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Marveltwin chords: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''Marveltwin chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the marveltwin comma, [[325/324]].
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>2011-07-28 04:06:22 UTC</tt>.<br>
There are 6 triads, 18 tetrads, 14 pentads and 3 hexads as 2.3.5.13 subgroup [[13-odd-limit]] essentially tempered chords.
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One marveltwin triad is a palindrome since it identifies [[13/9]] by a stack of two [[6/5]] minor thirds, that is,  
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
* 1–6/5–13/9 with steps of 6/5, 6/5, [[18/13]].
<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">The marveltwin triad is a 13-limit [[dyadic chord|essentially tempered dyadic chord]] which consists of two stacked minor thirds followed by an 18/13, that is, a 6/5-6/5-18/13 chord, tempered in [[marvelwin comma|marveltwin]]. In other words, an 1-6/5-13/9 chord tempered in marveltwin. It makes for an instructive comparison with the septimal diminished triad, 1-6/5-10/7 in starling, and might also be called a tridecimal diminished triad. It can be extended to the marveltwin tetrad, which is 1-6/5-13/9-26/15 in marveltwin, which is a 15-limit essentially tempered dyadic chord. Equal temperaments with marveltwin triads include 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333.</pre></div>
It makes for an instructive comparison with the septimal diminished triad, 1–6/5–[[10/7]] in [[starling]], and might also be called a tridecimal diminished triad.
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;marveltwin triad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The marveltwin triad is a 13-limit &lt;a class="wiki_link" href="/dyadic%20chord"&gt;essentially tempered dyadic chord&lt;/a&gt; which consists of two stacked minor thirds followed by an 18/13, that is, a 6/5-6/5-18/13 chord, tempered in &lt;a class="wiki_link" href="/marvelwin%20comma"&gt;marveltwin&lt;/a&gt;. In other words, an 1-6/5-13/9 chord tempered in marveltwin. It makes for an instructive comparison with the septimal diminished triad, 1-6/5-10/7 in starling, and might also be called a tridecimal diminished triad. It can be extended to the marveltwin tetrad, which is 1-6/5-13/9-26/15 in marveltwin, which is a 15-limit essentially tempered dyadic chord. Equal temperaments with marveltwin triads include 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333.&lt;/body&gt;&lt;/html&gt;</pre></div>
Another palindromic triad consists of [[16/13]] found as a stack of two [[10/9]] whole tones, that is,
* 1–10/9–16/13 with steps of 10/9, 10/9, [[13/8]].
 
We also have those built by
* 1–[[5/4]]–18/13 with steps of 5/4, 10/9, 13/9, and its inverse
* 1–10/9–18/13 with steps of 10/9, 5/4, 13/9;
* 1–[[5/3]]–[[24/13]] with steps of 5/3, 10/9, [[13/12]], and its inverse
* 1–10/9–24/13 with steps of 10/9, 5/3, 13/12.
 
For tetrads, there are four palindromic chords and seven pairs of chords in inverse relationship. The palindromic chords are
* 1–10/9–18/13–20/13 with steps of 10/9, 5/4, 10/9, 13/10;
* 1–10/9–5/4–18/13 with steps of 10/9, 9/8, 10/9, 13/9;
* 1–10/9–6/5–4/3 with steps of 10/9, 13/12, 10/9, 3/2;
* 1–13/12–6/5–13/10 with steps of 13/12, 10/9, 13/12, 20/13.
 
The inversely related pairs of chords are
* 1–18/13–3/2–5/3 with steps of 18/13, 13/12, 10/9, 6/5, and its inverse
* 1–13/12–3/2–9/5 with steps of 13/12, 18/13, 6/5, 10/9;
* 1–5/4–3/2–9/5 with steps of 5/4, 6/5, 6/5, 10/9, and its inverse
* 1–6/5–3/2–5/3 with steps of 6/5, 5/4, 10/9, 6/5;
* 1–5/4–18/13–3/2 with steps of 5/4, 10/9, 13/12, 4/3, and its inverse
* 1–13/12–6/5–3/2 with steps of 13/12, 10/9, 5/4, 4/3;
* 1–10/9–16/13–4/3 with steps of 10/9, 10/9, 13/12, 3/2, and its inverse
* 1–13/12–6/5–4/3 with steps of 13/12, 10/9, 10/9, 3/2;
* 1–5/4–18/13–20/13 with steps of 5/4, 10/9, 10/9, 13/10, and its inverse
* 1–10/9–16/13–20/13 with steps of 10/9, 10/9, 5/4, 13/10;
* 1–6/5–13/10–13/9 with steps of 6/5, 13/12, 10/9, 18/13, and its inverse
* 1–10/9–6/5–13/9 with steps of 10/9, 13/12, 6/5, 18/13;
* 1–9/8–5/4–18/13 with steps of 9/8, 10/9, 10/9, 13/9, and its inverse
* 1–10/9–16/13–18/13 with steps of 10/9, 10/9, 9/8, 13/9.
 
For pentads, there are two palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are
* 1–9/8–5/4–3/2–9/5 with steps of 9/8, 10/9, 6/5, 6/5, 10/9;
* 1–13/12–3/2–13/8–9/5 with steps of 13/12, 18/13, 13/12, 10/9, 10/9.
 
The inversely related pairs of chords are
* 1–18/13–3/2–5/3–9/5 with steps of 18/13, 13/12, 10/9, 13/12, 10/9, and its inverse
* 1–13/12–3/2–5/3–9/5 with steps of 13/12, 18/13, 10/9, 13/12, 10/9;
* 1–5/4–3/2–5/3–9/5 with steps of 5/4, 6/5, 10/9, 13/12, 10/9, and its inverse
* 1–6/5–3/2–5/3–9/5 with steps of 6/5, 5/4, 10/9, 13/12, 10/9;
* 1–5/4–3/2–13/8–9/5 with steps of 5/4, 6/5, 13/12, 10/9, 10/9, and its inverse
* 1–6/5–3/2–5/3–24/13 with steps of 6/5, 5/4, 10/9, 10/9, 13/12;
* 1–5/4–18/13–3/2–9/5 with steps of 5/4, 10/9, 13/12, 6/5, 10/9, and its inverse
* 1–13/12–6/5–3/2–5/3 with steps of 13/12, 10/9, 5/4, 10/9, 6/5;
* 1–9/8–5/4–18/13–3/2 with steps of 9/8, 10/9, 10/9, 13/12, 4/3, and its inverse
* 1–13/12–6/5–4/3–3/2 with steps of 13/12, 10/9, 10/9, 9/8, 4/3;
* 1–9/8–5/4–13/8–9/5 with steps of 9/8, 10/9, 13/10, 10/9, 10/9, and its inverse
* 1–9/8–5/4–18/13–9/5 with steps of 9/8, 10/9, 10/9, 13/10, 10/9.
 
For hexads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is
* 1–5/4–18/13–3/2–5/3–9/5 with steps of 5/4, 10/9, 13/12, 10/9, 13/12, 10/9.
 
The inversely related pair of chords is
* 1–6/5–4/3–3/2–5/3–24/13 with steps of 6/5, 10/9, 9/8, 10/9, 10/9, 13/12, and its inverse
* 1–9/8–5/4–3/2–13/8–9/5 with steps of 9/8, 10/9, 6/5, 13/12, 10/9, 10/9.
 
Equal temperaments with marveltwin chords include {{Optimal ET sequence| 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 246, 299 and 333 }}, with 333edo giving the [[optimal patent val]].
 
[[Category:13-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Marveltwin]]
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