Würschmidt family: Difference between revisions
Wikispaces>xenwolf **Imported revision 235960016 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 240555349 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-08 16:44:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>240555349</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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Commas: 2401/2400, 3136/3125 | Commas: 2401/2400, 3136/3125 | ||
[[POTE tuning|POTE generator]]: 193.898 | [[POTE tuning|POTE generator]]: ~28/25 = 193.898 | ||
Map: [<1 15 4 7|, <0 -16 -2 -5|] | Map: [<1 15 4 7|, <0 -16 -2 -5|] | ||
<<16 2 5 -34 -37 6|| | |||
EDOs: [[6edo|6]], [[31edo|31]], [[68edo|68]], [[99edo|99]], [[229edo|229]], [[328edo|328]] | |||
Badness: 0.0203 | |||
==11-limit== | |||
Commas: 243/242, 441/440, 3136/3125 | |||
[[POTE tuning|POTE generator]]: ~28/25 = 193.840 | |||
Map: [<1 15 4 7 37|, <0 -16 -2 -5 -40|] | |||
EDOs: 31, 130 | |||
Badness: 0.0211 | |||
</pre></div> | |||
<h4>Original HTML content:</h4> | <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><!-- ws:start:WikiTextTocRule: | <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><!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#Wuerschmidt">Wuerschmidt</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Wurschmidt">Wurschmidt</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Worschmidt">Worschmidt</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Whirrschmidt">Whirrschmidt</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Hemiwuerschmift">Hemiwuerschmift</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:22 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Wuerschmidt"></a><!-- ws:end:WikiTextHeadingRule:0 -->Wuerschmidt</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Wuerschmidt"></a><!-- ws:end:WikiTextHeadingRule:0 -->Wuerschmidt</h1> | ||
The <a class="wiki_link" href="/5-limit">5-limit</a> parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its <a class="wiki_link" href="/monzo">monzo</a> is |17 1 -8&gt;, and flipping that yields &lt;&lt;8 1 17|| for the wedgie. This tells us the <a class="wiki_link" href="/generator">generator</a> 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. 10\31, 11\34 or 21\65 are possible generators and other tunings include 96edo, 99edo 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 <a class="wiki_link" href="/minimax%20tuning">minimax tuning</a>. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28, 31 and 34 note <a class="wiki_link" href="/MOS">MOS</a> all possibilities.<br /> | The <a class="wiki_link" href="/5-limit">5-limit</a> parent comma for the wuerschmidt family is 393216/390625, known as Wuerschmidt's comma. Its <a class="wiki_link" href="/monzo">monzo</a> is |17 1 -8&gt;, and flipping that yields &lt;&lt;8 1 17|| for the wedgie. This tells us the <a class="wiki_link" href="/generator">generator</a> 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. 10\31, 11\34 or 21\65 are possible generators and other tunings include 96edo, 99edo 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 <a class="wiki_link" href="/minimax%20tuning">minimax tuning</a>. Wuerschmidt is well-supplied with MOS scales, with 10, 13, 16, 19, 22, 25, 28, 31 and 34 note <a class="wiki_link" href="/MOS">MOS</a> all possibilities.<br /> | ||
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Commas: 2401/2400, 3136/3125<br /> | Commas: 2401/2400, 3136/3125<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 193.898<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~28/25 = 193.898<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 15 4 7|, &lt;0 -16 -2 -5|]<br /> | Map: [&lt;1 15 4 7|, &lt;0 -16 -2 -5|]<br /> | ||
&lt;&lt;16 2 5 -34 -37 6||<br /> | |||
EDOs: <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/99edo">99</a>, <a class="wiki_link" href="/229edo">229</a>, <a class="wiki_link" href="/328edo">328</a><br /> | |||
Badness: 0.0203<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Hemiwuerschmift-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2> | |||
Commas: 243/242, 441/440, 3136/3125<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~28/25 = 193.840<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 15 4 7 37|, &lt;0 -16 -2 -5 -40|]<br /> | |||
EDOs: 31, 130<br /> | |||
Badness: 0.0211</body></html></pre></div> | |||