Schismatic 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>2010-09-20 12:47:04 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-20 13:30:09 UTC</tt>.<br>

: The original revision id was <tt>~~163976707~~</tt>.<br>

: The original revision id was <tt>163991491</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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===Garibaldi===

~~7-limit~~

Commas: {225/224, 3125/3087}

~~Minimax~~ tuning:

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>]

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[|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>]

~~Eigenmonzso~~: 2, 9/7

Eigenmonzos: 2, 9/7

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

Edos: 94, 135

===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

Edos: 94, ~~135~~

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

</pre></div>

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

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

~~<br />~~

~~7-limit<br />~~

Commas: {225/224, 3125/3087}<br />

<br />

~~Minimax~~ tuning:<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 />

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[|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 />

~~Eigenmonzso~~: 2, 9/7<br />

Eigenmonzos: 2, 9/7<br />

<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-Pontiac"></a>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 />

Edos: 94, ~~135~~</body></html></pre></div>

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

Edos: 171, 1079, 1250, 1421</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>2010-09-20 12:47:04 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-09-20 13:30:09 UTC</tt>.<br>
-: The original revision id was <tt>163976707</tt>.<br>
+: The original revision id was <tt>163991491</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 14: / Line 14: @@
 ===Garibaldi===
--limit
 Commas: {225/224, 3125/3087}
-Minimax tuning:
+-limit minimax tuning:
 -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;]
@@ Line 33: / Line 31: @@
 [|1 0 0 0 0&gt;, |25/16 1/8 0 -1/16 0&gt;, |5/2 -1 0 1/2 0&gt;,
 |25/8 -7/4 0 7/8 0&gt;, |47/16 23/8 0 -23/16 0&gt;]
-Eigenmonzso: 2, 9/7
+Eigenmonzos: 2, 9/7
 Map: [&lt;1 0 15 25 -33|, &lt;0 1 -8 -14 23|]
+Edos: 94, 135
+===Pontiac===
+Commas: {32805/32768, 4375/4374}
+-limit minimax:
+[|1 0 0 0&gt;, |74/47 0 -1/47 1/47&gt;, |113/47 0 8/47 -8/47&gt;,
+|113/47 0 -39/47 39/47&gt;]
+Eigenmonzos: 2, 7/5
+-limit minimax:
+[|1 0 0 0&gt;, |3/2 1/5 -1/10 0&gt;,
+|3 -8/5 4/5 0&gt;, |-1/2 39/5 -39/10 0&gt;]
+Eigenmonzos: 2, 10/9
-Edos: 94, 135
+Map: [&lt;1 0 15 -59|, &lt;0 1 -8 39|]
-</pre></div>
+Edos: 171, 1079, 1250, 1421</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 48: / Line 60: @@
 &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-Garibaldi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Garibaldi&lt;/h3&gt;
-&lt;br /&gt;
--limit&lt;br /&gt;
 Commas: {225/224, 3125/3087}&lt;br /&gt;
 &lt;br /&gt;
-Minimax tuning:&lt;br /&gt;
+-limit minimax tuning:&lt;br /&gt;
 -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;
@@ Line 67: / Line 77: @@
 [|1 0 0 0 0&amp;gt;, |25/16 1/8 0 -1/16 0&amp;gt;, |5/2 -1 0 1/2 0&amp;gt;,&lt;br /&gt;
 |25/8 -7/4 0 7/8 0&amp;gt;, |47/16 23/8 0 -23/16 0&amp;gt;]&lt;br /&gt;
-Eigenmonzso: 2, 9/7&lt;br /&gt;
+Eigenmonzos: 2, 9/7&lt;br /&gt;
 &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;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-Pontiac"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Pontiac&lt;/h3&gt;
+Commas: {32805/32768, 4375/4374}&lt;br /&gt;
+&lt;br /&gt;
+-limit minimax:&lt;br /&gt;
+[|1 0 0 0&amp;gt;, |74/47 0 -1/47 1/47&amp;gt;, |113/47 0 8/47 -8/47&amp;gt;, &lt;br /&gt;
+|113/47 0 -39/47 39/47&amp;gt;]&lt;br /&gt;
+Eigenmonzos: 2, 7/5&lt;br /&gt;
+&lt;br /&gt;
+-limit minimax:&lt;br /&gt;
+[|1 0 0 0&amp;gt;, |3/2 1/5 -1/10 0&amp;gt;, &lt;br /&gt;
+|3 -8/5 4/5 0&amp;gt;, |-1/2 39/5 -39/10 0&amp;gt;]&lt;br /&gt;
+Eigenmonzos: 2, 10/9&lt;br /&gt;
 &lt;br /&gt;
-Edos: 94, 135&lt;/body&gt;&lt;/html&gt;</pre></div>
+Map: [&amp;lt;1 0 15 -59|, &amp;lt;0 1 -8 39|]&lt;br /&gt;
+Edos: 171, 1079, 1250, 1421&lt;/body&gt;&lt;/html&gt;</pre></div>