Dakotismic chords

Dakotismic chords are essentially tempered dyadic chords tempered by the dakotisma, 595/594.

Dakotismic chords are numerous. If we disallow intervals that are typically too small for harmonic use, in this case the semitones 15/14, 18/17, 21/20, and 22/21, there are four pairs of triads in inverse relationship in the 21-odd-limit:

• 1-6/5-17/11 with steps 6/5-9/7-22/17, and
• 1-22/17-5/3 with steps 22/17-9/7-6/5;
• 1-7/6-22/17 with steps 7/6-10/9-17/11, and
• 1-17/11-12/7 with steps 17/11-10/9-7/6;
• 1-11/10-17/12 with steps 11/10-9/7-24/17, and
• 1-9/7-17/12 with steps 9/7-11/10-24/17;
• 1-14/11-24/17 with steps 14/11-10/9-17/12, and
• 1-10/9-24/17 with steps 10/9-14/11-17/12.

If we allow the semitones, there are four additional pairs of triads in inverse relationship:

• 1-9/5-21/11 with steps 9/5-18/17-22/21, and its inverse
• 1-9/5-17/9 with steps 9/5-22/21-18/17;
• 1-9/7-15/11 with steps 9/7-18/17-22/15, and its inverse
• 1-9/7-17/9 with steps 9/7-22/15-18/17;
• 1-11/7-5/3 with steps 11/7-18/17-6/5, and its inverse
• 1-11/7-17/9 with steps 11/7-6/5-18/17;
• 1-11/10-7/6 with steps 11/10-18/17-12/7, and its inverse
• 1-11/10-17/9 with steps 11/10-12/7-18/17.

For tetrads without the semitones, there are two pairs in inverse relationship:

• 1-6/5-17/11-12/7 with steps 6/5-9/7-10/9-7/6, and its inverse
• 1-7/6-22/17-5/3 with steps 7/6-10/9-9/7-6/5;
• 1-11/10-17/12-11/7 with steps 11/10-9/7-10/9-14/11, and its inverse
• 1-14/11-24/17-20/11 with steps 14/11-10/9-9/7-11/10;

And if we use the semitones, there are many more. Some of these involve the perfect fifth:

• 1-3/2-9/5-21/11 with steps 3/2-6/5-18/17-22/21, and its inverse
• 1-3/2-11/7-5/3 with steps 3/2-22/21-18/17-6/5;
• 1-9/7-15/11-3/2 with steps 9/7-18/17-11/10-4/3, and its inverse
• 1-11/10-7/6-3/2 with steps 11/10-18/17-9/7-4/3;
• 1-9/7-17/12-3/2 with steps 9/7-11/10-18/17-4/3, and its inverse
• 1-18/17-7/6-3/2 with steps 18/17-11/10-9/7-4/3.
• 1-11/10-17/12-3/2 with steps 11/10-9/7-18/17-4/3, and its inverse
• 1-18/17-15/11-3/2 with steps 18/17-9/7-11/10-4/3.

Others do not:

• 1-7/5-9/5-21/11 with steps 7/5-9/7-18/17-22/21, and its inverse
• 1-7/5-22/15-14/9 with steps 7/5-22/21-18/17-9/7;
• 1-10/7-11/7-5/3 with steps 10/7-11/10-18/17-6/5, and its inverse
• 1-10/7-12/7-20/11 with steps 10/7-6/5-18/17-11/10;
• 1-18/11-9/5-21/11 with steps 18/11-11/10-18/17-22/21, and its inverse
• 1-18/11-12/7-20/11 with steps 18/11-22/21-18/17-11/10;
• 1-9/7-15/11-18/11 with steps 9/7-18/17-6/5-11/9, and its inverse
• 1-6/5-14/11-18/11 with steps 6/5-18/17-9/7-11/9;
• 1-17/14-9/7-17/12 with steps 17/14-18/17-11/10-24/17, and its inverse
• 1-11/10-7/6-17/12 with steps 11/10-18/17-17/14-24/17;
• 1-11/10-6/5-17/9 with steps 11/10-12/11-11/7-18/17, and its inverse
• 1-11/7-12/7-17/9 with steps 11/7-12/11-11/10-18/17;

The following two tetrads are palindromic:

• 1-18/17-7/6-21/17 with steps 18/17-11/10-18/17-34/21;
• 1-18/17-5/3-30/17 with steps 18/17-11/7-18/17-17/15.

For pentads, there are at least six pairs in inverse relationship, all featuring the fifth and using the semitones:

• 1-3/2-18/11-9/5-21/11 with steps 3/2-12/11-11/10-18/17-22/21, and its inverse
• 1-3/2-11/7-5/3-11/6 with steps 3/2-22/21-18/17-11/10-12/11;
• 1-7/5-3/2-9/5-21/11 with steps 7/5-15/14-6/5-18/17-22/21, and its inverse
• 1-15/14-3/2-11/7-5/3 with steps 15/14-7/5-22/21-18/17-6/5;
• 1-9/7-15/11-3/2-18/11 with steps 9/7-18/17-11/10-12/11-11/9, and its inverse
• 1-11/10-7/6-3/2-11/6 with steps 11/10-18/17-9/7-11/9-12/11;
• 1-11/10-17/12-3/2-11/7 with steps 11/10-9/7-18/17-22/21-14/11, and its inverse
• 1-18/17-15/11-3/2-21/11 with steps 18/17-9/7-11/10-14/11-22/21;
• 1-9/7-15/11-10/7-3/2 with steps 9/7-18/17-22/21-21/20-4/3, and its inverse
• 1-21/20-11/10-7/6-3/2 with steps 21/20-22/21-18/17-9/7-4/3;
• 1-17/14-9/7-17/12-3/2 with steps 17/14-18/17-11/10-18/17-4/3, and its inverse
• 1-18/17-7/6-21/17-3/2 with steps 18/17-11/10-18/17-17/14-4/3;