Undecimal marvel chords: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 286550916 - Original comment: **
mNo edit summary
 
(9 intermediate revisions by 5 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
An '''undecimal marvel chord''' is an [[essentially tempered chord]] of undecimal ([[11-limit]]) [[marvel]], with intervals in the [[tonality diamond]] of the [[11-odd-limit]]. Since [[225/224]] is tempered out in undecimal marvel, [[9-odd-limit]] [[marvel chords]] are undecimal marvel chords. Since [[385/384]] is tempered out, [[keenanismic chords]] are also undecimal marvel chords. Finally, since [[540/539]] is tempered out, [[swetismic chords]] are undecimal marvel chords. There are also undecimal marvel chords which are none of these, the essentially undecimal marvel chords.  
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>2011-12-15 12:24:53 UTC</tt>.<br>
: The original revision id was <tt>286550916</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">An //undecimal marvel chord// is an [[Dyadic chord#Essentially tempered dyadic chord|essentially tempered chord]] of undecimal (11-limit) marvel, with intervals in the tonality diamond of the 11 odd limit. Since 225/224 is tempered out in undecimal marvel, 9-limit [[marvel chords]] are undecimal marvel chords. Since 385/384 is tempered out, [[keenanismic chords]] are also undecimal marvel chords. Finally, since 540/539 is tempered out, [[swetismic chords]] are undecimal marvel chords. There are also undecimal marvel chords which are none of these, the essentially undecimal marvel chords. These are four pairs of inversely related tetrads, 1-5/4-11/8-8/5 with steps 5/4-11/10-7/6-5/4 and 1-5/4-16/11-8/5 with steps 5/4-7/6-11/10-5/4; 1-9/8-8/5-7/4 with steps 9/8-10/7-12/11-8/7 and 1-9/8-9/7-7/5 with steps 9/8-8/7-12/11-10/7; 1-9/8-11/8-8/5 with steps 9/8-11/9-7/6-5/4 and 1-5/4-16/11-16/9 with steps 5/4-7/6-11/9-9/8; and 1-5/4-8/5-7/4 with steps 5/4-9/7-12/11-8/7 and 1-5/4-10/7-14/9 with steps 5/4-8/7-12/11-9/7. There are six pairs of inversely related essentially undecimal marvel pentads: 1-9/8-5/4-11/8-8/5 with steps 9/8-10/9-11/10-7/6-5/4 and 1-5/4-16/11-8/5-16/9 with steps 5/4-7/6-11/10-10/9-9/8; 1-5/4-7/5-8/5-7/4 with steps 5/4-9/8-8/7-12/11-8/7 and 1-9/8-7/5-8/5-7/4 with steps 9/8-5/4-8/7-12/11-8/7; 1-5/4-16/11-8/5-7/4 with steps 5/4-7/6-11/10-12/11-8/7 and 1-8/7-5/4-11/8-8/5 with steps 8/7-12/11-11/10-7/6-5/4; 1-5/4-11/8-8/5-7/4 with steps 5/4-11/10-7/6-12/11-8/7 and 1-8/7-5/4-16/11-8/5 with steps 8/7-12/11-7/6-11/10-5/4; 1-9/8-11/8-8/5-7/4 with steps 9/8-11/9-7/6-12/11-8/7 and 1-11/9-11/8-11/7-12/7 with steps 11/9-9/8-8/7-12/11-7/6; and 1-9/8-5/4-8/5-7/4 with steps 9/8-10/9-9/7-12/11-8/7 and 1-9/7-10/7-8/5-11/6 with steps 9/7-10/9-9/8-8/7-12/11.


The three essentially undecimal marvel hexads are particularly interesting. One is palindromic: 1-9/8-5/4-7/5-8/5-7/4 with steps 9/8-10/9-9/8-8/7-12/11-8/7. The two others are an inversive pair: 1-9/8-5/4-11/8-8/5-7/4 with steps 9/8-10/9-11/10-7/6-12/11-8/7 and 1-8/7-5/4-16/11-8/5-16/9 with steps 8/7-12/11-7/6-11/10-10/9-9/8. The latter two have steps which are permutations of the steps of the 11-limit JI hexads.
These are four pairs of inversely related tetrads:  
* 1–5/4–11/8–8/5 with steps 5/4, 11/10, 7/6, 5/4, and its inverse
* 1–5/4–16/11–8/5 with steps 5/4, 7/6, 11/10, 5/4;
* 1–9/8–8/5–7/4 with steps 9/8, 10/7, 12/11, 8/7, and its inverse
* 1–9/8–9/7–7/5 with steps 9/8, 8/7, 12/11, 10/7;
* 1–9/8–11/8–8/5 with steps 9/8, 11/9, 7/6, 5/4, and its inverse
* 1–5/4–16/11–16/9 with steps 5/4, 7/6, 11/9, 9/8;
* 1–5/4–8/5–7/4 with steps 5/4, 9/7, 12/11, 8/7, and its inverse
* 1–5/4–10/7–14/9 with steps 5/4, 8/7, 12/11, 9/7.  


Equal divisions with undecimal marvel chords include 19, 22, 31, 41, 50, 53, 72, 81, 94, 103, 166, 175, 197e, 269ce and 341ce.
There are six pairs of inversely related essentially undecimal marvel pentads:
* 1–9/8–5/4–11/8–8/5 with steps 9/8, 10/9, 11/10, 7/6, 5/4, and its inverse
* 1–5/4–16/11–8/5–16/9 with steps 5/4, 7/6, 11/10, 10/9, 9/8;
* 1–5/4–7/5–8/5–7/4 with steps 5/4, 9/8, 8/7, 12/11, 8/7, and its inverse
* 1–9/8–7/5–8/5–7/4 with steps 9/8, 5/4, 8/7, 12/11, 8/7;
* 1–5/4–16/11–8/5–7/4 with steps 5/4, 7/6, 11/10, 12/11, 8/7, and its inverse
* 1–8/7–5/4–11/8–8/5 with steps 8/7, 12/11, 11/10, 7/6, 5/4;
* 1–5/4–11/8–8/5–7/4 with steps 5/4, 11/10, 7/6, 12/11, 8/7, and its inverse
* 1–8/7–5/4–16/11–8/5 with steps 8/7, 12/11, 7/6, 11/10, 5/4;
* 1–9/8–11/8–8/5–7/4 with steps 9/8, 11/9, 7/6, 12/11, 8/7, and its inverse
* 1–11/9–11/8–11/7–12/7 with steps 11/9, 9/8, 8/7, 12/11, 7/6;
* 1–9/8–5/4–8/5–7/4 with steps 9/8, 10/9, 9/7, 12/11, 8/7, and its inverse
* 1–9/7–10/7–8/5–11/6 with steps 9/7, 10/9, 9/8, 8/7, 12/11.


The three essentially undecimal marvel hexads are particularly interesting. One is palindromic:
* 1–9/8–5/4–7/5–8/5–7/4 with steps 9/8, 10/9, 9/8, 8/7, 12/11, 8/7.


</pre></div>
The two others are an inversive pair:  
<h4>Original HTML content:</h4>
* 1–9/8–5/4–11/8–8/5–7/4 with steps 9/8, 10/9, 11/10, 7/6, 12/11, 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;undecimal marvel chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;An &lt;em&gt;undecimal marvel chord&lt;/em&gt; is an &lt;a class="wiki_link" href="/Dyadic%20chord#Essentially tempered dyadic chord"&gt;essentially tempered chord&lt;/a&gt; of undecimal (11-limit) marvel, with intervals in the tonality diamond of the 11 odd limit. Since 225/224 is tempered out in undecimal marvel, 9-limit &lt;a class="wiki_link" href="/marvel%20chords"&gt;marvel chords&lt;/a&gt; are undecimal marvel chords. Since 385/384 is tempered out, &lt;a class="wiki_link" href="/keenanismic%20chords"&gt;keenanismic chords&lt;/a&gt; are also undecimal marvel chords. Finally, since 540/539 is tempered out, &lt;a class="wiki_link" href="/swetismic%20chords"&gt;swetismic chords&lt;/a&gt; are undecimal marvel chords. There are also undecimal marvel chords which are none of these, the essentially undecimal marvel chords. These are four pairs of inversely related tetrads, 1-5/4-11/8-8/5 with steps 5/4-11/10-7/6-5/4 and 1-5/4-16/11-8/5 with steps 5/4-7/6-11/10-5/4; 1-9/8-8/5-7/4 with steps 9/8-10/7-12/11-8/7 and 1-9/8-9/7-7/5 with steps 9/8-8/7-12/11-10/7; 1-9/8-11/8-8/5 with steps 9/8-11/9-7/6-5/4 and 1-5/4-16/11-16/9 with steps 5/4-7/6-11/9-9/8; and 1-5/4-8/5-7/4 with steps 5/4-9/7-12/11-8/7 and 1-5/4-10/7-14/9 with steps 5/4-8/7-12/11-9/7. There are six pairs of inversely related essentially undecimal marvel pentads: 1-9/8-5/4-11/8-8/5 with steps 9/8-10/9-11/10-7/6-5/4 and 1-5/4-16/11-8/5-16/9 with steps 5/4-7/6-11/10-10/9-9/8; 1-5/4-7/5-8/5-7/4 with steps 5/4-9/8-8/7-12/11-8/7 and 1-9/8-7/5-8/5-7/4 with steps 9/8-5/4-8/7-12/11-8/7; 1-5/4-16/11-8/5-7/4 with steps 5/4-7/6-11/10-12/11-8/7 and 1-8/7-5/4-11/8-8/5 with steps 8/7-12/11-11/10-7/6-5/4; 1-5/4-11/8-8/5-7/4 with steps 5/4-11/10-7/6-12/11-8/7 and 1-8/7-5/4-16/11-8/5 with steps 8/7-12/11-7/6-11/10-5/4; 1-9/8-11/8-8/5-7/4 with steps 9/8-11/9-7/6-12/11-8/7 and 1-11/9-11/8-11/7-12/7 with steps 11/9-9/8-8/7-12/11-7/6; and 1-9/8-5/4-8/5-7/4 with steps 9/8-10/9-9/7-12/11-8/7 and 1-9/7-10/7-8/5-11/6 with steps 9/7-10/9-9/8-8/7-12/11.&lt;br /&gt;
* 1–8/7–5/4–16/11–8/5–16/9 with steps 8/7, 12/11, 7/6, 11/10, 10/9, 9/8.  
&lt;br /&gt;
 
The three essentially undecimal marvel hexads are particularly interesting. One is palindromic: 1-9/8-5/4-7/5-8/5-7/4 with steps 9/8-10/9-9/8-8/7-12/11-8/7. The two others are an inversive pair: 1-9/8-5/4-11/8-8/5-7/4 with steps 9/8-10/9-11/10-7/6-12/11-8/7 and 1-8/7-5/4-16/11-8/5-16/9 with steps 8/7-12/11-7/6-11/10-10/9-9/8. The latter two have steps which are permutations of the steps of the 11-limit JI hexads.&lt;br /&gt;
The latter two have steps which are permutations of the steps of the 11-limit JI hexads.
&lt;br /&gt;
 
Equal divisions with undecimal marvel chords include 19, 22, 31, 41, 50, 53, 72, 81, 94, 103, 166, 175, 197e, 269ce and 341ce.&lt;/body&gt;&lt;/html&gt;</pre></div>
The essentially undecimal marvel chords number tetrads: 8, pentads: 12, hexads: 3, for a total of 23.
 
[[Equal temperament]]s with undecimal marvel chords include {{EDOs| 19, 22, 31, 41, 50, 53, 72, 81, 94, 103, 166, 175, 197e, 269ce and 341ce }}.
 
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Marvel]]

Latest revision as of 14:01, 15 October 2024

An undecimal marvel chord is an essentially tempered chord of undecimal (11-limit) marvel, with intervals in the tonality diamond of the 11-odd-limit. Since 225/224 is tempered out in undecimal marvel, 9-odd-limit marvel chords are undecimal marvel chords. Since 385/384 is tempered out, keenanismic chords are also undecimal marvel chords. Finally, since 540/539 is tempered out, swetismic chords are undecimal marvel chords. There are also undecimal marvel chords which are none of these, the essentially undecimal marvel chords.

These are four pairs of inversely related tetrads:

  • 1–5/4–11/8–8/5 with steps 5/4, 11/10, 7/6, 5/4, and its inverse
  • 1–5/4–16/11–8/5 with steps 5/4, 7/6, 11/10, 5/4;
  • 1–9/8–8/5–7/4 with steps 9/8, 10/7, 12/11, 8/7, and its inverse
  • 1–9/8–9/7–7/5 with steps 9/8, 8/7, 12/11, 10/7;
  • 1–9/8–11/8–8/5 with steps 9/8, 11/9, 7/6, 5/4, and its inverse
  • 1–5/4–16/11–16/9 with steps 5/4, 7/6, 11/9, 9/8;
  • 1–5/4–8/5–7/4 with steps 5/4, 9/7, 12/11, 8/7, and its inverse
  • 1–5/4–10/7–14/9 with steps 5/4, 8/7, 12/11, 9/7.

There are six pairs of inversely related essentially undecimal marvel pentads:

  • 1–9/8–5/4–11/8–8/5 with steps 9/8, 10/9, 11/10, 7/6, 5/4, and its inverse
  • 1–5/4–16/11–8/5–16/9 with steps 5/4, 7/6, 11/10, 10/9, 9/8;
  • 1–5/4–7/5–8/5–7/4 with steps 5/4, 9/8, 8/7, 12/11, 8/7, and its inverse
  • 1–9/8–7/5–8/5–7/4 with steps 9/8, 5/4, 8/7, 12/11, 8/7;
  • 1–5/4–16/11–8/5–7/4 with steps 5/4, 7/6, 11/10, 12/11, 8/7, and its inverse
  • 1–8/7–5/4–11/8–8/5 with steps 8/7, 12/11, 11/10, 7/6, 5/4;
  • 1–5/4–11/8–8/5–7/4 with steps 5/4, 11/10, 7/6, 12/11, 8/7, and its inverse
  • 1–8/7–5/4–16/11–8/5 with steps 8/7, 12/11, 7/6, 11/10, 5/4;
  • 1–9/8–11/8–8/5–7/4 with steps 9/8, 11/9, 7/6, 12/11, 8/7, and its inverse
  • 1–11/9–11/8–11/7–12/7 with steps 11/9, 9/8, 8/7, 12/11, 7/6;
  • 1–9/8–5/4–8/5–7/4 with steps 9/8, 10/9, 9/7, 12/11, 8/7, and its inverse
  • 1–9/7–10/7–8/5–11/6 with steps 9/7, 10/9, 9/8, 8/7, 12/11.

The three essentially undecimal marvel hexads are particularly interesting. One is palindromic:

  • 1–9/8–5/4–7/5–8/5–7/4 with steps 9/8, 10/9, 9/8, 8/7, 12/11, 8/7.

The two others are an inversive pair:

  • 1–9/8–5/4–11/8–8/5–7/4 with steps 9/8, 10/9, 11/10, 7/6, 12/11, 8/7, and its inverse
  • 1–8/7–5/4–16/11–8/5–16/9 with steps 8/7, 12/11, 7/6, 11/10, 10/9, 9/8.

The latter two have steps which are permutations of the steps of the 11-limit JI hexads.

The essentially undecimal marvel chords number tetrads: 8, pentads: 12, hexads: 3, for a total of 23.

Equal temperaments with undecimal marvel chords include 19, 22, 31, 41, 50, 53, 72, 81, 94, 103, 166, 175, 197e, 269ce and 341ce.

Retrieved from "https://en.xen.wiki/index.php?title=Undecimal_marvel_chords&oldid=160261"