a class="wiki_link" href="/Marvel%20temperaments#Wizard"&gt;Wizard&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
&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;
[[Comma list]]: {{monzo| -59 5 22 }}
&lt;br /&gt;
 
POTE generator: ~3/2 = 703.829&lt;br /&gt;
{{Mapping|legend=1| 1 3 2 | 0 -22 5 }}
&lt;br /&gt;
 
Map: [&amp;lt;11 0 8|, &amp;lt;0 1 1|]&lt;br /&gt;
[[Optimal tuning]]s:  
EDOs: 22, 77c, 99c, 121c&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~17578125/16777216 = 77.186{{c}}
Badness: 0.7275&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~17578125/16777216 = 77.191{{c}}
&lt;br /&gt;
 
&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;
{{Optimal ET sequence|legend=1| 31, 109, 140, 171, 1679c, 1850c, 2021c, 2192c, 2363c, 2534c, 2705c, 2876c, 3047c }}
Commas: 875/864, 3200/3087&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 6.98
POTE generator: ~3/2 = 708.792&lt;br /&gt;
 
&lt;br /&gt;
== Untriton ==
Map: [&amp;lt;11 0 8 31|, &amp;lt;0 1 1 0|]&lt;br /&gt;
: ''For extensions, see [[Marvel temperaments #Untriton]], [[Porwell temperaments #Aufo]] and [[Triwellismic temperaments #Interaufo]].''
Wedgie: &amp;lt;&amp;lt;11 11 0 -8 -31 -31||&lt;br /&gt;
 
EDOs: 22&lt;br /&gt;
[[Subgroup]]: 2.3.5
Badness: 0.1418&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: {{monzo| -51 19 9 }}
&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;
{{Mapping|legend=1| 1 6 -7 | 0 -9 19 }}
&lt;br /&gt;
 
POTE generator: ~3/2 = 706.768&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 588.727{{c}}
Map: [&amp;lt;11 0 8 31 38|, &amp;lt;0 1 1 0 0|]&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 588.722{{c}}
EDOs: 22&lt;br /&gt;
 
Badness: 0.0687&lt;br /&gt;
{{Optimal ET sequence|legend=1| 51, 53, 267, 320, 373, 426, 479, 532, 2607bc }}
&lt;br /&gt;
 
&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;
[[Badness]] (Sintel): 7.20
Commas: 65/63, 100/99, 169/165, 352/343&lt;br /&gt;
 
&lt;br /&gt;
== Nessafof ==
POTE generator: ~3/2 = 707.764&lt;br /&gt;
: ''For extensions, see [[Porwell temperaments #Nessafof]].''
&lt;br /&gt;
 
Map: [&amp;lt;11 0 8 31 38 23|, &amp;lt;0 1 1 0 0 1|]&lt;br /&gt;
[[Subgroup]]: 2.3.5
EDOs: 22&lt;br /&gt;
 
Badness: 0.0565&lt;br /&gt;
[[Comma list]]: {{monzo| 25 15 -21 }}
&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;
{{Mapping|legend=1| 3 2 5 | 0 7 5 }}
Comma: 1220703125/1073741824&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
POTE generator: ~3/2 = 696.142&lt;br /&gt;
* [[CTE]]: ~78125/62208 = 400.000{{c}}, ~9765625/8957952 = 157.392{{c}}
&lt;br /&gt;
* [[CWE]]: ~78125/62208 = 400.000{{c}}, ~9765625/8957952 = 157.409{{c}}
Map: [&amp;lt;13 0 30|, &amp;lt;0 1 0|]&lt;br /&gt;
 
EDOs: 13, 26, 91c&lt;br /&gt;
{{Optimal ET sequence|legend=1| 15, 54b, 69, 84, 99, 183, 282, 465, 1212c, 1677cc }}
Badness: 2.2416&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 7.81
&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;
 
Commas: 1728/1715, 1875/1792&lt;br /&gt;
== Lemba ==
&lt;br /&gt;
: ''For extensions, see [[Jubilismic clan #Lemba]].''
POTE generator: ~3/2 = 694.143&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
Map: [&amp;lt;13 0 30 16|, &amp;lt;0 1 0 1|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;13 0 13 -30 -16 30||&lt;br /&gt;
[[Comma list]]: 140625/131072
EDOs: 26&lt;br /&gt;
 
Badness: 0.2190&lt;br /&gt;
{{Mapping|legend=1| 2 2 5 | 0 3 -1 }}
&lt;br /&gt;
: Mapping generators: ~375/256, ~75/64
&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;
[[Optimal tuning]]s:
&lt;br /&gt;
* [[CTE]]: ~375/256 = 600.000{{c}}, ~75/64 = 232.986{{c}}
POTE generator: ~3/2 = 696.296&lt;br /&gt;
: [[error map]]: {{val| 0.000 -2.998 -19.300 }}
&lt;br /&gt;
* [[CWE]]: ~375/256 = 600.000{{c}}, ~75/64 = 231.832{{c}}
Map: [&amp;lt;13 0 30 16 45|, &amp;lt;0 1 0 1 0|]&lt;br /&gt;
: error map: {{val| 0.000 -6.458 -18.146 }}
EDOs: 26, 91cd&lt;br /&gt;
 
Badness: 0.0988&lt;br /&gt;
{{Optimal ET sequence|legend=1| 10, 16, 26, 88cc }}
&lt;br /&gt;
 
&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;
[[Badness]] (Sintel): 7.85
Commas: 78/77, 99/98, 125/121, 1200/1183&lt;br /&gt;
 
&lt;br /&gt;
== Delorean ==
POTE generator: ~3/2 = 695.879&lt;br /&gt;
: ''For extensions, see [[Mint temperaments #Subklei]].''
&lt;br /&gt;
 
Map: [&amp;lt;13 0 30 16 45 48|, &amp;lt;0 1 0 1 0 0|]&lt;br /&gt;
[[Subgroup]]: 2.3.5
EDOs: 26, 91cdf&lt;br /&gt;
 
Badness: 0.0592&lt;br /&gt;
[[Comma list]]: 17496/15625
&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;
{{Mapping|legend=1| 1 3 4 | 0 -6 -7 }}
Comma: 9685512225/8589934592&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
POTE generator: ~3/2 = 691.455&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 284.817{{c}}
&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 284.293{{c}}
Map: [&amp;lt;2 0 33|, &amp;lt;0 1 -9|]&lt;br /&gt;
 
EDOs: 14, 26, 66b, 92bc, 118bc&lt;br /&gt;
{{Optimal ET sequence|legend=1| 4, 13c, 17c, 21, 38c }}
Badness: 2.2289&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 8.35
&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;
 
Comma: 145282683375/137438953472&lt;br /&gt;
== Majvam ==
&lt;br /&gt;
: ''For extensions, see [[No-sevens subgroup temperaments #Majvam]], [[Cataharry temperaments #Majvamoid]], and [[Parkleiness temperaments #Majvamic]].''
POTE generator: ~4096/3645 = 232.521&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
Map: [&amp;lt;1 1 6|, &amp;lt;0 3 -19|]&lt;br /&gt;
 
EDOs: 31, 98c, 129c, 160bc, 289bc&lt;br /&gt;
[[Comma list]]: 2404631929946112/2384185791015625
Badness: 1.2447&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 10 5 | 0 -22 -7 }}
&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;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~125/96 = 459.006{{c}}
POTE generator: ~1048576/885735 = 348.600&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~125/96 = 458.995{{c}}
&lt;br /&gt;
 
Map: [&amp;lt;1 1 9|, &amp;lt;0 2 -23|]&lt;br /&gt;
{{Optimal ET sequence|legend=1| 34, 115, 149, 183, 217, 400, 617 }}
EDOs: 31, 117c, 148bc, 179bc&lt;br /&gt;
 
Badness: 1.9867&lt;br /&gt;
[[Badness]] (Sintel): 8.37
&lt;br /&gt;
 
&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;
== Beatles ==
Comma: 2359296/1953125&lt;br /&gt;
: ''For extensions, see [[Archytas clan #Beatles]].''
&lt;br /&gt;
 
POTE generator: ~768/625 = 212.444&lt;br /&gt;
[[Subgroup]]: 2.3.5
&lt;br /&gt;
 
Map: [&amp;lt;1 0 2|, &amp;lt;0 9 2|]&lt;br /&gt;
[[Comma list]]: 524288/492075
EDOs: 17c&lt;br /&gt;
 
Badness: 1.4050&lt;br /&gt;
{{Mapping|legend=1| 1 1 5 | 0 2 -9 }}
&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;
[[Optimal tuning]]s:
Commas: 145964630126953125/144115188075855872&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~512/405 = 356.492{{c}}
&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~512/405 = 355.930{{c}}
POTE generator: ~16/15 = 113.240&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}
Map: [&amp;lt;1 3 1|, &amp;lt;0 -15 14|]&lt;br /&gt;
 
EDOs: 21, 32, 53, 392, 445, 498, 551, 604, 657c, 710c, 1367bc&lt;br /&gt;
[[Badness]] (Sintel): 8.41
Badness: 0.6095&lt;br /&gt;
 
&lt;br /&gt;
== Magus ==
&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;
: ''For extensions, see [[Sensamagic clan #Magus]] and [[Starling temperaments #Amigo]].''
Commas: 225/224, 4194304/4117715 &lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
POTE generator: ~16/15 = 113.235&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 50331648/48828125
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;
{{Mapping|legend=1| 1 -2 2 | 0 11 1 }}
EDOs: 21, 32, 53&lt;br /&gt;
 
Badness: 0.1410&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 391.068{{c}}
&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;
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 391.225{{c}}
Commas: 99/98, 176/175, 1310720/1294139&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 3, …, 40, 43, 46, 181c, 227c, 273c, 319c }}
POTE generator: ~16/15 = 113.323&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 8.45
Map: [&amp;lt;1 3 1 3 1|, &amp;lt;0 -15 14 -2 26|]&lt;br /&gt;
 
EDOS: 21, 53, 127, 180de&lt;br /&gt;
== Tritonic ==
Badness: 0.0854&lt;br /&gt;
: ''For extensions, see [[Marvel temperaments #Tritonic]].''
&lt;br /&gt;
 
&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;
[[Subgroup]]: 2.3.5
Commas: 99/98, 176/175, 640/637 847/845&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 553584375/536870912
POTE generator: ~16/15 = 113.323&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 4 -3 | 0 -5 11 }}
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;
[[Optimal tuning]]s:  
Badness: 0.0456&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 580.278{{c}}
&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 580.219{{c}}
&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;
 
Commas: 225/224, 385/384, 66550/64827&lt;br /&gt;
{{Optimal ET sequence|legend=1| 29, 31, 60, 91 }}
&lt;br /&gt;
 
POTE generator: ~16/15 = 113.142&lt;br /&gt;
[[Badness]] (Sintel): 8.88
&lt;br /&gt;
 
Map: [&amp;lt;1 3 1 3 6|, &amp;lt;0 -15 14 -2 -27|]&lt;br /&gt;
== Wizard ==
EDOS: 32, 53, 191de, 244cde, 297cde&lt;br /&gt;
: ''For extensions, see [[Marvel temperaments #Wizard]].''
Badness: 0.0873&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
&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;
 
Comma: 2270041927734375/2251799813685248&lt;br /&gt;
[[Comma list]]: 2197265625/2147483648
&lt;br /&gt;
 
POTE generator: ~45/32 = 588.722&lt;br /&gt;
{{Mapping|legend=1| 2 1 5 | 0 6 -1 }}
&lt;br /&gt;
: mapping generators: ~42875/32768, ~9375/8192
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;
[[Optimal tuning]]s:
Badness: 0.3071&lt;br /&gt;
* [[CTE]]: ~42875/32768 = 600.000{{c}}, ~9375/8192 = 216.950{{c}}
&lt;br /&gt;
* [[POTE]]: ~42875/32768 = 600.000{{c}}, ~9375/8192 = 216.788{{c}}
&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;
 
Commas: 225/224, 125000000/121060821&lt;br /&gt;
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 548bcc }}
&lt;br /&gt;
 
POTE generator: ~7/5 = 588.641&lt;br /&gt;
[[Badness]] (Sintel): 9.06
&lt;br /&gt;
 
Map: [&amp;lt;1 6 -7 -7|, &amp;lt;0 -9 19 20|]&lt;br /&gt;
Scales (Scala files): [[wizard22]]
Wedgie: &amp;lt;&amp;lt;9 -19 -20 -51 -57 7||&lt;br /&gt;
 
EDOs: 51, 53, 316cd, 369cd, 422cd&lt;br /&gt;
== Merman ==
Badness: 0.1440&lt;br /&gt;
: ''For extensions, see [[Marvel temperaments #Merman]].''
&lt;br /&gt;
 
&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;
[[Subgroup]]: 2.3.5
Commas: 121/120, 225/224, 22000/21609&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: {{monzo| -40 15 7 }}
POTE generator: ~7/5 = 588.626&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 5 -5 | 0 -7 15 }}
Map: [&amp;lt;1 6 -7 -7 1|, &amp;lt;0 -9 19 20 5|]&lt;br /&gt;
 
EDOs: 51, 53&lt;br /&gt;
[[Optimal tuning]]s:
Badness: 0.0743&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~45/32 = 585.653{{c}}
&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000{{c}}, ~45/32 = 585.634{{c}}
&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;
 
Commas: 121/120, 225/224, 275/273, 1040/1029&lt;br /&gt;
{{Optimal ET sequence|legend=1| 41, 84, 125, 209, 334c, 543bc }}
&lt;br /&gt;
 
POTE generator: ~7/5 = 588.654&lt;br /&gt;
[[Badness]] (Sintel): 10.6
&lt;br /&gt;
 
Map: [&amp;lt;1 6 -7 -7 1 -12|, &amp;lt;0 -9 19 20 5 32|]&lt;br /&gt;
== Nusecond ==
EDOs: 53&lt;br /&gt;
: ''For extensions, see [[Starling temperaments #Nusecond]].''
Badness: 0.0474&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5
&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;
[[Comma list]]: 51018336/48828125
&lt;br /&gt;
 
POTE generator: ~10/9 = 156.861&lt;br /&gt;
{{Mapping|legend=1| 1 3 4 | 0 -11 -13 }}
&lt;br /&gt;
 
Map: [&amp;lt;3 0 -5|, &amp;lt;0 2 5|]&lt;br /&gt;
[[Optimal tuning]]s:
EDOs: 15, 39c, 54, 69b, 84b&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000{{c}}, ~3125/2916 = 154.577{{c}}
Badness: 0.9030&lt;/body&gt;&lt;/html&gt;</pre></div>
* [[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]].''
 
[[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]]

Latest revision as of 08:53, 16 May 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

Below are listed some 5-limit temperaments that do not belong to some other temperament collection, the majority of which are restrictions to the 5-limit of temperaments that emerge more fully in higher limits or subgroups; 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:

Unidecmic

For extensions, see Gamelismic clan #Unidec.

Subgroup: 2.3.5

Comma list: 31381059609/31250000000

Mapping: [⟨2 -1 -3], ⟨0 6 11]]

mapping generators: ~177147/125000, ~25000/19683

Optimal tunings:

  • WE: ~177147/125000 = 600.0124 ¢, ~25000/19683 = 416.9619 ¢
error map: ⟨+0.025 -0.196 +0.235]
  • CWE: ~177147/125000 = 600.0000 ¢, ~25000/19683 = 416.9561 ¢
error map: ⟨0.000 -0.236 +0.172]

Optimal ET sequence: 26, 46, 72, 118, 2524, 2642, 2760

Badness (Sintel): 1.93

Quasithird

For extensions, see Ragismic microtemperaments #Quasithird.

Subgroup: 2.3.5

Comma list: [55 -64 20⟩

Mapping: [⟨4 0 -11], ⟨0 5 16]]

mapping generators: ~51200000/43046721, ~1594323/1280000

Optimal tunings:

  • WE: ~51200000/43046721 = 299.9990 ¢, ~1594323/1280000 = 380.3934 ¢
error map: ⟨-0.004 +0.012 -0.008]
  • CWE: ~51200000/43046721 = 300.0000 ¢, ~1594323/1280000 = 380.3944 ¢
error map: ⟨0.000 +0.017 -0.004]

Optimal ET sequence: 60, 104c, 164, 224, 388, 612, 1612, 2224, 2836, 6284, 9120, 15404

Badness (Sintel): 2.33

Supersharp

For extensions, see Trienstonic clan #Octokaidecal.

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 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.

Subgroup: 2.3.5

Comma list: 800/729

Mapping: [⟨2 0 -5], ⟨0 1 3]]

mapping generators: ~27/20, ~3

Optimal tunings:

  • WE: ~27/20 = 596.986 ¢, ~3/2 = 725.434 ¢ (~10/9 = 128.448 ¢)
error map: ⟨-6.029 +17.450 -13.027]
  • CWE: ~27/20 = 600.000 ¢, ~3/2 = 726.548 ¢ (~10/9 = 126.548 ¢)
error map: ⟨0.000 +24.593 -6.670]

Optimal ET sequence: 8, 10, 18, 28b

Badness (Sintel): 2.88

Avila

For extensions, see Septisemi temperaments #Avila.

Subgroup: 2.3.5

Comma list: 729/640

Mapping: [⟨1 0 -7], ⟨0 1 6]]

mapping generators: ~2, ~3

Optimal tunings:

  • WE: ~2 = 1210.600 ¢, ~3/2 = 667.437 ¢
error map: ⟨+10.600 -23.917 +7.711]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 663.474 ¢
error map: ⟨0.000 -38.481 -5.472]

Optimal ET sequence: 2c, 7c, 9, 20b, 29b

Badness (Sintel): 4.27

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[1]. Its ploidacot is therefore beta-dodecacot.

Subgroup: 2.3.5

Comma list: [77 -31 -12⟩

Mapping: [⟨1 -1 9], ⟨0 12 -31]]

mapping generators: ~2, ~[-32 13 5⟩

Optimal tunings:

  • WE: ~2 = 1199.9693 ¢, ~[-32 13 5⟩ = 258.4963 ¢
error map: ⟨-0.031 +0.031 +0.026]
  • CWE: ~2 = 1200.0000 ¢, ~[-32 13 5⟩ = 258.5031 ¢
error map: ⟨0.000 +0.082 +0.091]

Optimal ET sequence: 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: [⟨1 1 2], ⟨0 5 3]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~25/24 = 138.722 ¢
  • POTE: ~2 = 1200.000 ¢, ~25/24 = 140.995 ¢

Optimal ET sequence: 8, 9, 17c

Badness (Sintel): 4.70

Dodifo

For extensions, see Porwell temperaments #Dodifo.

Subgroup: 2.3.5

Comma list: [-67 -9 35⟩

Mapping: [⟨1 12 5], ⟨0 -35 -9]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~768/625 = 357.087 ¢
  • POTE: ~2 = 1200.000 ¢, ~768/625 = 357.088 ¢

Optimal ET sequence: 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: [⟨2 1 3], ⟨0 4 3]]

mapping generators: ~625/432, ~6/5

Optimal tunings:

  • WE: ~625/432 = 600.6814 ¢, ~6/5 = 325.8892 ¢ (~144/125 = 274.7921 ¢)
error map: ⟨+1.363 +2.283 -6.602]
  • CWE: ~625/432 = 600.0000 ¢, ~6/5 = 325.8147 ¢ (~144/125 = 274.185 ¢)
error map: ⟨0.000 +1.304 -8.869]

Optimal ET sequence: 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: [⟨1 4 5], ⟨0 -9 -10]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~6/5 = 321.773 ¢
  • POTE: ~2 = 1200.000 ¢, ~6/5 = 321.852 ¢

Optimal ET sequence: 15, 26, 41, 179c

Badness (Sintel): 5.34

Semidimfourth

For extensions, see Ragismic microtemperaments #Semidimfourth.

Subgroup: 2.3.5

Comma list: [7 41 -31⟩

Mapping: [⟨1 21 28], ⟨0 -31 -41]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~162/125 = 448.449 ¢
  • POTE: ~2 = 1200.000 ¢, ~162/125 = 448.449 ¢

Optimal ET sequence: 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: [⟨1 9 9], ⟨0 -10 -9]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~6/5 = 310.030 ¢
  • POTE: ~2 = 1200.000 ¢, ~6/5 = 310.140 ¢

Optimal ET sequence: 27, 31, 58, 89

Badness (Sintel): 5.86

Progress

For extensions, see Archytas clan #Progress.

Subgroup: 2.3.5

Comma list: 32768/30375

Mapping: [⟨1 0 5], ⟨0 3 -5]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~45/32 = 638.922 ¢
  • POTE: ~2 = 1200.000 ¢, ~45/32 = 638.736 ¢

Optimal ET sequence: 2, 13, 15, 32c, 47bc, 62bc

Badness (Sintel): 5.77

Abigail

For extensions, see Ragismic microtemperaments #Abigail.

Subgroup: 2.3.5

Comma list: [25 -48 22⟩

Mapping: [⟨2 7 13], ⟨0 -11 -24]]

Optimal tunings:

  • CTE: ~[-12 24 -11⟩ = 600.000 ¢, ~200000/177147 = 208.907 ¢
  • CWE: ~[-12 24 -11⟩ = 600.000 ¢, ~200000/177147 = 208.906 ¢

Optimal ET sequence: 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: [-13 -46 37⟩

Mapping: [⟨1 15 19], ⟨0 -37 -46]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~625/486 = 435.081 ¢
  • CWE: ~2 = 1200.000 ¢, ~625/486 = 435.081 ¢

Optimal ET sequence: 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: [10 -40 23⟩

Mapping: [⟨1 6 10], ⟨0 -23 -40]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~2500/2187 = 230.345 ¢
  • CWE: ~2 = 1200.000 ¢, ~2500/2187 = 230.345 ¢

Optimal ET sequence: 26, 73, 99, 224, 323, 547, 870

Badness (Sintel): 6.39

Tritriple

For extensions, see Gamelismic clan #Tritriple.

Subgroup: 2.3.5

Comma list: [31 20 -27⟩

Mapping: [⟨1 -11 -7], ⟨0 27 20]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~864/625 = 559.328 ¢
  • POTE: ~2 = 1200.000 ¢, ~864/625 = 559.332 ¢

Optimal ET sequence: 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: [⟨1 0 -3], ⟨0 3 10]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~40/27 = 637.879 ¢
  • POTE: ~2 = 1200.000 ¢, ~40/27 = 638.805 ¢

Optimal ET sequence: 15, 47b, 62b

Badness (Sintel): 6.94

Tertiaseptal

For extensions, see Breedsmic temperaments #Tertiaseptal.

Subgroup: 2.3.5

Comma list: [-59 5 22⟩

Mapping: [⟨1 3 2], ⟨0 -22 5]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~17578125/16777216 = 77.186 ¢
  • POTE: ~2 = 1200.000 ¢, ~17578125/16777216 = 77.191 ¢

Optimal ET sequence: 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: [-51 19 9⟩

Mapping: [⟨1 6 -7], ⟨0 -9 19]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~45/32 = 588.727 ¢
  • POTE: ~2 = 1200.000 ¢, ~45/32 = 588.722 ¢

Optimal ET sequence: 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: [25 15 -21⟩

Mapping: [⟨3 2 5], ⟨0 7 5]]

Optimal tunings:

  • CTE: ~78125/62208 = 400.000 ¢, ~9765625/8957952 = 157.392 ¢
  • CWE: ~78125/62208 = 400.000 ¢, ~9765625/8957952 = 157.409 ¢

Optimal ET sequence: 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: [⟨2 2 5], ⟨0 3 -1]]

Mapping generators: ~375/256, ~75/64

Optimal tunings:

  • CTE: ~375/256 = 600.000 ¢, ~75/64 = 232.986 ¢
error map: ⟨0.000 -2.998 -19.300]
  • CWE: ~375/256 = 600.000 ¢, ~75/64 = 231.832 ¢
error map: ⟨0.000 -6.458 -18.146]

Optimal ET sequence: 10, 16, 26, 88cc

Badness (Sintel): 7.85

Delorean

For extensions, see Mint temperaments #Subklei.

Subgroup: 2.3.5

Comma list: 17496/15625

Mapping: [⟨1 3 4], ⟨0 -6 -7]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~6/5 = 284.817 ¢
  • POTE: ~2 = 1200.000 ¢, ~6/5 = 284.293 ¢

Optimal ET sequence: 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: [⟨1 10 5], ⟨0 -22 -7]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~125/96 = 459.006 ¢
  • POTE: ~2 = 1200.000 ¢, ~125/96 = 458.995 ¢

Optimal ET sequence: 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: [⟨1 1 5], ⟨0 2 -9]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~512/405 = 356.492 ¢
  • POTE: ~2 = 1200.000 ¢, ~512/405 = 355.930 ¢

Optimal ET sequence: 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: [⟨1 -2 2], ⟨0 11 1]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~5/4 = 391.068 ¢
  • POTE: ~2 = 1200.000 ¢, ~5/4 = 391.225 ¢

Optimal ET sequence: 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: [⟨1 4 -3], ⟨0 -5 11]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~45/32 = 580.278 ¢
  • POTE: ~2 = 1200.000 ¢, ~45/32 = 580.219 ¢

Optimal ET sequence: 29, 31, 60, 91

Badness (Sintel): 8.88

Wizard

For extensions, see Marvel temperaments #Wizard.

Subgroup: 2.3.5

Comma list: 2197265625/2147483648

Mapping: [⟨2 1 5], ⟨0 6 -1]]

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

Optimal tunings:

  • CTE: ~42875/32768 = 600.000 ¢, ~9375/8192 = 216.950 ¢
  • POTE: ~42875/32768 = 600.000 ¢, ~9375/8192 = 216.788 ¢

Optimal ET sequence: 22, 50, 72, 166, 238c, 310c, 548bcc

Badness (Sintel): 9.06

Scales (Scala files): wizard22

Merman

For extensions, see Marvel temperaments #Merman.

Subgroup: 2.3.5

Comma list: [-40 15 7⟩

Mapping: [⟨1 5 -5], ⟨0 -7 15]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~45/32 = 585.653 ¢
  • POTE: ~2 = 1200.000 ¢, ~45/32 = 585.634 ¢

Optimal ET sequence: 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: [⟨1 3 4], ⟨0 -11 -13]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~3125/2916 = 154.577 ¢
  • POTE: ~2 = 1200.000 ¢, ~3125/2916 = 154.523 ¢

Optimal ET sequence: 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: [⟨2 1 -3], ⟨0 2 7]]

mapping generators: ~2187/1600, ~40/27

Optimal tunings:

  • WE: ~2187/1600 = 598.9674 ¢, ~40/27 = 654.2542 ¢ (~81/80 = 55.2868 ¢)
error map: ⟨-2.065 +5.521 -3.436]
  • CWE: ~2187/1600 = 600.0000 ¢, ~40/27 = 655.0201 ¢ (~81/80 = 55.0201 ¢)
error map: ⟨0.000 +8.085 -1.173]

Optimal ET sequence: 20c, 22, 86b, 108b, 130b

Badness (Sintel): 11.5

Sfourth

For extensions, see Ragismic microtemperaments #Sfourth.

Subgroup: 2.3.5

Comma list: [-5 31 -19⟩

Mapping: [⟨1 2 3], ⟨0 -19 -31]]

Optimal tunings:

  • CTE: ~2 = 1200.0000 ¢, ~1594323/1562500 = 26.2323 ¢
  • POTE: ~2 = 1200.0000 ¢, ~1594323/1562500 = 26.2342 ¢

Optimal ET sequence: 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: [⟨1 -4 0], ⟨0 12 5]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~3125/2304 = 558.404 ¢
  • POTE: ~2 = 1200.000 ¢, ~3125/2304 = 558.592 ¢

Optimal ET sequence: 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: [⟨1 0 -31], ⟨0 1 21]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~3/2 = 704.100 ¢
  • POTE: ~2 = 1200.000 ¢, ~3/2 = 704.179 ¢

Optimal ET sequence: 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: [⟨2 7 8], ⟨0 -8 -7]]

Optimal tunings:

  • CTE: ~390625/279936 = 600.000 ¢, ~6/5 = 312.636 ¢
  • POTE: ~390625/279936 = 600.000 ¢, ~6/5 = 312.713 ¢

Optimal ET sequence: 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: [-50 -8 27⟩

Mapping: [⟨1 14 6], ⟨0 -27 -8]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~9765625/7077888 = 551.777 ¢
  • POTE: ~2 = 1200.000 ¢, ~9765625/7077888 = 551.784 ¢

Optimal ET sequence: 37, 50, 87, 137, 224

Badness (Sintel): 12.8

Misneb

For extensions, see Marvel temperaments #Misneb.

Subgroup: 2.3.5

Comma list: [-57 14 15⟩

Mapping: [⟨1 3 1], ⟨0 -15 14]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~16/15 = 113.233 ¢
  • POTE: ~2 = 1200.000 ¢, ~16/15 = 113.240 ¢

Optimal ET sequence: 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: [⟨1 12 6], ⟨0 -17 -6]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~192/125 = 735.203 ¢
  • POTE: ~2 = 1200.000 ¢, ~192/125 = 735.146 ¢

Optimal ET sequence: 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: [⟨1 4 1], ⟨0 -11 6]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~75/64 = 263.571 ¢
  • POTE: ~2 = 1200.000 ¢, ~75/64 = 263.658 ¢

Optimal ET sequence: 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: [⟨1 2 3], ⟨0 -7 -11]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~27/25 = 72.659 ¢
  • POTE: ~2 = 1200.000 ¢, ~27/25 = 72.742 ¢

Optimal ET sequence: 16, 17c, 33

Badness (Sintel): 16.2

Pentadecal

For extensions, see Cloudy clan #Pentadecal.

Subgroup: 2.3.5

Comma list: 30517578125/29386561536

Mapping: [⟨15 0 11], ⟨0 1 1]]

Optimal tunings:

  • CTE: ~648/625 = 80.000 ¢, ~3/2 = 703.340 ¢
  • POTE: ~648/625 = 80.000 ¢, ~3/2 = 702.652 ¢

Optimal ET sequence: 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: [⟨1 8 2], ⟨0 -20 1]]

Optimal tunings:

  • WE: ~2 = 1200.303 ¢, ~5/4 = 385.024 ¢
  • CWE: ~2 = 1200.000 ¢, ~5/4 = 384.920 ¢

Optimal ET sequence: 25, 28, 53

Badness (Sintel): 16.5

Sentinel

For extensions, see Orwellismic temperaments #Sentinel.

Subgroup: 2.3.5

Comma list: 8968066875/8589934592

Mapping: [⟨1 3 -3], ⟨0 -4 15]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~512/405 = 425.590 ¢
  • POTE: ~2 = 1200.000 ¢, ~512/405 = 425.474 ¢

Optimal ET sequence: 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: [⟨1 4 4], ⟨0 -13 -9]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~144/125 = 223.076 ¢
  • POTE: ~2 = 1200.000 ¢, ~144/125 = 222.912 ¢

Optimal ET sequence: 16, 27, 43, 70, 183cc

Badness (Sintel): 17.1

Mirkat

For extensions, see Mirkwai clan #Mirkat.

Subgroup: 2.3.5

Comma list: [20 -39 18⟩

Mapping: [⟨3 2 1], ⟨0 6 13]]

Optimal tunings:

  • CTE: ~2000000/1594323 = 400.000 ¢, ~10/9 = 183.593 ¢
  • CWE: ~2000000/1594323 = 400.000 ¢, ~10/9 = 183.585 ¢

Optimal ET sequence: 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: [-12 -73 55⟩

Mapping: [⟨1 36 48], ⟨0 -55 -73]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~162/125 = 449.127 ¢
  • POTE: ~2 = 1200.000 ¢, ~162/125 = 449.127 ¢

Optimal ET sequence: 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: [-46 10 13⟩

Mapping: [⟨1 2 2], ⟨0 -13 10]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~16875/16384 = 38.380 ¢
  • CWE: ~2 = 1200.000 ¢, ~16875/16384 = 38.400 ¢

Optimal ET sequence: 31, 94, 125, 781bcc

Badness (Sintel): 17.8

Quasitemp

For extensions, see Keemic temperaments #Quasitemp.

Subgroup: 2.3.5

Comma list: 6103515625/5804752896

Mapping: [⟨1 5 5], ⟨0 -14 -11]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~3125/2592 = 292.591 ¢
  • POTE: ~2 = 1200.000 ¢, ~3125/2592 = 292.702 ¢

Optimal ET sequence: 4, …, 37, 41

Badness (Sintel): 18.0

Cypress

For extensions, see Starling temperaments #Cypress.

Subgroup: 2.3.5

Comma list: 258280326/244140625

Mapping: [⟨1 7 10], ⟨0 -12 -17]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~4374/3125 = 541.735 ¢
  • POTE: ~2 = 1200.000 ¢, ~4374/3125 = 541.726 ¢

Optimal ET sequence: 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: [⟨1 1 2], ⟨0 13 7]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~25/24 = 54.138 ¢
  • POTE: ~2 = 1200.000 ¢, ~25/24 = 53.922 ¢

Optimal ET sequence: 22, 45, 67c, 89c

Badness (Sintel): 19.8

Tertiosec

For extensions, see Marvel temperaments #Tertiosec.

Subgroup: 2.3.5

Comma list: [-89 21 24⟩

Mapping: [⟨3 7 5], ⟨0 -8 7]]

Optimal tunings:

  • CTE: ~[30 -7 -8⟩ = 400.000 ¢, ~16/15 = 112.275 ¢
  • POTE: ~[30 -7 -8⟩ = 400.000 ¢, ~16/15 = 112.281 ¢

Optimal ET sequence: 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: [⟨1 4 -2], ⟨0 -5 9]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~64/45 = 577.593 ¢
  • POTE: ~2 = 1200.000 ¢, ~64/45 = 577.705 ¢

Optimal ET sequence: 2, …, 25, 27

Badness (Sintel): 20.0

Bohpier

For extensions, see Sensamagic clan #Bohpier.

Subgroup: 2.3.5

Comma list: 1220703125/1162261467

Mapping: [⟨1 0 0], ⟨0 13 19]]

Optimal tunings:

  • CTE and POTE: ~2 = 1200.000 ¢, ~27/25 = 146.476 ¢

Optimal ET sequence: 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: [⟨2 1 10], ⟨0 2 -5]]

Optimal tunings:

  • CTE: ~6075/4096 = 600.000 ¢, ~64/45 = 644.844 ¢
  • POTE: ~6075/4096 = 600.000 ¢, ~64/45 = 645.454 ¢

Optimal ET sequence: 26, 80bc, 106bbcc, 132bbcc

Badness (Sintel): 20.7

Enneadecacot

Subgroup: 2.3.5

Comma list: [79 -22 -19⟩

Mapping: [⟨1 1 3], ⟨0 19 -22]]

Optimal tunings:

  • CTE: ~2 = 1200.0000 ¢, ~34171875/33554432 = 36.9607 ¢
  • POTE: ~2 = 1200.0000 ¢, ~34171875/33554432 = 36.9622 ¢

Optimal ET sequence: 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: [⟨3 0 -5], ⟨0 2 5]]

Optimal tunings:

  • CTE: ~243/200 = 400.000 ¢, ~4000/2187 = 955.656 ¢ (~10/9 = 155.656 ¢)
  • POTE: ~243/200 = 400.000 ¢, ~4000/2187 = 956.861 ¢ (~10/9 = 156.861 ¢)

Optimal ET sequence: 15, 39c, 54, 69b

Badness (Sintel): 21.2

Oolong

For extensions, see Starling temperaments #Oolong.

Subgroup: 2.3.5

Comma list: 793437161472/762939453125

Mapping: [⟨1 6 7], ⟨0 -17 -18]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~6/5 = 311.726 ¢
  • POTE: ~2 = 1200.000 ¢, ~6/5 = 311.694 ¢

Optimal ET sequence: 23, 27, 50, 77

Badness (Sintel): 22.1

Oncle

For extensions, see Gamelismic clan #Oncle.

Subgroup: 2.3.5

Comma list: 145282683375/137438953472

Mapping: [⟨1 1 6], ⟨0 3 -19]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~4096/3645 = 232.385 ¢
  • POTE: ~2 = 1200.000 ¢, ~4096/3645 = 232.521 ¢

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

Badness (Sintel): 29.2

Quasiorwell

For extensions, see Breedsmic temperaments #Quasiorwell.

Subgroup: 2.3.5

Comma list: [-93 3 38⟩

Mapping: [⟨1 31 0], ⟨0 -38 3]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~[-31 1 13⟩ = 928.896 ¢
  • CWE: ~2 = 1200.000 ¢, ~[-31 1 13⟩ = 928.893 ¢

Optimal ET sequence: 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: [⟨1 2 3], ⟨0 -13 -21]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~6561/6250 = 38.550 ¢
  • POTE: ~2 = 1200.000 ¢, ~6561/6250 = 38.571 ¢

Optimal ET sequence: 31, 156c

Badness (Sintel): 31.5

Quartemka

For extensions, see Gamelismic clan #Quartemka.

Subgroup: 2.3.5

Comma list: [2 -32 21⟩

Mapping: [⟨1 4 6], ⟨0 -21 -32]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~27/25 = 137.963 ¢
  • POTE: ~2 = 1200.000 ¢, ~27/25 = 137.962 ¢

Optimal ET sequence: 26, 61, 87, 287, 374, 461

Badness (Sintel): 32.4

Genocchi

Subgroup: 2.3.5

Comma list: 2359296/1953125

Mapping: [⟨1 0 2], ⟨0 9 2]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~768/625 = 210.920 ¢
  • POTE: ~2 = 1200.000 ¢, ~768/625 = 212.444 ¢

Optimal ET sequence: 6b, 11b, 17c

Badness (Sintel): 33.0

Casablanca

For extensions, see Starling temperaments #Casablanca.

Subgroup: 2.3.5

Comma list: [22 14 -19⟩

Mapping: [⟨1 -7 -14], ⟨0 19 14]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~864/625 = 542.142 ¢
  • POTE: ~2 = 1200.000 ¢, ~864/625 = 542.208 ¢

Optimal ET sequence: 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: [⟨1 1 5], ⟨0 3 -14]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~1215/1024 = 229.947 ¢
  • POTE: ~2 = 1200.000 ¢, ~1215/1024 = 230.351 ¢

Optimal ET sequence: 21, 26, 73bc, 99bc

Badness (Sintel): 33.7

Octacoid

Subgroup: 2.3.5

Comma list: 8589934592/7688671875

Mapping: [⟨1 1 3], ⟨0 8 -9]]

Mapping generators: ~2, ~16/15

Optimal tunings:

  • CTE: ~2 = 1200.0000 ¢, ~16/15 = 88.7331 ¢
  • CWE: ~2 = 1200.0000 ¢, ~16/15 = 88.8168 ¢

Optimal ET sequence: 13, 14, 27

Badness (Sintel): 41.1

Quasimoha

For extensions, see Breedsmic temperaments #Quasimoha.

Subgroup: 2.3.5

Comma list: [-41 23 2⟩

Mapping: [⟨1 1 9], ⟨0 2 -23]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~1048576/885735 = 348.462 ¢
  • POTE: ~2 = 1200.000 ¢, ~1048576/885735 = 348.600 ¢

Optimal ET sequence: 31, 117c, 148bc, 179bc

Badness (Sintel): 46.6

Phillips

For extensions, see Orwellismic temperaments #Phillips.

Subgroup: 2.3.5

Comma list: 9685512225/8589934592

Mapping: [⟨2 0 33], ⟨0 1 -9]]

Optimal tunings:

  • CTE: ~98415/65536 = 600.000 ¢, ~3/2 = 690.708 ¢
  • POTE: ~98415/65536 = 600.000 ¢, ~3/2 = 691.455 ¢

Optimal ET sequence: 14, 26, 66b, 92bc, 118bbc

Badness (Sintel): 52.3

Satin

For extensions, see Garischismic clan #Satin.

Subgroup: 2.3.5

Comma list: [104 -70 3⟩

Mapping: [⟨1 2 12], ⟨0 -3 -70]]

mapping generators: ~2, ~[-34 23 -1⟩

Optimal tunings:

  • WE: ~2 = 1199.9008 ¢, ~[-34 23 -1⟩ = 165.8930 ¢
error map: ⟨-0.099 +0.168 -0.015]
  • CWE: ~2 = 1200.0000 ¢, ~[-34 23 -1⟩ = 165.9079 ¢
error map: ⟨0.000 +0.321 +0.130]

Optimal ET sequence: 94, 217, 528, 745, 1273, 2018b

Badness (Sintel): 66.9

Lockerbie

For extensions, see Breedsmic temperaments #Lockerbie.

Subgroup: 2.3.5

Comma list: [91 51 -74⟩

Mapping: [⟨1 -25 -16], ⟨0 74 51]]

mapping generators: ~2, ~[36 20 -29⟩

Optimal tunings:

  • CTE: ~2 = 1200.0000 ¢, ~[36 20 -29⟩ = 431.1069 ¢
error map: ⟨0.0000 -0.0444 +0.1382]
  • CWE: ~2 = 1200.0000 ¢, ~[36 20 -29⟩ = 431.1073 ¢
error map: ⟨0.0000 -0.0174 +0.1568]

Optimal ET sequence: 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: [-57 17 13⟩

Mapping: [⟨1 11 -10], ⟨0 -13 17]]

Mapping generators: ~2, ~16384/10125

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~16384/10125 = 869.392 ¢
  • CWE: ~2 = 1200.000 ¢, ~16384/10125 = 869.402 ¢

Optimal ET sequence: 11, 29, 69, 98c

Badness (Sintel): 99.2

Jorgensen

For extensions, see Hemifamity temperaments #Jorgensen.

Subgroup: 2.3.5

Comma list: [111 -70⟩

Mapping: [⟨70 111 0], ⟨0 0 1]]

mapping generators: ~[46 -29⟩, ~5

Optimal tunings:

  • WE: ~[46 -29⟩ = 17.1388 ¢, ~5/4 = 386.8829 ¢
error map: ⟨-0.285 +0.451 -0.000]
  • CWE: ~[46 -29⟩ = 17.1429 ¢, ~5/4 = 386.7543 ¢
error map: ⟨0.000 +0.902 +0.441]

Optimal ET sequence: 70, 140, 350, 490

Badness (Sintel): 203

References

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
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