Marvel woo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-22 13:21:17 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-22 17:30:55 UTC</tt>.<br>

: The original revision id was <tt>~~479041360~~</tt>.<br>

: The original revision id was <tt>479062282</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>

<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 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 rows are fractional vals, 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.

<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 rows are fractional vals, 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.

=14 notes=

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[[dcon9marvwoo]]</pre></div>

<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 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 rows are fractional vals, which defines the tuning. This matrix is [&lt;0 -4 4 4 4|, &lt;-21 6 -6 15 8|, &lt;7 -18 18 11 4|, &lt;-28 -4 4 32 4|, &lt;0 0 0 0 28|]/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 is 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. <br />

<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 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 rows are fractional vals, which defines the tuning. This matrix is [&lt;0 -4 4 4 4|, &lt;-21 6 -6 15 8|, &lt;7 -18 18 11 4|, &lt;-28 -4 4 32 4|, &lt;0 0 0 0 28|]/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 is 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 />

<h1 id="toc0"><a name="x14 notes"></a>14 notes</h1>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-22 13:21:17 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-22 17:30:55 UTC</tt>.<br>
-: The original revision id was <tt>479041360</tt>.<br>
+: The original revision id was <tt>479062282</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>
 <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 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 rows are fractional vals, which defines the tuning. This matrix is [&lt;0 -4 4 4 4|, &lt;-21 6 -6 15 8|, &lt;7 -18 18 11 4|, &lt;-28 -4 4 32 4|, &lt;0 0 0 0 28|]/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 is 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.
+<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 rows are fractional vals, which defines the tuning. This matrix is [&lt;0 -4 4 4 4|, &lt;-21 6 -6 15 8|, &lt;7 -18 18 11 4|, &lt;-28 -4 4 32 4|, &lt;0 0 0 0 28|]/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 is 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.
 =14 notes=
@@ Line 23: / Line 23: @@
 [[dcon9marvwoo]]</pre></div>
 <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">&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 rows are fractional vals, which defines the tuning. This matrix is [&amp;lt;0 -4 4 4 4|, &amp;lt;-21 6 -6 15 8|, &amp;lt;7 -18 18 11 4|, &amp;lt;-28 -4 4 32 4|, &amp;lt;0 0 0 0 28|]/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 is 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. &lt;br /&gt;
+<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 rows are fractional vals, which defines the tuning. This matrix is [&amp;lt;0 -4 4 4 4|, &amp;lt;-21 6 -6 15 8|, &amp;lt;7 -18 18 11 4|, &amp;lt;-28 -4 4 32 4|, &amp;lt;0 0 0 0 28|]/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 is 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.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x14 notes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;14 notes&lt;/h1&gt;