Kleismic family: Difference between revisions

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<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>~~2010~~-12-~~10 14~~:26:27 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-15 19:03:07 UTC</tt>.<br>

: The original revision id was <tt>~~187190445~~</tt>.<br>

: The original revision id was <tt>193549270</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>

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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===

==Keemun==

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

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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

~~EDOs: 19, 91~~

==Catakleismic==

===Catakleismic===

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

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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

EDOs: 53, 72, ~~197~~

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

===Countercata===

==Countercata==

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

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Map: [<1 0 1 11|, <0 6 5 -31|]

Wedgie: <<6 5 -31 -6 -66 -86||

EDOs: 15, 19, 34, 53, 87, 140, 333, 473, 806

Badness: 0.0521

~~EDOs: 53, 140~~

==Hemikleismic==

===Hemikleismic===

Commas: 4000/3969, 6144/6125

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EDOs: 53, 121

===Clyde===

==Clyde==

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

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[[Edo|Edos]]: [[19edo|19]], [[49edo|49]], [[68edo|68]], [[87edo|87]], [[155edo|155]]

===Tritikleismic===

==Tritikleismic==

Commas: 15625/15552, 1029/1024

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EDOs: 72, 231

===Quadritikleismic===

==Quadritikleismic==

Commas: 15625/15552, 2401/2400

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The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> 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.<br />

<br />

<h3 id="toc1"><a name="x~~-Seven limit children~~-Keemun"></a>Keemun</h3>

<h2 id="toc1"><a name="x-Keemun"></a>Keemun</h2>

<a class="wiki_link" href="/Comma">Commas</a>: 49/48, 126/125<br />

<br />

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<br />

Map: [&lt;1 0 1 2|, &lt;0 6 5 3|]<br />

Wedgie: &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 />

Badness: 0.0274<br />

<br />

~~EDOs: 19, 91<br />~~

<h2 id="toc2"><a name="x-Catakleismic"></a>Catakleismic</h2>

~~<br />~~

<h3 id="toc2"><a name="x~~-Seven limit children~~-Catakleismic"></a>Catakleismic</h3>

<a class="wiki_link" href="/Comma">Commas</a>: 225/224, 4375/4374<br />

<br />

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<br />

Map: [&lt;1 0 1 -3|, &lt;0 6 5 22|]<br />

Wedgie: &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 />

Badness: 0.0215<br />

<br />

<h3 id="toc3"><a name="x-Catakleismic-11-limit"></a>11-limit</h3>

<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 />

EDOs: 53, 72, ~~197~~<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 />

Badness: 0.0218<br />

<br />

<h3 id="~~toc3~~"><a name="x~~-Seven limit children~~-Countercata"></a>Countercata</h3>

<h2 id="toc4"><a name="x-Countercata"></a>Countercata</h2>

<a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 5120/5103<br />

<br />

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<br />

Map: [&lt;1 0 1 11|, &lt;0 6 5 -31|]<br />

Wedgie: &lt;&lt;6 5 -31 -6 -66 -86||<br />

EDOs: 15, 19, 34, 53, 87, 140, 333, 473, 806<br />

Badness: 0.0521<br />

<br />

~~EDOs: 53, 140<br />~~

<h2 id="toc5"><a name="x-Hemikleismic"></a>Hemikleismic</h2>

~~<br />~~

<h3 id="~~toc4~~"><a name="x~~-Seven limit children~~-Hemikleismic"></a>Hemikleismic</h3>

Commas: 4000/3969, 6144/6125<br />

<br />

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EDOs: 53, 121<br />

<br />

<h3 id="~~toc5~~"><a name="x~~-Seven limit children~~-Clyde"></a>Clyde</h3>

<h2 id="toc6"><a name="x-Clyde"></a>Clyde</h2>

<a class="wiki_link" href="/Comma">Commas</a>: 245/243, 3136/3125<br />

<br />

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<br />

<h3 id="~~toc6~~"><a name="x~~-Seven limit children~~-Tritikleismic"></a>Tritikleismic</h3>

<h2 id="toc7"><a name="x-Tritikleismic"></a>Tritikleismic</h2>

Commas: 15625/15552, 1029/1024<br />

<br />

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EDOs: 72, 231<br />

<br />

<h3 id="~~toc7~~"><a name="x~~-Seven limit children~~-Quadritikleismic"></a>Quadritikleismic</h3>

<h2 id="toc8"><a name="x-Quadritikleismic"></a>Quadritikleismic</h2>

Commas: 15625/15552, 2401/2400<br />

<br />

@@ 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>2010-12-10 14:26:27 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-15 19:03:07 UTC</tt>.<br>
-: The original revision id was <tt>187190445</tt>.<br>
+: The original revision id was <tt>193549270</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 15: / Line 15: @@
 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===
+==Keemun==
 [[Comma|Commas]]: 49/48, 126/125
@@ Line 21: / Line 21: @@
 Map: [&lt;1 0 1 2|, &lt;0 6 5 3|]
+Wedgie: &lt;&lt;6 5 3 -6 -12 -7||
+EDOs: [[15edo|15]], [[19edo|19]], [[91edo|91]]
+Badness: 0.0274
-EDOs: 19, 91
+==Catakleismic==
-===Catakleismic===
 [[Comma|Commas]]: 225/224, 4375/4374
@@ Line 30: / Line 31: @@
 Map: [&lt;1 0 1 -3|, &lt;0 6 5 22|]
+Wedgie: &lt;&lt;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
-EDOs: 53, 72, 197
+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
-===Countercata===
+==Countercata==
 [[Comma|Commas]]: 15625/15552, 5120/5103
@@ Line 39: / Line 50: @@
 Map: [&lt;1 0 1 11|, &lt;0 6 5 -31|]
+Wedgie: &lt;&lt;6 5 -31 -6 -66 -86||
+EDOs: 15, 19, 34, 53, 87, 140, 333, 473, 806
+Badness: 0.0521
-EDOs: 53, 140
+==Hemikleismic==
-===Hemikleismic===
 Commas: 4000/3969, 6144/6125
@@ Line 50: / Line 62: @@
 EDOs: 53, 121
-===Clyde===
+==Clyde==
 [[Comma|Commas]]: 245/243, 3136/3125
@@ Line 65: / Line 77: @@
 [[Edo|Edos]]: [[19edo|19]], [[49edo|49]], [[68edo|68]], [[87edo|87]], [[155edo|155]]
-===Tritikleismic===
+==Tritikleismic==
 Commas: 15625/15552, 1029/1024
@@ Line 74: / Line 86: @@
 EDOs: 72, 231
-===Quadritikleismic===
+==Quadritikleismic==
 Commas: 15625/15552, 2401/2400
@@ Line 92: / Line 104: @@
 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;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Seven limit children-Keemun"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Keemun&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Keemun"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Keemun&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 49/48, 126/125&lt;br /&gt;
 &lt;br /&gt;
@@ Line 98: / Line 110: @@
 &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;
+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;br /&gt;
-EDOs: 19, 91&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Catakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Catakleismic&lt;/h2&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Seven limit children-Catakleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Catakleismic&lt;/h3&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 4375/4374&lt;br /&gt;
 &lt;br /&gt;
@@ Line 107: / Line 120: @@
 &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;
+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;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Catakleismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11-limit&lt;/h3&gt;
+&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 385/384, 4375/4374&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 316.719&lt;br /&gt;
 &lt;br /&gt;
-EDOs: 53, 72, 197&lt;br /&gt;
+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;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Seven limit children-Countercata"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Countercata&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Countercata"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Countercata&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 15625/15552, 5120/5103&lt;br /&gt;
 &lt;br /&gt;
@@ Line 116: / Line 139: @@
 &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;
+EDOs: 15, 19, 34, 53, 87, 140, 333, 473, 806&lt;br /&gt;
+Badness: 0.0521&lt;br /&gt;
 &lt;br /&gt;
-EDOs: 53, 140&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Hemikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Hemikleismic&lt;/h2&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Seven limit children-Hemikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hemikleismic&lt;/h3&gt;
 Commas: 4000/3969, 6144/6125&lt;br /&gt;
 &lt;br /&gt;
@@ Line 127: / Line 151: @@
 EDOs: 53, 121&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-Seven limit children-Clyde"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Clyde&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Clyde"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Clyde&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 245/243, 3136/3125&lt;br /&gt;
 &lt;br /&gt;
@@ Line 142: / Line 166: @@
 &lt;a class="wiki_link" href="/Edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/49edo"&gt;49&lt;/a&gt;, &lt;a class="wiki_link" href="/68edo"&gt;68&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87&lt;/a&gt;, &lt;a class="wiki_link" href="/155edo"&gt;155&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Seven limit children-Tritikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Tritikleismic&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-Tritikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Tritikleismic&lt;/h2&gt;
 Commas: 15625/15552, 1029/1024&lt;br /&gt;
 &lt;br /&gt;
@@ Line 151: / Line 175: @@
 EDOs: 72, 231&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Seven limit children-Quadritikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Quadritikleismic&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-Quadritikleismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Quadritikleismic&lt;/h2&gt;
 Commas: 15625/15552, 2401/2400&lt;br /&gt;
 &lt;br /&gt;