Kleismic family: Difference between revisions

Revision as of 12:51, 11 June 2011

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[[toc|flat]]


The [[5-limit]] parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].

[[POTE tuning|POTE generator]]: 317.007

Map: [<1 0 1|, <0 6 5|]
EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[458edo|458]]

Music:
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Parizek/Hanson%20%20Improv.mp3|Hanson Improv]] by [[Petr Parizek]]
[[http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3|In Hanson11]] by [[Chris Vaisvil]]

=Seven limit children=
The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.

=Keemun=
[[Comma|Commas]]: 49/48, 126/125

[[POTE tuning|POTE generator]]: ~6/5 = 316.473

Map: [<1 0 1 2|, <0 6 5 3|]
[[Wedgie]]: <<6 5 3 -6 -12 -7||
EDOs: [[15edo|15]], [[19edo|19]], [[91edo|91]]
[[Badness]]: 0.0274

==11-limit==
[[Comma]]s: 49/48, 56/55, 100/99

[[POTE tuning|POTE generator]]: ~6/5 = 317.576

Map: [<1 0 1 2 4|, <0 6 5 3 -2|]
EDOs: [[4edo|4]], [[15edo|15]], [[19edo|19]], [[34edo|34]]
[[Badness]]: 0.0274

==13-limit==
[[Comma]]s: 49/48, 56/55, 78/77, 100/99

[[POTE tuning|POTE generator]]: ~6/5 = 316.611

Map: [<1 0 1 2 4 5|, <0 6 5 3 -2 -5|]
EDOs: [[4edo|4]], [[15edo|15]], [[19edo|19]], [[72edo|72]]
[[Badness]]: 0.0297

=Catakleismic=
[[Comma|Commas]]: 225/224, 4375/4374

[[POTE tuning|POTE generator]]: 316.732

Map: [<1 0 1 -3|, <0 6 5 22|]
[[Wedgie]]: <<6 5 22 -6 18 37||
EDOs: [[19edo|19]], [[53edo|15]], [[72edo|72]], [[197edo|197]], [[269edo|269]]
[[Badness]]: 0.0215

==11-limit==
[[Comma|Commas]]: 225/224, 385/384, 4375/4374

[[POTE tuning|POTE generator]]: 316.719

Map: [<1 0 1 -3 9|, <0 6 5 22 -21|]
EDOs: [[15edo|15]], [[19edo|19]], [[53edo|53]], [[72edo|72]], [[269edo|269]], [[341edo|341]]
[[Badness]]: 0.0218

==13-limit==
[[Comma|Commas]]: 169/168, 225/224, 325/324, 540/539

[[POTE tuning|POTE generator]]: 316.738

Map: [<1 0 1 -3 9 0|, <0 6 5 22 -21 14|]
EDOs: [[15edo|15]], [[19edo|19]], [[53edo|53]], [[72edo|72]], [[197edo|197]], [[269edo|269]], [[466edo|466]]
[[Badness]]: 0.0169

=Countercata=
[[Comma|Commas]]: 15625/15552, 5120/5103

[[POTE tuning|POTE generator]]: 317.121

Map: [<1 0 1 11|, <0 6 5 -31|]
[[Wedgie]]: <<6 5 -31 -6 -66 -86||
EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[333edo|333]], [[473edo|473]], [[806edo|806]]
[[Badness]]: 0.0521

==11-limit==
[[Comma]]s: 385/384, 2200/2187, 3388/3375

POTE generator: ~6/5 = 317.162

Map: [<1 0 1 11 -5|, <0 6 5 -31 32|]
EDOs: [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[227edo|227]]
[[Badness]]: 0.0398

==13-limit==
[[Comma]]s: 325/324, 352/351, 385/384, 625/624

POTE generator: ~6/5 = 317.162

Map: [<1 0 1 11 -5 0|, <0 6 5 -31 32 14|]
EDOs: [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[367edo|367]]
[[Badness]]: 0.0202

=Metakleismic=
[[Comma]]s: 15625/15552, 179200/177147

POTE generator: ~6/5 = 317.314

Map: [<1 0 1 -12|, <0 6 5 56|]
Wedgie: <<6 5 56 -6 72 116||
EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]]
[[Badness]]: 0.1635

==11-limit==
[[Comma]]s: 896/891, 2200/2187, 14700/14641

POTE generator: ~6/5 = 317.311

Map: [<1 0 1 -12 -5|, <0 6 5 56 32|]
EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]]
[[Badness]]: 0.0486

==13-limit==
[[Comma]]s: 325/324, 352/351, 364/363, 625/624

POTE generator: ~6/5 = 317.311

Map: [<1 0 1 -12 -5 0|, <0 6 5 56 32 14|]
EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]]
[[Badness]]: 0.0244

=Hemikleismic=
Commas: 4000/3969, 6144/6125

[[POTE tuning|POTE generator]]: 158.649

Map: [<1 0 1 4|, <0 12 10 -9|]
EDOs: [[53edo|53]], [[121edo|121]]

=Clyde=
[[Comma|Commas]]: 245/243, 3136/3125

7 and 9 limit minimax
[|1 0 0 0>, |6/25 0 0 12/25>, |6/5 0 0 2/5>, |0 0 0 1>]
[[Eigenmonzo|Eigenmonzos]]: 2, 7

[[POTE tuning|POTE generator]]: 441.335

Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 [[Cent|cents]]. Associated recurrence relationship quickly converges.

Map: [<1 6 6 12|, <0 -12 -10 -25|]
[[Generator|Generators]]: 2, 9/7
[[Edo|Edos]]: [[19edo|19]], [[49edo|49]], [[68edo|68]], [[87edo|87]], [[155edo|155]]

=Tritikleismic=
[[Comma]]s: 15625/15552, 1029/1024

[[POTE tuning|POTE generator]]: 316.872

Map: [<3 0 3 10|, <0 6 5 -2|]
[[Wedgie]]: <<18 15 -6 -18 -60 -56||
EDOs: [[12edo|12]], [[15edo|15]], [[57edo|57]], [[72edo|72]], [[159edo|159]], [[231edo|231]]
[[Badness]]: 0.0563

==11-limit==
[[Comma]]s: 385/384, 441/440, 4000/3993

[[POTE tuning|POTE generator]]: 316.881

Map: [<3 0 3 10 8|, <0 6 5 -2 3|]
EDOs: [[12edo|12]], [[15edo|15]], [[57edo|57]], [[72edo|72]], [[159edo|159]], [[231edo|231]]
[[Badness]]: 0.0193

==13-limit==
[[Comma]]s: 325/324, 364/363, 441/440, 625/624

[[POTE tuning|POTE generator]]: 316.959

Map: [<3 0 3 10 8 0|, <0 6 5 -2 3 14|]
EDOs: [[12edo|12]], [[15edo|15]], [[72edo|72]], 87, 159, 867, 1026
[[Badness]]: 0.0157

=Quadritikleismic=
[[Comma]]s: 15625/15552, 2401/2400

[[POTE tuning|POTE generator]]: 316.9999

Map: [<4 0 4 7|, <0 6 5 4|]
Wedgie: <<24 20 16 -24 -42 -19||
EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[1200edo|1200]]
[[Badness]]: 0.0392

==11-limit==
Commas: 385/384, 1375/1372, 6250/6237

[[POTE tuning|POTE generator]]: 316.925

Map: [<4 0 4 7 17|, <0 6 5 4 -3|]
EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[284edo|284]], [[496edo|496]], [[780edo|780]]
[[Badness]]: 0.0234

==13-limit==
Commas: 325/324, 385/384, 625/624, 1573/1568

[[POTE tuning|POTE generator]]: 316.989

Map: [<4 0 4 7 17 0|, <0 6 5 4 -3 14|]
EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]]
[[Badness]]: 0.0187

Original HTML content:

<html><head><title>Kleismic family</title></head><body><!-- ws:start:WikiTextTocRule:42:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Keemun">Keemun</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --> | <a href="#Catakleismic">Catakleismic</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Countercata">Countercata</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Metakleismic">Metakleismic</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Hemikleismic">Hemikleismic</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --> | <a href="#Clyde">Clyde</a><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Tritikleismic">Tritikleismic</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#Quadritikleismic">Quadritikleismic</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: -->
<!-- ws:end:WikiTextTocRule:64 --><br />
<br />
The <a class="wiki_link" href="/5-limit">5-limit</a> parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</a>.<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.007<br />
<br />
Map: [&lt;1 0 1|, &lt;0 6 5|]<br />
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/458edo">458</a><br />
<br />
Music:<br />
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Parizek/Hanson%20%20Improv.mp3" rel="nofollow">Hanson Improv</a> by <a class="wiki_link" href="/Petr%20Parizek">Petr Parizek</a><br />
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3" rel="nofollow">In Hanson11</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h1>
The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Keemun"></a><!-- ws:end:WikiTextHeadingRule:2 -->Keemun</h1>
<a class="wiki_link" href="/Comma">Commas</a>: 49/48, 126/125<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 316.473<br />
<br />
Map: [&lt;1 0 1 2|, &lt;0 6 5 3|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;6 5 3 -6 -12 -7||<br />
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/91edo">91</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0274<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Keemun-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2>
<a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 56/55, 100/99<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 317.576<br />
<br />
Map: [&lt;1 0 1 2 4|, &lt;0 6 5 3 -2|]<br />
EDOs: <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0274<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Keemun-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2>
<a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 56/55, 78/77, 100/99<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 316.611<br />
<br />
Map: [&lt;1 0 1 2 4 5|, &lt;0 6 5 3 -2 -5|]<br />
EDOs: <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/72edo">72</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0297<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Catakleismic"></a><!-- ws:end:WikiTextHeadingRule:8 -->Catakleismic</h1>
<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 4375/4374<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.732<br />
<br />
Map: [&lt;1 0 1 -3|, &lt;0 6 5 22|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;6 5 22 -6 18 37||<br />
EDOs: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">15</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/197edo">197</a>, <a class="wiki_link" href="/269edo">269</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0215<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Catakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2>
<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 385/384, 4375/4374<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.719<br />
<br />
Map: [&lt;1 0 1 -3 9|, &lt;0 6 5 22 -21|]<br />
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/269edo">269</a>, <a class="wiki_link" href="/341edo">341</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0218<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Catakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2>
<a class="wiki_link" href="/Comma">Commas</a>: 169/168, 225/224, 325/324, 540/539<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.738<br />
<br />
Map: [&lt;1 0 1 -3 9 0|, &lt;0 6 5 22 -21 14|]<br />
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/197edo">197</a>, <a class="wiki_link" href="/269edo">269</a>, <a class="wiki_link" href="/466edo">466</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0169<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Countercata"></a><!-- ws:end:WikiTextHeadingRule:14 -->Countercata</h1>
<a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 5120/5103<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.121<br />
<br />
Map: [&lt;1 0 1 11|, &lt;0 6 5 -31|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;6 5 -31 -6 -66 -86||<br />
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/333edo">333</a>, <a class="wiki_link" href="/473edo">473</a>, <a class="wiki_link" href="/806edo">806</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0521<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Countercata-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2>
<a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 2200/2187, 3388/3375<br />
<br />
POTE generator: ~6/5 = 317.162<br />
<br />
Map: [&lt;1 0 1 11 -5|, &lt;0 6 5 -31 32|]<br />
EDOs: <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/227edo">227</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0398<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Countercata-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h2>
<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 385/384, 625/624<br />
<br />
POTE generator: ~6/5 = 317.162<br />
<br />
Map: [&lt;1 0 1 11 -5 0|, &lt;0 6 5 -31 32 14|]<br />
EDOs: <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/367edo">367</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0202<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Metakleismic"></a><!-- ws:end:WikiTextHeadingRule:20 -->Metakleismic</h1>
<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 179200/177147<br />
<br />
POTE generator: ~6/5 = 317.314<br />
<br />
Map: [&lt;1 0 1 -12|, &lt;0 6 5 56|]<br />
Wedgie: &lt;&lt;6 5 56 -6 72 116||<br />
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/208edo">208</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.1635<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Metakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2>
<a class="wiki_link" href="/Comma">Comma</a>s: 896/891, 2200/2187, 14700/14641<br />
<br />
POTE generator: ~6/5 = 317.311<br />
<br />
Map: [&lt;1 0 1 -12 -5|, &lt;0 6 5 56 32|]<br />
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/208edo">208</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0486<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Metakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h2>
<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 364/363, 625/624<br />
<br />
POTE generator: ~6/5 = 317.311<br />
<br />
Map: [&lt;1 0 1 -12 -5 0|, &lt;0 6 5 56 32 14|]<br />
EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/208edo">208</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0244<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Hemikleismic"></a><!-- ws:end:WikiTextHeadingRule:26 -->Hemikleismic</h1>
Commas: 4000/3969, 6144/6125<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 158.649<br />
<br />
Map: [&lt;1 0 1 4|, &lt;0 12 10 -9|]<br />
EDOs: <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/121edo">121</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Clyde"></a><!-- ws:end:WikiTextHeadingRule:28 -->Clyde</h1>
<a class="wiki_link" href="/Comma">Commas</a>: 245/243, 3136/3125<br />
<br />
7 and 9 limit minimax<br />
[|1 0 0 0&gt;, |6/25 0 0 12/25&gt;, |6/5 0 0 2/5&gt;, |0 0 0 1&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 441.335<br />
<br />
Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 <a class="wiki_link" href="/Cent">cents</a>. Associated recurrence relationship quickly converges.<br />
<br />
Map: [&lt;1 6 6 12|, &lt;0 -12 -10 -25|]<br />
<a class="wiki_link" href="/Generator">Generators</a>: 2, 9/7<br />
<a class="wiki_link" href="/Edo">Edos</a>: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/155edo">155</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:30 -->Tritikleismic</h1>
<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 1029/1024<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.872<br />
<br />
Map: [&lt;3 0 3 10|, &lt;0 6 5 -2|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;18 15 -6 -18 -60 -56||<br />
EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/231edo">231</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0563<br />
<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2>
<a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 441/440, 4000/3993<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.881<br />
<br />
Map: [&lt;3 0 3 10 8|, &lt;0 6 5 -2 3|]<br />
EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/231edo">231</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0193<br />
<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2>
<a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 364/363, 441/440, 625/624<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.959<br />
<br />
Map: [&lt;3 0 3 10 8 0|, &lt;0 6 5 -2 3 14|]<br />
EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/72edo">72</a>, 87, 159, 867, 1026<br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0157<br />
<br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Quadritikleismic"></a><!-- ws:end:WikiTextHeadingRule:36 -->Quadritikleismic</h1>
<a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 2401/2400<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.9999<br />
<br />
Map: [&lt;4 0 4 7|, &lt;0 6 5 4|]<br />
Wedgie: &lt;&lt;24 20 16 -24 -42 -19||<br />
EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a>, <a class="wiki_link" href="/1200edo">1200</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0392<br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Quadritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2>
Commas: 385/384, 1375/1372, 6250/6237<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.925<br />
<br />
Map: [&lt;4 0 4 7 17|, &lt;0 6 5 4 -3|]<br />
EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a>, <a class="wiki_link" href="/284edo">284</a>, <a class="wiki_link" href="/496edo">496</a>, <a class="wiki_link" href="/780edo">780</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0234<br />
<br />
<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Quadritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->13-limit</h2>
Commas: 325/324, 385/384, 625/624, 1573/1568<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.989<br />
<br />
Map: [&lt;4 0 4 7 17 0|, &lt;0 6 5 4 -3 14|]<br />
EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a><br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0187</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-07 19:36:00 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-11 12:51:42 UTC</tt>.<br>
-: The original revision id was <tt>234998158</tt>.<br>
+: The original revision id was <tt>235943316</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>
@@ Line 9: / Line 9: @@
-The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].
+The [[5-limit]] parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].
 [[POTE tuning|POTE generator]]: 317.007
 Map: [&lt;1 0 1|, &lt;0 6 5|]
-EDOs: 15, 19, 34, 53, 458
+EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[458edo|458]]
 Music:
@@ Line 21: / Line 21: @@
 =Seven limit children=
-The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.
+The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.
 =Keemun=
@@ Line 29: / Line 29: @@
 Map: [&lt;1 0 1 2|, &lt;0 6 5 3|]
-Wedgie: &lt;&lt;6 5 3 -6 -12 -7||
+[[Wedgie]]: &lt;&lt;6 5 3 -6 -12 -7||
 EDOs: [[15edo|15]], [[19edo|19]], [[91edo|91]]
-Badness: 0.0274
+[[Badness]]: 0.0274
 ==11-limit==
-Commas: 49/48, 56/55, 100/99
+[[Comma]]s: 49/48, 56/55, 100/99
 [[POTE tuning|POTE generator]]: ~6/5 = 317.576
 Map: [&lt;1 0 1 2 4|, &lt;0 6 5 3 -2|]
-EDOs: 4, 15, 19, 34
+EDOs: [[4edo|4]], [[15edo|15]], [[19edo|19]], [[34edo|34]]
-Badness: 0.0274
+[[Badness]]: 0.0274
 ==13-limit==
-Commas: 49/48, 56/55, 78/77, 100/99
+[[Comma]]s: 49/48, 56/55, 78/77, 100/99
 [[POTE tuning|POTE generator]]: ~6/5 = 316.611
 Map: [&lt;1 0 1 2 4 5|, &lt;0 6 5 3 -2 -5|]
-EDOs: 4, 15, 19, 72
+EDOs: [[4edo|4]], [[15edo|15]], [[19edo|19]], [[72edo|72]]
-Badness: 0.0297
+[[Badness]]: 0.0297
 =Catakleismic=
@@ Line 57: / Line 57: @@
 Map: [&lt;1 0 1 -3|, &lt;0 6 5 22|]
-Wedgie: &lt;&lt;6 5 22 -6 18 37||
+[[Wedgie]]: &lt;&lt;6 5 22 -6 18 37||
 EDOs: [[19edo|19]], [[53edo|15]], [[72edo|72]], [[197edo|197]], [[269edo|269]]
-Badness: 0.0215
+[[Badness]]: 0.0215
 ==11-limit==
@@ Line 68: / Line 68: @@
 Map: [&lt;1 0 1 -3 9|, &lt;0 6 5 22 -21|]
 EDOs: [[15edo|15]], [[19edo|19]], [[53edo|53]], [[72edo|72]], [[269edo|269]], [[341edo|341]]
-Badness: 0.0218
+[[Badness]]: 0.0218
 ==13-limit==
@@ Line 77: / Line 77: @@
 Map: [&lt;1 0 1 -3 9 0|, &lt;0 6 5 22 -21 14|]
 EDOs: [[15edo|15]], [[19edo|19]], [[53edo|53]], [[72edo|72]], [[197edo|197]], [[269edo|269]], [[466edo|466]]
-Badness: 0.0169
+[[Badness]]: 0.0169
 =Countercata=
@@ Line 85: / Line 85: @@
 Map: [&lt;1 0 1 11|, &lt;0 6 5 -31|]
-Wedgie: &lt;&lt;6 5 -31 -6 -66 -86||
+[[Wedgie]]: &lt;&lt;6 5 -31 -6 -66 -86||
-EDOs: 15, 19, 34, 53, 87, 140, 333, 473, 806
+EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[333edo|333]], [[473edo|473]], [[806edo|806]]
-Badness: 0.0521
+[[Badness]]: 0.0521
 ==11-limit==
-Commas: 385/384, 2200/2187, 3388/3375
+[[Comma]]s: 385/384, 2200/2187, 3388/3375
 POTE generator: ~6/5 = 317.162
 Map: [&lt;1 0 1 11 -5|, &lt;0 6 5 -31 32|]
-EDOs: 34, 53, 87, 140, 227
+EDOs: [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[227edo|227]]
-Badness: 0.0398
+[[Badness]]: 0.0398
 ==13-limit==
-Commas: 325/324, 352/351, 385/384, 625/624
+[[Comma]]s: 325/324, 352/351, 385/384, 625/624
 POTE generator: ~6/5 = 317.162
 Map: [&lt;1 0 1 11 -5 0|, &lt;0 6 5 -31 32 14|]
-EDOs: 34, 53, 87, 140, 367
+EDOs: [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[367edo|367]]
-Badness: 0.0202
+[[Badness]]: 0.0202
 =Metakleismic=
-Commas: 15625/15552, 179200/177147
+[[Comma]]s: 15625/15552, 179200/177147
 POTE generator: ~6/5 = 317.314
@@ Line 114: / Line 114: @@
 Map: [&lt;1 0 1 -12|, &lt;0 6 5 56|]
 Wedgie: &lt;&lt;6 5 56 -6 72 116||
-EDOs: 15, 19, 34, 87, 121, 208
+EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]]
-Badness: 0.1635
+[[Badness]]: 0.1635
 ==11-limit==
-Commas: 896/891, 2200/2187, 14700/14641
+[[Comma]]s: 896/891, 2200/2187, 14700/14641
 POTE generator: ~6/5 = 317.311
 Map: [&lt;1 0 1 -12 -5|, &lt;0 6 5 56 32|]
-EDOs: 15, 19, 34, 87, 121, 208
+EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]]
-Badness: 0.0486
+[[Badness]]: 0.0486
 ==13-limit==
-Commas: 325/324, 352/351, 364/363, 625/624
+[[Comma]]s: 325/324, 352/351, 364/363, 625/624
 POTE generator: ~6/5 = 317.311
 Map: [&lt;1 0 1 -12 -5 0|, &lt;0 6 5 56 32 14|]
-EDOs: 15, 19, 34, 87, 121, 208
+EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]]
-Badness: 0.0244
+[[Badness]]: 0.0244
 =Hemikleismic=
@@ Line 141: / Line 141: @@
 Map: [&lt;1 0 1 4|, &lt;0 12 10 -9|]
-EDOs: 53, 121
+EDOs: [[53edo|53]], [[121edo|121]]
 =Clyde=
@@ Line 159: / Line 159: @@
 =Tritikleismic=
-Commas: 15625/15552, 1029/1024
+[[Comma]]s: 15625/15552, 1029/1024
 [[POTE tuning|POTE generator]]: 316.872
 Map: [&lt;3 0 3 10|, &lt;0 6 5 -2|]
-Wedgie: &lt;&lt;18 15 -6 -18 -60 -56||
+[[Wedgie]]: &lt;&lt;18 15 -6 -18 -60 -56||
-EDOs: 12, 15, 57, 72, 159, 231
+EDOs: [[12edo|12]], [[15edo|15]], [[57edo|57]], [[72edo|72]], [[159edo|159]], [[231edo|231]]
-Badness: 0.0563
+[[Badness]]: 0.0563
 ==11-limit==
-Commas: 385/384, 441/440, 4000/3993
+[[Comma]]s: 385/384, 441/440, 4000/3993
 [[POTE tuning|POTE generator]]: 316.881
 Map: [&lt;3 0 3 10 8|, &lt;0 6 5 -2 3|]
-EDOs: 12, 15, 57, 72, 159, 231
+EDOs: [[12edo|12]], [[15edo|15]], [[57edo|57]], [[72edo|72]], [[159edo|159]], [[231edo|231]]
-Badness: 0.0193
+[[Badness]]: 0.0193
 ==13-limit==
-Commas: 325/324, 364/363, 441/440, 625/624
+[[Comma]]s: 325/324, 364/363, 441/440, 625/624
 [[POTE tuning|POTE generator]]: 316.959
 Map: [&lt;3 0 3 10 8 0|, &lt;0 6 5 -2 3 14|]
-EDOs: 12, 15, 72, 87, 159, 867, 1026
+EDOs: [[12edo|12]], [[15edo|15]], [[72edo|72]], 87, 159, 867, 1026
-Badness: 0.0157
+[[Badness]]: 0.0157
 =Quadritikleismic=
-Commas: 15625/15552, 2401/2400
+[[Comma]]s: 15625/15552, 2401/2400
 [[POTE tuning|POTE generator]]: 316.9999
@@ Line 194: / Line 194: @@
 Wedgie: &lt;&lt;24 20 16 -24 -42 -19||
 EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[1200edo|1200]]
-Badness: 0.0392
+[[Badness]]: 0.0392
 ==11-limit==
@@ Line 203: / Line 203: @@
 Map: [&lt;4 0 4 7 17|, &lt;0 6 5 4 -3|]
 EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[284edo|284]], [[496edo|496]], [[780edo|780]]
-Badness: 0.0234
+[[Badness]]: 0.0234
 ==13-limit==
@@ Line 211: / Line 211: @@
 Map: [&lt;4 0 4 7 17 0|, &lt;0 6 5 4 -3 14|]
-EDOs: 68, 72, 140, 212
+EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]]
-Badness: 0.0187</pre></div>
+[[Badness]]: 0.0187</pre></div>
 <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;Kleismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:42:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;a href="#Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt; | &lt;a href="#Keemun"&gt;Keemun&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt; | &lt;a href="#Catakleismic"&gt;Catakleismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt; | &lt;a href="#Countercata"&gt;Countercata&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt; | &lt;a href="#Metakleismic"&gt;Metakleismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Hemikleismic"&gt;Hemikleismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt; | &lt;a href="#Clyde"&gt;Clyde&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Tritikleismic"&gt;Tritikleismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt; | &lt;a href="#Quadritikleismic"&gt;Quadritikleismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;
 &lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&amp;gt;, and flipping that yields &amp;lt;&amp;lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87edo&lt;/a&gt; and &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt;.&lt;br /&gt;
+The &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6&amp;gt;, and flipping that yields &amp;lt;&amp;lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament is commonly called hanson, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense and 5\19 is possible. Other tunings include &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87edo&lt;/a&gt; and &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 317.007&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1|, &amp;lt;0 6 5|]&lt;br /&gt;
-EDOs: 15, 19, 34, 53, 458&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/458edo"&gt;458&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 Music:&lt;br /&gt;
@@ Line 229: / Line 229: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h1&gt;
-The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.&lt;br /&gt;
+The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Keemun"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Keemun&lt;/h1&gt;
@@ Line 237: / Line 237: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 2|, &amp;lt;0 6 5 3|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;6 5 3 -6 -12 -7||&lt;br /&gt;
+&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;6 5 3 -6 -12 -7||&lt;br /&gt;
 EDOs: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/91edo"&gt;91&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0274&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0274&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Keemun-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
-Commas: 49/48, 56/55, 100/99&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 56/55, 100/99&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~6/5 = 317.576&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 2 4|, &amp;lt;0 6 5 3 -2|]&lt;br /&gt;
-EDOs: 4, 15, 19, 34&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/4edo"&gt;4&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0274&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0274&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Keemun-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
-Commas: 49/48, 56/55, 78/77, 100/99&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 56/55, 78/77, 100/99&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~6/5 = 316.611&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 2 4 5|, &amp;lt;0 6 5 3 -2 -5|]&lt;br /&gt;
-EDOs: 4, 15, 19, 72&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/4edo"&gt;4&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0297&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0297&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Catakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Catakleismic&lt;/h1&gt;
@@ Line 265: / Line 265: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 -3|, &amp;lt;0 6 5 22|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;6 5 22 -6 18 37||&lt;br /&gt;
+&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;6 5 22 -6 18 37||&lt;br /&gt;
 EDOs: &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/197edo"&gt;197&lt;/a&gt;, &lt;a class="wiki_link" href="/269edo"&gt;269&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0215&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0215&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Catakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;11-limit&lt;/h2&gt;
@@ Line 276: / Line 276: @@
 Map: [&amp;lt;1 0 1 -3 9|, &amp;lt;0 6 5 22 -21|]&lt;br /&gt;
 EDOs: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/269edo"&gt;269&lt;/a&gt;, &lt;a class="wiki_link" href="/341edo"&gt;341&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0218&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0218&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Catakleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
@@ Line 285: / Line 285: @@
 Map: [&amp;lt;1 0 1 -3 9 0|, &amp;lt;0 6 5 22 -21 14|]&lt;br /&gt;
 EDOs: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/197edo"&gt;197&lt;/a&gt;, &lt;a class="wiki_link" href="/269edo"&gt;269&lt;/a&gt;, &lt;a class="wiki_link" href="/466edo"&gt;466&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0169&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0169&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Countercata"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Countercata&lt;/h1&gt;
@@ Line 293: / Line 293: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 11|, &amp;lt;0 6 5 -31|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;6 5 -31 -6 -66 -86||&lt;br /&gt;
+&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;6 5 -31 -6 -66 -86||&lt;br /&gt;
-EDOs: 15, 19, 34, 53, 87, 140, 333, 473, 806&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/333edo"&gt;333&lt;/a&gt;, &lt;a class="wiki_link" href="/473edo"&gt;473&lt;/a&gt;, &lt;a class="wiki_link" href="/806edo"&gt;806&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0521&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0521&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Countercata-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;11-limit&lt;/h2&gt;
-Commas: 385/384, 2200/2187, 3388/3375&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 385/384, 2200/2187, 3388/3375&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.162&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 11 -5|, &amp;lt;0 6 5 -31 32|]&lt;br /&gt;
-EDOs: 34, 53, 87, 140, 227&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/227edo"&gt;227&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0398&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0398&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Countercata-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;13-limit&lt;/h2&gt;
-Commas: 325/324, 352/351, 385/384, 625/624&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 325/324, 352/351, 385/384, 625/624&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.162&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 11 -5 0|, &amp;lt;0 6 5 -31 32 14|]&lt;br /&gt;
-EDOs: 34, 53, 87, 140, 367&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/367edo"&gt;367&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0202&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0202&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Metakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Metakleismic&lt;/h1&gt;
-Commas: 15625/15552, 179200/177147&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 15625/15552, 179200/177147&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.314&lt;br /&gt;
@@ Line 322: / Line 322: @@
 Map: [&amp;lt;1 0 1 -12|, &amp;lt;0 6 5 56|]&lt;br /&gt;
 Wedgie: &amp;lt;&amp;lt;6 5 56 -6 72 116||&lt;br /&gt;
-EDOs: 15, 19, 34, 87, 121, 208&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/121edo"&gt;121&lt;/a&gt;, &lt;a class="wiki_link" href="/208edo"&gt;208&lt;/a&gt;&lt;br /&gt;
-Badness: 0.1635&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.1635&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Metakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h2&gt;
-Commas: 896/891, 2200/2187, 14700/14641&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 896/891, 2200/2187, 14700/14641&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.311&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 -12 -5|, &amp;lt;0 6 5 56 32|]&lt;br /&gt;
-EDOs: 15, 19, 34, 87, 121, 208&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/121edo"&gt;121&lt;/a&gt;, &lt;a class="wiki_link" href="/208edo"&gt;208&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0486&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0486&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Metakleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;13-limit&lt;/h2&gt;
-Commas: 325/324, 352/351, 364/363, 625/624&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 325/324, 352/351, 364/363, 625/624&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~6/5 = 317.311&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 -12 -5 0|, &amp;lt;0 6 5 56 32 14|]&lt;br /&gt;
-EDOs: 15, 19, 34, 87, 121, 208&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/121edo"&gt;121&lt;/a&gt;, &lt;a class="wiki_link" href="/208edo"&gt;208&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0244&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0244&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Hemikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Hemikleismic&lt;/h1&gt;
@@ Line 349: / Line 349: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 1 4|, &amp;lt;0 12 10 -9|]&lt;br /&gt;
-EDOs: 53, 121&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/121edo"&gt;121&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Clyde"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Clyde&lt;/h1&gt;
@@ Line 367: / Line 367: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Tritikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Tritikleismic&lt;/h1&gt;
-Commas: 15625/15552, 1029/1024&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 15625/15552, 1029/1024&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.872&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;3 0 3 10|, &amp;lt;0 6 5 -2|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;18 15 -6 -18 -60 -56||&lt;br /&gt;
+&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;18 15 -6 -18 -60 -56||&lt;br /&gt;
-EDOs: 12, 15, 57, 72, 159, 231&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/57edo"&gt;57&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/231edo"&gt;231&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0563&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0563&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Tritikleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
-Commas: 385/384, 441/440, 4000/3993&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 385/384, 441/440, 4000/3993&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.881&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;3 0 3 10 8|, &amp;lt;0 6 5 -2 3|]&lt;br /&gt;
-EDOs: 12, 15, 57, 72, 159, 231&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/57edo"&gt;57&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/231edo"&gt;231&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0193&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0193&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Tritikleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;13-limit&lt;/h2&gt;
-Commas: 325/324, 364/363, 441/440, 625/624&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 325/324, 364/363, 441/440, 625/624&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.959&lt;br /&gt;
 &lt;br /&gt;
 Map: [&amp;lt;3 0 3 10 8 0|, &amp;lt;0 6 5 -2 3 14|]&lt;br /&gt;
-EDOs: 12, 15, 72, 87, 159, 867, 1026&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, 87, 159, 867, 1026&lt;br /&gt;
-Badness: 0.0157&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0157&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Quadritikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Quadritikleismic&lt;/h1&gt;
-Commas: 15625/15552, 2401/2400&lt;br /&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 15625/15552, 2401/2400&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.9999&lt;br /&gt;
@@ Line 402: / Line 402: @@
 Wedgie: &amp;lt;&amp;lt;24 20 16 -24 -42 -19||&lt;br /&gt;
 EDOs: &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212&lt;/a&gt;, &lt;a class="wiki_link" href="/1200edo"&gt;1200&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0392&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0392&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Quadritikleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
@@ Line 411: / Line 411: @@
 Map: [&amp;lt;4 0 4 7 17|, &amp;lt;0 6 5 4 -3|]&lt;br /&gt;
 EDOs: &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212&lt;/a&gt;, &lt;a class="wiki_link" href="/284edo"&gt;284&lt;/a&gt;, &lt;a class="wiki_link" href="/496edo"&gt;496&lt;/a&gt;, &lt;a class="wiki_link" href="/780edo"&gt;780&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0234&lt;br /&gt;
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0234&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Quadritikleismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
@@ Line 419: / Line 419: @@
 &lt;br /&gt;
 Map: [&amp;lt;4 0 4 7 17 0|, &amp;lt;0 6 5 4 -3 14|]&lt;br /&gt;
-EDOs: 68, 72, 140, 212&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0187&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0187&lt;/body&gt;&lt;/html&gt;</pre></div>

Kleismic family: Difference between revisions

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