Xenharmonic Wiki

Swetismic chords: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 243619319 - Original comment: **
m Improve readability; recategorize
 
(19 intermediate revisions by 7 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A '''swetismic chord''' is an [[essentially tempered chord]] tempered by the swetisma, [[540/539]].
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 17:03:40 UTC</tt>.<br>
Swetismic 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.  
: The original revision id was <tt>243619319</tt>.<br>
 
: The revision comment was: <tt></tt><br>
There are six swetismic triads, consisting of three pairs of chords in inverse relationship:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
* 1–7/5–12/7 with steps 7/5, 11/9, 7/6, and its inverse
<h4>Original Wikitext content:</h4>
* 1–7/6–10/7 with steps 7/6, 11/9, 7/5;
<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">The swetismic triad is either the 540/539-tempered version of a 7/6-11/9-7/5 chord or its inversion, an 11/9-7/6-7/5 chord. It is an 11-limit [[dyadic chord|essentially tempered triad]], and can also be characterized as the tempering of 1-7/6-10/7 or 1-11/9-10/7. It can be extended to the swetismic tetrad, the 7/6-11/9-7/6-6/5 chord, the swetismic tempering of 1-7/6-10/7-5/3. Equal temperaments with swetismic tetrads include 19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 130, 152, 183, 224, 354, 537 and 578.</pre></div>
* 1–7/6–9/7 with steps 7/6, 11/10, 14/9, and its inverse
<h4>Original HTML content:</h4>
* 1–14/9–12/7 with steps 14/9, 11/10, 7/6;
<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;swetismic chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The swetismic triad is either the 540/539-tempered version of a 7/6-11/9-7/5 chord or its inversion, an 11/9-7/6-7/5 chord. It is an 11-limit &lt;a class="wiki_link" href="/dyadic%20chord"&gt;essentially tempered triad&lt;/a&gt;, and can also be characterized as the tempering of 1-7/6-10/7 or 1-11/9-10/7. It can be extended to the swetismic tetrad, the 7/6-11/9-7/6-6/5 chord, the swetismic tempering of 1-7/6-10/7-5/3. Equal temperaments with swetismic tetrads include 19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 130, 152, 183, 224, 354, 537 and 578.&lt;/body&gt;&lt;/html&gt;</pre></div>
* 1–9/7–7/5 with steps 9/7, 12/11, 10/7, and its inverse
* 1–10/7–14/9 with steps 10/7, 12/11, 9/7.
 
There are fifteen swetismic tetrads, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:
 
* 1–7/6–9/7–3/2 with steps 7/6, 11/10, 7/6, 4/3;
* 1–6/5–7/5–12/7 with steps 6/5, 7/6, 11/9, 7/6;
* 1–9/7–7/5–9/5 with steps 9/7, 12/11, 9/7, 10/9.
 
The six pairs are:
 
* 1–9/7–3/2–11/6 with steps 9/7, 7/6, 11/9, 12/11, and its inverse
* 1–7/6–3/2–18/11 with steps 7/6, 9/7, 12/11, 11/9;
* 1–7/6–9/7–10/7 with steps 7/6, 11/10, 10/9, 7/5, and its inverse
* 1–7/5–14/9–12/7 with steps 7/5, 10/9, 11/10, 7/6;
* 1–7/6–9/7–18/11 with steps 7/6, 11/10, 14/11, 11/9, and its inverse
* 1–14/11–7/5–18/11 with steps 14/11, 11/10, 7/6, 11/9;
* 1–7/6–10/7–11/6 with steps 7/6, 11/9, 9/7, 12/11, and its inverse
* 1–9/7–11/7–11/6 with steps 9/7, 11/9, 7/6, 12/11;
* 1–7/6–9/7–11/6 with steps 7/6, 11/10, 10/7, 12/11, and its inverse
* 1–10/7–11/7–11/6 with steps 10/7, 11/10, 7/6, 12/11;
* 1–10/7–14/9–12/7 with steps 10/7, 12/11, 11/10, 7/6, and its inverse
* 1–7/6–9/7–7/5 with steps 7/6, 11/10, 12/11, 10/7.
 
Finally, there are six swetismic pentads coming in three pairs:
 
* 1–7/6–9/7–3/2–11/6 with steps 7/6, 11/10, 7/6, 11/9, 12/11, and its inverse
* 1–7/6–9/7–3/2–18/11 with steps 7/6, 11/10, 7/6, 12/11, 11/9;
* 1–7/6–10/7–5/3–11/6 with steps 7/6, 11/9, 7/6, 11/10, 12/11, and its inverse
* 1–7/6–10/7–5/3–20/11 with steps 7/6, 11/9, 7/6, 12/11, 11/10;  
* 1–7/6–9/7–10/7–11/6 with steps 7/6, 11/10, 10/9, 9/7, 12/11, and its inverse
* 1–9/7–10/7–11/7–11/6 with steps 9/7, 10/9, 11/10, 7/6, 12/11.
 
If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads, including something important for functional harmony. The ''swetismic dominant seventh chord'' is a tempering of
* 1–9/7–3/2–7/4 with steps 9/7, 7/6, 7/6, 8/7.
 
Its inversion might be called the ''swetismic half-diminished chord'', a tempering of  
* 1–7/6–3/2–12/7 with steps 7/6, 9/7, 8/7, 7/6.
 
We also have
* 1–11/9–10/7–5/3 with steps 11/9, 7/6, 7/6, 6/5; and its inverse
* 1–7/6–15/11–5/3 with steps 7/6, 7/6, 11/9, 6/5.
 
[[Equal temperament]]s with swetismic chords include {{EDOs| 19, 22, 31, 41, 53, 58, 72, 80, 94, 103, 111, 121, 130, 152, 183, 205, 224, 354, 537, 578, 761d, 1115de, 1339de, 1491de, 1715de and 1845de }}.
 
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Swetismic]]
Retrieved from "https://en.xen.wiki/w/Swetismic_chords"