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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox Interval |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Ratio = 896/891 |
| : This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2012-10-07 12:53:52 UTC</tt>.<br>
| | | Name = pentacircle comma, undecimal semicomma |
| : The original revision id was <tt>370889996</tt>.<br>
| | | Color name = s1uz2, Saluzo comma |
| : The revision comment was: <tt></tt><br>
| | | Comma = yes |
| 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>
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| <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 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.
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| 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.
| | The '''pentacircle comma''' or '''undecimal semicomma''', '''896/891''' (9.68796 [[cent]]s), is an [[11-limit]] [[comma]] with monzo {{monzo|7 -4 0 1 -1}}. It 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]]. |
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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 is tempered out by the following edos, using their patent vals: {{EDOs|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}}. |
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| 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.) | | Pentacircle can be factored into two [[13-limit]] [[superparticular]] commas, [[364/363]] (which is {{monzo| 2 -1 0 1 -2 1 }}) and [[352/351]] (which is {{monzo| 5 -3 0 0 1 -1 }}). |
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| 352/351 is the minthma: See the article on [[minthmic chords]]. | | 364/363 is the gentle comma, which 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.) |
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| Finally, see the article on [[Pentacircle Chords]].
| | 352/351 is the minthma: see the article on [[minthmic chords]]. |
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| 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> | | Finally, see the article on [[Pentacircle chords]]. |
| <h4>Original HTML content:</h4>
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| <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 />
| | 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. |
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| 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 />
| | == Sagittal notation == |
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| | In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | )!( }} and is called the '''11/7 kleisma''', or '''11/7k''' for short, because the simplest interval it notates is 11/7, as for example in A-F{{nbhsp}}{{sagittal | )!( }}. The upward version is called '''7/11k''' or '''11/7k up''' and is represented by {{sagittal| )|( }}. |
| 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 />
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| | == See also == |
| 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 />
| | * [[Pentacircle clan]], the clan of rank-3 temperaments where it is tempered out |
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| | * [[Small comma]] |
| 352/351 is the minthma: See the article on <a class="wiki_link" href="/minthmic%20chords">minthmic chords</a>.<br />
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| | [[Category:Pentacircle]] |
| Finally, see the article on <a class="wiki_link" href="/Pentacircle%20Chords">Pentacircle Chords</a>.<br />
| | [[Category:Commas named for their regular temperament properties]] |
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| 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></pre></div>
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