Sycamore 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>2011-06-19 15:23:52 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-19 16:23:22 UTC</tt>.<br>

: The original revision id was <tt>~~237577799~~</tt>.<br>

: The original revision id was <tt>237584385</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 head of the sycamore family is 5-limit sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11> = 48828125/47775744. The dual of the monzo is the wedgie, <<11 6 -16||, which tells us that six chromatic semitone ~~generators~~ give 5/4 (and hence five 6/5) and eleven give 3/2. [[94edo]] supports sycamore, and 5\94 is reommendable as a generator. It can be described as the 19&94 temperament, and uses a decidedly flat version of the chromatic semitone as a generator. MOS of 18 or 19 notes to the octave give enough room for sycamore's triads, but 37 notes can be tried by the adventurous.

<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 head of the sycamore family is [[5-limit]] sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11> = 48828125/47775744. The dual of the [[monzo]] is the [[wedgie]], <<11 6 -16||, which tells us that six chromatic semitone [[generator]]s give 5/4 (and hence five 6/5) and eleven give 3/2. [[94edo]] supports sycamore, and 5\94 is reommendable as a generator. It can be described as the 19&94 temperament, and uses a decidedly flat version of the chromatic semitone as a generator. [[MOS]] of 18 or 19 notes to the octave give enough room for sycamore's triads, but 37 notes can be tried by the adventurous.

Another possible tuning uses a generator which is a pure 3/2 divided into 11 parts, and this makes the generator chain of sycamore exactly the same as [[Carlos Beta]]. In fact, Carlos Beta is characterized by Carlos as taking five steps to reach 6/5 and six to reach 5/4, which means it tempers out the sycamore comma. It can be described as the generator chain of sycamore, or sycamore can be called Carlos Beta with octaves.

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Map: [<1 1 2|, <0 11 6|]

EDOs: 18, 19, 56, 75, 94, 207, 508

EDOs: [[18edo|18]], [[19edo|19]], [[56edo|56]], [[75edo|75]], [[94edo|94]], 207, 508

==Seven limit children==

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Map: [<1 1 2 2 4|, <0 11 6 15 -10|]

EDOs: 18, 19, 37, 56

EDOs: 18, 19, [[37edo|37]], 56

===Betic===

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EDOs: 19, 75, 94, 207</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>Sycamore family</title></head><body>The head of the sycamore family is 5-limit sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11&gt; = 48828125/47775744. The dual of the monzo is the wedgie, &lt;&lt;11 6 -16||, which tells us that six chromatic semitone ~~generators~~ 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. MOS 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 />

<br />

Another possible tuning uses a generator which is a pure 3/2 divided into 11 parts, and this makes the generator chain of sycamore exactly the same as <a class="wiki_link" href="/Carlos%20Beta">Carlos Beta</a>. In fact, Carlos Beta is characterized by Carlos as taking five steps to reach 6/5 and six to reach 5/4, which means it tempers out the sycamore comma. It can be described as the generator chain of sycamore, or sycamore can be called Carlos Beta with octaves.<br />

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<br />

Map: [&lt;1 1 2|, &lt;0 11 6|]<br />

EDOs: 18, 19, 56, 75, 94, 207, 508<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>, 207, 508<br />

<br />

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

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<br />

Map: [&lt;1 1 2 2 4|, &lt;0 11 6 15 -10|]<br />

EDOs: 18, 19, 37, 56<br />

EDOs: 18, 19, <a class="wiki_link" href="/37edo">37</a>, 56<br />

<br />

<h3 id="toc2"><a name="x-Seven limit children-Betic"></a>Betic</h3>

@@ 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>2011-06-19 15:23:52 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-19 16:23:22 UTC</tt>.<br>
-: The original revision id was <tt>237577799</tt>.<br>
+: The original revision id was <tt>237584385</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 head of the sycamore family is 5-limit sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11&gt; = 48828125/47775744. The dual of the monzo is the wedgie, &lt;&lt;11 6 -16||, which tells us that six chromatic semitone generators give 5/4 (and hence five 6/5) and eleven give 3/2. [[94edo]] 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. MOS of 18 or 19 notes to the octave give enough room for sycamore's triads, but 37 notes can be tried by the adventurous.
+<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 head of the sycamore family is [[5-limit]] sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11&gt; = 48828125/47775744. The dual of the [[monzo]] is the [[wedgie]], &lt;&lt;11 6 -16||, which tells us that six chromatic semitone [[generator]]s give 5/4 (and hence five 6/5) and eleven give 3/2. [[94edo]] 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. [[MOS]] of 18 or 19 notes to the octave give enough room for sycamore's triads, but 37 notes can be tried by the adventurous.
 Another possible tuning uses a generator which is a pure 3/2 divided into 11 parts, and this makes the generator chain of sycamore exactly the same as [[Carlos Beta]]. In fact, Carlos Beta is characterized by Carlos as taking five steps to reach 6/5 and six to reach 5/4, which means it tempers out the sycamore comma. It can be described as the generator chain of sycamore, or sycamore can be called Carlos Beta with octaves.
@@ Line 13: / Line 13: @@
 Map: [&lt;1 1 2|, &lt;0 11 6|]
-EDOs: 18, 19, 56, 75, 94, 207, 508
+EDOs: [[18edo|18]], [[19edo|19]], [[56edo|56]], [[75edo|75]], [[94edo|94]], 207, 508
 ==Seven limit children==
@@ Line 34: / Line 34: @@
 Map: [&lt;1 1 2 2 4|, &lt;0 11 6 15 -10|]
-EDOs: 18, 19, 37, 56
+EDOs: 18, 19, [[37edo|37]], 56
 ===Betic===
@@ Line 54: / Line 54: @@
 EDOs: 19, 75, 94, 207</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;Sycamore family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The head of the sycamore family is 5-limit sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11&amp;gt; = 48828125/47775744. The dual of the monzo is the wedgie, &amp;lt;&amp;lt;11 6 -16||, which tells us that six chromatic semitone generators give 5/4 (and hence five 6/5) and eleven give 3/2. &lt;a class="wiki_link" href="/94edo"&gt;94edo&lt;/a&gt; supports sycamore, and 5\94 is reommendable as a generator. It can be described as the 19&amp;amp;94 temperament, and uses a decidedly flat version of the chromatic semitone as a generator. MOS of 18 or 19 notes to the octave give enough room for sycamore's triads, but 37 notes can be tried by the adventurous.&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;Sycamore family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The head of the sycamore family is &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; sycamore, which tempers out (25/24)^6/(5/4) = |-16 -6 11&amp;gt; = 48828125/47775744. The dual of the &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;, &amp;lt;&amp;lt;11 6 -16||, which tells us that six chromatic semitone &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt;s give 5/4 (and hence five 6/5) and eleven give 3/2. &lt;a class="wiki_link" href="/94edo"&gt;94edo&lt;/a&gt; supports sycamore, and 5\94 is reommendable as a generator. It can be described as the 19&amp;amp;94 temperament, and uses a decidedly flat version of the chromatic semitone as a generator. &lt;a class="wiki_link" href="/MOS"&gt;MOS&lt;/a&gt; of 18 or 19 notes to the octave give enough room for sycamore's triads, but 37 notes can be tried by the adventurous.&lt;br /&gt;
 &lt;br /&gt;
 Another possible tuning uses a generator which is a pure 3/2 divided into 11 parts, and this makes the generator chain of sycamore exactly the same as &lt;a class="wiki_link" href="/Carlos%20Beta"&gt;Carlos Beta&lt;/a&gt;. In fact, Carlos Beta is characterized by Carlos as taking five steps to reach 6/5 and six to reach 5/4, which means it tempers out the sycamore comma. It can be described as the generator chain of sycamore, or sycamore can be called Carlos Beta with octaves.&lt;br /&gt;
@@ Line 61: / Line 61: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 2|, &amp;lt;0 11 6|]&lt;br /&gt;
-EDOs: 18, 19, 56, 75, 94, 207, 508&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/18edo"&gt;18&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/56edo"&gt;56&lt;/a&gt;, &lt;a class="wiki_link" href="/75edo"&gt;75&lt;/a&gt;, &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, 207, 508&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;
@@ Line 82: / Line 82: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 2 2 4|, &amp;lt;0 11 6 15 -10|]&lt;br /&gt;
-EDOs: 18, 19, 37, 56&lt;br /&gt;
+EDOs: 18, 19, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;, 56&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Seven limit children-Betic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Betic&lt;/h3&gt;