Valinorsmic chords: Difference between revisions

Revision as of 23:29, 13 December 2011

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This revision was by author genewardsmith and made on 2011-12-13 23:29:31 UTC.

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A //valinorsmic chord// is a valinorsma (176/175) tempered [[Dyadic chord|essentially tempered chord]] in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.

If we are willing to go to the 15 odd limit, we get four alternative, valinorsmic, temperings of the four
[[keenanismic chords|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.

Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.

Original HTML content:

<html><head><title>valinorsmic chords</title></head><body>A <em>valinorsmic chord</em> is a valinorsma (176/175) tempered <a class="wiki_link" href="/Dyadic%20chord">essentially tempered chord</a> in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.<br />
<br />
If we are willing to go to the 15 odd limit, we get four alternative, valinorsmic, temperings of the four <br />
<a class="wiki_link" href="/keenanismic%20chords">keenanismic tetrads</a> which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.<br />
<br />
Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.</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:genewardsmith|genewardsmith]] and made on <tt>2011-12-10 21:45:42 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-13 23:29:31 UTC</tt>.<br>
-: The original revision id was <tt>284568832</tt>.<br>
+: The original revision id was <tt>285749696</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>
 <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">A valinorsmic tetrad is any of five 15-limit [[Dyadic chord|essentially tempered tetrads]] which are tempered by the valinorsma, 176/175. Four of them represent alternative, valinorsmic, temperings of the four 7-limit tetrads with steps 5/4-6/5-8/7-7/6 and 5/4-8/7-6/5-7/6 and their inversions 6/5-5/4-7/6-8/7 and 5/4-7/6-6/5-8/7, leading to 176/175 temperings of 1-5/4-10/7-12/7, 1-5/4-3/2-12/7, 1-6/5-3/2-7/4 and 1-5/4-22/15-7/4. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords. Aside from these, there are many more with smaller step sizes such as 11/10.</pre></div>
+<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 //valinorsmic chord// is a valinorsma (176/175) tempered [[Dyadic chord|essentially tempered chord]] in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.
+If we are willing to go to the 15 odd limit, we get four alternative, valinorsmic, temperings of the four
+[[keenanismic chords|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.
+Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.</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;valinorsmic chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A valinorsmic tetrad is any of five 15-limit &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;essentially tempered tetrads&lt;/a&gt; which are tempered by the valinorsma, 176/175. Four of them represent alternative, valinorsmic, temperings of the four 7-limit tetrads with steps 5/4-6/5-8/7-7/6 and 5/4-8/7-6/5-7/6 and their inversions 6/5-5/4-7/6-8/7 and 5/4-7/6-6/5-8/7, leading to 176/175 temperings of 1-5/4-10/7-12/7, 1-5/4-3/2-12/7, 1-6/5-3/2-7/4 and 1-5/4-22/15-7/4. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords. Aside from these, there are many more with smaller step sizes such as 11/10.&lt;/body&gt;&lt;/html&gt;</pre></div>
+<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;valinorsmic chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;em&gt;valinorsmic chord&lt;/em&gt; is a valinorsma (176/175) tempered &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;essentially tempered chord&lt;/a&gt; in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.&lt;br /&gt;
+&lt;br /&gt;
+If we are willing to go to the 15 odd limit, we get four alternative, valinorsmic, temperings of the four &lt;br /&gt;
+&lt;a class="wiki_link" href="/keenanismic%20chords"&gt;keenanismic tetrads&lt;/a&gt; which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.&lt;br /&gt;
+&lt;br /&gt;
+Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.&lt;/body&gt;&lt;/html&gt;</pre></div>

Valinorsmic chords: Difference between revisions

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