Pentacircle comma: Difference between revisions

Revision as of 15:08, 9 October 2012

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This revision was by author jdfreivald and made on 2012-10-09 15:08:48 UTC.

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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.

Pentacircle is an 11-limit comma with monzo | 7 -4 0 1 -1 >. It is tempered out by the following EDOs, using their patent vals: 5, 12, 17, 19, 22, 24, 27, 29, 36, 41, 44, 46, 51, 58, 60, 63, 65, 68, 80, 82, 85, 87, 90, 92, 104, 109, 114, 121, 123, 126, 128, 131, 133, 136, 138, 145, 150, 155, 167, 169, 172, 174, 177, 184, 189, 191, 196, 201, 208, 213, 218, 230, 232, 237, 242, 254, 259, 271, 278, 283, and 295.

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 (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]].

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.

Original HTML content:

<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 />
<br />
Pentacircle is an 11-limit comma with monzo | 7 -4 0 1 -1 &gt;. It is tempered out by the following EDOs, using their patent vals: 5, 12, 17, 19, 22, 24, 27, 29, 36, 41, 44, 46, 51, 58, 60, 63, 65, 68, 80, 82, 85, 87, 90, 92, 104, 109, 114, 121, 123, 126, 128, 131, 133, 136, 138, 145, 150, 155, 167, 169, 172, 174, 177, 184, 189, 191, 196, 201, 208, 213, 218, 230, 232, 237, 242, 254, 259, 271, 278, 283, and 295.<br />
<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 />
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 />
352/351 is the minthma: See the article on <a class="wiki_link" href="/minthmic%20chords">minthmic chords</a>.<br />
<br />
Finally, see the article on <a class="wiki_link" href="/Pentacircle%20Chords">Pentacircle Chords</a>.<br />
<br />
Example scales: <a class="wiki_link" href="/Cantonpenta">Cantonpenta</a> 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.</body></html>

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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:jdfreivald|jdfreivald]] and made on <tt>2012-10-07 12:53:52 UTC</tt>.<br>
+: 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>370889996</tt>.<br>
+: The original revision id was <tt>371566222</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>
@@ Line 12: / Line 12: @@
 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; ).
-/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.)
+/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.)
 /351 is the minthma: See the article on [[minthmic chords]].
@@ Line 18: / Line 18: @@
 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>
 <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;pentacircle comma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;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.&lt;br /&gt;
@@ Line 26: / Line 26: @@
 Pentacircle can be factored into two 13-limit superparticular commas, 364/363 (which is | 2 -1 0 1 -2 1 &amp;gt; ) and 352/351 (which is | 5 -3 0 0 1 -1 &amp;gt; ).&lt;br /&gt;
 &lt;br /&gt;
-/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.)&lt;br /&gt;
+/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.)&lt;br /&gt;
 &lt;br /&gt;
 /351 is the minthma: See the article on &lt;a class="wiki_link" href="/minthmic%20chords"&gt;minthmic chords&lt;/a&gt;.&lt;br /&gt;

Pentacircle comma: Difference between revisions

Revision as of 15:08, 9 October 2012

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