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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>
The '''jubilismic clan''' tempers out the jubilisma, [[50/49]], which means [[7/5]] and [[10/7]] are both equated to the 600-cent tritone and the [[octave]] is divided in two.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-03-21 06:15:18 UTC</tt>.<br>
: The original revision id was <tt>497311818</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<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]]


The **Jubilismic clan** tempers out the jubilisma, [[50_49|50/49]], which means [[7_5|7/5]] and [[10_7|10/7]] are identified and the [[octave]] is divided in two. Doublewide lemba and diminished are discussed below; others in the clan are pajara, decimal, injera, octokaidecal, hedgehog, bipelog and hexe, which are discussed elsewhere.
== Jubilic ==
The head of this clan, jubilic, is generated by [[~]][[5/4]]. That and a semioctave give ~[[7/4]]. As such, a reasonable tuning would tune the 5/4 flat and 7/4 sharp.  


No-threes [[POTE tuning|POTE generator]]: 380.840
[[Subgroup]]: 2.5.7


No-threes map: [&lt;2 0 1 1|, &lt;0 0 1 1|]
[[Comma list]]: 50/49
EDOs: [[10edo|10]], [[12edo|12]], [[16edo|16]], [[22edo|22]], [[104edo|104]]


=Diminished=
{{Mapping|legend=2| 2 0 1 | 0 1 1 }}
Commas: 36/35, 50/49


[[POTE tuning|POTE generator]]: ~3/2 = 699.523
: sval mapping generators: ~7/5, ~5


Map: [&lt;4 0 3 5|, &lt;0 1 1 1|]
{{Mapping|legend=3| 2 0 0 1 | 0 0 1 1 }}
EDOs: [[4edo|4]], [[12edo|12]]
Badness: 0.0224


==11-limit==
[[Optimal tuning]]s:
Commas: 36/35, 50/49, 56/55
* [[WE]]: ~7/5 = 599.6673{{c}}, ~5/4 = 380.6287{{c}} (~8/7 = 219.0386{{c}})
: [[error map]]: {{val| -0.665 -7.016 +10.139 }}
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~5/4 = 380.0086{{c}} (~8/7 = 219.9914{{c}})
: error map: {{val| 0.000 -6.305 +11.183 }}


[[POTE tuning|POTE generator]]: ~3/2 = 709.109
{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 60d }}


Map: [&lt;4 0 3 5 14|, &lt;0 1 1 1 0|]
[[Badness]] (Sintel): 0.140
EDOs: [[4edo|4]], [[8edo|8]], [[12edo|12]], [[44edo|44]]
Badness: 0.0221


==13-limit==
=== Overview to extensions ===
Commas: 36/35, 40/39, 50/49, 66/65
Lemba finds the perfect fifth three steps away by tempering out [[1029/1024]]. Astrology, five steps away by tempering out [[3125/3072]]. Decimal, two steps away by tempering out [[25/24]] and [[49/48]]. Walid merges ~5/4 and ~4/3 by tempering out [[16/15]].


POTE generator: ~3/2 = 713.773
Diminished adds 36/35 and splits the ~7/5 period in a further two. Pajara adds 64/63 and slices the ~7/4 in two, with antikythera being every other step thereof. Dubbla adds 78125/73728 and slices the ~5/4 in two. Injera adds 81/80 and slices the ~5/1 in four. Octokaidecal adds 28/27. Bipelog adds 135/128. Those splits the generator into three in various ways. Hexe adds 128/125 and slices the period in three. Hedgehog adds 250/243. Elvis adds 8505/8192. Those slice the generator in five. Comic adds 2240/2187. Crepuscular adds 4375/4374. Those slice the generator in seven. Byhearted adds 19683/19208. Bipyth adds 20480/19683. Those slice the generator in nine.  


Map: [&lt;4 0 3 5 14 15|, &lt;0 1 1 1 0 0|]
Temperaments discussed elsewhere are:  
EDOs: 4, 8d, 12f, 20cdef
* [[Decimal]] (+25/24) → [[Dicot family #Decimal|Dicot family]]
Badness: 0.0195
* [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]]
* [[Pajara]] (+64/63) → [[Diaschismic family #Pajara|Diaschismic family]]
* ''[[Dubbla]]'' (+78125/73728) → [[Wesley family #Dubbla|Wesley family]]
* ''[[Injera]]'' (+81/80) → [[Meantone family #Injera|Meantone family]]
* ''[[Octokaidecal]]'' (+28/27) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
* ''[[Bipelog]]'' (+135/128) → [[Mavila #Bipelog|Mavila family]]
* ''[[Hexe]]'' (+128/125) → [[Augmented family #Hexe|Augmented family]]
* ''[[Hedgehog]]'' (+250/243) → [[Porcupine family #Hedgehog|Porcupine family]]
* ''[[Crepuscular]]'' (+4375/4374) → [[Fifive family #Crepuscular|Fifive family]]
* ''[[Byhearted]]'' (+19683/19208) → [[Tetracot family #Byhearted|Tetracot family]]


==Demolished==
Considered below are lemba, astrology, walid, antikythera, doublewide, elvis, comic, and bipyth.
Commas: 36/35, 45/44, 50/49


POTE generator: ~3/2 = 689.881
== Lemba ==
{{Main| Lemba }}
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Lemba]].''


Map: [&lt;4 0 3 5 -5|, &lt;0 1 1 1 3|]
Lemba tempers out 1029/1024, the gamelisma, and a stack of three ~8/7 generators gives an approximate perfect fifth. It may be described as the {{nowrap| 10 & 16 }} temperament; its [[ploidacot]] is diploid tricot.  
EDOs: 12, 28, 40de
Badness: 0.0266


==Hemidim==
[[Subgroup]]: 2.3.5.7
Commas: 36/35, 50/49, 125/121


POTE generator: ~12/11 = 101.679
[[Comma list]]: 50/49, 525/512


Map: [&lt;4 1 4 6 6|, &lt;0 2 2 2 3|]
{{Mapping|legend=1| 2 2 5 6 | 0 3 -1 -1 }}
EDOs: 12, 20b
Badness: 0.0550


=Doublewide=
: mapping generators: ~7/5, ~8/7
Commas: 50/49, 875/864


[[POTE tuning|POTE generator]]: ~6/5 = 325.719
[[Optimal tuning]]s:
* [[WE]]: ~7/5 = 601.4623{{c}}, ~8/7 = 232.6544{{c}}
: [[error map]]: {{val| +2.925 -1.067 -11.656 +7.294 }}
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~8/7 = 232.2655{{c}}
: error map: {{val| 0.000 -5.158 -18.579 -1.091 }}


Map: [&lt;2 1 3 4|, &lt;0 4 3 3|]
{{Optimal ET sequence|legend=1| 10, 16, 26, 36c, 62c }}
EDOs: [[18edo|18]], [[22edo|22]], [[26edo]], [[48edo|48]], [[70edo|70c]]
Badness: 0.0435


==11-limit==
[[Badness]] (Sintel): 1.57
Commas: 50/49, 99/98, 875/864


[[POTE tuning|POTE generator]]: ~6/5 = 325.548
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;2 1 3 4 8|, &lt;0 4 3 3 -2|]
Comma list: 45/44, 50/49, 385/384
EDOs: [[18edo|18]], [[22edo|22]], [[48edo|48]], [[70edo|70c]], [[118edo|118cd]]
Badness: 0.0321


==Fleetwood==
Mapping: {{mapping| 2 2 5 6 5 | 0 3 -1 -1 5 }}
Commas: 50/49, 55/54, 176/175


POTE generator: ~6/5 = 327.038
Optimal tunings:
* WE: ~7/5 = 601.1769{{c}}, ~8/7 = 231.4273{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~8/7 = 231.1781{{c}}


Map: [&lt;2 1 3 4 2|, &lt;0 4 3 3 9|]
{{Optimal ET sequence|legend=0| 10, 16, 26 }}
EDOs: 22, 26e
Badness: 0.0352


===13-limit===
Badness (Sintel): 1.37
Commas: 50/49, 55/54, 65/63, 176/175


POTE generator: ~6/5 = 327.841
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [&lt;2 1 3 4 2 3|, &lt;0 4 3 3 9 8|]
Comma list: 45/44, 50/49, 65/64, 78/77
EDOs: 22, 84bdf
Badness: 0.0318


==Cavalier==
Mapping: {{mapping| 2 2 5 6 5 7 | 0 3 -1 -1 5 1 }}
Commas: 45/44, 50/49, 875/864


POTE generator: ~6/5 = 323.427
Optimal tunings:
* WE: ~7/5 = 601.1939{{c}}, ~8/7 = 231.4261{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~8/7 = 231.1617{{c}}


Map: [&lt;2 1 3 4 1|, &lt;0 4 3 3 11|]
{{Optimal ET sequence|legend=0| 10, 16, 26 }}
EDOs: 26
Badness: 0.0529


===13-limit===
Badness (Sintel): 1.05
Commas: 45/44 50/49 78/77 325/324


POTE generator: ~6/5 = 323.396
== Astrology ==
Astrology tempers out 3125/3072, the magic comma, and a stack of five ~5/4 generators gives an approximate harmonic 3. It may be described as the {{nowrap| 16 & 22 }} temperament; its ploidacot is diploid pentacot.  


Map: [&lt;2 1 3 4 1 2|, &lt;0 4 3 3 11 10|]
[[Subgroup]]: 2.3.5.7
EDOs: 26
Badness: 0.0350


=Lemba=
[[Comma list]]: 50/49, 3125/3072
Commas: 50/49, 525/512


[[POTE tuning|POTE generator]]: ~8/7 = 232.089
{{Mapping|legend=1| 2 0 4 5 | 0 5 1 1 }}


Map: [&lt;2 2 5 6|, &lt;0 3 -1 -1|]
: mapping geenerators: ~7/5, ~5/4
EDOs: [[10edo|10]], [[16edo|16]], [[26edo|26]], [[62edo|62]]
Badness: 0.0622


==11-limit==
[[Optimal tuning]]s:
Commas: 45/44, 50/49, 385/384
* [[WE]]: ~7/5 = 599.6999{{c}}, ~5/4 = 380.3881{{c}} (~8/7 = 219.3119{{c}})
: [[error map]]: {{val| -0.600 -0.015 -7.126 +10.062 }}
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~5/4 = 380.5123{{c}} (~8/7 = 219.4877{{c}})
: error map: {{val| 0.000 +0.606 -5.801 +11.686 }}


POTE generator: ~8/7 = 230.974
{{Optimal ET sequence|legend=1| 6, 16, 22, 60d }}


Map: [&lt;2 2 5 6 5|, &lt;0 3 -1 -1 5|]
[[Badness]] (Sintel): 2.09
EDOs: 10, 16, 26
Badness: 0.0416


==13-limit==
=== 11-limit ===
Commas: 45/44, 50/49, 65/64, 78/77
Subgroup: 2.3.5.7.11


POTE generator: ~8/7 = 230.966
Comma list: 50/49, 121/120, 176/175


Map: [&lt;2 2 5 6 5 7|, &lt;0 3 -1 -1 5 1|]
Mapping: {{mapping| 2 0 4 5 5 | 0 5 1 1 3 }}
EDOs: 10, 16, 26
Badness: 0.0255


=Vigintiduo=
Optimal tunings:
Commas: 50/49, 64/63, 245/243
* WE: ~7/5 = 600.0538{{c}}, ~5/4 = 380.5640{{c}} (~8/7 = 219.4897{{c}})
* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 380.5419{{c}} (~8/7 = 219.4581{{c}})


POTE generator: ~11/8 = 557.563
{{Optimal ET sequence|legend=0| 6, 16, 22 }}


Map: [&lt;22 35 51 62 0|, &lt;0 0 0 0 1|]
Badness (Sintel): 1.29
EDOs: 22, 66de, 88bde, 110bd, 198bcdde
Badness: 0.0484


=Vigin=
==== 13-limit ====
Commas: 50/49, 55/54, 64/63, 99/98
Subgroup: 2.3.5.7.11.13


POTE generator: ~13/8 = 844.624
Comma list: 50/49, 65/64, 78/77, 121/120


Map: [&lt;22 35 51 62 76 0|, &lt;0 0 0 0 0 1|]
Mapping: {{mapping| 2 0 4 5 5 8 | 0 5 1 1 3 -1 }}
EDOs: 22, 44
Badness: 0.0298


=Duodecim=
Optimal tunings:
Commas: 36/35, 50/49, 64/63
* WE: ~7/5 = 600.7886{{c}}, ~5/4 = 380.2857{{c}} (~8/7 = 220.5028{{c}})
* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 379.9119{{c}} (~8/7 = 220.0881{{c}})


POTE generator: ~11/8 = 565.023
{{Optimal ET sequence|legend=0| 6, 16, 22, 38f }}


Map: [&lt;12 19 28 34 0|, &lt;0 0 0 0 1|]
Badness (Sintel): 1.42
EDOs: 12, 24d, 36d
Badness: 30.536


=Crepuscular=
; Music
Commas: 50/49, 4375/4374
* [https://soundcloud.com/joelgranttaylor/astrology-percussion-quintet ''Astrology Percussion Quintet No 1'']{{dead link}} [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/AstrologyPercQuintet1_c.mp3 play]{{dead link}} by [[Joel Taylor]]


POTE generator: ~27/25 = 140.349
==== Horoscope ====
Subgroup: 2.3.5.7.11.13


Map: [&lt;2 2 3 4|, &lt;0 5 7 7|]
Comma list: 50/49, 66/65, 105/104, 121/120
Wedgie: &lt;&lt;10 14 14 -1 -6 -7||
EDOs: 26, 34d, 60d, 94d
Badness: 0.0867


==11-limit==
Mapping: {{mapping| 2 0 4 5 5 3 | 0 5 1 1 3 7 }}
Commas: 50/49, 99/98, 1944/1925


POTE generator: ~12/11 = 140.587
Optimal tunings:  
* WE: ~7/5 = 599.8927{{c}}, ~5/4 = 379.7688{{c}} (~8/7 = 220.1239{{c}})
* CWE: ~7/5 = 600.0000{{c}}, ~5/4 = 379.8117{{c}} (~8/7 = 220.1883{{c}})


Map: [&lt;2 2 3 4 6|, &lt;0 5 7 7 4|]
{{Optimal ET sequence|legend=0| 6f, 16, 22f, 38 }}
EDOs: 26, 34d, 60d, 94de
Badness: 0.0408


==13-limit==
Badness (Sintel): 1.46
Commas: 50/49, 78/77, 99/98, 144/143


POTE generator: ~12/11 = 140.554
== Walid ==
This low-accuracy extension tempers out 16/15, so the perfect fifth stands in for ~8/5 as in [[father]]. Its ploidacot is diploid monocot.  


Map: [&lt;2 2 3 4 6 6|, &lt;0 5 7 7 4 6|]
[[Subgroup]]: 2.3.5.7
EDOs: 26, 34d, 60d, 94de
Badness: 0.0244


=Bipyth=
[[Comma list]]: 16/15, 50/49
Commas: 50/49, 20480/19683


POTE generator: ~3/2 = 709.437
{{Mapping|legend=1| 2 0 8 9 | 0 1 -1 -1 }}


Map: [&lt;2 0 -24 -23|, &lt;0 1 9 9|]
: mapping generators: ~7/5, ~3
Wedgie: &lt;&lt;2 18 18 24 23 -9||
Badness: 0.1650


==11-limit==
[[Optimal tuning]]s:
Commas: 50/49, 121/120, 896/891
* [[WE]]: ~7/5 = 589.0384{{c}}, ~3/2 = 735.7242{{c}} (~15/14 = 146.6857{{c}})
: [[error map]]: {{val| -21.923 +11.846 +12.193 +18.719 }}
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 750.4026{{c}} (~15/14 = 150.4026{{c}})
: error map: {{val| 0.000 +48.448 +63.284 +80.771 }}


POTE generator: ~3/2 = 709.310
{{Optimal ET sequence|legend=1| 2, 6, 8d }}


Map: [&lt;2 0 -24 -23 -9|, &lt;0 1 9 9 5|]
[[Badness]] (Sintel): 1.24
EDOs: 22
Badness: 0.0709


=Elvis=
=== 11-limit ===
Comma: 33554432/36905625
Subgroup: 2.3.5.7.11


POTE generator: ~45/32 = 554.546
Comma list: 16/15, 22/21, 50/49


Map: [&lt;2 1 10|, &lt;0 2 -5|]
Mapping: {{mapping| 2 0 8 9 7 | 0 1 -1 -1 0 }}
EDOs: 24c, 26, 80bc, 106bc, 132bc
Badness: 0.8840


==7-limit==
Optimal tunings:
Commas: 50/49, 8505/8192
* WE: ~7/5 = 589.7684{{c}}, ~3/2 = 736.9708{{c}} (~12/11 = 147.2023{{c}})
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 750.5221{{c}} (~12/11 = 150.5221{{c}})


POTE generator: ~45/32 = 553.721
{{Optimal ET sequence|legend=0| 2, 6, 8d }}


Map: [&lt;2 1 10 11|, &lt;0 2 -5 -5|]
Badness (Sintel): 0.965
Wedgie: &lt;&lt;4 -10 -10 -25 -27 5||
EDOs: 24c, 26
Badness: 0.1415


==11-limit==
== Antikythera ==
Commas: 45/44, 50/49, 1344/1331
Named by [[Gene Ward Smith]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101481.html Yahoo! Tuning Group | ''Antikythera'']</ref>, antikythera is every other step of [[pajara]].


POTE generator: ~11/8 = 553.882
[[Subgroup]]: 2.9.5.7


Map: [&lt;2 1 10 11 8|, &lt;0 2 -5 -5 -1|]
[[Comma list]]: 50/49, 64/63
EDOs: 24c, 26
Badness: 0.0632


==13-limit==
{{Mapping|legend=2| 2 0 11 12 | 0 1 -1 -1 }}
Commas: 45/44, 50/49, 78/77, 1053/1024


POTE generator: ~11/8 = 553.892
: mapping generators: ~7/5, ~9


Map: [&lt;2 1 10 11 8 16|, &lt;0 2 -5 -5 -1 -8|]
{{Mapping|legend=3| 2 3 5 6 | 0 1/2 -1 -1 }}
EDOs: 26
 
Badness: 0.0440</pre></div>
: [[gencom]]: [7/5 8/7; 50/49 64/63]
<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;Jubilismic clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:52:&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:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Diminished"&gt;Diminished&lt;/a&gt;&lt;/div&gt;
[[Optimal tuning]]s:
&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Diminished-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
* [[WE]]: ~7/5 = 598.8483{{c}}, ~9/8 = 213.6844{{c}}
&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Diminished-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
: [[error map]]: {{val| -2.303 +2.864 -5.756 +10.580 }}
&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Diminished-Demolished"&gt;Demolished&lt;/a&gt;&lt;/div&gt;
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~9/8 = 214.6875{{c}}
&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Diminished-Hemidim"&gt;Hemidim&lt;/a&gt;&lt;/div&gt;
: error map: {{val| 0.000 +10.778 -1.001 +16.487 }}
&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Doublewide"&gt;Doublewide&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Doublewide-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
{{Optimal ET sequence|legend=1| 2, 4, 6, 16, 22, 28 }}
&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Doublewide-Fleetwood"&gt;Fleetwood&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Doublewide-Fleetwood-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
[[Badness]] (Sintel): 0.253
&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Doublewide-Cavalier"&gt;Cavalier&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Doublewide-Cavalier-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
== Doublewide ==
&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Lemba"&gt;Lemba&lt;/a&gt;&lt;/div&gt;
: ''For the 5-limit version, see [[Superpyth–22 equivalence continuum #Doublewide (5-limit)]].''
&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Lemba-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Lemba-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
Doublewide is generated by a sharply tuned ~6/5 minor third, four of which and a semi-octave period give the 3rd harmonic. It may be described as the {{nowrap| 22 & 26 }} temperament; its ploidacot is diploid alpha-tetracot. An 11-limit extension is immediately available by identifying two generator steps as ~16/11. [[48edo]] makes for an excellent tuning.
&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Vigintiduo"&gt;Vigintiduo&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="#Vigin"&gt;Vigin&lt;/a&gt;&lt;/div&gt;
[[Subgroup]]: 2.3.5.7
&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Duodecim"&gt;Duodecim&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Crepuscular"&gt;Crepuscular&lt;/a&gt;&lt;/div&gt;
[[Comma list]]: 50/49, 875/864
&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Crepuscular-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Crepuscular-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
{{Mapping|legend=1| 2 1 3 4 | 0 4 3 3 }}
&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Bipyth"&gt;Bipyth&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="#Bipyth-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
: mapping generators: ~7/5, ~6/5
&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Elvis"&gt;Elvis&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="#Elvis-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
[[Optimal tuning]]s:  
&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Elvis-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
* [[WE]]: ~7/5 = 600.0365{{c}}, ~6/5 = 325.7389{{c}} (~7/6 = 274.2975{{c}})
&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Elvis-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
: [[error map]]: {{val| -2.303 +2.864 -5.756 +10.580 }}
&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;/div&gt;
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~6/5 = 325.7353{{c}} (~7/6 = 274.2647{{c}})
&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;br /&gt;
: error map: {{val| 0.000 +10.778 -1.001 +16.487 }}
The &lt;strong&gt;Jubilismic clan&lt;/strong&gt; tempers out the jubilisma, &lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;, which means &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt; and &lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt; are identified and the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; is divided in two. Doublewide lemba and diminished are discussed below; others in the clan are pajara, decimal, injera, octokaidecal, hedgehog, bipelog and hexe, which are discussed elsewhere.&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 4, 14bd, 18, 22, 48 }}
No-threes &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 380.840&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 1.10
No-threes map: [&amp;lt;2 0 1 1|, &amp;lt;0 0 1 1|]&lt;br /&gt;
 
EDOs: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/104edo"&gt;104&lt;/a&gt;&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Diminished"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Diminished&lt;/h1&gt;
 
Commas: 36/35, 50/49&lt;br /&gt;
Comma list: 50/49, 99/98, 385/384
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 699.523&lt;br /&gt;
Mapping: {{mapping| 2 1 3 4 8 | 0 4 3 3 -2 }}
&lt;br /&gt;
 
Map: [&amp;lt;4 0 3 5|, &amp;lt;0 1 1 1|]&lt;br /&gt;
Optimal tunings:  
EDOs: &lt;a class="wiki_link" href="/4edo"&gt;4&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;&lt;br /&gt;
* WE: ~7/5 = 600.1818{{c}}, ~6/5 = 325.6434{{c}} (~7/6 = 274.5384{{c}})
Badness: 0.0224&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 325.5854{{c}} (~7/6 = 274.4146{{c}})
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Diminished-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
{{Optimal ET sequence|legend=0| 4, 18, 22, 48 }}
Commas: 36/35, 50/49, 56/55&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.06
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 709.109&lt;br /&gt;
 
&lt;br /&gt;
=== Fleetwood ===
Map: [&amp;lt;4 0 3 5 14|, &amp;lt;0 1 1 1 0|]&lt;br /&gt;
Subgroup: 2.3.5.7.11
EDOs: &lt;a class="wiki_link" href="/4edo"&gt;4&lt;/a&gt;, &lt;a class="wiki_link" href="/8edo"&gt;8&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/44edo"&gt;44&lt;/a&gt;&lt;br /&gt;
 
Badness: 0.0221&lt;br /&gt;
Comma list: 50/49, 55/54, 176/175
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Diminished-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
Mapping: {{mapping| 2 1 3 4 2 | 0 4 3 3 9 }}
Commas: 36/35, 40/39, 50/49, 66/65&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
POTE generator: ~3/2 = 713.773&lt;br /&gt;
* WE: ~7/5 = 599.6049{{c}}, ~6/5 = 326.8229{{c}} (~7/6 = 272.7819{{c}})
&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 326.8890{{c}} (~7/6 = 273.1110{{c}})
Map: [&amp;lt;4 0 3 5 14 15|, &amp;lt;0 1 1 1 0 0|]&lt;br /&gt;
 
EDOs: 4, 8d, 12f, 20cdef&lt;br /&gt;
{{Optimal ET sequence|legend=0| 4e, …, 18e, 22 }}
Badness: 0.0195&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.16
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Diminished-Demolished"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Demolished&lt;/h2&gt;
 
Commas: 36/35, 45/44, 50/49&lt;br /&gt;
==== 13-limit ====
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
POTE generator: ~3/2 = 689.881&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 50/49, 55/54, 65/63, 176/175
Map: [&amp;lt;4 0 3 5 -5|, &amp;lt;0 1 1 1 3|]&lt;br /&gt;
 
EDOs: 12, 28, 40de&lt;br /&gt;
Mapping: {{mapping| 2 1 3 4 2 3 | 0 4 3 3 9 8 }}
Badness: 0.0266&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:  
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Diminished-Hemidim"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hemidim&lt;/h2&gt;
* WE: ~7/5 = 599.5482{{c}}, ~6/5 = 327.5939{{c}} (~7/6 = 271.9543{{c}})
Commas: 36/35, 50/49, 125/121&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 327.6706{{c}} (~7/6 = 272.3294{{c}})
&lt;br /&gt;
 
POTE generator:  ~12/11 = 101.679&lt;br /&gt;
{{Optimal ET sequence|legend=0| 4ef, …, 18e, 22 }}
&lt;br /&gt;
 
Map: [&amp;lt;4 1 4 6 6|, &amp;lt;0 2 2 2 3|]&lt;br /&gt;
Badness (Sintel): 1.32
EDOs: 12, 20b&lt;br /&gt;
 
Badness: 0.0550&lt;br /&gt;
=== Cavalier ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Doublewide"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Doublewide&lt;/h1&gt;
 
Commas: 50/49, 875/864&lt;br /&gt;
Comma list: 45/44, 50/49, 875/864
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~6/5 = 325.719&lt;br /&gt;
Mapping: {{mapping| 2 1 3 4 1 | 0 4 3 3 11 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 1 3 4|, &amp;lt;0 4 3 3|]&lt;br /&gt;
Optimal tunings:
EDOs: &lt;a class="wiki_link" href="/18edo"&gt;18&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26edo&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48&lt;/a&gt;, &lt;a class="wiki_link" href="/70edo"&gt;70c&lt;/a&gt;&lt;br /&gt;
* WE: ~7/5 = 600.9467{{c}}, ~6/5 = 323.9369{{c}} (~7/6 = 277.0098{{c}})
Badness: 0.0435&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 323.7272{{c}} (~7/6 = 276.2728{{c}})
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Doublewide-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11-limit&lt;/h2&gt;
{{Optimal ET sequence|legend=0| 4e, 22e, 26 }}
Commas: 50/49, 99/98, 875/864&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.75
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~6/5 = 325.548&lt;br /&gt;
 
&lt;br /&gt;
==== 13-limit ====
Map: [&amp;lt;2 1 3 4 8|, &amp;lt;0 4 3 3 -2|]&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
EDOs: &lt;a class="wiki_link" href="/18edo"&gt;18&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48&lt;/a&gt;, &lt;a class="wiki_link" href="/70edo"&gt;70c&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118cd&lt;/a&gt;&lt;br /&gt;
 
Badness: 0.0321&lt;br /&gt;
Comma list: 45/44, 50/49, 78/77, 325/324
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Doublewide-Fleetwood"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Fleetwood&lt;/h2&gt;
Mapping: {{mapping| 2 1 3 4 1 2 | 0 4 3 3 11 10 }}
Commas: 50/49, 55/54, 176/175&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
POTE generator: ~6/5 = 327.038&lt;br /&gt;
* WE: ~7/5 = 600.9537{{c}}, ~6/5 = 323.9097{{c}} (~7/6 = 277.0440{{c}})
&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~6/5 = 323.6876{{c}} (~7/6 = 276.3124{{c}})
Map: [&amp;lt;2 1 3 4 2|, &amp;lt;0 4 3 3 9|]&lt;br /&gt;
 
EDOs: 22, 26e&lt;br /&gt;
{{Optimal ET sequence|legend=0| 4ef, 22ef, 26 }}
Badness: 0.0352&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.45
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Doublewide-Fleetwood-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h3&gt;
 
Commas: 50/49, 55/54, 65/63, 176/175&lt;br /&gt;
== Elvis ==
&lt;br /&gt;
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Elvis]].''
POTE generator: ~6/5 = 327.841&lt;br /&gt;
 
&lt;br /&gt;
Elvis is generated by a ptolemaic diminished fifth, tuned sharp such that two generators and a semi-octave period give the 3rd harmonic. Its ploidacot is diploid alpha-dicot. [[26edo]] makes for an obvious tuning.
Map: [&amp;lt;2 1 3 4 2 3|, &amp;lt;0 4 3 3 9 8|]&lt;br /&gt;
 
EDOs: 22, 84bdf&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
Badness: 0.0318&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 50/49, 8505/8192
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Doublewide-Cavalier"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Cavalier&lt;/h2&gt;
 
Commas: 45/44, 50/49, 875/864&lt;br /&gt;
{{Mapping|legend=1| 2 1 10 11 | 0 2 -5 -5 }}
&lt;br /&gt;
 
POTE generator: ~6/5 = 323.427&lt;br /&gt;
: mapping generators: ~7/5, ~64/45
&lt;br /&gt;
 
Map: [&amp;lt;2 1 3 4 1|, &amp;lt;0 4 3 3 11|]&lt;br /&gt;
[[Optimal tuning]]s:  
EDOs: 26&lt;br /&gt;
* [[WE]]: ~7/5 = 601.6846{{c}}, ~64/45 = 648.0937{{c}} (~64/63 = 46.4091{{c}})
Badness: 0.0529&lt;br /&gt;
: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}
&lt;br /&gt;
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~64/45 = 646.0539{{c}} (~64/63 = 46.0539{{c}})
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Doublewide-Cavalier-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit&lt;/h3&gt;
: error map: {{val| 0.000 -9.847 -16.583 +0.904 }}
Commas: 45/44 50/49 78/77 325/324&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 2, 24c, 26 }}
POTE generator: ~6/5 = 323.396&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 3.58
Map: [&amp;lt;2 1 3 4 1 2|, &amp;lt;0 4 3 3 11 10|]&lt;br /&gt;
 
EDOs: 26&lt;br /&gt;
=== 11-limit ===
Badness: 0.0350&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Lemba"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Lemba&lt;/h1&gt;
Comma list: 45/44, 50/49, 1344/1331
Commas: 50/49, 525/512&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 2 1 10 11 8 | 0 2 -5 -5 -1 }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~8/7 = 232.089&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:  
Map: [&amp;lt;2 2 5 6|, &amp;lt;0 3 -1 -1|]&lt;br /&gt;
* WE: ~7/5 = 601.2186{{c}}, ~16/11 = 647.4300{{c}} (~56/55 = 46.2114{{c}})
EDOs: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/62edo"&gt;62&lt;/a&gt;&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 645.9681{{c}} (~56/55 = 45.9681{{c}})
Badness: 0.0622&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 2, 24c, 26 }}
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Lemba-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;11-limit&lt;/h2&gt;
 
Commas: 45/44, 50/49, 385/384&lt;br /&gt;
Badness (Sintel): 2.09
&lt;br /&gt;
 
POTE generator: ~8/7 = 230.974&lt;br /&gt;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
Map: [&amp;lt;2 2 5 6 5|, &amp;lt;0 3 -1 -1 5|]&lt;br /&gt;
 
EDOs: 10, 16, 26&lt;br /&gt;
Comma list: 45/44, 50/49, 78/77, 1053/1024
Badness: 0.0416&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 2 1 10 11 8 16 | 0 2 -5 -5 -1 -8 }}
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Lemba-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h2&gt;
 
Commas: 45/44, 50/49, 65/64, 78/77&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~7/5 = 601.2206{{c}}, ~16/11 = 647.4219{{c}} (~56/55 = 46.2013{{c}})
POTE generator: ~8/7 = 230.966&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 645.9362{{c}} (~56/55 = 45.9362{{c}})
&lt;br /&gt;
 
Map: [&amp;lt;2 2 5 6 5 7|, &amp;lt;0 3 -1 -1 5 1|]&lt;br /&gt;
{{Optimal ET sequence|legend=0| 2f, 24cf, 26 }}
EDOs: 10, 16, 26&lt;br /&gt;
 
Badness: 0.0255&lt;br /&gt;
Badness (Sintel): 1.82
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Vigintiduo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Vigintiduo&lt;/h1&gt;
== Comic ==
Commas: 50/49, 64/63, 245/243&lt;br /&gt;
: ''For the 5-limit version, see [[Superpyth–22 equivalence continuum #Comic (5-limit)]].''
&lt;br /&gt;
 
POTE generator: ~11/8 = 557.563&lt;br /&gt;
Comic is generated by a grave fifth, tuned flat such that two generators and a semi-octave period give the 3rd harmonic. Its ploidacot is diploid alpha-dicot. [[22edo]] makes for an obvious tuning.
&lt;br /&gt;
 
Map: [&amp;lt;22 35 51 62 0|, &amp;lt;0 0 0 0 1|]&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
EDOs: 22, 66de, 88bde, 110bd, 198bcdde&lt;br /&gt;
 
Badness: 0.0484&lt;br /&gt;
[[Comma list]]: 50/49, 2240/2187
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Vigin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Vigin&lt;/h1&gt;
{{Mapping|legend=1| 2 1 -3 -2 | 0 2 7 7 }}
Commas: 50/49, 55/54, 64/63, 99/98&lt;br /&gt;
 
&lt;br /&gt;
: mapping generators: ~7/5, ~40/27
POTE generator: ~13/8 = 844.624&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
Map: [&amp;lt;22 35 51 62 76 0|, &amp;lt;0 0 0 0 0 1|]&lt;br /&gt;
* [[WE]]: ~7/5 = 598.9554{{c}}, ~40/27 = 653.5596{{c}} (~28/27 = 54.6042{{c}})
EDOs: 22, 44&lt;br /&gt;
: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}
Badness: 0.0298&lt;br /&gt;
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~40/27 = 654.3329{{c}} (~28/27 = 54.3329{{c}})
&lt;br /&gt;
: error map: {{val| 0.000 -9.847 -16.583 +0.904 }}
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Duodecim"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Duodecim&lt;/h1&gt;
 
Commas: 36/35, 50/49, 64/63&lt;br /&gt;
{{Optimal ET sequence|legend=1| 2cd, …, 20cd, 22 }}
&lt;br /&gt;
 
POTE generator: ~11/8 = 565.023&lt;br /&gt;
[[Badness]] (Sintel): 2.14
&lt;br /&gt;
 
Map: [&amp;lt;12 19 28 34 0|, &amp;lt;0 0 0 0 1|]&lt;br /&gt;
=== 11-limit ===
EDOs: 12, 24d, 36d&lt;br /&gt;
Subgroup: 2.3.5.7.11
Badness: 30.536&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 50/49, 99/98, 2662/2625
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Crepuscular"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Crepuscular&lt;/h1&gt;
 
Commas: 50/49, 4375/4374&lt;br /&gt;
Mapping: {{mapping| 2 1 -3 -2 -4 | 0 2 7 7 10 }}
&lt;br /&gt;
 
POTE generator: ~27/25 = 140.349&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~7/5 = 598.8161{{c}}, ~22/15 = 653.8909{{c}} (~28/27 = 55.0747{{c}})
Map: [&amp;lt;2 2 3 4|, &amp;lt;0 5 7 7|]&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~22/15 = 654.7898{{c}} (~28/27 = 54.7898{{c}})
Wedgie: &amp;lt;&amp;lt;10 14 14 -1 -6 -7||&lt;br /&gt;
 
EDOs: 26, 34d, 60d, 94d&lt;br /&gt;
{{Optimal ET sequence|legend=0| 2cde, …, 20cde, 22 }}
Badness: 0.0867&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.49
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Crepuscular-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;11-limit&lt;/h2&gt;
 
Commas: 50/49, 99/98, 1944/1925&lt;br /&gt;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
POTE generator: ~12/11 = 140.587&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 50/49, 65/63, 99/98, 968/945
Map: [&amp;lt;2 2 3 4 6|, &amp;lt;0 5 7 7 4|]&lt;br /&gt;
 
EDOs: 26, 34d, 60d, 94de&lt;br /&gt;
Mapping: {{mapping| 2 1 -3 -2 -4 3 | 0 2 7 7 10 4 }}
Badness: 0.0408&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Crepuscular-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;13-limit&lt;/h2&gt;
* WE: ~7/5 = 600.1030{{c}}, ~22/15 = 654.5470{{c}} (~28/27 = 54.4440{{c}})
Commas: 50/49, 78/77, 99/98, 144/143&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~22/15 = 654.4665{{c}} (~28/27 = 54.4665{{c}})
&lt;br /&gt;
 
POTE generator: ~12/11 = 140.554&lt;br /&gt;
{{Optimal ET sequence|legend=0| 2cde, 20cde, 22 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 2 3 4 6 6|, &amp;lt;0 5 7 7 4 6|]&lt;br /&gt;
Badness (Sintel): 1.71
EDOs: 26, 34d, 60d, 94de&lt;br /&gt;
 
Badness: 0.0244&lt;br /&gt;
== Bipyth ==
&lt;br /&gt;
Bipyth tempers out the 5-limit [[superpyth comma]], 20480/19683, making it an alternative extension of 5-limit [[superpyth]]. Its ploidacot is diploid monocot.
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Bipyth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Bipyth&lt;/h1&gt;
 
Commas: 50/49, 20480/19683&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
POTE generator: ~3/2 = 709.437&lt;br /&gt;
[[Comma list]]: 50/49, 20480/19683
&lt;br /&gt;
 
Map: [&amp;lt;2 0 -24 -23|, &amp;lt;0 1 9 9|]&lt;br /&gt;
{{Mapping|legend=1| 2 0 -24 -23 | 0 1 9 9 }}
Wedgie: &amp;lt;&amp;lt;2 18 18 24 23 -9||&lt;br /&gt;
 
Badness: 0.1650&lt;br /&gt;
: mapping generators: ~7/5, ~3
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Bipyth-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11-limit&lt;/h2&gt;
[[Optimal tuning]]s:  
Commas: 50/49, 121/120, 896/891&lt;br /&gt;
* [[WE]]: ~7/5 = 598.7533{{c}}, ~3/2 = 707.9630{{c}} (~15/14 = 109.2098{{c}})
&lt;br /&gt;
: [[error map]]: {{val| +3.369 -4.083 -9.936 +9.236 }}
POTE generator: ~3/2 = 709.310&lt;br /&gt;
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 709.1579{{c}} (~15/14 = 109.1579{{c}})
&lt;br /&gt;
: error map: {{val| 0.000 -9.847 -16.583 +0.904 }}
Map: [&amp;lt;2 0 -24 -23 -9|, &amp;lt;0 1 9 9 5|]&lt;br /&gt;
 
EDOs: 22&lt;br /&gt;
{{Optimal ET sequence|legend=1| 10cd, 12cd, 22 }}
Badness: 0.0709&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 4.18
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Elvis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Elvis&lt;/h1&gt;
 
Comma: 33554432/36905625&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
POTE generator: ~45/32 = 554.546&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 50/49, 121/120, 896/891
Map: [&amp;lt;2 1 10|, &amp;lt;0 2 -5|]&lt;br /&gt;
 
EDOs: 24c, 26, 80bc, 106bc, 132bc&lt;br /&gt;
Mapping: {{mapping| 2 0 -24 -23 -9 | 0 1 9 9 5 }}
Badness: 0.8840&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Elvis-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;7-limit&lt;/h2&gt;
* WE: ~7/5 = 599.2296{{c}}, ~3/2 = 708.3992{{c}} (~15/14 = 109.1697{{c}})
Commas: 50/49, 8505/8192&lt;br /&gt;
* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 709.1395{{c}} (~15/14 = 109.1395{{c}})
&lt;br /&gt;
 
POTE generator: ~45/32 = 553.721&lt;br /&gt;
{{Optimal ET sequence|legend=0| 10cd, 12cde, 22 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 1 10 11|, &amp;lt;0 2 -5 -5|]&lt;br /&gt;
Badness (Sintel): 2.34
Wedgie: &amp;lt;&amp;lt;4 -10 -10 -25 -27 5||&lt;br /&gt;
 
EDOs: 24c, 26&lt;br /&gt;
== Sedecic ==
Badness: 0.1415&lt;br /&gt;
Sedecic has 1/16-octave period and may be thought of as 16edo with an independent generator for prime 3. Its ploidacot is 16-ploid monocot.  
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Elvis-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;11-limit&lt;/h2&gt;
[[Subgroup]]: 2.3.5.7
Commas: 45/44, 50/49, 1344/1331&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 50/49, 546875/524288
POTE generator: ~11/8 = 553.882&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 16 0 37 45 | 0 1 0 0 }}
Map: [&amp;lt;2 1 10 11 8|, &amp;lt;0 2 -5 -5 -1|]&lt;br /&gt;
 
EDOs: 24c, 26&lt;br /&gt;
[[Optimal tuning]]s:
Badness: 0.0632&lt;br /&gt;
* [[WE]]: ~128/125 = 75.0539{{c}}, ~3/2 = 701.0578{{c}} (~525/512 = 25.5726{{c}})
&lt;br /&gt;
: [[error map]]: {{val| 0.000 0.000 -11.314 +6.174 }}
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Elvis-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;13-limit&lt;/h2&gt;
* [[CWE]]: ~128/125 = 75.0000{{c}}, ~3/2 = 700.8957{{c}} (~525/512 = 25.8957{{c}})
Commas: 45/44, 50/49, 78/77, 1053/1024&lt;br /&gt;
: error map: {{val| 0.000 -1.401 -11.314 +6.174 }}
&lt;br /&gt;
 
POTE generator: ~11/8 = 553.892&lt;br /&gt;
{{Optimal ET sequence|legend=1| 16, 32, 48 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 1 10 11 8 16|, &amp;lt;0 2 -5 -5 -1 -8|]&lt;br /&gt;
[[Badness]] (Sintel): 6.73
EDOs: 26&lt;br /&gt;
 
Badness: 0.0440&lt;/body&gt;&lt;/html&gt;</pre></div>
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 50/49, 385/384, 1331/1323
 
Mapping: {{mapping| 16 0 37 45 30 | 0 1 0 0 1 }}
 
Optimal tunings:
* WE: ~22/21 = 75.0000{{c}}, ~3/2 = 700.7810{{c}} (~45/44 = 25.3476{{c}})
* CWE: ~22/21 = 75.0000{{c}}, ~3/2 = 700.6780{{c}} (~45/44 = 25.6780{{c}})
 
{{Optimal ET sequence|legend=0| 16, 32, 48 }}
 
Badness (Sintel): 3.07
 
== Notes ==
 
[[Category:Temperament clans]]
[[Category:Pages with mostly numerical content]]
[[Category:Jubilismic clan| ]] <!-- main article -->
[[Category:Jubilismic| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Jubilismic_clan"