Dakotismic chords

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

Dakotismic chords are numerous, including 14 triads and 51 tetrads as 2.3.5.7.11.17 subgroup 17-odd-limit essentially tempered chords.

For triads, there are seven pairs of chords in inverse relationship:

  • 1-6/5-17/11 with steps 6/5-9/7-22/17 and its inverse 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 its inverse 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 its inverse 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 its inverse 1-10/9-24/17 with steps 10/9-14/11-17/12;
  • 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, there are three palindromic chords and twenty-four pairs of chords in inverse relationship. The palindromic chords are

  • 1-6/5-9/7-17/11 with steps 6/5-15/14-6/5-22/17;
  • 1-18/17-9/7-15/11 with steps 18/17-17/14-18/17-22/15;
  • 1-18/17-5/3-30/17 with steps 18/17-11/7-18/17-17/15.

The inversely related pairs of chords are

  • 1-14/11-17/11-9/5 with steps 14/11-17/14-7/6-10/9 and its inverse 1-7/6-17/12-9/5 with steps 7/6-17/14-14/11-10/9;
  • 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;
  • 1-6/5-17/11-9/5 with steps 6/5-9/7-7/6-10/9 and its inverse 1-10/9-22/17-5/3 with steps 10/9-7/6-9/7-6/5;
  • 1-9/7-17/12-11/7 with steps 9/7-11/10-10/9-14/11 and its inverse 1-14/11-24/17-14/9 with steps 14/11-10/9-11/10-9/7;
  • 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;
  • 1-11/10-17/12-17/10 with steps 11/10-9/7-6/5-20/17 and its inverse 1-6/5-17/11-17/10 with steps 6/5-9/7-11/10-20/17;
  • 1-17/12-11/7-11/6 with steps 17/12-10/9-7/6-12/11 and its inverse 1-17/12-17/11-9/5 with steps 17/12-12/11-7/6-10/9;
  • 1-22/17-5/3-11/6 with steps 22/17-9/7-11/10-12/11 and its inverse 1-11/10-17/12-11/6 with steps 11/10-9/7-22/17-12/11;
  • 1-17/12-3/2-9/5 with steps 17/12-18/17-6/5-10/9 and its inverse 1-18/17-3/2-5/3 with steps 18/17-17/12-10/9-6/5;
  • 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;
  • 1-9/7-15/11-5/3 with steps 9/7-18/17-11/9-6/5 and its inverse 1-9/7-17/11-17/9 with steps 9/7-6/5-11/9-18/17;
  • 1-9/7-15/11-18/11 with steps 9/7-18/17-6/5-11/9 and its inverse 1-9/7-11/7-17/9 with steps 9/7-11/9-6/5-18/17;
  • 1-9/7-17/11-18/11 with steps 9/7-6/5-18/17-11/9 and its inverse 1-6/5-17/11-17/9 with steps 6/5-9/7-11/9-18/17;
  • 1-6/5-14/9-17/9 with steps 6/5-22/17-17/14-18/17 and its inverse 1-17/14-11/7-17/9 with steps 17/14-22/17-6/5-18/17;
  • 1-9/7-5/3-17/9 with steps 9/7-22/17-17/15-18/17 and its inverse 1-17/15-22/15-17/9 with steps 17/15-22/17-9/7-18/17;
  • 1-6/5-17/10-17/9 with steps 6/5-17/12-10/9-18/17 and its inverse 1-10/9-11/7-17/9 with steps 10/9-17/12-6/5-18/17;
  • 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;
  • 1-10/7-11/7-5/3 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;
  • 1-11/10-11/9-17/9 with steps 11/10-10/9-17/11-18/17 and its inverse 1-17/11-12/7-17/9 with steps 17/11-10/9-11/10-18/17;
  • 1-10/9-12/7-17/9 with steps 10/9-17/11-11/10-18/17 and its inverse 1-11/10-17/10-17/9 with steps 11/10-17/11-10/9-18/17;
  • 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;
  • 1-15/14-9/7-15/11 with steps 15/14-6/5-18/17-22/15 and its inverse 1-18/17-14/11-15/11 with steps 18/17-6/5-15/14-22/15.

Equal temperaments with dakotismic chords include 12, 14c, 15g, 19eg, 22, 26, 27eg, 31g, 41, 46, 50, 58, 72, 94, 118, 121, 140, 239 and 311.

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