Pentacircle comma: Difference between revisions
Wikispaces>jdfreivald **Imported revision 370866044 - Original comment: ** |
Wikispaces>jdfreivald **Imported revision 370886248 - 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>2012-10-07 | : This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2012-10-07 12:28:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>370886248</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">The Pentacircle Comma, 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. | <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">The Pentacircle Comma, 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. | ||
Pentacircle can be factored into two superparticular commas, 364/363 and 352/351. 364/363 is the difference between (14/11 * 13/11) and 3/2. Tempering out this comma ensures that a major third and a 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. | |||
[[Cantonpenta]] is an example of 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. Finally, see the article on [[Pentacircle Chords]].</pre></div> | [[Cantonpenta]] is an example of 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. Finally, see the article on [[Pentacircle Chords]].</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, 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, 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 /> | ||
<br /> | |||
Pentacircle can be factored into two superparticular commas, 364/363 and 352/351. 364/363 is the difference between (14/11 * 13/11) and 3/2. Tempering out this comma ensures that a major third and a 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 /> | ||
<a class="wiki_link" href="/Cantonpenta">Cantonpenta</a> is an example of 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. Finally, see the article on <a class="wiki_link" href="/Pentacircle%20Chords">Pentacircle Chords</a>.</body></html></pre></div> | <a class="wiki_link" href="/Cantonpenta">Cantonpenta</a> is an example of 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. Finally, see the article on <a class="wiki_link" href="/Pentacircle%20Chords">Pentacircle Chords</a>.</body></html></pre></div> | ||