Marvel woo
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- This revision was by author genewardsmith and made on 2013-12-24 00:41:10 UTC.
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Original Wikitext content:
[[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>, |-21 6 -6 15 8>, |7 -18 18 11 4>, |-28 -4 4 32 4>, |0 0 0 0 28>]/28. It leads to a tuning where the octave is sharp by |-7 -1 1 1 1>/7 = (385/384)^(1/7), about 0.643 cents. In this tuning, 9/5 is sharp by only |-49 -26 -2 19 12>/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= [[genus1125marvwoo]] [[duohexmarvwoo]] [[bluesmarvwoo]] [[dwarf12_11marvwoo]] [[glummamarvwoo]] =14 notes= [[pum14marvwoo]] =15 notes= [[pummelmarvwoo]] [[dwarf15marvwoo]] [[dekanymarvwoo]] [[genus5625marvwoo]] =16 notes= [[stellarhexmarvwoo]] =17 notes= [[diam7plusmarvwoo]] [[dwarf17marvwoo]] [[elf17marvwoo]] =18 notes= [[genus28125marvwoo]] =19 notes= [[marvel19woo]] =20 notes= [[genus16875marvwoo]] =21 notes= [[dcon9marvwoo]] =22 notes= [[marvel22woo]] [[marvel22_11woo]] =24 notes= [[bimarveldenewoo]]
Original HTML content:
<html><head><title>Marvel woo</title></head><body><a class="wiki_link" href="/Marvel">Marvel</a> 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>, |-21 6 -6 15 8>, |7 -18 18 11 4>, |-28 -4 4 32 4>, |0 0 0 0 28>]/28. It leads to a tuning where the octave is sharp by |-7 -1 1 1 1>/7 = (385/384)^(1/7), about 0.643 cents. In this tuning, 9/5 is sharp by only |-49 -26 -2 19 12>/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.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x12 notes"></a><!-- ws:end:WikiTextHeadingRule:0 -->12 notes</h1> <a class="wiki_link" href="/genus1125marvwoo">genus1125marvwoo</a><br /> <a class="wiki_link" href="/duohexmarvwoo">duohexmarvwoo</a><br /> <a class="wiki_link" href="/bluesmarvwoo">bluesmarvwoo</a><br /> <a class="wiki_link" href="/dwarf12_11marvwoo">dwarf12_11marvwoo</a><br /> <a class="wiki_link" href="/glummamarvwoo">glummamarvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="x14 notes"></a><!-- ws:end:WikiTextHeadingRule:2 -->14 notes</h1> <a class="wiki_link" href="/pum14marvwoo">pum14marvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="x15 notes"></a><!-- ws:end:WikiTextHeadingRule:4 -->15 notes</h1> <a class="wiki_link" href="/pummelmarvwoo">pummelmarvwoo</a><br /> <a class="wiki_link" href="/dwarf15marvwoo">dwarf15marvwoo</a><br /> <a class="wiki_link" href="/dekanymarvwoo">dekanymarvwoo</a><br /> <a class="wiki_link" href="/genus5625marvwoo">genus5625marvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="x16 notes"></a><!-- ws:end:WikiTextHeadingRule:6 -->16 notes</h1> <a class="wiki_link" href="/stellarhexmarvwoo">stellarhexmarvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="x17 notes"></a><!-- ws:end:WikiTextHeadingRule:8 -->17 notes</h1> <a class="wiki_link" href="/diam7plusmarvwoo">diam7plusmarvwoo</a><br /> <a class="wiki_link" href="/dwarf17marvwoo">dwarf17marvwoo</a><br /> <a class="wiki_link" href="/elf17marvwoo">elf17marvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="x18 notes"></a><!-- ws:end:WikiTextHeadingRule:10 -->18 notes</h1> <a class="wiki_link" href="/genus28125marvwoo">genus28125marvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="x19 notes"></a><!-- ws:end:WikiTextHeadingRule:12 -->19 notes</h1> <a class="wiki_link" href="/marvel19woo">marvel19woo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="x20 notes"></a><!-- ws:end:WikiTextHeadingRule:14 -->20 notes</h1> <a class="wiki_link" href="/genus16875marvwoo">genus16875marvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="x21 notes"></a><!-- ws:end:WikiTextHeadingRule:16 -->21 notes</h1> <a class="wiki_link" href="/dcon9marvwoo">dcon9marvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="x22 notes"></a><!-- ws:end:WikiTextHeadingRule:18 -->22 notes</h1> <a class="wiki_link" href="/marvel22woo">marvel22woo</a><br /> <a class="wiki_link" href="/marvel22_11woo">marvel22_11woo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h1> --><h1 id="toc10"><a name="x24 notes"></a><!-- ws:end:WikiTextHeadingRule:20 -->24 notes</h1> <a class="wiki_link" href="/bimarveldenewoo">bimarveldenewoo</a></body></html>