Würschmidt family: Difference between revisions
Wikispaces>Natebedell **Imported revision 250966732 - Original comment: ** |
Wikispaces>guest **Imported revision 262338164 - 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:guest|guest]] and made on <tt>2011-10-06 16:34:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>262338164</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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EDOs: [[6edo|6]], [[31edo|31]], [[68edo|68]], [[99edo|99]], [[229edo|229]], [[328edo|328]] | EDOs: [[6edo|6]], [[31edo|31]], [[68edo|68]], [[99edo|99]], [[229edo|229]], [[328edo|328]] | ||
Badness: 0.0203 | Badness: 0.0203 | ||
=Doppelwuerschmidt= | |||
Doppelwuerschmidt uses a generator an approximate 25th harmonic for the genarator. To arrive exactly at 6/1, cents (775.489)^4 is best, and yields a spanking 14-note sLsssLssssLssss scale. In addition to 25/16 and 6/1, it also arrives approximates many other consonanzen, like 7/4, 7/6, 11/9, etc. and especially 11/8. | |||
Commas: 390625/279963 etc. | |||
[[POTE tuning|POTE generator]]: ~25/16 = 775 c | |||
Map: | |||
EDOs: (if it works for wuerschmidt it works for doppelwuerschmidt) | |||
Badness: | |||
==11-limit== | ==11-limit== | ||
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Map: [<1 15 4 7 37|, <0 -16 -2 -5 -40|] | Map: [<1 15 4 7 37|, <0 -16 -2 -5 -40|] | ||
EDOs: 31, 130 | EDOs: 31, 130 | ||
Badness: 0.0211</pre></div> | Badness: 0.0211 | ||
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;">around 775.489 which is approximately </span></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:16:&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:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#Wuerschmidt">Wuerschmidt</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Wurschmidt">Wurschmidt</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Worschmidt">Worschmidt</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Whirrschmidt">Whirrschmidt</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Hemiwuerschmidt">Hemiwuerschmidt</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Doppelwuerschmidt">Doppelwuerschmidt</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:25 --><!-- 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, and named after José Würschmidt, 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, and named after José Würschmidt, 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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Badness: 0.0203<br /> | Badness: 0.0203<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id=" | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Doppelwuerschmidt"></a><!-- ws:end:WikiTextHeadingRule:12 -->Doppelwuerschmidt</h1> | ||
Doppelwuerschmidt uses a generator an approximate 25th harmonic for the genarator. To arrive exactly at 6/1, cents (775.489)^4 is best, and yields a spanking 14-note sLsssLssssLssss scale. In addition to 25/16 and 6/1, it also arrives approximates many other consonanzen, like 7/4, 7/6, 11/9, etc. and especially 11/8.<br /> | |||
<br /> | |||
Commas: 390625/279963 etc.<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~25/16 = 775 c<br /> | |||
<br /> | |||
Map:<br /> | |||
EDOs: (if it works for wuerschmidt it works for doppelwuerschmidt)<br /> | |||
Badness:<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Doppelwuerschmidt-11-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->11-limit</h2> | |||
Commas: 243/242, 441/440, 3136/3125<br /> | Commas: 243/242, 441/440, 3136/3125<br /> | ||
<br /> | <br /> | ||
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Map: [&lt;1 15 4 7 37|, &lt;0 -16 -2 -5 -40|]<br /> | Map: [&lt;1 15 4 7 37|, &lt;0 -16 -2 -5 -40|]<br /> | ||
EDOs: 31, 130<br /> | EDOs: 31, 130<br /> | ||
Badness: 0.0211</body></html></pre></div> | Badness: 0.0211<br /> | ||
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: -25px; width: 1px;">around 775.489 which is approximately </span></body></html></pre></div> | |||