Marvel woo: 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">[[Marvel]] 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 columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [|0 -4 4 4 4&gt;, |-21 6 -6 15 8&gt;, |7 -18 18 11 4&gt;, |-28 -4 4 32 4&gt;, |0 0 0 0 28&gt;]/28. It leads to a tuning where the octave is sharp by |-7 -1 1 1 1&gt;/7 = (385/384)^(1/7), about 0.643 cents. In this tuning, 9/5 and 12/7 are sharp by only |-49 -26 -2 19 12&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.

=12 notes=

<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 columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [|0 -4 4 4 4&amp;gt;, |-21 6 -6 15 8&amp;gt;, |7 -18 18 11 4&amp;gt;, |-28 -4 4 32 4&amp;gt;, |0 0 0 0 28&amp;gt;]/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 and 12/7 are 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;br /&gt;

&lt;a class="wiki_link" href="/genus1125marvwoo"&gt;genus1125marvwoo&lt;/a&gt;&lt;br /&gt;

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

&lt;a class="wiki_link" href="/tertiadie3marvwoo"&gt;tertiadie3marvwoo&lt;/a&gt;&lt;br /&gt;

&lt;br /&gt;

&lt;a class="wiki_link" href="/pum14marvwoo"&gt;pum14marvwoo&lt;/a&gt;&lt;br /&gt;

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

&lt;a class="wiki_link" href="/dwarf15marvwoo"&gt;dwarf15marvwoo&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="/genus5625marvwoo"&gt;genus5625marvwoo&lt;/a&gt;&lt;br /&gt;

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&lt;a class="wiki_link" href="/stellarhexmarvwoo"&gt;stellarhexmarvwoo&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;

&lt;a class="wiki_link" href="/genus3375plusmarvwoo"&gt;genus3375plusmarvwoo&lt;/a&gt;&lt;br /&gt;

&lt;br /&gt;

&lt;a class="wiki_link" href="/genus28125marvwoo"&gt;genus28125marvwoo&lt;/a&gt;&lt;br /&gt;

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&lt;a class="wiki_link" href="/marvel19woo"&gt;marvel19woo&lt;/a&gt;&lt;br /&gt;

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&lt;a class="wiki_link" href="/genus16875marvwoo"&gt;genus16875marvwoo&lt;/a&gt;&lt;br /&gt;

&lt;br /&gt;

&lt;a class="wiki_link" href="/dcon9marvwoo"&gt;dcon9marvwoo&lt;/a&gt;&lt;br /&gt;

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

&lt;br /&gt;

&lt;a class="wiki_link" href="/marvel22woo"&gt;marvel22woo&lt;/a&gt;&lt;br /&gt;

&lt;a class="wiki_link" href="/marvel22_11woo"&gt;marvel22_11woo&lt;/a&gt;&lt;br /&gt;

&lt;br /&gt;

&lt;a class="wiki_link" href="/bimarveldenewoo"&gt;bimarveldenewoo&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>