Marvel woo: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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[[dwarf15marvwoo]]

[[dekanymarvwoo]]

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<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;Marvel woo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/Marvel"&gt;Marvel&lt;/a&gt; is the 11-limit planar temperament tempering out 225/224 and 385/384. Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as eigenmonzos. This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose rows are fractional vals, which defines the tuning. This matrix is [&amp;lt;0 -4 4 4 4|, &amp;lt;-21 6 -6 15 8|, &amp;lt;7 -18 18 11 4|, &amp;lt;-28 -4 4 32 4|, &amp;lt;0 0 0 0 28|]/28. It leads to a tuning where the octave is sharp by |-7 -1 1 1 1&amp;gt;/7 = (385/384)^(1/7), about 0.643 cents. In this tuning, 9/5 is sharp by only |-49 -26 -2 19 12&amp;gt;/28 = (385/384)^(3/7)/(225/224)^(1/4), about 0.0018 cents. Putting 10/3, 7/2, 11 and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the beat ratios of everything in the 11-limit diamond are closely approximated by small integer ratios. For instance, for every eight beats of the octave in the chord 1-5/4-3/2-7/4-2, the approximate 5/4 beats approximately 20 times, 3/2 12 times, and 7/4 7 times; the actual numbers being 19.968, 11.977, 6.997 and 8 respectively. Aside from these facts about beats, it should be noted that marvel woo tuning is very close to the TE tuning for marvel.&lt;br /&gt;

&lt;a class="wiki_link" href="/dekanymarvwoo"&gt;dekanymarvwoo&lt;/a&gt;&lt;br /&gt;

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&lt;a class="wiki_link" href="/diam7plusmarvwoo"&gt;diam7plusmarvwoo&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="/dwarf17marvwoo"&gt;dwarf17marvwoo&lt;/a&gt;&lt;br /&gt;

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