Meantone 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>2010-05-~~31 02~~:55:57 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-11-13 16:35:15 UTC</tt>.<br>

: The original revision id was <tt>~~145972469~~</tt>.<br>

: The original revision id was <tt>179212561</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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===Mothra===

Mothra, with wedgie <<3 12 -1 12 -10 -36||, splits the fifth into three 8/7 generators. It uses 1029/1024, the gamelisma, to accomplish this deed and also tempers out 1728/1715, the orwell comma. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a MOS should be used as a scale to get the most out of mothra.

Commas: 81/80, 1029/1024

7 and 9 limit minimax 1/4 comma

[|1 0 0 0>, |1 0 1/4 0>, |0 0 1 0>, |3 0 -1/12 0>]

Eigenmonzos: 2, 5

Algebraic generator: Rabrindanath, largest real root of x^8-3x^2+1, or 232.0774 cents.

Map: [<1 1 0 3|, <0 3 12 -1|]

Generators: 2, 8/7

===Squares===

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<h3 id="toc8"><a name="x-Seven limit children-Mothra"></a>Mothra</h3>

Mothra, with wedgie &lt;&lt;3 12 -1 12 -10 -36||, splits the fifth into three 8/7 generators. It uses 1029/1024, the gamelisma, to accomplish this deed and also tempers out 1728/1715, the orwell comma. Using <a class="wiki_link" href="/31edo">31edo</a> with a generator of 6/31 is an excellent tuning choice. Once again something other than a MOS should be used as a scale to get the most out of mothra.<br />

<br />

Commas: 81/80, 1029/1024<br />

<br />

7 and 9 limit minimax 1/4 comma <br />

[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |3 0 -1/12 0&gt;]<br />

Eigenmonzos: 2, 5<br />

<br />

Algebraic generator: Rabrindanath, largest real root of x^8-3x^2+1, or 232.0774 cents.<br />

Map: [&lt;1 1 0 3|, &lt;0 3 12 -1|]<br />

Generators: 2, 8/7<br />

<br />

<h3 id="toc9"><a name="x-Seven limit children-Squares"></a>Squares</h3>

@@ 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>2010-05-31 02:55:57 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-11-13 16:35:15 UTC</tt>.<br>
-: The original revision id was <tt>145972469</tt>.<br>
+: The original revision id was <tt>179212561</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 34: / Line 34: @@
 ===Mothra===
 Mothra, with wedgie &lt;&lt;3 12 -1 12 -10 -36||, splits the fifth into three 8/7 generators. It uses 1029/1024, the gamelisma, to accomplish this deed and also tempers out 1728/1715, the orwell comma. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a MOS should be used as a scale to get the most out of mothra.
+Commas: 81/80, 1029/1024
+and 9 limit minimax 1/4 comma
+[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |3 0 -1/12 0&gt;]
+Eigenmonzos: 2, 5
+Algebraic generator: Rabrindanath, largest real root of x^8-3x^2+1, or 232.0774 cents.
+Map: [&lt;1 1 0 3|, &lt;0 3 12 -1|]
+Generators: 2, 8/7
 ===Squares===
@@ Line 69: / Line 79: @@
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x-Seven limit children-Mothra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Mothra&lt;/h3&gt;
 Mothra, with wedgie &amp;lt;&amp;lt;3 12 -1 12 -10 -36||, splits the fifth into three 8/7 generators. It uses 1029/1024, the gamelisma, to accomplish this deed and also tempers out 1728/1715, the orwell comma. Using &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; with a generator of 6/31 is an excellent tuning choice. Once again something other than a MOS should be used as a scale to get the most out of mothra.&lt;br /&gt;
+&lt;br /&gt;
+Commas: 81/80, 1029/1024&lt;br /&gt;
+&lt;br /&gt;
+and 9 limit minimax 1/4 comma &lt;br /&gt;
+[|1 0 0 0&amp;gt;, |1 0 1/4 0&amp;gt;, |0 0 1 0&amp;gt;, |3 0 -1/12 0&amp;gt;]&lt;br /&gt;
+Eigenmonzos: 2, 5&lt;br /&gt;
+&lt;br /&gt;
+Algebraic generator: Rabrindanath, largest real root of x^8-3x^2+1, or 232.0774 cents.&lt;br /&gt;
+Map: [&amp;lt;1 1 0 3|, &amp;lt;0 3 12 -1|]&lt;br /&gt;
+Generators: 2, 8/7&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x-Seven limit children-Squares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Squares&lt;/h3&gt;