Würschmidt 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>2011-03-18 18:26:38 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-02 18:38:54 UTC</tt>.<br>

: The original revision id was <tt>~~211898060~~</tt>.<br>

: The original revision id was <tt>233912702</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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=Wuerschmidt=

The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8>, and flipping that yields <<8 1 -17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.

The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8>, and flipping that yields <<8 1 17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.

[[POTE tuning|POTE generator]]: 387.799

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<br />

<h1 id="toc0"><a name="Wuerschmidt"></a>Wuerschmidt</h1>

The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8&gt;, and flipping that yields &lt;&lt;8 1 -17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.<br />

The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8&gt;, and flipping that yields &lt;&lt;8 1 17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 387.799<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>2011-03-18 18:26:38 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-02 18:38:54 UTC</tt>.<br>
-: The original revision id was <tt>211898060</tt>.<br>
+: The original revision id was <tt>233912702</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 9: / Line 9: @@
 =Wuerschmidt=
-The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8&gt;, and flipping that yields &lt;&lt;8 1 -17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.
+The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8&gt;, and flipping that yields &lt;&lt;8 1 17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.
 [[POTE tuning|POTE generator]]: 387.799
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 &lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Wuerschmidt"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Wuerschmidt&lt;/h1&gt;
-The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8&amp;gt;, and flipping that yields &amp;lt;&amp;lt;8 1 -17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.&lt;br /&gt;
+The 5-limit parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its monzo is |17 1 -8&amp;gt;, and flipping that yields &amp;lt;&amp;lt;8 1 17|| for the wedgie. This tells us the generator is a major third, and that to get to the interval class of fifths will require eight of these. In fact, (5/4)^8 * 393216/390625 = 6. 14/53 or 21/65 are excellent generators, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo, 140edo and 164edo. Another tuning solution is to sharpen the major third by 1/8th of a Wuerschmift comma, which is to say by 1.43 cents, and thereby achieve pure fifths; this is the minimax tuning. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 387.799&lt;br /&gt;