Sycamore family: Difference between revisions

Revision as of 19:58, 19 November 2011

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This revision was by author genewardsmith and made on 2011-11-19 19:58:12 UTC.

The original revision id was 277285838.

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Original Wikitext content:

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.

[[POTE tuning|POTE generator]]: 63.779

Map: [<1 1 2|, <0 11 6|]
EDOs: [[18edo|18]], [[19edo|19]], [[56edo|56]], [[75edo|75]], [[94edo|94]], [[207edo|207c]], [[301edo|301c]]

==Seven limit children== 

===Septimal sycamore=== 
The second element of the [[Normal lists|normal comma list]] for septimal sycamore is 875/864, the keema, and it also tempers out 686/675, the senga, and 3136/3125, hemimean. It has <<11 6 15 -16 -7 18|| for a wedgie, and may also be called the 19&56 temperament. This may also be used as the name for the temperament obtained by adding 100/99 to sycamore's commas, giving unidecimal sycamore, where 10 generator steps reaches 16/11, 11 reach 3/2, and 15 give 7/4, adding a considerable dose of 11-limit harmonies to the 19-note MOS. [[75edo]] is an excellent tuning for 7-limit sycamore, and [[56edo]] for the 11-limit version.

Commas: 686/675, 875/864

[[POTE tuning|POTE generator]]: 63.995

Map: [<1 1 2 2|, <0 11 6 15|]
EDOs: 18, 19, 56, 75d


11-limit
Commas: 100/99, 385/384, 686/675

[[POTE tuning|POTE generator]]: 64.268

Map: [<1 1 2 2 4|, <0 11 6 15 -10|]
EDOs: 18, 19, [[37edo|37]], [[56edo|56]]

===Betic=== 
Septimal sycamore sharpens the fifth from where it stands in the 5-limit, and lowers accuracy in order to reach 7-limit harmonies. If we retain tunings approximately (eg 94et) or exactly those of Carlos Beta, we get the 19&94 temperament, betic, for the 7-limit. This adds 225/224 to the sycamore comma, and has <<11 6 34 -16 23 62|| as a wedgie. The Carlos Beta tuning, with pure fifths, is a good tuning choice, but 94 or 113 equal are as well. Betic extends to the 11-limit upon addition of 385/384 or 540/539 to the list of commas, which means it supports both 7 and 11-limit marvel. The wedgie starts <<11 6 34 -29 ...||.

Commas: 225/224, 1071875/1062882

[[POTE tuning|POTE generator]]: 63.701

Map: [<1 1 2 1|, <0 11 6 34|]
EDOs: 19, 75, 94, [[113edo|113]], [[133edo|133]], [[320edo|320c]], [[433edo|433cd]]

11-limit
Commas: 225/224, 385/384, 218750/216513

[[POTE tuning|POTE generator]]: 63.776

Map: [<1 1 2 1 5|, <0 11 6 34 -29|]
EDOs: 19, 75, 94, 207c

Original HTML content:

<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 />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 63.779<br />
<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">207c</a>, <a class="wiki_link" href="/301edo">301c</a><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>
 <br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Seven limit children-Septimal sycamore"></a><!-- ws:end:WikiTextHeadingRule:2 -->Septimal sycamore</h3>
 The second element of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> for septimal sycamore is 875/864, the keema, and it also tempers out 686/675, the senga, and 3136/3125, hemimean. It has &lt;&lt;11 6 15 -16 -7 18|| for a wedgie, and may also be called the 19&amp;56 temperament. This may also be used as the name for the temperament obtained by adding 100/99 to sycamore's commas, giving unidecimal sycamore, where 10 generator steps reaches 16/11, 11 reach 3/2, and 15 give 7/4, adding a considerable dose of 11-limit harmonies to the 19-note MOS. <a class="wiki_link" href="/75edo">75edo</a> is an excellent tuning for 7-limit sycamore, and <a class="wiki_link" href="/56edo">56edo</a> for the 11-limit version.<br />
<br />
Commas: 686/675, 875/864<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 63.995<br />
<br />
Map: [&lt;1 1 2 2|, &lt;0 11 6 15|]<br />
EDOs: 18, 19, 56, 75d<br />
<br />
<br />
11-limit<br />
Commas: 100/99, 385/384, 686/675<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 64.268<br />
<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>, <a class="wiki_link" href="/56edo">56</a><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>
 Septimal sycamore sharpens the fifth from where it stands in the 5-limit, and lowers accuracy in order to reach 7-limit harmonies. If we retain tunings approximately (eg 94et) or exactly those of Carlos Beta, we get the 19&amp;94 temperament, betic, for the 7-limit. This adds 225/224 to the sycamore comma, and has &lt;&lt;11 6 34 -16 23 62|| as a wedgie. The Carlos Beta tuning, with pure fifths, is a good tuning choice, but 94 or 113 equal are as well. Betic extends to the 11-limit upon addition of 385/384 or 540/539 to the list of commas, which means it supports both 7 and 11-limit marvel. The wedgie starts &lt;&lt;11 6 34 -29 ...||.<br />
<br />
Commas: 225/224, 1071875/1062882<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 63.701<br />
<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="/133edo">133</a>, <a class="wiki_link" href="/320edo">320c</a>, <a class="wiki_link" href="/433edo">433cd</a><br />
<br />
11-limit<br />
Commas: 225/224, 385/384, 218750/216513<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 63.776<br />
<br />
Map: [&lt;1 1 2 1 5|, &lt;0 11 6 34 -29|]<br />
EDOs: 19, 75, 94, 207c</body></html>

@@ 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:xenwolf|xenwolf]] and made on <tt>2011-06-22 16:02:06 UTC</tt>.<br>
+: 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>238243837</tt>.<br>
+: The original revision id was <tt>277285838</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>
@@ Line 13: / Line 13: @@
 Map: [&lt;1 1 2|, &lt;0 11 6|]
-EDOs: [[18edo|18]], [[19edo|19]], [[56edo|56]], [[75edo|75]], [[94edo|94]], [[207edo|207]], [[508edo|508]]
+EDOs: [[18edo|18]], [[19edo|19]], [[56edo|56]], [[75edo|75]], [[94edo|94]], [[207edo|207c]], [[301edo|301c]]
 ==Seven limit children==
@@ Line 25: / Line 25: @@
 Map: [&lt;1 1 2 2|, &lt;0 11 6 15|]
-EDOs: 18, 19, 56, 75
+EDOs: 18, 19, 56, 75d
@@ Line 34: / Line 34: @@
 Map: [&lt;1 1 2 2 4|, &lt;0 11 6 15 -10|]
-EDOs: 18, 19, [[37edo|37]], 56
+EDOs: 18, 19, [[37edo|37]], [[56edo|56]]
 ===Betic===
@@ Line 44: / Line 44: @@
 Map: [&lt;1 1 2 1|, &lt;0 11 6 34|]
-EDOs: 19, 75, 94, [[113edo|113]], [[433edo|433]]
+EDOs: 19, 75, 94, [[113edo|113]], [[133edo|133]], [[320edo|320c]], [[433edo|433cd]]
 -limit
@@ Line 52: / Line 52: @@
 Map: [&lt;1 1 2 1 5|, &lt;0 11 6 34 -29|]
-EDOs: 19, 75, 94, 207</pre></div>
+EDOs: 19, 75, 94, 207c</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 &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;
@@ Line 61: / Line 61: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 2|, &amp;lt;0 11 6|]&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;, &lt;a class="wiki_link" href="/207edo"&gt;207&lt;/a&gt;, &lt;a class="wiki_link" href="/508edo"&gt;508&lt;/a&gt;&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;, &lt;a class="wiki_link" href="/207edo"&gt;207c&lt;/a&gt;, &lt;a class="wiki_link" href="/301edo"&gt;301c&lt;/a&gt;&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 73: / Line 73: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 2 2|, &amp;lt;0 11 6 15|]&lt;br /&gt;
-EDOs: 18, 19, 56, 75&lt;br /&gt;
+EDOs: 18, 19, 56, 75d&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&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, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;, 56&lt;br /&gt;
+EDOs: 18, 19, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;, &lt;a class="wiki_link" href="/56edo"&gt;56&lt;/a&gt;&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;
@@ Line 92: / Line 92: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 2 1|, &amp;lt;0 11 6 34|]&lt;br /&gt;
-EDOs: 19, 75, 94, &lt;a class="wiki_link" href="/113edo"&gt;113&lt;/a&gt;, &lt;a class="wiki_link" href="/433edo"&gt;433&lt;/a&gt;&lt;br /&gt;
+EDOs: 19, 75, 94, &lt;a class="wiki_link" href="/113edo"&gt;113&lt;/a&gt;, &lt;a class="wiki_link" href="/133edo"&gt;133&lt;/a&gt;, &lt;a class="wiki_link" href="/320edo"&gt;320c&lt;/a&gt;, &lt;a class="wiki_link" href="/433edo"&gt;433cd&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
 -limit&lt;br /&gt;
@@ Line 100: / Line 100: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 1 2 1 5|, &amp;lt;0 11 6 34 -29|]&lt;br /&gt;
-EDOs: 19, 75, 94, 207&lt;/body&gt;&lt;/html&gt;</pre></div>
+EDOs: 19, 75, 94, 207c&lt;/body&gt;&lt;/html&gt;</pre></div>

Sycamore family: Difference between revisions

Revision as of 19:58, 19 November 2011

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