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A ''swetismic chord'' is a swetismic (540/539) 11-odd-limit [[Dyadic chord|essentially tempered chord]].
A '''swetismic chord''' is an [[essentially tempered chord]] tempered by the swetisma, [[540/539]].
 
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:
There are six swetismic triads, consisting of three pairs of chords in inverse relationship:
* 1–7/5–12/7 with steps 7/5, 11/9, 7/6, and its inverse
* 1–7/6–10/7 with steps 7/6, 11/9, 7/5;
* 1–7/6–9/7 with steps 7/6, 11/10, 14/9, and its inverse
* 1–14/9–12/7 with steps 14/9, 11/10, 7/6;
* 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.


<ul><li>1-7/5-12/7 with steps 7/5-11/9-7/6 and 1-7/6-10/7 with steps 7/6-11/9-7/5;</li><li>1-7/6-9/7 with steps 7/6-11/10-14/9 and 1-14/9-12/7 with steps 14/9-11/10-7/6;</li><li>and 1-9/7-7/5 with steps 9/7-12/11-10/7 and 1-10/7-14/9 with steps 10/7-12/11-9/7.</li></ul>
There are fifteen swetismic tetrads, 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;
* 1–6/5–7/5–12/7 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.


<ul><li>1-7/6-9/7-3/2 with steps 7/6-11/10-7/6-4/3;</li><li>1-6/5-7/5-12/7 with steps 6/5-7/6-11/9-7/6;</li><li>and 1-9/7-7/5-9/5 with steps 9/7-12/11-9/7-10/9.</li></ul>The six pairs are:
The six pairs are:


<ul><li>1-9/7-3/2-11/6 with steps 9/7-7/6-11/9-12/11 and 1-7/6-3/2-18/11 with steps 7/6-9/7-12/11-11/9;</li><li>1-7/6-9/7-10/7 with steps 7/6-11/10-10/9-7/5 and 1-7/5-14/9-12/7 with steps 7/5-10/9-11/10-7/6;</li><li>1-7/6-9/7-18/11 with steps 7/6-11/10-14/11-11/9 and 1-14/11-7/5-18/11 with steps 14/11-11/10-7/6-11/9;</li><li>1-7/6-10/7-11/6 with steps 7/6-11/9-9/7-12/11 and 1-9/7-11/7-11/6 with steps 9/7-11/9-7/6-12/11;</li><li>1-7/6-9/7-11/6 with steps 7/6-11/10-10/7-12/11 and 1-10/7-11/7-11/6 with steps 10/7-11/10-7/6-12/11;</li><li>and 1-10/7-14/9-12/7 with steps 10/7-12/11-11/10-7/6 and 1-7/6-9/7-7/5 with steps 7/6-11/10-12/11-10/7.</li></ul>
* 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:
Finally, there are six swetismic pentads coming in three pairs:


<ul><li>1-7/6-9/7-3/2-11/6 with steps 7/6-11/10-7/6-11/9-12/11 and 1-7/6-9/7-3/2-18/11 with steps 7/6-11/10-7/6-12/11-11/9;</li><li>1-7/6-10/7-5/3-11/6 with steps 7/6-11/9-7/6-11/10-12/11 and 1-7/6-10/7-5/3-20/11 with steps 7/6-11/9-7/6-12/11-11/10;</li><li>and 1-7/6-9/7-10/7-11/6 with steps 7/6-11/10-10/9-9/7-12/11 and 1-9/7-10/7-11/7-11/6 with steps 9/7-10/9-11/10-7/6-12/11.</li></ul>
* 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.


The 11 limit swetismic chords number triads: 6, tetrads: 15, pentads: 6 for a total of 27.
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.


If we are willing to consider the 15-limit, there are also 15-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.
[[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 }}.


Equal temperaments with swetismic chords include 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:11-limit]]
[[Category:Essentially tempered chords]]
[[Category:Chords]]
[[Category:Triads]]
[[Category:Dyadic]]
[[Category:Tetrads]]
[[Category:Swetisma]]
[[Category:Pentads]]
[[Category:Todo:add links]]
[[Category:Swetismic]]
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