Marvel woo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 568330695 - Original comment: ** |
Wikispaces>jollybard **Imported revision 615626511 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:jollybard|jollybard]] and made on <tt>2017-07-14 18:21:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>615626511</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">[[Marvel]] is the | <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 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. | ||
The marvel woo tuning map is <1200.643223 1901.313567 2785.029055 3369.469129 4151.317943|. | |||
=7 notes= | =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]] | [[max7amarvwoo]] | ||
=12 notes= | =12 notes= | ||
[[genus1125marvwoo]] | [[genus1125marvwoo]] | ||
[[duohexmarvwoo]] | [[duohexmarvwoo]] | ||
| Line 22: | Line 26: | ||
[[sixtetwoo]] | [[sixtetwoo]] | ||
=14 notes= | =14 notes= | ||
[[pum14marvwoo]] | [[pum14marvwoo]] | ||
=15 notes= | =15 notes= | ||
[[pummelmarvwoo]] | [[pummelmarvwoo]] | ||
[[dwarf15marvwoo]] | [[dwarf15marvwoo]] | ||
| Line 31: | Line 35: | ||
[[genus5625marvwoo]] | [[genus5625marvwoo]] | ||
=16 notes= | =16 notes= | ||
[[stellarhexmarvwoo]] | [[stellarhexmarvwoo]] | ||
=17 notes= | =17 notes= | ||
[[diam7plusmarvwoo]] | [[diam7plusmarvwoo]] | ||
[[dwarf17marvwoo]] | [[dwarf17marvwoo]] | ||
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[[genus3375plusmarvwoo]] | [[genus3375plusmarvwoo]] | ||
=18 notes= | =18 notes= | ||
[[genus28125marvwoo]] | [[genus28125marvwoo]] | ||
=19 notes= | =19 notes= | ||
[[marvel19woo]] | [[marvel19woo]] | ||
=20 notes= | =20 notes= | ||
[[genus16875marvwoo]] | [[genus16875marvwoo]] | ||
=21 notes= | =21 notes= | ||
[[dcon9marvwoo]] | [[dcon9marvwoo]] | ||
[[blackwoo]] | [[blackwoo]] | ||
=22 notes= | =22 notes= | ||
[[marvel22woo]] | [[marvel22woo]] | ||
[[marvel22_11woo]] | [[marvel22_11woo]] | ||
=24 notes= | =24 notes= | ||
[[bimarveldenewoo]] | [[bimarveldenewoo]] | ||
=Music= | =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]]</pre></div> | [[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> | <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"><html><head><title>Marvel woo</title></head><body><a class="wiki_link" href="/Marvel">Marvel</a> is the | <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 temperament 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 /> | ||
<br /> | |||
The marvel woo tuning map is &lt;1200.643223 1901.313567 2785.029055 3369.469129 4151.317943|.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Math"></a><!-- ws:end:WikiTextHeadingRule:0 -->Math</h1> | |||
<br /> | |||
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 /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x7 notes"></a><!-- ws:end:WikiTextHeadingRule:2 -->7 notes</h1> | ||
<a class="wiki_link" href="/max7amarvwoo">max7amarvwoo</a><br /> | <a class="wiki_link" href="/max7amarvwoo">max7amarvwoo</a><br /> | ||
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<a class="wiki_link" href="/genus1125marvwoo">genus1125marvwoo</a><br /> | <a class="wiki_link" href="/genus1125marvwoo">genus1125marvwoo</a><br /> | ||
<a class="wiki_link" href="/duohexmarvwoo">duohexmarvwoo</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="/bluesmarvwoo">bluesmarvwoo</a><br /> | ||
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<a class="wiki_link" href="/sixtetwoo">sixtetwoo</a><br /> | <a class="wiki_link" href="/sixtetwoo">sixtetwoo</a><br /> | ||
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<a class="wiki_link" href="/pum14marvwoo">pum14marvwoo</a><br /> | <a class="wiki_link" href="/pum14marvwoo">pum14marvwoo</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="x15 notes"></a><!-- ws:end:WikiTextHeadingRule:8 -->15 notes</h1> | ||
<a class="wiki_link" href="/pummelmarvwoo">pummelmarvwoo</a><br /> | <a class="wiki_link" href="/pummelmarvwoo">pummelmarvwoo</a><br /> | ||
<a class="wiki_link" href="/dwarf15marvwoo">dwarf15marvwoo</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="/dekanymarvwoo">dekanymarvwoo</a><br /> | ||
<a class="wiki_link" href="/genus5625marvwoo">genus5625marvwoo</a><br /> | <a class="wiki_link" href="/genus5625marvwoo">genus5625marvwoo</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="x16 notes"></a><!-- ws:end:WikiTextHeadingRule:10 -->16 notes</h1> | ||
<a class="wiki_link" href="/stellarhexmarvwoo">stellarhexmarvwoo</a><br /> | <a class="wiki_link" href="/stellarhexmarvwoo">stellarhexmarvwoo</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="x17 notes"></a><!-- ws:end:WikiTextHeadingRule:12 -->17 notes</h1> | ||
<a class="wiki_link" href="/diam7plusmarvwoo">diam7plusmarvwoo</a><br /> | <a class="wiki_link" href="/diam7plusmarvwoo">diam7plusmarvwoo</a><br /> | ||
<a class="wiki_link" href="/dwarf17marvwoo">dwarf17marvwoo</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="/elf17marvwoo">elf17marvwoo</a><br /> | ||
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<a class="wiki_link" href="/genus3375plusmarvwoo">genus3375plusmarvwoo</a><br /> | <a class="wiki_link" href="/genus3375plusmarvwoo">genus3375plusmarvwoo</a><br /> | ||
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<a class="wiki_link" href="/genus28125marvwoo">genus28125marvwoo</a><br /> | <a class="wiki_link" href="/genus28125marvwoo">genus28125marvwoo</a><br /> | ||
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<a class="wiki_link" href="/marvel19woo">marvel19woo</a><br /> | <a class="wiki_link" href="/marvel19woo">marvel19woo</a><br /> | ||
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<a class="wiki_link" href="/genus16875marvwoo">genus16875marvwoo</a><br /> | <a class="wiki_link" href="/genus16875marvwoo">genus16875marvwoo</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="x21 notes"></a><!-- ws:end:WikiTextHeadingRule:20 -->21 notes</h1> | ||
<a class="wiki_link" href="/dcon9marvwoo">dcon9marvwoo</a><br /> | <a class="wiki_link" href="/dcon9marvwoo">dcon9marvwoo</a><br /> | ||
<a class="wiki_link" href="/blackwoo">blackwoo</a><br /> | <a class="wiki_link" href="/blackwoo">blackwoo</a><br /> | ||
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<a class="wiki_link" href="/marvel22woo">marvel22woo</a><br /> | <a class="wiki_link" href="/marvel22woo">marvel22woo</a><br /> | ||
<a class="wiki_link" href="/marvel22_11woo">marvel22_11woo</a><br /> | <a class="wiki_link" href="/marvel22_11woo">marvel22_11woo</a><br /> | ||
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<a class="wiki_link" href="/bimarveldenewoo">bimarveldenewoo</a><br /> | <a class="wiki_link" href="/bimarveldenewoo">bimarveldenewoo</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:26 -->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></pre></div> | <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> | ||