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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | [[Marvel_family|Marvel]] is the rank-3 [[Tour_of_Regular_Temperaments|temperament]] tempering out 225/224, the [https://en.wikipedia.org/wiki/Septimal_kleisma septimal kleisma]. For Marvel woo, we extend Marvel into the 11-limit by tempering out [[385/384|385/384]]. Marvel woo is a particular tuning of Marvel which is optimized for synchronized beating, and which also happens to be very close to the [[Tenney-Euclidean_Tuning|TE tuning]] for Marvel. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-07-21 01:22:14 UTC</tt>.<br>
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| : The original revision id was <tt>615800081</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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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 family|Marvel]] is the rank-3 [[Tour of Regular Temperaments|temperament]] tempering out 225/224, the [[https://en.wikipedia.org/wiki/Septimal_kleisma|septimal kleisma]]. For Marvel woo, we extend Marvel into the 11-limit by tempering out [[385_384|385/384]]. Marvel woo is a particular tuning of Marvel which is optimized for synchronized beating, and which also happens to be very close to the [[Tenney-Euclidean Tuning|TE tuning]] for Marvel.
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| The marvel woo tuning map is <1200.643223 1901.313567 2785.029055 3369.469129 4151.317943|. | | The marvel woo tuning map is <1200.643223 1901.313567 2785.029055 3369.469129 4151.317943|. |
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| =Math= | | =Math= |
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| 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.. | | 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.. |
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| =7 notes= | | =7 notes= |
| [[max7amarvwoo]] | | [[max7amarvwoo|max7amarvwoo]] |
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| =12 notes= | | =12 notes= |
| [[genus1125marvwoo]] | | [[genus1125marvwoo|genus1125marvwoo]] |
| [[duohexmarvwoo]]
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| [[bluesmarvwoo]]
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| [[dwarf12_11marvwoo]]
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| [[glummamarvwoo]]
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| [[tertiadie3marvwoo]]
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| [[sixtetwoo]]
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| =14 notes=
| | [[duohexmarvwoo|duohexmarvwoo]] |
| [[pum14marvwoo]] | |
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| =15 notes=
| | [[bluesmarvwoo|bluesmarvwoo]] |
| [[pummelmarvwoo]] | |
| [[dwarf15marvwoo]]
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| [[dekanymarvwoo]]
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| [[genus5625marvwoo]]
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| =16 notes=
| | [[dwarf12_11marvwoo|dwarf12_11marvwoo]] |
| [[stellarhexmarvwoo]] | |
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| =17 notes=
| | [[glummamarvwoo|glummamarvwoo]] |
| [[diam7plusmarvwoo]] | |
| [[dwarf17marvwoo]]
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| [[elf17marvwoo]]
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| [[diamond_chess11marvwoo]]
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| [[rectsp6amarvwoo]]
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| [[chalmers_17marvwoo]]
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| [[genus3375plusmarvwoo]]
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| =18 notes=
| | [[tertiadie3marvwoo|tertiadie3marvwoo]] |
| [[genus28125marvwoo]] | |
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| =19 notes=
| | [[sixtetwoo|sixtetwoo]] |
| [[marvel19woo]] | |
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| =20 notes= | | =14 notes= |
| [[genus16875marvwoo]] | | [[pum14marvwoo|pum14marvwoo]] |
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| =21 notes= | | =15 notes= |
| [[dcon9marvwoo]] | | [[pummelmarvwoo|pummelmarvwoo]] |
| [[blackwoo]]
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| =22 notes=
| | [[dwarf15marvwoo|dwarf15marvwoo]] |
| [[marvel22woo]] | |
| [[marvel22_11woo]]
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| =24 notes=
| | [[dekanymarvwoo|dekanymarvwoo]] |
| [[bimarveldenewoo]] | |
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| =Music=
| | [[genus5625marvwoo|genus5625marvwoo]] |
| [[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]]</pre></div> | | |
| <h4>Original HTML content:</h4>
| | =16 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"><html><head><title>Marvel woo</title></head><body><a class="wiki_link" href="/Marvel%20family">Marvel</a> is the rank-3 <a class="wiki_link" href="/Tour%20of%20Regular%20Temperaments">temperament</a> tempering out 225/224, the <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Septimal_kleisma" rel="nofollow">septimal kleisma</a>. For Marvel woo, we extend Marvel into the 11-limit by tempering out <a class="wiki_link" href="/385_384">385/384</a>. Marvel woo is a particular tuning of Marvel which is optimized for synchronized beating, and which also happens to be very close to the <a class="wiki_link" href="/Tenney-Euclidean%20Tuning">TE tuning</a> for Marvel.<br />
| | [[stellarhexmarvwoo|stellarhexmarvwoo]] |
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| The marvel woo tuning map is &lt;1200.643223 1901.313567 2785.029055 3369.469129 4151.317943|.<br />
| | =17 notes= |
| <br />
| | [[diam7plusmarvwoo|diam7plusmarvwoo]] |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Math"></a><!-- ws:end:WikiTextHeadingRule:0 -->Math</h1>
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| | [[dwarf17marvwoo|dwarf17marvwoo]] |
| 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..<br />
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| | [[elf17marvwoo|elf17marvwoo]] |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x7 notes"></a><!-- ws:end:WikiTextHeadingRule:2 -->7 notes</h1>
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| <a class="wiki_link" href="/max7amarvwoo">max7amarvwoo</a><br />
| | [[diamond_chess11marvwoo|diamond_chess11marvwoo]] |
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| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="x12 notes"></a><!-- ws:end:WikiTextHeadingRule:4 -->12 notes</h1>
| | [[rectsp6amarvwoo|rectsp6amarvwoo]] |
| <a class="wiki_link" href="/genus1125marvwoo">genus1125marvwoo</a><br />
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| <a class="wiki_link" href="/duohexmarvwoo">duohexmarvwoo</a><br />
| | [[chalmers_17marvwoo|chalmers_17marvwoo]] |
| <a class="wiki_link" href="/bluesmarvwoo">bluesmarvwoo</a><br />
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| <a class="wiki_link" href="/dwarf12_11marvwoo">dwarf12_11marvwoo</a><br />
| | [[genus3375plusmarvwoo|genus3375plusmarvwoo]] |
| <a class="wiki_link" href="/glummamarvwoo">glummamarvwoo</a><br />
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| <a class="wiki_link" href="/tertiadie3marvwoo">tertiadie3marvwoo</a><br />
| | =18 notes= |
| <a class="wiki_link" href="/sixtetwoo">sixtetwoo</a><br />
| | [[genus28125marvwoo|genus28125marvwoo]] |
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| <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="x14 notes"></a><!-- ws:end:WikiTextHeadingRule:6 -->14 notes</h1>
| | =19 notes= |
| <a class="wiki_link" href="/pum14marvwoo">pum14marvwoo</a><br />
| | [[marvel19woo|marvel19woo]] |
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| <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="x15 notes"></a><!-- ws:end:WikiTextHeadingRule:8 -->15 notes</h1>
| | =20 notes= |
| <a class="wiki_link" href="/pummelmarvwoo">pummelmarvwoo</a><br />
| | [[genus16875marvwoo|genus16875marvwoo]] |
| <a class="wiki_link" href="/dwarf15marvwoo">dwarf15marvwoo</a><br />
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| <a class="wiki_link" href="/dekanymarvwoo">dekanymarvwoo</a><br />
| | =21 notes= |
| <a class="wiki_link" href="/genus5625marvwoo">genus5625marvwoo</a><br />
| | [[dcon9marvwoo|dcon9marvwoo]] |
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| <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="x16 notes"></a><!-- ws:end:WikiTextHeadingRule:10 -->16 notes</h1>
| | [[blackwoo|blackwoo]] |
| <a class="wiki_link" href="/stellarhexmarvwoo">stellarhexmarvwoo</a><br />
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| | =22 notes= |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="x17 notes"></a><!-- ws:end:WikiTextHeadingRule:12 -->17 notes</h1>
| | [[marvel22woo|marvel22woo]] |
| <a class="wiki_link" href="/diam7plusmarvwoo">diam7plusmarvwoo</a><br />
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| <a class="wiki_link" href="/dwarf17marvwoo">dwarf17marvwoo</a><br />
| | [[marvel22_11woo|marvel22_11woo]] |
| <a class="wiki_link" href="/elf17marvwoo">elf17marvwoo</a><br />
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| <a class="wiki_link" href="/diamond_chess11marvwoo">diamond_chess11marvwoo</a><br />
| | =24 notes= |
| <a class="wiki_link" href="/rectsp6amarvwoo">rectsp6amarvwoo</a><br />
| | [[bimarveldenewoo|bimarveldenewoo]] |
| <a class="wiki_link" href="/chalmers_17marvwoo">chalmers_17marvwoo</a><br />
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| <a class="wiki_link" href="/genus3375plusmarvwoo">genus3375plusmarvwoo</a><br />
| | =Music= |
| <br />
| | [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] |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="x18 notes"></a><!-- ws:end:WikiTextHeadingRule:14 -->18 notes</h1>
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| <a class="wiki_link" href="/genus28125marvwoo">genus28125marvwoo</a><br />
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| <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="x19 notes"></a><!-- ws:end:WikiTextHeadingRule:16 -->19 notes</h1>
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| <a class="wiki_link" href="/marvel19woo">marvel19woo</a><br />
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| <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="x20 notes"></a><!-- ws:end:WikiTextHeadingRule:18 -->20 notes</h1>
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| <a class="wiki_link" href="/genus16875marvwoo">genus16875marvwoo</a><br />
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| <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="x21 notes"></a><!-- ws:end:WikiTextHeadingRule:20 -->21 notes</h1>
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| <a class="wiki_link" href="/dcon9marvwoo">dcon9marvwoo</a><br />
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| <a class="wiki_link" href="/blackwoo">blackwoo</a><br />
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| <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="x22 notes"></a><!-- ws:end:WikiTextHeadingRule:22 -->22 notes</h1>
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| <a class="wiki_link" href="/marvel22woo">marvel22woo</a><br />
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| <a class="wiki_link" href="/marvel22_11woo">marvel22_11woo</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="x24 notes"></a><!-- ws:end:WikiTextHeadingRule:24 -->24 notes</h1>
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| <a class="wiki_link" href="/bimarveldenewoo">bimarveldenewoo</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:26 -->Music</h1>
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| <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></pre></div>
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Marvel is the rank-3 temperament tempering out 225/224, the septimal kleisma. For Marvel woo, we extend Marvel into the 11-limit by tempering out 385/384. Marvel woo is a particular tuning of Marvel which is optimized for synchronized beating, and which also happens to be very close to the TE tuning for Marvel.
The marvel woo tuning map is <1200.643223 1901.313567 2785.029055 3369.469129 4151.317943|.
Math
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..
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
The Mysteries of Motivation in diam7plusmarvwoo by Chris Vaisvil