Marvel woo
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[[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 and 12/7 are 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. In terms of cents, the marvel woo tuning map is <1200.643223 1901.313567 2785.029055 3369.469129 4151.317943|. =7 notes= [[max7amarvwoo]] =12 notes= [[genus1125marvwoo]] [[duohexmarvwoo]] [[bluesmarvwoo]] [[dwarf12_11marvwoo]] [[glummamarvwoo]] [[tertiadie3marvwoo]] [[sixtetwoo]] =14 notes= [[pum14marvwoo]] =15 notes= [[pummelmarvwoo]] [[dwarf15marvwoo]] [[dekanymarvwoo]] [[genus5625marvwoo]] =16 notes= [[stellarhexmarvwoo]] =17 notes= [[diam7plusmarvwoo]] [[dwarf17marvwoo]] [[elf17marvwoo]] [[diamond_chess11marvwoo]] [[rectsp6amarvwoo]] [[chalmers_17marvwoo]] [[genus3375plusmarvwoo]] =18 notes= [[genus28125marvwoo]] =19 notes= [[marvel19woo]] =20 notes= [[genus16875marvwoo]] =21 notes= [[dcon9marvwoo]] [[blackwoo]] =22 notes= [[marvel22woo]] [[marvel22_11woo]] =24 notes= [[bimarveldenewoo]] =Music= [[http://micro.soonlabel.com/marvel/20140425_diam7_plus_woo.mp3|The Mysteries of Motivation]] in diam7plusmarvwoo by [[http://chrisvaisvil.com/the-mysteries-of-motivation-piano-tuned-to-marvel-woo/|Chris Vaisvil]]
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 and 12/7 are 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 /> In terms of cents, the marvel woo tuning map is <1200.643223 1901.313567 2785.029055 3369.469129 4151.317943|.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x7 notes"></a><!-- ws:end:WikiTextHeadingRule:0 -->7 notes</h1> <a class="wiki_link" href="/max7amarvwoo">max7amarvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="x12 notes"></a><!-- ws:end:WikiTextHeadingRule:2 -->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 /> <a class="wiki_link" href="/tertiadie3marvwoo">tertiadie3marvwoo</a><br /> <a class="wiki_link" href="/sixtetwoo">sixtetwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="x14 notes"></a><!-- ws:end:WikiTextHeadingRule:4 -->14 notes</h1> <a class="wiki_link" href="/pum14marvwoo">pum14marvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="x15 notes"></a><!-- ws:end:WikiTextHeadingRule:6 -->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:8:<h1> --><h1 id="toc4"><a name="x16 notes"></a><!-- ws:end:WikiTextHeadingRule:8 -->16 notes</h1> <a class="wiki_link" href="/stellarhexmarvwoo">stellarhexmarvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="x17 notes"></a><!-- ws:end:WikiTextHeadingRule:10 -->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 /> <a class="wiki_link" href="/diamond_chess11marvwoo">diamond_chess11marvwoo</a><br /> <a class="wiki_link" href="/rectsp6amarvwoo">rectsp6amarvwoo</a><br /> <a class="wiki_link" href="/chalmers_17marvwoo">chalmers_17marvwoo</a><br /> <a class="wiki_link" href="/genus3375plusmarvwoo">genus3375plusmarvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="x18 notes"></a><!-- ws:end:WikiTextHeadingRule:12 -->18 notes</h1> <a class="wiki_link" href="/genus28125marvwoo">genus28125marvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="x19 notes"></a><!-- ws:end:WikiTextHeadingRule:14 -->19 notes</h1> <a class="wiki_link" href="/marvel19woo">marvel19woo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="x20 notes"></a><!-- ws:end:WikiTextHeadingRule:16 -->20 notes</h1> <a class="wiki_link" href="/genus16875marvwoo">genus16875marvwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="x21 notes"></a><!-- ws:end:WikiTextHeadingRule:18 -->21 notes</h1> <a class="wiki_link" href="/dcon9marvwoo">dcon9marvwoo</a><br /> <a class="wiki_link" href="/blackwoo">blackwoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h1> --><h1 id="toc10"><a name="x22 notes"></a><!-- ws:end:WikiTextHeadingRule:20 -->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:22:<h1> --><h1 id="toc11"><a name="x24 notes"></a><!-- ws:end:WikiTextHeadingRule:22 -->24 notes</h1> <a class="wiki_link" href="/bimarveldenewoo">bimarveldenewoo</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h1> --><h1 id="toc12"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:24 -->Music</h1> <a class="wiki_link_ext" href="http://micro.soonlabel.com/marvel/20140425_diam7_plus_woo.mp3" rel="nofollow">The Mysteries of Motivation</a> in diam7plusmarvwoo by <a class="wiki_link_ext" href="http://chrisvaisvil.com/the-mysteries-of-motivation-piano-tuned-to-marvel-woo/" rel="nofollow">Chris Vaisvil</a></body></html>