Schismatic family: Difference between revisions

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>2010-09-21 00:37:00 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-09-21 02:55:52 UTC</tt>.<br>

: The original revision id was <tt>~~164157035~~</tt>.<br>

: The original revision id was <tt>164168875</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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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>]

~~Eigenmonzos~~: 2, 7/6

[[Eigenmonzo]]s: 2, 7/6

9-limit: [|1 0 0 0>, |25/16 1/8 0 -1/16>,

Line 34:

Map: [<1 0 15 25 -33|, <0 1 -8 -14 23|]

Edos: 94, 135

[[edo|Edos]]: [[94edo|94]], [[135edo|135]]

===Guiron===

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Map: [<1 1 7 3 -2|, <0 3 -24 -1 28|]

Edos: 118, 159, 200

[[edo|Edos]]: [[118edo|118]], [[159edo|159]], [[200edo|200]]

===Pontiac===

Line 68:

Map: [<1 0 15 -59|, <0 1 -8 39|]

Edos: 171, 1079, 1250, 1421

[[edo|Edos]]: [[171edo|171]], [[1079edo|1079]], [[1250edo|1250]], [[1421edo|1421]]

===Grackle===

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Map: [<1 0 15 -44|, <0 1 -8 -26|]

Edos: 77, 89

[[edo|Edos]]: [[77edo|77]], [[89edo|89]]

===Bischismic===

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Map: [<2 0 30 69|, <0 1 -8 -20|]

Edos: 118, 130, 248, 378, 508

[[edo|Edos]]: [[118edo|118]], [[130edo|130]], [[248edo|248]], [[378edo|378]], [[508edo|508]]

===Term===

Line 104:

Map: [<3 0 45 94|, <0 1 -8 -18|]

Edos: 171, 1038, 1209

[[edo|Edos]]: [[171edo|171]], [[1038edo|1038]], [[1209edo|1209]]

===Sesquiquartififths===

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Map: [<1 1 7 5|, <0 4 -32 -15|]

Edos: 171, 643</pre></div>

[[edo|Edos]]: [[171edo|171]], [[643edo|643]]</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"><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 />

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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 />

~~Eigenmonzos~~: 2, 7/6<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 />

Line 146:

<br />

Map: [&lt;1 0 15 25 -33|, &lt;0 1 -8 -14 23|]<br />

Edos: 94, 135<br />

<br />

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

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<br />

Map: [&lt;1 1 7 3 -2|, &lt;0 3 -24 -1 28|]<br />

Edos: 118, 159, 200<br />

<br />

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

Line 180:

<br />

Map: [&lt;1 0 15 -59|, &lt;0 1 -8 39|]<br />

Edos: 171, 1079, 1250, 1421<br />

<br />

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

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<br />

Map: [&lt;1 0 15 -44|, &lt;0 1 -8 -26|]<br />

Edos: 77, 89<br />

<br />

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

Line 204:

<br />

Map: [&lt;2 0 30 69|, &lt;0 1 -8 -20|]<br />

Edos: 118, 130, 248, 378, 508<br />

<br />

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

Line 216:

<br />

Map: [&lt;3 0 45 94|, &lt;0 1 -8 -18|]<br />

Edos: 171, 1038, 1209<br />

<br />

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

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<br />

Map: [&lt;1 1 7 5|, &lt;0 4 -32 -15|]<br />

Edos: 171, 643</body></html></pre></div>

@@ 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>2010-09-21 00:37:00 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-09-21 02:55:52 UTC</tt>.<br>
-: The original revision id was <tt>164157035</tt>.<br>
+: The original revision id was <tt>164168875</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 19: / Line 19: @@
 -limit: [|1 0 0 0&gt;, |5/3 1/15 0 -1/15&gt;,
 |5/3 -8/15 0 8/15&gt;, |5/3 -14/15 0 14/15&gt;]
-Eigenmonzos: 2, 7/6
+[[Eigenmonzo]]s: 2, 7/6
 -limit: [|1 0 0 0&gt;, |25/16 1/8 0 -1/16&gt;,
@@ Line 34: / Line 34: @@
 Map: [&lt;1 0 15 25 -33|, &lt;0 1 -8 -14 23|]
-Edos: 94, 135
+[[edo|Edos]]: [[94edo|94]], [[135edo|135]]
 ===Guiron===
@@ Line 52: / Line 52: @@
 Map: [&lt;1 1 7 3 -2|, &lt;0 3 -24 -1 28|]
-Edos: 118, 159, 200
+[[edo|Edos]]: [[118edo|118]], [[159edo|159]], [[200edo|200]]
 ===Pontiac===
@@ Line 68: / Line 68: @@
 Map: [&lt;1 0 15 -59|, &lt;0 1 -8 39|]
-Edos: 171, 1079, 1250, 1421
+[[edo|Edos]]: [[171edo|171]], [[1079edo|1079]], [[1250edo|1250]], [[1421edo|1421]]
 ===Grackle===
@@ Line 80: / Line 80: @@
 Map: [&lt;1 0 15 -44|, &lt;0 1 -8 -26|]
-Edos: 77, 89
+[[edo|Edos]]: [[77edo|77]], [[89edo|89]]
 ===Bischismic===
@@ Line 92: / Line 92: @@
 Map: [&lt;2 0 30 69|, &lt;0 1 -8 -20|]
-Edos: 118, 130, 248, 378, 508
+[[edo|Edos]]: [[118edo|118]], [[130edo|130]], [[248edo|248]], [[378edo|378]], [[508edo|508]]
 ===Term===
@@ Line 104: / Line 104: @@
 Map: [&lt;3 0 45 94|, &lt;0 1 -8 -18|]
-Edos: 171, 1038, 1209
+[[edo|Edos]]: [[171edo|171]], [[1038edo|1038]], [[1209edo|1209]]
 ===Sesquiquartififths===
@@ Line 116: / Line 116: @@
 Map: [&lt;1 1 7 5|, &lt;0 4 -32 -15|]
-Edos: 171, 643</pre></div>
+[[edo|Edos]]: [[171edo|171]], [[643edo|643]]</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;Schismatic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;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 &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |-15 8 1&amp;gt;, and flipping that yields &amp;lt;&amp;lt;1 -8 -15|| for the &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;. 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. &lt;br /&gt;
@@ Line 131: / Line 131: @@
 -limit: [|1 0 0 0&amp;gt;, |5/3 1/15 0 -1/15&amp;gt;,&lt;br /&gt;
 |5/3 -8/15 0 8/15&amp;gt;, |5/3 -14/15 0 14/15&amp;gt;]&lt;br /&gt;
-Eigenmonzos: 2, 7/6&lt;br /&gt;
+&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 7/6&lt;br /&gt;
 &lt;br /&gt;
 -limit: [|1 0 0 0&amp;gt;, |25/16 1/8 0 -1/16&amp;gt;, &lt;br /&gt;
@@ Line 146: / Line 146: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 15 25 -33|, &amp;lt;0 1 -8 -14 23|]&lt;br /&gt;
-Edos: 94, 135&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;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 164: / Line 164: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 7 3 -2|, &amp;lt;0 3 -24 -1 28|]&lt;br /&gt;
-Edos: 118, 159, 200&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;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 180: / Line 180: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 15 -59|, &amp;lt;0 1 -8 39|]&lt;br /&gt;
-Edos: 171, 1079, 1250, 1421&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;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;
@@ Line 192: / Line 192: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 15 -44|, &amp;lt;0 1 -8 -26|]&lt;br /&gt;
-Edos: 77, 89&lt;br /&gt;
+&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/77edo"&gt;77&lt;/a&gt;, &lt;a class="wiki_link" href="/89edo"&gt;89&lt;/a&gt;&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-Bischismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Bischismic&lt;/h3&gt;
@@ Line 204: / Line 204: @@
 &lt;br /&gt;
 Map: [&amp;lt;2 0 30 69|, &amp;lt;0 1 -8 -20|]&lt;br /&gt;
-Edos: 118, 130, 248, 378, 508&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="/130edo"&gt;130&lt;/a&gt;, &lt;a class="wiki_link" href="/248edo"&gt;248&lt;/a&gt;, &lt;a class="wiki_link" href="/378edo"&gt;378&lt;/a&gt;, &lt;a class="wiki_link" href="/508edo"&gt;508&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-Term"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Term&lt;/h3&gt;
@@ Line 216: / Line 216: @@
 &lt;br /&gt;
 Map: [&amp;lt;3 0 45 94|, &amp;lt;0 1 -8 -18|]&lt;br /&gt;
-Edos: 171, 1038, 1209&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="/1038edo"&gt;1038&lt;/a&gt;, &lt;a class="wiki_link" href="/1209edo"&gt;1209&lt;/a&gt;&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-Sesquiquartififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Sesquiquartififths&lt;/h3&gt;
@@ Line 228: / Line 228: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 7 5|, &amp;lt;0 4 -32 -15|]&lt;br /&gt;
-Edos: 171, 643&lt;/body&gt;&lt;/html&gt;</pre></div>
+&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="/643edo"&gt;643&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>