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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''Island chords''' are [[dyadic chord|essentially tempered chords]] tempered by the island comma, [[676/675]].
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>2014-06-06 11:10:16 UTC</tt>.<br>
There are 9 triads, 37 tetrads, 51 pentads, 29 hexads and 6 heptads as 2.3.5.13 subgroup [[15-odd-limit]] essentially tempered chords.
: The original revision id was <tt>513103752</tt>.<br>
 
: The revision comment was: <tt></tt><br>
For triads, there are one palindromic chord and four 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>
 
<h4>Original Wikitext content:</h4>
The palindromic triad consists of two [[semifourth]]s and one [[perfect fifth]], splitting a fourth in two:
<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 **island tetrad** is an [[Dyadic chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] which under [[octave reduction]] consists of three [[15_13|15/13]] intervals followed by a [[13_10|13/10]], which closes on the octave since the [[island comma]], [[676_675|676/675]], is [[tempering out|tempered out]]; in other words a 15/13-15/13-15/13-13/10 chord. It can also be viewed as an island tempered version of 1-15/13-[[4_3|4/3]]-[[20_13|20/13]]. Contained within it are a [[barbados triad]], the 1-13/10-[[3_2|3/2]] chord, and an [[island triad]], the 1-15/13-4/3 chord, which in another position is the 1-3/2-[[26_15|26/15]] chord. Another island chord of interest is a 26/15 over a major triad, 1-5/4-3/2-26/15, 5/4-6/5-15/13-15/13 in terms of intervals.</pre></div>
* 1–15/13–4/3 with steps of 15/13, 15/13, 3/2.
<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;island tetrad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;strong&gt;island tetrad&lt;/strong&gt; is an &lt;a class="wiki_link" href="/Dyadic%20chord#Essentially tempered dyadic chords"&gt;essentially tempered dyadic chord&lt;/a&gt; which under &lt;a class="wiki_link" href="/octave%20reduction"&gt;octave reduction&lt;/a&gt; consists of three &lt;a class="wiki_link" href="/15_13"&gt;15/13&lt;/a&gt; intervals followed by a &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt;, which closes on the octave since the &lt;a class="wiki_link" href="/island%20comma"&gt;island comma&lt;/a&gt;, &lt;a class="wiki_link" href="/676_675"&gt;676/675&lt;/a&gt;, is &lt;a class="wiki_link" href="/tempering%20out"&gt;tempered out&lt;/a&gt;; in other words a 15/13-15/13-15/13-13/10 chord. It can also be viewed as an island tempered version of 1-15/13-&lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;-&lt;a class="wiki_link" href="/20_13"&gt;20/13&lt;/a&gt;. Contained within it are a &lt;a class="wiki_link" href="/barbados%20triad"&gt;barbados triad&lt;/a&gt;, the 1-13/10-&lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; chord, and an &lt;a class="wiki_link" href="/island%20triad"&gt;island triad&lt;/a&gt;, the 1-15/13-4/3 chord, which in another position is the 1-3/2-&lt;a class="wiki_link" href="/26_15"&gt;26/15&lt;/a&gt; chord. Another island chord of interest is a 26/15 over a major triad, 1-5/4-3/2-26/15, 5/4-6/5-15/13-15/13 in terms of intervals.&lt;/body&gt;&lt;/html&gt;</pre></div>
The inversely related pairs of chords are
* 1–5/4–13/9 with steps of 5/4, 15/13, 18/13, and its inverse
* 1–15/13–13/9 with steps of 15/13, 5/4, 18/13;
* 1–13/10–18/13 with steps of 13/10, 16/15, 13/9, and its inverse
* 1–16/15–18/13 with steps of 16/15, 13/10, 13/9;
* 1–15/13–13/10 with steps of 15/13, 9/8, 20/13, and its inverse
* 1–9/8–13/10 with steps of 9/8, 15/13, 20/13;
* 1–13/12–15/13 with steps of 13/12, 16/15, 26/15, and its inverse
* 1–16/15–15/13 with steps of 13/12, 16/15, 26/15.
 
For tetrads, there are seven palindromic chords and fifteen pairs of chords in inverse relationship.
 
One of the palindromic tetrads consists of three semifourths and one [[semisixth]],
* 1–13/10–3/2–26/15 with steps of 13/10, 15/13, 15/13, 15/13.
 
Aside from above, the following palindromic tetrad also contains a barbados triad (otonal [[10:13:15|1–13/10–3/2]] chord) and its inversion (utonal [[26:30:39|1–15/13–3/2]] chord),  
* 1–15/13–13/10–3/2 with steps of 15/13, 9/8, 15/13, 4/3.
 
The rest five palindromic tetrads are
* 1–15/13–13/9–5/3 with steps of 15/13, 5/4, 15/13, 6/5;
* 1–10/9–13/9–20/13 with steps of 10/9, 13/10, 16/15, 13/10;
* 1–15/13–5/4–13/9 with steps of 15/13, 13/12, 15/13, 18/13;
* 1–13/12–15/13–5/4 with steps of 13/12, 16/15, 13/12, 8/5;
* 1–16/15–15/13–16/13 with steps of 16/15, 13/12, 16/15, 13/8.
 
The inversely related pairs of chords are
* 1–9/8–13/10–13/8 with steps of 9/8, 15/13, 5/4, 16/13, and its inverse
* 1–5/4–13/9–13/8 with steps of 5/4, 15/13, 9/8, 16/13;
* 1–5/4–3/2–26/15 with steps of 5/4, 6/5, 15/13, 15/13, and its inverse
* 1–6/5–3/2–26/15 with steps of 6/5, 5/4, 15/13, 15/13;
* 1–5/4–13/9–20/13 with steps of 5/4, 15/13, 16/15, 13/10, and its inverse
* 1–5/4–13/8–26/15 with steps of 5/4, 13/10, 16/15, 15/13;
* 1–13/10–3/2–15/8 with steps of 13/10, 15/13, 5/4, 16/15, and its inverse
* 1–15/13–3/2–8/5 with steps of 15/13, 13/10, 16/15, 5/4;
* 1–13/10–18/13–3/2 with steps of 13/10, 16/15, 13/12, 4/3, and its inverse
* 1–13/12–15/13–3/2 with steps of 13/12, 16/15, 13/10, 4/3;
* 1–15/13–4/3–3/2 with steps of 15/13, 15/13, 9/8, 4/3, and its inverse
* 1–9/8–13/10–3/2 with steps of 9/8, 15/13, 15/13, 4/3;
* 1–18/13–3/2–8/5 with steps of 18/13, 13/12, 16/15, 5/4, and its inverse
* 1–13/12–3/2–15/8 with steps of 13/12, 18/13, 5/4, 16/15;
* 1–15/13–13/10–13/9 with steps of 15/13, 9/8, 10/9, 18/13, and its inverse
* 1–10/9–5/4–13/9 with steps of 10/9, 9/8, 15/13, 18/13;
* 1–18/13–3/2–26/15 with steps of 18/13, 13/12, 15/13, 15/13, and its inverse
* 1–13/12–3/2–26/15 with steps of 13/12, 18/13, 15/13, 15/13;
* 1–6/5–13/10–18/13 with steps of 6/5, 13/12, 16/15, 13/9, and its inverse
* 1–16/15–15/13–18/13 with steps of 16/15, 13/12, 6/5, 13/9;
* 1–15/13–13/10–18/13 with steps of 15/13, 9/8, 16/15, 13/9, and its inverse
* 1–16/15–6/5–18/13 with steps of 16/15, 9/8, 15/13, 13/9;
* 1–9/8–13/10–18/13 with steps of 9/8, 15/13, 16/15, 13/9, and its inverse
* 1–16/15–16/13–18/13 with steps of 16/15, 15/13, 9/8, 13/9;
* 1–15/13–16/13–4/3 with steps of 15/13, 16/15, 13/12, 3/2, and its inverse
* 1–13/12–15/13–4/3 with steps of 13/12, 16/15, 15/13, 3/2;
* 1–15/13–5/4–4/3 with steps of 15/13, 13/12, 16/15, 3/2, and its inverse
* 1–16/15–15/13–4/3 with steps of 16/15, 13/12, 15/13, 3/2;
* 1–9/8–6/5–13/10 with steps of 9/8, 16/15, 13/12, 20/13, and its inverse
* 1–13/12–15/13–13/10 with steps of 13/12, 16/15, 9/8, 20/13.
 
For pentads, there are one palindromic chord and twenty-five pairs of chords in inverse relationship.
 
The palindromic pentad consists of four semifourths and one [[whole tone]],
* 1–9/8–13/10–3/2–26/15 with steps of 9/8, 15/13, 15/13, 15/13, 15/13.
 
The inversely related pairs of chords are
* 1–6/5–18/13–3/2–26/15 with steps of 6/5, 15/13, 13/12, 15/13, 15/13, and its inverse
* 1–13/12–5/4–3/2–26/15 with steps of 13/12, 15/13, 6/5, 15/13, 15/13;
* 1–9/8–5/4–3/2–26/15 with steps of 9/8, 10/9, 6/5, 15/13, 15/13, and its inverse
* 1–6/5–4/3–3/2–26/15 with steps of 6/5, 10/9, 9/8, 15/13, 15/13;
* 1–6/5–18/13–3/2–26/15 with steps of 6/5, 13/12, 15/13, 15/13, 15/13, and its inverse
* 1–15/13–5/4–3/2–26/15 with steps of 15/13, 13/12, 6/5, 15/13, 15/13;
* 1–9/8–18/13–3/2–26/15 with steps of 9/8, 16/13, 13/12, 15/13, 15/13, and its inverse
* 1–9/8–13/10–3/2–13/8 with steps of 9/8, 15/13, 15/13, 13/12, 16/13;
* 1–5/4–3/2–8/5–26/15 with steps of 5/4, 6/5, 16/15, 13/12, 15/13, and its inverse
* 1–6/5–3/2–26/15–15/8 with steps of 6/5, 5/4, 15/13, 13/12, 16/15;
* 1–5/4–3/2–13/8–26/15 with steps of 5/4, 6/5, 13/12, 16/15, 15/13, and its inverse
* 1–6/5–3/2–26/15–24/13 with steps of 6/5, 5/4, 15/13, 16/15, 13/12;
* 1–15/13–13/9–5/3–15/8 with steps of 15/13, 5/4, 15/13, 9/8, 16/15, and its inverse
* 1–9/8–13/10–13/8–15/8 with steps of 9/8, 15/13, 5/4, 15/13, 16/15;
* 1–15/13–18/13–3/2–8/5 with steps of 15/13, 6/5, 13/12, 16/15, 5/4, and its inverse
* 1–13/12–13/10–3/2–15/8 with steps of 13/12, 6/5, 15/13, 5/4, 16/15;
* 1–5/4–4/3–3/2–26/15 with steps of 5/4, 16/15, 9/8, 15/13, 15/13, and its inverse
* 1–9/8–6/5–3/2–26/15 with steps of 9/8, 16/15, 5/4, 15/13, 15/13;
* 1–15/13–13/10–3/2–15/8 with steps of 15/13, 9/8, 15/13, 5/4, 16/15, and its inverse
* 1–15/13–13/10–3/2–8/5 with steps of 15/13, 9/8, 15/13, 16/15, 5/4;
* 1–13/10–18/13–3/2–8/5 with steps of 13/10, 16/15, 13/12, 16/15, 5/4, and its inverse
* 1–13/12–15/13–3/2–15/8 with steps of 13/12, 16/15, 13/10, 5/4, 16/15;
* 1–13/10–18/13–3/2–9/5 with steps of 13/10, 16/15, 13/12, 6/5, 10/9, and its inverse
* 1–13/12–15/13–3/2–5/3 with steps of 13/12, 16/15, 13/10, 10/9, 6/5;
* 1–9/8–5/4–13/8–26/15 with steps of 9/8, 10/9, 13/10, 16/15, 15/13, and its inverse
* 1–15/13–16/13–8/5–16/9 with steps of 15/13, 16/15, 13/10, 10/9, 9/8;
* 1–13/10–3/2–13/8–26/15 with steps of 13/10, 15/13, 13/12, 16/15, 15/13, and its inverse
* 1–13/10–3/2–8/5–26/15 with steps of 13/10, 15/13, 16/15, 13/12, 15/13;
* 1–13/10–3/2–26/15–15/8 with steps of 13/10, 15/13, 15/13, 13/12, 16/15, and its inverse
* 1–13/10–18/13–3/2–26/15 with steps of 13/10, 16/15, 13/12, 15/13, 15/13;
* 1–13/10–3/2–13/8–15/8 with steps of 13/10, 15/13, 13/12, 15/13, 16/15, and its inverse
* 1–15/13–3/2–8/5–24/13 with steps of 15/13, 13/10, 16/15, 15/13, 13/12;
* 1–6/5–13/10–18/13–3/2 with steps of 6/5, 13/12, 16/15, 13/12, 4/3, and its inverse
* 1–13/12–15/13–5/4–3/2 with steps of 13/12, 16/15, 13/12, 6/5, 4/3;
* 1–15/13–5/4–4/3–3/2 with steps of 15/13, 13/12, 16/15, 9/8, 4/3, and its inverse
* 1–9/8–6/5–13/10–3/2 with steps of 9/8, 16/15, 13/12, 15/13, 4/3;
* 1–9/8–13/10–18/13–3/2 with steps of 9/8, 15/13, 16/15, 13/12, 4/3, and its inverse
* 1–13/12–15/13–4/3–3/2 with steps of 13/12, 16/15, 15/13, 9/8, 4/3;
* 1–15/13–13/10–18/13–3/2 with steps of 15/13, 9/8, 16/15, 13/12, 4/3, and its inverse
* 1–13/12–15/13–13/10–3/2 with steps of 13/12, 16/15, 9/8, 15/13, 4/3;
* 1–18/13–3/2–8/5–26/15 with steps of 18/13, 13/12, 16/15, 13/12, 15/13, and its inverse
* 1–13/12–3/2–26/15–15/8 with steps of 13/12, 18/13, 15/13, 13/12, 16/15;
* 1–18/13–3/2–8/5–9/5 with steps of 18/13, 13/12, 16/15, 9/8, 10/9, and its inverse
* 1–13/12–3/2–5/3–15/8 with steps of 13/12, 18/13, 10/9, 9/8, 16/15;
* 1–13/12–3/2–13/8–15/8 with steps of 13/12, 18/13, 13/12, 15/13, 16/15, and its inverse
* 1–13/12–3/2–13/8–26/15 with steps of 13/12, 18/13, 13/12, 16/15, 15/13;
* 1–9/8–6/5–13/10–18/13 with steps of 9/8, 16/15, 13/12, 16/15, 13/9, and its inverse
* 1–16/15–15/13–16/13–18/13 with steps of 16/15, 13/12, 16/15, 9/8, 13/9;
* 1–13/12–15/13–5/4–4/3 with steps of 13/12, 16/15, 13/12, 16/15, 3/2, and its inverse
* 1–16/15–15/13–16/13–4/3 with steps of 16/15, 13/12, 16/15, 13/12, 3/2.
 
For hexads, there are three palindromic chords and thirteen pairs of chords in inverse relationship. The palindromic chords are
* 1–13/12–5/4–3/2–26/15–15/8 with steps of 13/12, 15/13, 6/5, 15/13, 13/12, 16/15;
* 1–13/12–15/13–5/4–3/2–5/3 with steps of 13/12, 16/15, 13/12, 6/5, 10/9, 6/5;
* 1–13/12–3/2–13/8–26/15–15/8 with steps of 13/12, 18/13, 13/12, 16/15, 13/12, 16/15.
 
The inversely related pairs of chords are
* 1–15/13–5/4–4/3–3/2–26/15 with steps of 15/13, 13/12, 16/15, 9/8, 15/13, 15/13, and its inverse
* 1–9/8–6/5–13/10–3/2–26/15 with steps of 9/8, 16/15, 13/12, 15/13, 15/13, 15/13;
* 1–9/8–13/10–3/2–13/8–26/15 with steps of 9/8, 15/13, 15/13, 13/12, 16/15, 15/13, and its inverse
* 1–9/8–13/10–18/13–3/2–26/15 with steps of 9/8, 15/13, 16/15, 13/12, 15/13, 15/13;
* 1–9/8–6/5–18/13–3/2–26/15 with steps of 9/8, 16/15, 15/13, 13/12, 15/13, 15/13, and its inverse
* 1–13/12–5/4–4/3–3/2–26/15 with steps of 13/12, 15/13, 16/15, 9/8, 15/13, 15/13;
* 1–6/5–4/3–3/2–8/5–26/15 with steps of 6/5, 10/9, 9/8, 16/15, 13/12, 15/13, and its inverse
* 1–9/8–5/4–3/2–26/15–15/8 with steps of 9/8, 10/9, 6/5, 15/13, 13/12, 16/15;
* 1–6/5–13/10–18/13–3/2–26/15 with steps of 6/5, 13/12, 16/15, 13/12, 15/13, 15/13, and its inverse
* 1–13/12–15/13–5/4–3/2–26/15 with steps of 13/12, 16/15, 13/12, 6/5, 15/13, 15/13;
* 1–6/5–18/13–3/2–26/15–24/13 with steps of 6/5, 15/13, 13/12, 15/13, 16/15, 13/12, and its inverse
* 1–13/12–5/4–3/2–13/8–26/15 with steps of 13/12, 15/13, 6/5, 13/12, 16/15, 15/13;
* 1–6/5–13/10–3/2–8/5–26/15 with steps of 6/5, 13/12, 15/13, 16/15, 13/12, 15/13, and its inverse
* 1–15/13–5/4–3/2–26/15–15/8 with steps of 15/13, 13/12, 6/5, 15/13, 13/12, 16/15;
* 1–6/5–4/3–3/2–26/15–24/13 with steps of 6/5, 10/9, 9/8, 15/13, 16/15, 13/12, and its inverse
* 1–9/8–5/4–3/2–8/5–26/15 with steps of 9/8, 10/9, 6/5, 13/12, 16/15, 15/13;
* 1–5/4–3/2–13/8–26/15–15/8 with steps of 5/4, 6/5, 13/12, 16/15, 13/12, 16/15, and its inverse
* 1–6/5–3/2–8/5–26/15–24/13 with steps of 6/5, 5/4, 16/15, 13/12, 16/15, 13/12;
* 1–15/13–13/10–18/13–3/2–8/5 with steps of 15/13, 9/8, 16/15, 13/12, 16/15, 5/4, and its inverse
* 1–13/12–15/13–13/10–3/2–15/8 with steps of 13/12, 16/15, 9/8, 15/13, 5/4, 16/15;
* 1–13/10–18/13–3/2–8/5–26/15 with steps of 13/10, 16/15, 13/12, 16/15, 13/12, 15/13, and its inverse
* 1–13/12–15/13–3/2–26/15–15/8 with steps of 13/12, 16/15, 13/10, 15/13, 13/12, 16/15;
* 1–13/10–18/13–3/2–8/5–9/5 with steps of 13/10, 16/15, 13/12, 16/15, 9/8, 10/9, and its inverse
* 1–13/12–15/13–3/2–5/3–15/8 with steps of 13/12, 16/15, 13/10, 10/9, 9/8, 16/15;
* 1–9/8–6/5–13/10–18/13–3/2 with steps of 9/8, 16/15, 13/12, 16/15, 13/12, 4/3, and its inverse
* 1–13/12–15/13–5/4–4/3–3/2 with steps of 13/12, 16/15, 13/12, 16/15, 9/8, 4/3.
 
Finally, there are three pairs of heptads in inverse relationship:
* 1–9/8–6/5–13/10–18/13–3/2–26/15 with steps of 9/8, 16/15, 13/12, 16/15, 13/12, 15/13, 15/13, and its inverse
* 1–13/12–15/13–5/4–4/3–3/2–26/15 with steps of 13/12, 16/15, 13/12, 16/15, 9/8, 15/13, 15/13;
* 1–13/12–5/4–3/2–13/8–26/15–15/8 with steps of 13/12, 15/13, 6/5, 13/12, 16/15, 13/12, 16/15, and its inverse
* 1–13/12–15/13–5/4–3/2–26/15–15/8 with steps of 13/12, 16/15, 13/12, 6/5, 15/13, 13/12, 16/15;
* 1–13/12–15/13–5/4–4/3–3/2–5/3 with steps of 13/12, 16/15, 13/12, 16/15, 9/8, 10/9, 6/5, and its inverse
* 1–13/12–15/13–5/4–3/2–5/3–15/8 with steps of 13/12, 16/15, 13/12, 6/5, 10/9, 9/8, 16/15.
 
Equal temperaments with island chords include {{Optimal ET sequence| 10, 15, 19, 24, 29, 34, 43, 53, 58, 72, 77, 87, 111, 130, 140, 164, 183 and 217 }}.
 
== See also ==
* [[Arto and tendo theory]]
* [[The Archipelago]]
 
[[Category:15-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Heptads]]
[[Category:Island]]
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