Valinorsmic chords: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 287092170 - Original comment: **
m Improve readability; recategorize
 
(10 intermediate revisions by 4 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A '''valinorsmic chord''' is a [[valinorsma]] (176/175) tempered [[essentially tempered chord]].  
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>2011-12-17 17:04:32 UTC</tt>.<br>
: The original revision id was <tt>287092170</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 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.


The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.
Valinorsmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.5.7.11 [[subgroup]] [[11-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.  


If we are willing to go to the 15 odd limit, we get four alternative, valinorsmic, temperings of the four
There are three valinorsmic triads: the valinorsmic version of the augmented triad,
[[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.
* 1–5/4–8/5 with steps 5/4, 14/11, 5/4,


Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.</pre></div>
and an inversely related pair,  
<h4>Original HTML content:</h4>
* 1–8/5–7/4 with steps 8/5, 11/10, 8/7, 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">&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;
* 1–8/7–5/4 with steps 8/7, 11/10, 8/5.  
&lt;br /&gt;
 
The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.&lt;br /&gt;
Valinorsmic tetrads are six in number, consisting of two palindromic chords and two pairs of inversely related chords. The palindromes are  
&lt;br /&gt;
* 1–11/10–5/4–7/4 with steps 11/10, 8/7, 7/5, 8/7, and its inverse
If we are willing to go to the 15 odd limit, we get four alternative, valinorsmic, temperings of the four &lt;br /&gt;
* 1–11/10–5/4–11/8 with steps 11/10, 8/7, 11/10, 16/11.  
&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;
The rest are  
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>
* 1–5/4–8/5–7/4 with steps 5/4, 14/11, 11/10, 8/7, and its inverse
* 1–5/4–10/7–11/7 with steps 5/4, 8/7, 11/10, 14/11;
* 1–5/4–11/8–11/7 with steps 5/4, 11/10, 8/7, 14/11, and its inverse
* 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 its inverse
* 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 temperament]]s with valinorsmic chords include {{EDOs| 22, 31, 43, 46, 53, 58, 68, 80, 89, 111 }} with 111edo giving the [[optimal patent val]].
 
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Valinorsmic]]

Latest revision as of 09:20, 10 October 2024

A valinorsmic chord is a valinorsma (176/175) tempered essentially tempered chord.

Valinorsmic chords are of pattern 1a in the 2.5.7.11 subgroup 11-odd-limit, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

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 its inverse
  • 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 two 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 its inverse
  • 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 its inverse
  • 1–5/4–10/7–11/7 with steps 5/4, 8/7, 11/10, 14/11;
  • 1–5/4–11/8–11/7 with steps 5/4, 11/10, 8/7, 14/11, and its inverse
  • 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 its inverse
  • 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 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 with 111edo giving the optimal patent val.

Retrieved from "https://en.xen.wiki/index.php?title=Valinorsmic_chords&oldid=159386"