896/891: Difference between revisions
Wikispaces>jdfreivald **Imported revision 370889996 - Original comment: ** |
Wikispaces>jdfreivald **Imported revision 371566222 - 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:jdfreivald|jdfreivald]] and made on <tt>2012-10- | : This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2012-10-09 15:08:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>371566222</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> | ||
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Pentacircle can be factored into two 13-limit superparticular commas, 364/363 (which is | 2 -1 0 1 -2 1 > ) and 352/351 (which is | 5 -3 0 0 1 -1 > ). | Pentacircle can be factored into two 13-limit superparticular commas, 364/363 (which is | 2 -1 0 1 -2 1 > ) and 352/351 (which is | 5 -3 0 0 1 -1 > ). | ||
364/363 is the difference between (14/11 * 13/11) and 3/2. If both Pentacircle and 364/363 are tempered out, a 14/11 major third and a 13/11 minor third together add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 * 6/5 = 3/2.) | 364/363 is the difference between (14/11 * 13/11) and 3/2. If both Pentacircle and 364/363 are tempered out (which implies that 352/351 is also tempered out, of course), a 14/11 major third and a 13/11 minor third together add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 * 6/5 = 3/2.) | ||
352/351 is the minthma: See the article on [[minthmic chords]]. | 352/351 is the minthma: See the article on [[minthmic chords]]. | ||
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Finally, see the article on [[Pentacircle Chords]]. | Finally, see the article on [[Pentacircle Chords]]. | ||
Example scales: [[Cantonpenta]] is a scale that tempers out the pentacircle comma. Also, the MOSes with an octave period and 17\29 as a generator temper out the Pentacircle comma. </pre></div> | Example scales: [[Cantonpenta]] is a scale that tempers out the pentacircle comma. Also, the MOSes with an octave period and 17\29 as a generator temper out the Pentacircle comma.</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>pentacircle comma</title></head><body>The Pentacircle Comma or undecimal semicomma, 896/891, is similar to the Didymus or syntonic comma, 81/80, in that it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Pentacircle comma, the major third is 14/11.<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>pentacircle comma</title></head><body>The Pentacircle Comma or undecimal semicomma, 896/891, is similar to the Didymus or syntonic comma, 81/80, in that it makes a stack of four fifths equal a major third (octave equivalent). In the case of 81/80, however, the major third is 5/4, while with the Pentacircle comma, the major third is 14/11.<br /> | ||
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Pentacircle can be factored into two 13-limit superparticular commas, 364/363 (which is | 2 -1 0 1 -2 1 &gt; ) and 352/351 (which is | 5 -3 0 0 1 -1 &gt; ).<br /> | Pentacircle can be factored into two 13-limit superparticular commas, 364/363 (which is | 2 -1 0 1 -2 1 &gt; ) and 352/351 (which is | 5 -3 0 0 1 -1 &gt; ).<br /> | ||
<br /> | <br /> | ||
364/363 is the difference between (14/11 * 13/11) and 3/2. If both Pentacircle and 364/363 are tempered out, a 14/11 major third and a 13/11 minor third together add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 * 6/5 = 3/2.)<br /> | 364/363 is the difference between (14/11 * 13/11) and 3/2. If both Pentacircle and 364/363 are tempered out (which implies that 352/351 is also tempered out, of course), a 14/11 major third and a 13/11 minor third together add up to a perfect fifth. (This isn't necessary for traditional minor and major thirds, because 5/4 * 6/5 = 3/2.)<br /> | ||
<br /> | <br /> | ||
352/351 is the minthma: See the article on <a class="wiki_link" href="/minthmic%20chords">minthmic chords</a>.<br /> | 352/351 is the minthma: See the article on <a class="wiki_link" href="/minthmic%20chords">minthmic chords</a>.<br /> | ||