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A '''swetismic chord''' is a [[Swetismic temperaments|swetismic]] ([[540/539]]) [[11-odd-limit]], [[essentially tempered chord]].
A '''swetismic chord''' is an [[essentially tempered chord]] tempered by the swetisma, [[540/539]].


There are six swetismic [[triad]]s, consisting of three pairs of chords in inverse relationship:
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.
 
There are six swetismic triads, consisting of three pairs of chords in inverse relationship:
* 1-7/5-12/7 with [[step]]s 7/5-11/9-7/6, and its inverse
* 1-7/5-12/7 with [[step]]s 7/5-11/9-7/6, and its inverse
* 1-7/6-10/7 with steps 7/6-11/9-7/5;
* 1-7/6-10/7 with steps 7/6-11/9-7/5;
Line 9: Line 11:
* 1-10/7-14/9 with steps 10/7-12/11-9/7.
* 1-10/7-14/9 with steps 10/7-12/11-9/7.


There are fifteen swetismic [[tetrad]]s, consisting of three palindromic (self-inverse) chords and six pairs of chords in inverse relationship. The palindromic tetrads are:
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;
* 1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;
Line 26: Line 28:
* 1-9/7-11/7-11/6 with steps 9/7-11/9-7/6-12/11;
* 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
* 1-7/6-9/7-11/6 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;
* 1-10/7-11/7-11/6 with steps 10/7-11/10-7/6-12/11; and
* and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6, and its inverse
* 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.
* 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.


Finally, there are six swetismic [[pentad]]s coming in three pairs:
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
* 1-7/6-9/7-3/2-11/6 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;
* 1-7/6-9/7-3/2-18/11 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
* 1-7/6-10/7-5/3-11/6 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;
* 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10; and
* and 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11, and its inverse
* 1-7/6-9/7-10/7-11/6 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.
* 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.
The 11-odd-limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.


If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.
If we are willing to consider the [[15-odd-limit]], there are also 15-odd-limit swetismic tetrads of 1-9/7-3/2-7/4, 1-7/6-3/2-12/7, 1-11/9-10/7-5/3 and 1-7/6-15/11-5/3 with steps 9/7-7/6-7/6-8/7, 7/6-9/7-8/7-7/6, 11/9-7/6-7/6-6/5 and 7/6-7/6-11/9-6/5.
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