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>2010-08-10 15:19:09 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-08-10 15:21:00 UTC</tt>.<br>

: The original revision id was <tt>~~155965685~~</tt>.<br>

: The original revision id was <tt>155965947</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>

<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">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 is about perfect as a generator, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo and 140edo. 21/65 makes an excellent wuerschmidt generator and 53/164 is even more accurate, but deciding between [[31edo]] or [34edo]] on the basis of whether you prefer flat fifths or sharp ones ~~does~~ also. 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. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.

<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;white-space: pre-wrap ! important" class="old-revision-html">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 is about perfect as a generator, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo and 140edo. 21/65 makes an excellent wuerschmidt generator and 53/164 is even more accurate, but deciding between [[31edo]] or [[34edo]] on the basis of whether you prefer flat fifths or sharp ones is also possible. 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. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.

==Seven limit children==

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Hemiwuerschmidt, which splits the major third in two and uses that for a generator, is the most important of these temperaments even with the rather large complexity for the fifth. It tempers out 3136/3125, 6144/6125 and 2401/2400. [[68edo]], [[99edo]] and [[130edo]] can all be used as tunings, but 130 is not only the most accurate, it shows how hemiwuerschmidt extends to a higher limit temperament, <<16 2 5 40 -39 -49 -48 28...</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>Würschmidt family</title></head><body>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 is about perfect as a generator, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo and 140edo. 21/65 makes an excellent wuerschmidt generator and 53/164 is even more accurate, but deciding between <a class="wiki_link" href="/31edo">31edo</a> or [34edo]] on the basis of whether you prefer flat fifths or sharp ones ~~does~~ also. 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. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.<br />

<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>Würschmidt family</title></head><body>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 is about perfect as a generator, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo and 140edo. 21/65 makes an excellent wuerschmidt generator and 53/164 is even more accurate, but deciding between <a class="wiki_link" href="/31edo">31edo</a> or <a class="wiki_link" href="/34edo">34edo</a> on the basis of whether you prefer flat fifths or sharp ones is also possible. 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. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.<br />

<br />

<h2 id="toc0"><a name="x-Seven limit children"></a>Seven limit children</h2>

@@ 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>2010-08-10 15:19:09 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-08-10 15:21:00 UTC</tt>.<br>
-: The original revision id was <tt>155965685</tt>.<br>
+: The original revision id was <tt>155965947</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>
 <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">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 is about perfect as a generator, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo  and 140edo. 21/65 makes an excellent wuerschmidt generator and 53/164 is even more accurate, but deciding between [[31edo]] or [34edo]] on the basis of whether you prefer flat fifths or sharp ones does also. 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. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.
+<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;white-space: pre-wrap ! important" class="old-revision-html">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 is about perfect as a generator, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo  and 140edo. 21/65 makes an excellent wuerschmidt generator and 53/164 is even more accurate, but deciding between [[31edo]] or [[34edo]] on the basis of whether you prefer flat fifths or sharp ones is also possible. 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. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28 31 and 34 note MOS all possibilities.
 ==Seven limit children==
@@ Line 23: / Line 23: @@
 Hemiwuerschmidt, which splits the major third in two and uses that for a generator, is the most important of these temperaments even with the rather large complexity for the fifth. It tempers out 3136/3125, 6144/6125 and 2401/2400. [[68edo]], [[99edo]] and [[130edo]] can all be used as tunings, but 130 is not only the most accurate, it shows how hemiwuerschmidt extends to a higher limit temperament, &lt;&lt;16 2 5 40 -39 -49 -48 28...</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;Würschmidt family&lt;/title&gt;&lt;/head&gt;&lt;body&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 is about perfect as a generator, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo  and 140edo. 21/65 makes an excellent wuerschmidt generator and 53/164 is even more accurate, but deciding between &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; or [34edo]] on the basis of whether you prefer flat fifths or sharp ones does also. 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. 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;
+<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;Würschmidt family&lt;/title&gt;&lt;/head&gt;&lt;body&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 is about perfect as a generator, though 9/34 also makes sense and using 19edo is possible. Other tunings include 72edo, 87edo  and 140edo. 21/65 makes an excellent wuerschmidt generator and 53/164 is even more accurate, but deciding between &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; or &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; on the basis of whether you prefer flat fifths or sharp ones is also possible. 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. 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;!-- 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;