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Pentacircle chords: Difference between revisions

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**Imported revision 264503164 - Original comment: **
 
It's important to single ou the palindromic triad cuz it's the most fundamental form of these chords. The rest can be viewed as variations on it
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A '''pentacircle chord''' is an [[essentially tempered dyadic chord]] in the 2.9.7.11 [[subgroup]] in the [[11-odd-limit]], [[tempering out]] the pentacircle comma, [[896/891]].  
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>2011-10-13 14:44:59 UTC</tt>.<br>
Pentacircle chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.9.7.11 [[subgroup]] [[11-odd-limit]], meaning that there are 3 [[triad]]s, 6 [[tetrad]]s and 2 [[pentad]]s, for a total of 11 distinct chord structures.
: The original revision id was <tt>264503164</tt>.<br>
 
: The revision comment was: <tt></tt><br>
The three pentacircle triads include a palindrome since it identifies [[14/11]] by a stack of two [[9/8]]'s:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
* 1–9/8–14/11 with steps 9/8, 9/8, 11/7.
<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 pentacircle tetrad is one of three [[Dyadic chord#Essentially tempered dyadic chords|essentially tempered dyadic chords]]. It is either 1-9/8-11/8-14/9, 1-9/8-11/8-16/9, 1-11/9-11/8-14/9, with steps 9/8-11/9-9/8-9/7, 9/8-11/9-9/7-9/8, 11/9-9/8-9/8-9/7.</pre></div>
And an inversely related pair:
<h4>Original HTML content:</h4>
* 1–9/8–16/11 with steps 9/8, 9/7, 11/8;
<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;pentacircle chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A pentacircle tetrad is one of three &lt;a class="wiki_link" href="/Dyadic%20chord#Essentially tempered dyadic chords"&gt;essentially tempered dyadic chords&lt;/a&gt;. It is either 1-9/8-11/8-14/9, 1-9/8-11/8-16/9, 1-11/9-11/8-14/9, with steps 9/8-11/9-9/8-9/7, 9/8-11/9-9/7-9/8, 11/9-9/8-9/8-9/7.&lt;/body&gt;&lt;/html&gt;</pre></div>
* 1–9/8–14/9 with steps 9/8, 11/8, 9/7;
 
The tetrads include the palindromic
* 1–9/8–14/9–7/4 with steps 9/8, 11/8, 9/8, 8/7;
* 1–9/8–11/8–14/9 with steps 9/8, 11/9, 9/8, 9/7.  
 
And the inversely related pairs
* 1–11/8–11/7–16/9 with steps 11/8, 8/7, 9/8, 9/8, and its inverse
* 1–11/8–14/9–7/4 with steps 11/8, 9/8, 9/8, 8/7;
* 1–11/9–11/7–16/9 with steps 11/9, 9/7, 9/8, 9/8, and its inverse
* 1–11/9–11/8–14/9 with steps 11/9, 9/8, 9/8, 9/7.
 
Finally, there are two pentacircle pentads, inversely related:
* 1–11/9–11/8–11/7–16/9 with steps 11/9, 9/8, 8/7, 9/8, 9/8, and its inverse
* 1–11/9–11/8–14/9–16/9 with steps 11/9, 9/8, 9/8, 8/7, 9/8.
 
[[Equal temperament]]s with pentacircle chords include {{EDOs| 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, and 208 }}, with 208edo giving the [[optimal patent val]].
 
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Pentacircle]]
Retrieved from "https://en.xen.wiki/w/Pentacircle_chords"