Sycamore family: Difference between revisions
Wikispaces>xenwolf **Imported revision 238243837 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 277285838 - 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>2011-11-19 19:58:12 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>277285838</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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Map: [<1 1 2|, <0 11 6|] | Map: [<1 1 2|, <0 11 6|] | ||
EDOs: [[18edo|18]], [[19edo|19]], [[56edo|56]], [[75edo|75]], [[94edo|94]], [[207edo| | EDOs: [[18edo|18]], [[19edo|19]], [[56edo|56]], [[75edo|75]], [[94edo|94]], [[207edo|207c]], [[301edo|301c]] | ||
==Seven limit children== | ==Seven limit children== | ||
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Map: [<1 1 2 2|, <0 11 6 15|] | Map: [<1 1 2 2|, <0 11 6 15|] | ||
EDOs: 18, 19, 56, | EDOs: 18, 19, 56, 75d | ||
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Map: [<1 1 2 2 4|, <0 11 6 15 -10|] | Map: [<1 1 2 2 4|, <0 11 6 15 -10|] | ||
EDOs: 18, 19, [[37edo|37]], 56 | EDOs: 18, 19, [[37edo|37]], [[56edo|56]] | ||
===Betic=== | ===Betic=== | ||
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Map: [<1 1 2 1|, <0 11 6 34|] | Map: [<1 1 2 1|, <0 11 6 34|] | ||
EDOs: 19, 75, 94, [[113edo|113]], [[433edo| | EDOs: 19, 75, 94, [[113edo|113]], [[133edo|133]], [[320edo|320c]], [[433edo|433cd]] | ||
11-limit | 11-limit | ||
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Map: [<1 1 2 1 5|, <0 11 6 34 -29|] | Map: [<1 1 2 1 5|, <0 11 6 34 -29|] | ||
EDOs: 19, 75, 94, | EDOs: 19, 75, 94, 207c</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>Sycamore family</title></head><body>The head of the sycamore family is <a class="wiki_link" href="/5-limit">5-limit</a> sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11&gt; = 48828125/47775744. The dual of the <a class="wiki_link" href="/monzo">monzo</a> is the <a class="wiki_link" href="/wedgie">wedgie</a>, &lt;&lt;11 6 -16||, which tells us that six chromatic semitone <a class="wiki_link" href="/generator">generator</a>s give 5/4 (and hence five 6/5) and eleven give 3/2. <a class="wiki_link" href="/94edo">94edo</a> supports sycamore, and 5\94 is reommendable as a generator. It can be described as the 19&amp;94 temperament, and uses a decidedly flat version of the chromatic semitone as a generator. <a class="wiki_link" href="/MOS">MOS</a> of 18 or 19 notes to the octave give enough room for sycamore's triads, but 37 notes can be tried by the adventurous.<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>Sycamore family</title></head><body>The head of the sycamore family is <a class="wiki_link" href="/5-limit">5-limit</a> sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11&gt; = 48828125/47775744. The dual of the <a class="wiki_link" href="/monzo">monzo</a> is the <a class="wiki_link" href="/wedgie">wedgie</a>, &lt;&lt;11 6 -16||, which tells us that six chromatic semitone <a class="wiki_link" href="/generator">generator</a>s give 5/4 (and hence five 6/5) and eleven give 3/2. <a class="wiki_link" href="/94edo">94edo</a> supports sycamore, and 5\94 is reommendable as a generator. It can be described as the 19&amp;94 temperament, and uses a decidedly flat version of the chromatic semitone as a generator. <a class="wiki_link" href="/MOS">MOS</a> of 18 or 19 notes to the octave give enough room for sycamore's triads, but 37 notes can be tried by the adventurous.<br /> | ||
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<br /> | <br /> | ||
Map: [&lt;1 1 2|, &lt;0 11 6|]<br /> | Map: [&lt;1 1 2|, &lt;0 11 6|]<br /> | ||
EDOs: <a class="wiki_link" href="/18edo">18</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/56edo">56</a>, <a class="wiki_link" href="/75edo">75</a>, <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/207edo"> | EDOs: <a class="wiki_link" href="/18edo">18</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/56edo">56</a>, <a class="wiki_link" href="/75edo">75</a>, <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/207edo">207c</a>, <a class="wiki_link" href="/301edo">301c</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> | ||
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<br /> | <br /> | ||
Map: [&lt;1 1 2 2|, &lt;0 11 6 15|]<br /> | Map: [&lt;1 1 2 2|, &lt;0 11 6 15|]<br /> | ||
EDOs: 18, 19, 56, | EDOs: 18, 19, 56, 75d<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
Map: [&lt;1 1 2 2 4|, &lt;0 11 6 15 -10|]<br /> | Map: [&lt;1 1 2 2 4|, &lt;0 11 6 15 -10|]<br /> | ||
EDOs: 18, 19, <a class="wiki_link" href="/37edo">37</a>, 56<br /> | EDOs: 18, 19, <a class="wiki_link" href="/37edo">37</a>, <a class="wiki_link" href="/56edo">56</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Betic"></a><!-- ws:end:WikiTextHeadingRule:4 -->Betic</h3> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Betic"></a><!-- ws:end:WikiTextHeadingRule:4 -->Betic</h3> | ||
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Map: [&lt;1 1 2 1|, &lt;0 11 6 34|]<br /> | Map: [&lt;1 1 2 1|, &lt;0 11 6 34|]<br /> | ||
EDOs: 19, 75, 94, <a class="wiki_link" href="/113edo">113</a>, <a class="wiki_link" href="/433edo"> | EDOs: 19, 75, 94, <a class="wiki_link" href="/113edo">113</a>, <a class="wiki_link" href="/133edo">133</a>, <a class="wiki_link" href="/320edo">320c</a>, <a class="wiki_link" href="/433edo">433cd</a><br /> | ||
<br /> | <br /> | ||
11-limit<br /> | 11-limit<br /> | ||
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<br /> | <br /> | ||
Map: [&lt;1 1 2 1 5|, &lt;0 11 6 34 -29|]<br /> | Map: [&lt;1 1 2 1 5|, &lt;0 11 6 34 -29|]<br /> | ||
EDOs: 19, 75, 94, | EDOs: 19, 75, 94, 207c</body></html></pre></div> | ||