Schismatic family: Difference between revisions

Revision as of 00:40, 17 December 2010

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2010-12-17 00:40:15 UTC.

The original revision id was 188868111.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

The 5-limit parent comma for the schismatic family is the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymus comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. Its [[monzo]] is |-15 8 1>, and flipping that yields <<1 -8 -15|| for the [[Wedgies and Multivals|wedgie]]. This tells us the generator is a fifth and that we will need eight fourths in succession to reach the pitch class of a major third. In fact, 10 = (4/3)^8 * 32805/32768. 

The 5-limit version of the temperament is a [[Microtempering|microtemperament]], sometimes called helmholtz or schismatic, which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. [[53edo]] is a possible tuning for schismatic, but you need [[118edo]] if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schisma schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244 cents, this falls into the range of microtempering.

[[POTE tuning|POTE generator]]: 701.736

Map: [<1 0 15|, <0 1 -8|]
EDOs: 12, 29, 41, 53, 118, 171, 289, 460, 749

==Seven limit children==
The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. Adding |25 -14 0 -1> gives garibaldi, |-44 26 0 1> grackle, |6 -2 0 -1> schism and |-59 39 0 -1> pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2> and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3>, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3> with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4> and slices the fifth in four.

===Garibaldi===
Commas: 225/224, 3125/3087

7-limit minimax tuning:
7-limit: [|1 0 0 0>, |5/3 1/15 0 -1/15>,
|5/3 -8/15 0 8/15>, |5/3 -14/15 0 14/15>]
[[Eigenmonzo]]s: 2, 7/6

9-limit: [|1 0 0 0>, |25/16 1/8 0 -1/16>, 
|5/2 -1 0 1/2>, |25/8 -7/4 0 7/8>]
Eigenmonzos: 2, 9/7

[[POTE tuning|POTE generator]]: 702.085

Map: [<1 0 15 25|, <0 1 -8 -14|]
EDOs: 12, 29, 41, 53, 94

11-limit
Commas: 225/224, 385/384, 2200/2187

Minimax tuning:
[|1 0 0 0 0>, |25/16 1/8 0 -1/16 0>, |5/2 -1 0 1/2 0>,
|25/8 -7/4 0 7/8 0>, |47/16 23/8 0 -23/16 0>]
Eigenmonzos: 2, 9/7

[[POTE tuning|POTE generator]]: 702.157

Map: [<1 0 15 25 -33|, <0 1 -8 -14 23|]
[[edo|Edos]]: [[41edo|41]], [[53edo|53]], [[94edo|94]], [[135edo|135]]

===Guiron===
Commas: 1029/1024, 10976/10935

7-limit minimax
Eigenmonzos: 2, 5/4

9-limit minimax
Eigenmonzos: 2, 5/4

[[POTE tuning|POTE generator]]: 233.930

Map: [<1 1 7 3|, <0 3 -24 -1|]
EDOs: 36, 41, 77, 118

11-limit
Commas: 385/384, 441/440, 10976/10935

11-limit minimax
Eigenmonzos: 2, 5/4

[[POTE tuning|POTE generator]]: 233.931

Map: [<1 1 7 3 -2|, <0 3 -24 -1 28|]
[[edo|Edos]]: [[41edo|41]], [[77edo|77]], [[118edo|118]], [[159edo|159]], [[200edo|200]]

===Pontiac===
Commas: 32805/32768, 4375/4374

7-limit minimax:
[|1 0 0 0>, |74/47 0 -1/47 1/47>, |113/47 0 8/47 -8/47>, 
|113/47 0 -39/47 39/47>]
Eigenmonzos: 2, 7/5

9-limit minimax:
[|1 0 0 0>, |3/2 1/5 -1/10 0>, 
|3 -8/5 4/5 0>, |-1/2 39/5 -39/10 0>]
Eigenmonzos: 2, 10/9

[[POTE tuning|POTE generator]]: 701.757

Map: [<1 0 15 -59|, <0 1 -8 39|]
[[edo|Edos]]: [[53edo|53]], [[118edo|118]], [[171edo|171]], [[1079edo|1079]], [[1250edo|1250]], [[1421edo|1421]]

===Grackle===
Commas: 126/125, 32805/32768

7-limit minimax
Eigenmonzos: 2, 7/6

9-limit minimax
Eigenmonzos: 2, 9/7

[[POTE tuning|POTE generator]]: 701.239

Map: [<1 0 15 -44|, <0 1 -8 -26|]
[[edo|Edos]]: [[77edo|77]], [[89edo|89]], [[101edo|101]]

===Bischismic===
Commas: 3136/3125, 32805/32768

7-limit minimax
Eigenmonzos: 2, 7/6

9-limit minimax
Eigenmonzos: 2, 9/7

[[POTE tuning|POTE generator]]: 701.592

Map: [<2 0 30 69|, <0 1 -8 -20|]
[[edo|Edos]]: [[118edo|118]], [[130edo|130]], [[248edo|248]], [[378edo|378]], [[508edo|508]]

===Term===
Commas: 32805/32768, 250047/250000

7-limit minimax
Eigenmonzos: 2, 6/5

9-limit minimax
Eigenmonzos: 2, 9/7

[[POTE tuning|POTE generator]]: 701.742

Map: [<3 0 45 94|, <0 1 -8 -18|]
[[edo|Edos]]: [[171edo|171]], [[1038edo|1038]], [[1209edo|1209]]

===Sesquiquartififths===
Commas: 2401/2400, 32805/32768

7-limit minimax
Eigenmonzos: 2, 7/6

9-limit minimax
Eigenmonzos: 2, 9/7

[[POTE tuning|POTE generator]]: 175.434

Map: [<1 1 7 5|, <0 4 -32 -15|]
[[edo|Edos]]: [[171edo|171]], [[643edo|643]]

Original HTML content:

<html><head><title>Schismatic family</title></head><body>The 5-limit parent comma for the schismatic family is the schisma of 32805/32768, which is the amount by which the Pythagorean comma exceeds the Didymus comma (81/80), or alternatively put, the difference between a just major third and a just diminished fourth. Its <a class="wiki_link" href="/monzo">monzo</a> is |-15 8 1&gt;, and flipping that yields &lt;&lt;1 -8 -15|| for the <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>. This tells us the generator is a fifth and that we will need eight fourths in succession to reach the pitch class of a major third. In fact, 10 = (4/3)^8 * 32805/32768. <br />
<br />
The 5-limit version of the temperament is a <a class="wiki_link" href="/Microtempering">microtemperament</a>, sometimes called helmholtz or schismatic, which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. <a class="wiki_link" href="/53edo">53edo</a> is a possible tuning for schismatic, but you need <a class="wiki_link" href="/118edo">118edo</a> if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schisma schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244 cents, this falls into the range of microtempering.<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.736<br />
<br />
Map: [&lt;1 0 15|, &lt;0 1 -8|]<br />
EDOs: 12, 29, 41, 53, 118, 171, 289, 460, 749<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2>
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. Adding |25 -14 0 -1&gt; gives garibaldi, |-44 26 0 1&gt; grackle, |6 -2 0 -1&gt; schism and |-59 39 0 -1&gt; pontiac; these all have a fifth as generator. Bischismic adds |-69 40 0 2&gt; and has a fifth generator with a half-octave period. Guiron adds 1029/1024 = |-10 1 0 3&gt;, with an 8/7 generator, three of which give the fifth, and term adds |-94 54 0 3&gt; with a 1/3 octave period. Sesquiquartififths adds |-35 15 0 4&gt; and slices the fifth in four.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Seven limit children-Garibaldi"></a><!-- ws:end:WikiTextHeadingRule:2 -->Garibaldi</h3>
Commas: 225/224, 3125/3087<br />
<br />
7-limit minimax tuning:<br />
7-limit: [|1 0 0 0&gt;, |5/3 1/15 0 -1/15&gt;,<br />
|5/3 -8/15 0 8/15&gt;, |5/3 -14/15 0 14/15&gt;]<br />
<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 7/6<br />
<br />
9-limit: [|1 0 0 0&gt;, |25/16 1/8 0 -1/16&gt;, <br />
|5/2 -1 0 1/2&gt;, |25/8 -7/4 0 7/8&gt;]<br />
Eigenmonzos: 2, 9/7<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 702.085<br />
<br />
Map: [&lt;1 0 15 25|, &lt;0 1 -8 -14|]<br />
EDOs: 12, 29, 41, 53, 94<br />
<br />
11-limit<br />
Commas: 225/224, 385/384, 2200/2187<br />
<br />
Minimax tuning:<br />
[|1 0 0 0 0&gt;, |25/16 1/8 0 -1/16 0&gt;, |5/2 -1 0 1/2 0&gt;,<br />
|25/8 -7/4 0 7/8 0&gt;, |47/16 23/8 0 -23/16 0&gt;]<br />
Eigenmonzos: 2, 9/7<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 702.157<br />
<br />
Map: [&lt;1 0 15 25 -33|, &lt;0 1 -8 -14 23|]<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/135edo">135</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Guiron"></a><!-- ws:end:WikiTextHeadingRule:4 -->Guiron</h3>
Commas: 1029/1024, 10976/10935<br />
<br />
7-limit minimax<br />
Eigenmonzos: 2, 5/4<br />
<br />
9-limit minimax<br />
Eigenmonzos: 2, 5/4<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 233.930<br />
<br />
Map: [&lt;1 1 7 3|, &lt;0 3 -24 -1|]<br />
EDOs: 36, 41, 77, 118<br />
<br />
11-limit<br />
Commas: 385/384, 441/440, 10976/10935<br />
<br />
11-limit minimax<br />
Eigenmonzos: 2, 5/4<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 233.931<br />
<br />
Map: [&lt;1 1 7 3 -2|, &lt;0 3 -24 -1 28|]<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/77edo">77</a>, <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/200edo">200</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Seven limit children-Pontiac"></a><!-- ws:end:WikiTextHeadingRule:6 -->Pontiac</h3>
Commas: 32805/32768, 4375/4374<br />
<br />
7-limit minimax:<br />
[|1 0 0 0&gt;, |74/47 0 -1/47 1/47&gt;, |113/47 0 8/47 -8/47&gt;, <br />
|113/47 0 -39/47 39/47&gt;]<br />
Eigenmonzos: 2, 7/5<br />
<br />
9-limit minimax:<br />
[|1 0 0 0&gt;, |3/2 1/5 -1/10 0&gt;, <br />
|3 -8/5 4/5 0&gt;, |-1/2 39/5 -39/10 0&gt;]<br />
Eigenmonzos: 2, 10/9<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.757<br />
<br />
Map: [&lt;1 0 15 -59|, &lt;0 1 -8 39|]<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/171edo">171</a>, <a class="wiki_link" href="/1079edo">1079</a>, <a class="wiki_link" href="/1250edo">1250</a>, <a class="wiki_link" href="/1421edo">1421</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Seven limit children-Grackle"></a><!-- ws:end:WikiTextHeadingRule:8 -->Grackle</h3>
Commas: 126/125, 32805/32768<br />
<br />
7-limit minimax<br />
Eigenmonzos: 2, 7/6<br />
<br />
9-limit minimax<br />
Eigenmonzos: 2, 9/7<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.239<br />
<br />
Map: [&lt;1 0 15 -44|, &lt;0 1 -8 -26|]<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/77edo">77</a>, <a class="wiki_link" href="/89edo">89</a>, <a class="wiki_link" href="/101edo">101</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-Seven limit children-Bischismic"></a><!-- ws:end:WikiTextHeadingRule:10 -->Bischismic</h3>
Commas: 3136/3125, 32805/32768<br />
<br />
7-limit minimax<br />
Eigenmonzos: 2, 7/6<br />
<br />
9-limit minimax<br />
Eigenmonzos: 2, 9/7<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.592<br />
<br />
Map: [&lt;2 0 30 69|, &lt;0 1 -8 -20|]<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/118edo">118</a>, <a class="wiki_link" href="/130edo">130</a>, <a class="wiki_link" href="/248edo">248</a>, <a class="wiki_link" href="/378edo">378</a>, <a class="wiki_link" href="/508edo">508</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-Seven limit children-Term"></a><!-- ws:end:WikiTextHeadingRule:12 -->Term</h3>
Commas: 32805/32768, 250047/250000<br />
<br />
7-limit minimax<br />
Eigenmonzos: 2, 6/5<br />
<br />
9-limit minimax<br />
Eigenmonzos: 2, 9/7<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.742<br />
<br />
Map: [&lt;3 0 45 94|, &lt;0 1 -8 -18|]<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/171edo">171</a>, <a class="wiki_link" href="/1038edo">1038</a>, <a class="wiki_link" href="/1209edo">1209</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="x-Seven limit children-Sesquiquartififths"></a><!-- ws:end:WikiTextHeadingRule:14 -->Sesquiquartififths</h3>
Commas: 2401/2400, 32805/32768<br />
<br />
7-limit minimax<br />
Eigenmonzos: 2, 7/6<br />
<br />
9-limit minimax<br />
Eigenmonzos: 2, 9/7<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 175.434<br />
<br />
Map: [&lt;1 1 7 5|, &lt;0 4 -32 -15|]<br />
<a class="wiki_link" href="/edo">Edos</a>: <a class="wiki_link" href="/171edo">171</a>, <a class="wiki_link" href="/643edo">643</a></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>2010-12-09 12:12:56 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-17 00:40:15 UTC</tt>.<br>
-: The original revision id was <tt>186789115</tt>.<br>
+: The original revision id was <tt>188868111</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 11: / Line 11: @@
 [[POTE tuning|POTE generator]]: 701.736
+Map: [&lt;1 0 15|, &lt;0 1 -8|]
+EDOs: 12, 29, 41, 53, 118, 171, 289, 460, 749
 ==Seven limit children==
@@ Line 28: / Line 31: @@
 [[POTE tuning|POTE generator]]: 702.085
+Map: [&lt;1 0 15 25|, &lt;0 1 -8 -14|]
+EDOs: 12, 29, 41, 53, 94
 -limit
@@ Line 40: / Line 46: @@
 Map: [&lt;1 0 15 25 -33|, &lt;0 1 -8 -14 23|]
-[[edo|Edos]]: [[94edo|94]], [[135edo|135]]
+[[edo|Edos]]: [[41edo|41]], [[53edo|53]], [[94edo|94]], [[135edo|135]]
 ===Guiron===
@@ Line 52: / Line 58: @@
 [[POTE tuning|POTE generator]]: 233.930
+Map: [&lt;1 1 7 3|, &lt;0 3 -24 -1|]
+EDOs: 36, 41, 77, 118
 -limit
@@ Line 62: / Line 71: @@
 Map: [&lt;1 1 7 3 -2|, &lt;0 3 -24 -1 28|]
-[[edo|Edos]]: [[118edo|118]], [[159edo|159]], [[200edo|200]]
+[[edo|Edos]]: [[41edo|41]], [[77edo|77]], [[118edo|118]], [[159edo|159]], [[200edo|200]]
 ===Pontiac===
@@ Line 80: / Line 89: @@
 Map: [&lt;1 0 15 -59|, &lt;0 1 -8 39|]
-[[edo|Edos]]: [[171edo|171]], [[1079edo|1079]], [[1250edo|1250]], [[1421edo|1421]]
+[[edo|Edos]]: [[53edo|53]], [[118edo|118]], [[171edo|171]], [[1079edo|1079]], [[1250edo|1250]], [[1421edo|1421]]
 ===Grackle===
@@ Line 143: / Line 152: @@
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.736&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 0 15|, &amp;lt;0 1 -8|]&lt;br /&gt;
+EDOs: 12, 29, 41, 53, 118, 171, 289, 460, 749&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
@@ Line 160: / Line 172: @@
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 702.085&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 0 15 25|, &amp;lt;0 1 -8 -14|]&lt;br /&gt;
+EDOs: 12, 29, 41, 53, 94&lt;br /&gt;
 &lt;br /&gt;
 -limit&lt;br /&gt;
@@ Line 172: / Line 187: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 15 25 -33|, &amp;lt;0 1 -8 -14 23|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, &lt;a class="wiki_link" href="/135edo"&gt;135&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, &lt;a class="wiki_link" href="/135edo"&gt;135&lt;/a&gt;&lt;br /&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-Guiron"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Guiron&lt;/h3&gt;
@@ Line 184: / Line 199: @@
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 233.930&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 1 7 3|, &amp;lt;0 3 -24 -1|]&lt;br /&gt;
+EDOs: 36, 41, 77, 118&lt;br /&gt;
 &lt;br /&gt;
 -limit&lt;br /&gt;
@@ Line 194: / Line 212: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 7 3 -2|, &amp;lt;0 3 -24 -1 28|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/118edo"&gt;118&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/200edo"&gt;200&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/77edo"&gt;77&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118&lt;/a&gt;, &lt;a class="wiki_link" href="/159edo"&gt;159&lt;/a&gt;, &lt;a class="wiki_link" href="/200edo"&gt;200&lt;/a&gt;&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-Pontiac"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Pontiac&lt;/h3&gt;
@@ Line 212: / Line 230: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 15 -59|, &amp;lt;0 1 -8 39|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/171edo"&gt;171&lt;/a&gt;, &lt;a class="wiki_link" href="/1079edo"&gt;1079&lt;/a&gt;, &lt;a class="wiki_link" href="/1250edo"&gt;1250&lt;/a&gt;, &lt;a class="wiki_link" href="/1421edo"&gt;1421&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118&lt;/a&gt;, &lt;a class="wiki_link" href="/171edo"&gt;171&lt;/a&gt;, &lt;a class="wiki_link" href="/1079edo"&gt;1079&lt;/a&gt;, &lt;a class="wiki_link" href="/1250edo"&gt;1250&lt;/a&gt;, &lt;a class="wiki_link" href="/1421edo"&gt;1421&lt;/a&gt;&lt;br /&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-Grackle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Grackle&lt;/h3&gt;

Schismatic family: Difference between revisions

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