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'''Quadrantonismic chords''' are [[essentially tempered dyadic chord]]s tempered by the quadrantonisma, [[1156/1155]].  
'''Quadrantonismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the quadrantonisma, [[1156/1155]].  


Quadrantonismic chords are numerous. There are seven pairs of quadrantonismic triads of inverse relationship in the no-13 21-odd-limit:
There are six triads, fifteen tetrads and six pentads as no-thirteen [[subgroup]] 17-odd-limit essentially tempered chords.
* 1-5/4-17/11 with steps 5/4-21/17-22/17, and its inverse
* 1-5/4-34/21 with steps 5/4-22/17-21/17;
* 1-21/16-17/11 with steps 21/16-20/17-22/17, and its inverse
* 1-21/16-17/10 with steps 21/16-22/17-20/17;
* 1-17/11-7/4 with steps 17/11-17/15-8/7, and its inverse
* 1-17/15-7/4 with steps 17/15-17/11-8/7;
* 1-17/11-15/8 with steps 17/11-17/14-16/15, and its inverse
* 1-17/14-15/8 with steps 17/14-17/11-15/8;
* 1-11/8-17/10 with steps 11/8-21/17-20/17, and its inverse
* 1-11/8-34/21 with steps 11/8-20/17-21/17;
* 1-17/14-11/8 with steps 17/14-17/15-16/11, and its inverse
* 1-17/15-11/8 with steps 17/15-17/14-16/11;
* 1-12/11-30/17 with steps 12/11-34/21-17/15, and its inverse
* 1-12/11-21/17 with steps 12/11-17/15-34/21.  


They can be extended to the following palindromic tetrads:  
For triads, there are three pairs of chords in inverse relationship:
* 1-5/4-17/11-34/21 with steps 5/4-21/17-22/21-21/17;
* 1-17/11-7/4 with steps 17/11-17/15-8/7 and its inverse 1-17/15-7/4 with steps 17/15-17/11-8/7;
* 1-21/16-17/11-17/10 with steps 21/16-20/17-11/10-20/17;
* 1-17/11-15/8 with steps 17/11-17/14-16/15 and its inverse 1-17/14-15/8 with steps 17/14-17/11-15/8;
* 1-17/15-17/11-7/4 with steps 17/15-15/11-17/15-7/4;  
* 1-17/14-11/8 with steps 17/14-17/15-16/11 and its inverse 1-17/15-11/8 with steps 17/15-17/14-16/11.
* 1-17/14-17/11-15/8 with steps 17/14-14/11-17/14-16/15;
* 1-11/8-34/21-17/10 with steps 11/8-20/17-21/20-20/17;  
* 1-17/15-17/14-11/8 with steps 17/15-15/14-17/15-16/11;
* 1-12/11-21/17-30/17 with steps 12/11-17/15-10/7-17/15.  


As well as the following inversely related tetrads:  
For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are
* 1-17/14-3/2-30/17 with steps 17/14-21/17-20/17-17/15, and its inverse
* 1-17/15-17/11-7/4 with steps 17/15-15/11-17/15-8/7;
* 1-21/17-3/2-17/10 with steps 21/17-17/14-17/15-20/17;  
* 1-17/14-17/11-15/8 with steps 17/14-14/11-17/14-16/15;
* 1-17/14-3/2-15/8 with steps 17/14-21/17-5/4-16/15, and its inverse
* 1-17/15-17/14-11/8 with steps 17/15-15/14-17/15-16/11.
* 1-21/17-3/2-8/5 with steps 21/17-17/14-16/15-5/4;  
 
* 1-21/16-3/2-17/10 with steps 21/16-8/7-17/15-20/17, and its inverse
The inversely related pairs of chords are
* 1-8/7-3/2-30/17 with steps 8/7-21/16-20/17-17/15;  
* 1-17/11-7/4-15/8 with steps 17/11-17/15-15/14-16/15 and its inverse 1-17/11-28/17-30/17 with steps 17/11-16/15-15/14-17/15;
* 1-17/14-11/8-3/2 with steps 17/14-17/15-12/11-4/3, and its inverse
* 1-17/15-11/8-7/4 with steps 17/15-17/14-14/11-8/7 and its inverse 1-17/14-11/8-11/7 with steps 17/14-17/15-8/7-14/11;
* 1-12/11-21/17-3/2 with steps 12/11-17/15-17/14-4/3;  
* 1-17/14-11/8-15/8 with steps 17/14-17/15-15/11-16/15 and its inverse 1-17/15-11/8-22/15 with steps 17/15-17/14-16/15-15/11;
* 1-11/8-3/2-17/10 with steps 11/8-12/11-17/15-20/17, and its inverse
* 1-17/16-17/15-7/4 with steps 17/16-16/15-17/11-8/7 and its inverse 1-17/11-28/17-7/4 with steps 17/11-16/15-17/16-8/7;
* 1-12/11-3/2-30/17 with step 12/11-11/8-20/17-17/15;  
* 1-17/15-22/17-11/8 with steps 17/15-8/7-17/16-16/11 and its inverse 1-17/16-17/14-11/8 with steps 17/16-8/7-17/15-16/11;
* 1-5/4-17/11-7/4 with steps 5/4-21/17-17/15-8/7, and its inverse
* 1-17/14-22/17-11/8 with steps 17/14-16/15-17/16-16/11 and its inverse 1-17/16-17/15-11/8 with steps 17/16-16/15-17/14-16/11.
* 1-21/17-17/11-30/17 with steps 21/17-5/4-8/7-17/15;  
 
* 1-21/16-17/11-15/8 with steps 21/16-20/17-17/14-16/15, and its inverse
For pentads, there are three pairs of chords in inverse relationship:
* 1-20/17-17/11-28/17 with steps 20/17-21/16-16/15-17/14.
* 1-17/15-17/14-22/17-11/8 with steps 17/15-15/14-16/15-17/16-16/11 and its inverse 1-17/16-17/15-17/14-11/8 with steps 17/16-16/15-15/14-17/15-16/11;
* 1-5/4-21/16-17/11 with steps 5/4-21/20-20/17-22/17, and its inverse
* 1-17/16-17/14-11/8-15/8 with steps 17/16-8/7-17/15-15/11-16/15 and its inverse 1-17/15-22/17-11/8-22/15 with steps 17/15-8/7-17/16-16/15-15/11;
* 1-20/17-21/17-17/11 with steps 20/17-21/20-5/4-22/17;
* 1-17/16-17/15-11/8-7/4 with steps 17/16-16/15-17/14-14/11-8/7 and its inverse 1-17/14-22/17-11/8-11/7 with steps 17/14-16/15-17/16-8/7-14/11.
* 1-17/11-7/4-15/8 with steps 17/11-17/15-15/14-16/15, and its invere
 
* 1-17/11-28/17-30/17 with steps 17/11-16/15-15/14-17/15;  
If we are willing to go to the 21-odd-limit, There are four additional pairs of triads of inverse relationship:
* 1-17/14-11/8-17/10 with steps 17/14-17/15-21/17-20/17, and its inverse
* 1-5/4-17/11 with steps 5/4-21/17-22/17 and its inverse 1-5/4-34/21 with steps 5/4-22/17-21/17;
* 1-17/15-11/8-34/21 with steps 17/15-17/14-20/17-21/17;  
* 1-21/16-17/11 with steps 21/16-20/17-22/17 and its inverse 1-21/16-17/10 with steps 21/16-22/17-20/17;
* 1-5/4-11/8-34/21 with steps 5/4-11/10-20/17-21/17, and its inverse
* 1-11/8-17/10 with steps 11/8-21/17-20/17 and its inverse 1-11/8-34/21 with steps 11/8-20/17-21/17;
* 1-11/10-11/8-17/10 with steps 11/10-5/4-21/17-20/17;  
* 1-12/11-30/17 with steps 12/11-34/21-17/15 and its inverse 1-12/11-21/17 with steps 12/11-17/15-34/21.
* 1-21/16-11/8-17/10 with steps 21/16-22/21-21/17-20/17 and its inverse
 
* 1-22/21-11/8-34/21 with steps 22/21-21/16-20/17-21/17;
They can be extended to the following palindromic tetrads:
* 1-17/15-11/8-7/4 with steps 17/15-17/14-14/11-8/7, and its inverse
* 1-5/4-17/11-34/21 with steps 5/4-21/17-22/21-21/17;
* 1-17/14-11/8-11/7 with steps 17/14-17/15-8/7-14/11;
* 1-21/16-17/11-17/10 with steps 21/16-20/17-11/10-20/17;
* 1-17/14-11/8-15/8 with steps 17/14-17/15-15/11-16/15, and its inverse
* 1-11/8-34/21-17/10 with steps 11/8-20/17-21/20-20/17;
* 1-17/15-11/8-22/15 with steps 17/15-17/14-16/15-15/11.  
* 1-12/11-21/17-30/17 with steps 12/11-17/15-10/7-17/15.
 
As well as the following additional pairs of triads of inverse relationship:
* 1-17/14-3/2-30/17 with steps 17/14-21/17-20/17-17/15 and its inverse 1-21/17-3/2-17/10 with steps 21/17-17/14-17/15-20/17;
* 1-17/14-3/2-15/8 with steps 17/14-21/17-5/4-16/15 and its inverse 1-21/17-3/2-8/5 with steps 21/17-17/14-16/15-5/4;
* 1-21/16-3/2-17/10 with steps 21/16-8/7-17/15-20/17 and its inverse 1-8/7-3/2-30/17 with steps 8/7-21/16-20/17-17/15;
* 1-17/14-11/8-3/2 with steps 17/14-17/15-12/11-4/3 and its inverse 1-12/11-21/17-3/2 with steps 12/11-17/15-17/14-4/3;
* 1-11/8-3/2-17/10 with steps 11/8-12/11-17/15-20/17 and its inverse 1-12/11-3/2-30/17 with step 12/11-11/8-20/17-17/15;
* 1-5/4-17/11-7/4 with steps 5/4-21/17-17/15-8/7 and its inverse 1-21/17-17/11-30/17 with steps 21/17-5/4-8/7-17/15;
* 1-21/16-17/11-15/8 with steps 21/16-20/17-17/14-16/15 and its inverse 1-20/17-17/11-28/17 with steps 20/17-21/16-16/15-17/14;
* 1-5/4-21/16-17/11 with steps 5/4-21/20-20/17-22/17 and its inverse 1-20/17-21/17-17/11 with steps 20/17-21/20-5/4-22/17;
* 1-17/14-11/8-17/10 with steps 17/14-17/15-21/17-20/17 and its inverse 1-17/15-11/8-34/21 with steps 17/15-17/14-20/17-21/17;
* 1-5/4-11/8-34/21 with steps 5/4-11/10-20/17-21/17 and its inverse 1-11/10-11/8-17/10 with steps 11/10-5/4-21/17-20/17;
* 1-21/16-11/8-17/10 with steps 21/16-22/21-21/17-20/17 and its inverse 1-22/21-11/8-34/21 with steps 22/21-21/16-20/17-21/17.


For pentads, there are
For pentads, there are
* 1-17/14-3/2-30/17-15/8 with steps 17/14-21/17-20/17-17/16-16/15, and its inverse
* 1-17/14-3/2-30/17-15/8 with steps 17/14-21/17-20/17-17/16-16/15 and its inverse 1-21/17-3/2-8/5-17/10 with steps 21/17-17/14-16/15-17/16-20/17;
* 1-21/17-3/2-8/5-17/10 with steps 21/17-17/14-16/15-17/16-20/17;  
* 1-21/17-21/16-3/2-17/10 with steps 21/17-17/16-8/7-17/15-20/17 and its inverse 1-8/7-17/14-3/2-30/17 with steps 8/7-17/16-21/17-20/17-17/15;
* 1-21/17-21/16-3/2-17/10 with steps 21/17-17/16-8/7-17/15-20/17, and its inverse
* 1-17/14-11/8-3/2-15/8 with steps 17/14-17/15-12/11-5/4-16/15 and its inverse 1-12/11-21/17-3/2-8/5 with steps 12/11-17/15-17/14-16/15-5/4;
* 1-8/7-17/14-3/2-30/17 with steps 8/7-17/16-21/17-20/17-17/15;  
* 1-21/16-11/8-3/2-17/10 with steps 21/16-22/21-12/11-17/15-20/17 and its inverse 1-12/11-8/7-3/2-30/17 with steps 12/11-22/21-21/16-20/17-17/15;
* 1-17/14-11/8-3/2-15/8 with steps 17/14-17/15-12/11-5/4-16/15, and its inverse
* 1-17/14-11/8-3/2-17/10 with steps 17/14-17/15-12/11-17/15-20/17 and its inverse 1-12/11-21/17-3/2-30/17 with steps 12/11-17/15-17/14-20/17-17/15.
* 1-12/11-21/17-3/2-8/5 with steps 12/11-17/15-17/14-16/15-5/4;  
 
* 1-21/16-11/8-3/2-17/10 with steps 21/16-22/21-12/11-17/15-20/17, and its inverse
Equal temperaments with quadrantonismic chords include {{Optimal ET sequence|22, 26, 43, 46, 50, 68, 72, 89, 94, 111, 118, 121, 140, 183, 239, 311, 400, 422 and 494}}.
* 1-12/11-8/7-3/2-30/17 with steps 12/11-22/21-21/16-20/17-17/15;  
* 1-17/14-11/8-3/2-17/10 with steps 17/14-17/15-12/11-17/15-20/17, and its inverse
* 1-12/11-21/17-3/2-30/17 with steps 12/11-17/15-17/14-20/17-17/15.  


[[Category:21-odd-limit]]
[[Category:17-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Triads]]
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