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Werckismic chords: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A '''werckismic chord''' is an [[essentially tempered dyadic chord]] tempered by the werckisma, [[441/440]].  
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>2011-07-31 16:41:55 UTC</tt>.<br>
Werckismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the [[11-odd-limit]], meaning that there are 6 [[triad]]s, 15 [[tetrad]]s and 6 [[pentad]]s, for a total of 27 distinct chord structures.  
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The werckismic triads consist of three pairs of inversely related chords:  
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
* 1–11/9–7/5 with steps 11/9, 8/7, 10/7, and its inverse
<h4>Original Wikitext content:</h4>
* 1–11/9–7/4 with steps 11/9, 10/7, 8/7;
<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 //werckismic triad// is one of two 11-limit [[dyadic chord|essentially tempered dyadic chords]] in inverse relation, constructed from the intervals 8/7, 11/9 and 10/7 which make up an octave under werckismic (441/440) tempering. That is, tempered versions of either 1-8/7-7/5 or 1-11/9-7/5. The triads can be extended to the //werckismic tetrad//, 1-8/7-7/5-8/5, with steps of size 8/7-11/9-8/7-5/4. Equal temperaments with werckismic triads and tetrads include 31, 41, 46, 58, 72, 77, 84, 103, 118, 130, 159, 171, 190, 248, 289 and 320.</pre></div>
* 1–11/7–7/4 with steps 11/7, 10/9, 8/7, and its inverse
<h4>Original HTML content:</h4>
* 1–11/7–9/5 with steps 11/7, 8/7, 10/9;
<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;werckismic chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;em&gt;werckismic triad&lt;/em&gt; is one of two 11-limit &lt;a class="wiki_link" href="/dyadic%20chord"&gt;essentially tempered dyadic chords&lt;/a&gt; in inverse relation, constructed from the intervals 8/7, 11/9 and 10/7 which make up an octave under werckismic (441/440) tempering. That is, tempered versions of either 1-8/7-7/5 or 1-11/9-7/5. The triads can be extended to the &lt;em&gt;werckismic tetrad&lt;/em&gt;, 1-8/7-7/5-8/5, with steps of size 8/7-11/9-8/7-5/4. Equal temperaments with werckismic triads and tetrads include 31, 41, 46, 58, 72, 77, 84, 103, 118, 130, 159, 171, 190, 248, 289 and 320.&lt;/body&gt;&lt;/html&gt;</pre></div>
* 1–7/5–11/7 with steps 7/5, 9/8, 14/11, and its inverse
* 1–14/11–10/7 with steps 14/11, 9/8, 7/5.
 
The werckismic tetrads consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are
* 1–5/4–10/7–7/4 with steps 5/4, 8/7, 11/9, 8/7;
* 1–9/8–10/7–11/7 with steps 9/8, 14/11, 11/10, 14/11;
* 1–14/11–7/5–16/9 with steps 14/11, 11/10, 14/11, 9/8.
 
The pairs of chords are:
* 1–11/9–11/7–7/4 with steps 11/9, 9/7, 10/9, 8/7, and its inverse
* 1–9/7–11/7–9/5 with steps 9/7, 11/9, 8/7, 10/9;
* 1–10/7–11/7–7/4 with steps 10/7, 11/10, 10/9, 8/7, and its inverse
* 1–8/7–14/11–7/5 with steps 8/7, 10/9, 11/10, 10/7;
* 1–9/8–10/7–7/4 with steps 9/8, 14/11, 11/9, 8/7, and its inverse
* 1–11/9–14/9–7/4 with steps 11/9, 14/11, 9/8, 8/7;
* 1–11/9–11/8–7/4 with steps 11/9, 9/8, 14/11, 8/7, and its inverse
* 1–14/11–10/7–7/4 with steps 14/11, 9/8, 11/9, 8/7;
* 1–9/8–5/4–10/7 with steps 9/8, 10/9, 8/7, 7/5, and its inverse
* 1–10/9–5/4–7/4 with steps 10/9, 9/8, 7/5, 8/7;
* 1–9/8–9/7–10/7 with steps 9/8, 8/7, 10/9, 7/5, and its inverse
* 1–9/8–11/7–7/4 with steps 9/8, 7/5, 10/9, 8/7.
 
The werckismic pentads consist of three pairs of chords in an inverse relationship:
* 1–9/8–5/4–10/7–7/4 with steps 9/8, 10/9, 8/7, 11/9, 8/7, and its inverse
* 1–11/9–7/5–14/9–7/4 with steps 11/9, 8/7, 10/9, 9/8, 8/7;
* 1–11/9–11/8–11/7–7/4 with steps 11/9, 9/8, 8/7, 10/9, 8/7, and its inverse
* 1–9/8–11/8–11/7–7/4 with steps 9/8, 11/9, 8/7, 10/9, 8/7;  
* 1–9/8–9/7–10/7–11/7 with steps 9/8, 8/7, 10/9, 11/10, 14/11, and its inverse
* 1–9/8–10/7–11/7–7/4 with steps 9/8, 14/11, 11/10, 10/9, 8/7.
 
[[Equal temperament]]s with werckismic chords include {{EDOs| 31, 41, 43, 46, 58, 72, 77, 84, 103, 118, 130, 159, 171, 190, 248, 289, and 320 }}, with [[320edo]] giving the [[optimal patent val]].
 
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Werckismic]]
Retrieved from "https://en.xen.wiki/w/Werckismic_chords"