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An '''island chord''' is an [[15-odd-limit]] [[essentially tempered dyadic chord]] which is tempered by [[676/675]] (island comma).  
'''Island chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the island comma, [[676/675]].


The island tetrad under [[octave reduction]] consists of three [[15/13]] intervals followed by a [[13/10]], which closes on the octave since the island comma, [[676/675]], is [[tempering out|tempered out]]; in other words an island tempered version of
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.
* 1-15/13-[[4/3]]-[[20/13]], with steps 15/13-15/13-15/13-13/10.  


Contained within it are a '''barbados triad''',
For triads, there are one palindromic chord and four pairs of chords in inverse relationship.
* 1-13/10-[[3/2]], with steps 13/10-15/13-4/3,


its inversion,  
The palindromic triad consists of two [[semifourth]]s and one [[perfect fifth]], equating two [[15/13]]s and one [[4/3]]:
* 1-15/13-3/2, with steps 15/13-13/10-4/3,
* 1-15/13-4/3 with steps of 15/13-15/13-3/2.


and an '''island triad''',  
The inversely related pairs of chords are
* 1-15/13-4/3, with steps 15/13-15/13-3/2,  
* 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.


which in another position is the 1-3/2-[[26/15]] chord.  
For tetrads, there are seven palindromic chords and fifteen pairs of chords in inverse relationship.


Another island tetrad of interest is a 26/15 over a major triad,  
One of the palindromic tetrads consists of three semifourths and one [[semisixth]],
* 1-5/4-3/2-26/15, with steps 5/4-6/5-15/13-15/13,
* 1-13/10-3/2-26/15 with steps of 13/10-15/13-15/13-15/13.


and its inversion,  
Aside from above, the following palindromic tetrad also contains a [[List of root-3rd-P5 triads in JI|barbados triad]] (otonal 1-13/10-3/2 chord) and its inversion (utonal 1-15/13-3/2 chord),
* 1-6/5-3/2-26/15, with steps 6/5-5/4-15/13-15/13.  
* 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
* 1-15/13-4/3-16/9 with steps of 15/13-15/13-4/3-9/8;
* 1-5/4-4/3-13/9 with steps of 5/4-16/15-13/12-18/13, and its inverse
* 1-13/12-15/13-13/9 with steps of 13/12-16/15-5/4-18/13;
* 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;
* 1-15/13-4/3-13/9 with steps of 15/13-15/13-13/12-18/13, and its inverse
* 1-13/12-5/4-13/9 with steps of 13/12-15/13-15/13-18/13;
* 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;
* 1-15/13-5/4-4/3-20/13 with steps of 15/13-13/12-16/15-15/13-13/10, and its inverse
* 1-15/13-16/13-4/3-20/13 with steps of 15/13-16/15-13/12-15/13-13/10;
* 1-15/13-4/3-13/9-20/13 with steps of 15/13-15/13-13/12-16/15-13/10, and its inverse
* 1-16/15-15/13-4/3-20/13 with steps of 16/15-13/12-15/13-15/13-13/10;
* 1-15/13-5/4-13/9-20/13 with steps of 15/13-13/12-15/13-16/15-13/10, and its inverse
* 1-16/15-16/13-4/3-20/13 with steps of 16/15-15/13-13/12-15/13-13/10;
* 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 ==
== See also ==
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[[Category:Triads]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Heptads]]
[[Category:Island]]
[[Category:Island]]
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