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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''Cuthbert chords''' are [[essentially tempered dyadic chord]]s tempered by the cuthbert comma, [[847/845]]. |
| 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:xenwolf|xenwolf]] and made on <tt>2011-10-19 17:58:06 UTC</tt>.<br>
| | Cuthbert chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.5.7.11.13 [[subgroup]] [[13-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. |
| : The original revision id was <tt>266575852</tt>.<br>
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| : The revision comment was: <tt></tt><br>
| | The most basic cuthbert triad is a palindrome, consisting of two [[13/11]]'s making up [[7/5]], which implies tempering by cuthbert, the 847/845 comma. It is, in other words, the 847/845-tempered version of |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | * 1–13/11–7/5 chord with steps of 13/11, 13/11, 10/7. |
| <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 **cuthbert triad** is an [[dyadic chord|essentially tempered dyadic triad]] which consists of two [[13_11|13/11]] thirds making up a (sort of) [[7_5|7/5]], which implies tempering by [[cuthbert]], the [[847_845|847/845]] comma. It is, in other words, the 847/845-tempered version of 1-13/11-7/5. The cuthbert triad can be extended to the [[garibert tetrad]], which is the {275/273, 847/845} garibert tempering of a tetrad with steps of size 13/11-13/11-13/11-[[6_5|6/5]], leading to a garibert tempering of 1-13/11-7/5-[[5_3|5/3]]. Equal temperaments with cuthbert triads include [[29edo]], [[33edo]], [[37edo]], [[41edo]], [[46edo]], [[50edo]], [[53edo]], [[58edo]], [[70edo]], [[87edo]], [[94edo]], [[99edo]], [[103edo]], [[111edo]], [[128edo]], [[140edo]], [[149edo]], [[177edo]], [[190edo]], 198, 205, 227, 264, 284 and 388. Equal temperaments with garibert tetrads include 41, 53, and 94; and it is a characteristic chord of [[13-limit]] [[Schismatic family#Garibaldi|garibaldi temperament]].</pre></div>
| | There is an inversely related pair which is more squeezed and fit for a sort of secundal harmony: |
| <h4>Original HTML content:</h4>
| | * 1–11/10–13/11 with steps of 11/10, 14/13, 22/13, 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>cuthbert triad</title></head><body>The <strong>cuthbert triad</strong> is an <a class="wiki_link" href="/dyadic%20chord">essentially tempered dyadic triad</a> which consists of two <a class="wiki_link" href="/13_11">13/11</a> thirds making up a (sort of) <a class="wiki_link" href="/7_5">7/5</a>, which implies tempering by <a class="wiki_link" href="/cuthbert">cuthbert</a>, the <a class="wiki_link" href="/847_845">847/845</a> comma. It is, in other words, the 847/845-tempered version of 1-13/11-7/5. The cuthbert triad can be extended to the <a class="wiki_link" href="/garibert%20tetrad">garibert tetrad</a>, which is the {275/273, 847/845} garibert tempering of a tetrad with steps of size 13/11-13/11-13/11-<a class="wiki_link" href="/6_5">6/5</a>, leading to a garibert tempering of 1-13/11-7/5-<a class="wiki_link" href="/5_3">5/3</a>. Equal temperaments with cuthbert triads include <a class="wiki_link" href="/29edo">29edo</a>, <a class="wiki_link" href="/33edo">33edo</a>, <a class="wiki_link" href="/37edo">37edo</a>, <a class="wiki_link" href="/41edo">41edo</a>, <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/50edo">50edo</a>, <a class="wiki_link" href="/53edo">53edo</a>, <a class="wiki_link" href="/58edo">58edo</a>, <a class="wiki_link" href="/70edo">70edo</a>, <a class="wiki_link" href="/87edo">87edo</a>, <a class="wiki_link" href="/94edo">94edo</a>, <a class="wiki_link" href="/99edo">99edo</a>, <a class="wiki_link" href="/103edo">103edo</a>, <a class="wiki_link" href="/111edo">111edo</a>, <a class="wiki_link" href="/128edo">128edo</a>, <a class="wiki_link" href="/140edo">140edo</a>, <a class="wiki_link" href="/149edo">149edo</a>, <a class="wiki_link" href="/177edo">177edo</a>, <a class="wiki_link" href="/190edo">190edo</a>, 198, 205, 227, 264, 284 and 388. Equal temperaments with garibert tetrads include 41, 53, and 94; and it is a characteristic chord of <a class="wiki_link" href="/13-limit">13-limit</a> <a class="wiki_link" href="/Schismatic%20family#Garibaldi">garibaldi temperament</a>.</body></html></pre></div>
| | * 1–14/13–13/11 with steps of 14/13, 11/10, 22/13. |
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| | They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic tetrads are |
| | * 1–11/10–13/11–13/10 chord with steps of 11/10, 14/13, 11/10, 20/13; |
| | * 1–14/13–13/11–14/11 chord with steps of 14/13, 11/10, 14/13, 11/7. |
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| | The inversely related pairs of tetrads are |
| | * 1–13/11–14/11–7/5 with steps of 13/11, 14/13, 11/10, 10/7, and its inverse |
| | * 1–11/10–13/11–7/5 with steps of 11/10, 14/13, 13/11, 10/7; |
| | * 1–13/11–13/10–7/5 with steps of 13/11, 11/10, 14/13, 10/7, and its inverse |
| | * 1–14/13–13/11–7/5 with steps of 14/13, 11/10, 13/11, 10/7. |
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| | Then there is an inversely related pair of pentads: |
| | * 1–11/10–13/11–13/10–7/5 with steps of 11/10, 14/13, 11/10, 14/13, 10/7, and its inverse |
| | * 1–14/13–13/11–14/11–7/5 with steps of 14/13, 11/10, 14/13, 11/10, 10/7. |
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| | Equal temperaments with cuthbert triads include {{Optimal ET sequence| 29, 33, 37, 41, 46, 50, 53, 58, 70, 87, 94, 99, 103, 111, 128, 140, 149, 177, 190, 198, 205, 227, 264, 284 and 388 }}. |
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| | == Garibert tetrad == |
| | The first cuthbert triad can be extended to the '''garibert tetrad''', which is the {[[275/273]], 847/845} garibert tempering of a tetrad, |
| | * 1–13/11–7/5–[[5/3]] with steps of size 13/11, 13/11, 13/11, [[6/5]]. |
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| | Equal temperaments with the garibert tetrad include {{Optimal ET sequence| 16, 29, 37, 41, 53 and 94 }}; and it is a characteristic chord of [[13-limit]] [[garibaldi temperament]]. |
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| | [[Category:13-odd-limit chords]] |
| | [[Category:Essentially tempered chords]] |
| | [[Category:Triads]] |
| | [[Category:Tetrads]] |
| | [[Category:Pentads]] |
| | [[Category:Cuthbert]] |
| | [[Category:Garibaldi]] |
| | [[Category:Garibert]] |
| | [[Category:Gassormic]] |