Sycamore family: Difference between revisions

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<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">[[toc|flat]]

 

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]]: ~25/24 = 63.779

==7-limit==  

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 &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. [[75edo]] is an excellent tuning for 7-limit sycamore, and [[56edo]] for the 11-limit version.

[[POTE tuning|POTE generator]]: ~25/24 = 63.995

[[POTE tuning|POTE generator]]: ~25/24 = 64.268

[[POTE tuning|POTE generator]]: 63.701

[[POTE tuning|POTE generator]]: 63.776

EDOs: 19, 75, 94, 207c</pre></div>

<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;&lt;!-- ws:start:WikiTextTocRule:10:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;a href="#Sycamore"&gt;Sycamore&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Betic"&gt;Betic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;

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

&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Sycamore-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit&lt;/h2&gt;

The second element of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; for septimal sycamore is 875/864, the keema, and it also tempers out 686/675, the senga, and 3136/3125, hemimean. It has &amp;lt;&amp;lt;11 6 15 -16 -7 18|| for a wedgie, and may also be called the 19&amp;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. &lt;a class="wiki_link" href="/75edo"&gt;75edo&lt;/a&gt; is an excellent tuning for 7-limit sycamore, and &lt;a class="wiki_link" href="/56edo"&gt;56edo&lt;/a&gt; for the 11-limit version.&lt;br /&gt;

Commas: 686/675, 875/864&lt;br /&gt;

Map: [&amp;lt;1 1 2 2|, &amp;lt;0 11 6 15|]&lt;br /&gt;

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

Map: [&amp;lt;1 1 2 2 4 3|, &amp;lt;0 11 6 15 -10 13|]&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Betic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Betic&lt;/h1&gt;

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;amp;94 temperament, betic, for the 7-limit. This adds 225/224 to the sycamore comma, and has &amp;lt;&amp;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 &amp;lt;&amp;lt;11 6 34 -29 ...||.&lt;br /&gt;

Map: [&amp;lt;1 1 2 1|, &amp;lt;0 11 6 34|]&lt;br /&gt;

Map: [&amp;lt;1 1 2 1 5|, &amp;lt;0 11 6 34 -29|]&lt;br /&gt;