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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A '''pentacircle chord''' is an [[essentially tempered dyadic chord]] in the 2.9.7.11 [[subgroup]] in the [[11-odd-limit]], [[tempering out]] the pentacircle comma, [[896/891]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-13 13:26:50 UTC</tt>.<br>
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| : The original revision id was <tt>285563084</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <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">A //pentacircle chord// is an [[Dyadic chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] in the 2.9.7.11 subgroup of the 11-limit, tempering out the pentacircle comma, 896/891. The pentacircle triads are three in number, 1-9/7-16/9 with steps 9/7-11/8-9/8; 1-9/7-16/11 with steps 9/7-9/8-11/8; and 1-11/7-16/9 with steps 11/7-9/8-9/8. There are six pentacircle tetrads: the palindromic 1-9/8-14/9-7/4 with steps 9/8-11/8-9/8-8/7; the palindromic 1-9/8-11/8-14/9 with steps 9/8-11/9-9/8-9/7; the inverse pair 1-11/8-11/7-16/9 with steps 11/8-8/7-9/8-9/8 and 1-11/8-14/9-7/4 with steps 11/8-9/8-9/8-8/7; and the inverse pair 1-11/9-11/7-16/9 with steps 11/9-9/7-9/8-9/8 and 1-11/9-11/8-14/9 with steps 11/9-9/8-9/8-9/7. Finally, there are two pentacircle pentads, inversely related: 1-11/9-11/8-11/7-16/9 with steps 11/9-9/8-8/7-9/8-9/8 and 1-11/9-11/8-14/9-16/9 with steps 11/9-9/8-9/8-8/7-9/8.
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| Equal divisions with pentacircle chords include 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, 208, 266e and 433bce.
| | Pentacircle chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.9.7.11 [[subgroup]] [[11-odd-limit]], meaning that there are 3 [[triad]]s, 6 [[tetrad]]s and 2 [[pentad]]s, for a total of 11 distinct chord structures. |
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| | The three pentacircle triads include a palindrome since it identifies [[14/11]] by a stack of two [[9/8]]'s: |
| | * 1–9/8–14/11 with steps 9/8, 9/8, 11/7. |
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| | And an inversely related pair: |
| | * 1–9/8–16/11 with steps 9/8, 9/7, 11/8; |
| | * 1–9/8–14/9 with steps 9/8, 11/8, 9/7; |
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| | The tetrads include the palindromic |
| | * 1–9/8–14/9–7/4 with steps 9/8, 11/8, 9/8, 8/7; |
| | * 1–9/8–11/8–14/9 with steps 9/8, 11/9, 9/8, 9/7. |
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| </pre></div>
| | And the inversely related pairs |
| <h4>Original HTML content:</h4>
| | * 1–11/8–11/7–16/9 with steps 11/8, 8/7, 9/8, 9/8, and its inverse |
| <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 chords</title></head><body>A <em>pentacircle chord</em> is an <a class="wiki_link" href="/Dyadic%20chord#Essentially tempered dyadic chords">essentially tempered dyadic chord</a> in the 2.9.7.11 subgroup of the 11-limit, tempering out the pentacircle comma, 896/891. The pentacircle triads are three in number, 1-9/7-16/9 with steps 9/7-11/8-9/8; 1-9/7-16/11 with steps 9/7-9/8-11/8; and 1-11/7-16/9 with steps 11/7-9/8-9/8. There are six pentacircle tetrads: the palindromic 1-9/8-14/9-7/4 with steps 9/8-11/8-9/8-8/7; the palindromic 1-9/8-11/8-14/9 with steps 9/8-11/9-9/8-9/7; the inverse pair 1-11/8-11/7-16/9 with steps 11/8-8/7-9/8-9/8 and 1-11/8-14/9-7/4 with steps 11/8-9/8-9/8-8/7; and the inverse pair 1-11/9-11/7-16/9 with steps 11/9-9/7-9/8-9/8 and 1-11/9-11/8-14/9 with steps 11/9-9/8-9/8-9/7. Finally, there are two pentacircle pentads, inversely related: 1-11/9-11/8-11/7-16/9 with steps 11/9-9/8-8/7-9/8-9/8 and 1-11/9-11/8-14/9-16/9 with steps 11/9-9/8-9/8-8/7-9/8.<br />
| | * 1–11/8–14/9–7/4 with steps 11/8, 9/8, 9/8, 8/7; |
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| | * 1–11/9–11/7–16/9 with steps 11/9, 9/7, 9/8, 9/8, and its inverse |
| Equal divisions with pentacircle chords include 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, 208, 266e and 433bce.</body></html></pre></div> | | * 1–11/9–11/8–14/9 with steps 11/9, 9/8, 9/8, 9/7. |
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| | Finally, there are two pentacircle pentads, inversely related: |
| | * 1–11/9–11/8–11/7–16/9 with steps 11/9, 9/8, 8/7, 9/8, 9/8, and its inverse |
| | * 1–11/9–11/8–14/9–16/9 with steps 11/9, 9/8, 9/8, 8/7, 9/8. |
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| | [[Equal temperament]]s with pentacircle chords include {{EDOs| 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, and 208 }}, with 208edo giving the [[optimal patent val]]. |
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| | [[Category:11-odd-limit chords]] |
| | [[Category:Essentially tempered chords]] |
| | [[Category:Triads]] |
| | [[Category:Tetrads]] |
| | [[Category:Pentads]] |
| | [[Category:Pentacircle]] |