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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:genewardsmith|genewardsmith]] and made on <tt>2011-08-06 19:43:11 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>244647213</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 thirds making up a 7/5, which implies tempering by cuthbert, the 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, leading to a garibert tempering of 1-13/11-7/5-5/3. Equal temperaments with cuthbert triads include 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. 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 <em>cuthbert triad</em> is an <a class="wiki_link" href="/dyadic%20chord">essentially tempered dyadic triad</a> which consists of two 13/11 thirds making up a 7/5, which implies tempering by cuthbert, the 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, leading to a garibert tempering of 1-13/11-7/5-5/3. Equal temperaments with cuthbert triads include 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. Equal temperaments with garibert tetrads include 41, 53, and 94; and it is a characteristic chord of 13-limit <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]] |