Ainismic chords: Difference between revisions

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An '''ainic chord''' is an [[Dyadic chord|essentially tempered dyadic chord]] tempered by [[936/935]], the ainos comma. So far, only a handful of ainic triads are known, however, other triads, as well as tetrads, pentads and so forth are likely to exist.  
'''Ainismic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by [[936/935]], the ainisma.  


The known ainic triads are:
Ainismic chords are numerous, including 22 triads and 99 tetrads as 2.3.5.11.13.17 subgroup [[17-odd-limit]] essentially tempered chords.
* 1-17/16-13/11 with steps 17/16-10/9-22/13, and its inversions;
* 1-10/9-13/11 with steps 10/9-17/16-22/13, and its inversions;
* 1-13/11-17/12 with steps 13/11-6/5-24/17, and its inversions;
* 1-6/5-17/12 with steps 6/5-13/11-24/17, and its inversions;
* 1-18/17-5/4 with steps 18/17-13/11-8/5, and its inversions;
* 1-13/11-5/4 with steps 13/11-18/17-8/5, and its inversions;


[[Category:17-limit]]
For triads, there are eleven pairs of chords in inverse relationship:
[[Category:Chords]]
* 1-5/4-26/17 with steps of 5/4-11/9-17/13 (ainismic major triad), and its inversion
[[Category:Dyadic]]
* 1-11/9-26/17 with steps of 11/9-5/4-17/13 (ainismic neutral triad);
[[Category:Ainos]]
* 1-11/8-26/17 with steps of 11/8-10/9-17/13 (ainismic suspended demisharp four), and its inversion
[[Category:todo]]
* 1-10/9-26/17 with steps of 10/9-11/8-17/13 (ainismic suspended two);
* 1-6/5-17/12 with steps of 6/5-13/11-24/17, and its inversion
* 1-13/11-17/12 with steps of 13/11-6/5-24/17;
* 1-13/10-17/12 with steps of 13/10-12/11-24/17, and its inversion
* 1-12/11-17/12 with steps of 12/11-13/10-24/17;
* 1-11/9-24/17 with steps of 11/9-15/13-17/12, and its inversion
* 1-15/13-24/17 with steps of 15/13-11/9-17/12;
* 1-13/10-11/8 with steps of 13/10-18/17-16/11, and its inversion
* 1-18/17-11/8 with steps of 18/17-13/10-16/11;
* 1-6/5-17/13 with steps of 6/5-12/11-26/17, and its inversion
* 1-12/11-17/13 with steps of 12/11-6/5-26/17;
* 1-11/9-13/10 with steps of 11/9-17/16-20/13, and its inversion
* 1-17/16-13/10 with steps of 17/16-11/9-20/13;
* 1-13/11-5/4 with steps of 13/11-18/17-8/5, and its inversion
* 1-18/17-5/4 with steps of 18/17-13/11-8/5;
* 1-10/9-13/11 with steps of 10/9-17/16-22/13, and its inversion
* 1-17/16-13/11 with steps of 17/16-10/9-22/13;
* 1-12/11-15/13 with steps of 12/11-18/17-26/15, and its inversion
* 1-18/17-15/13 with steps of 18/17-12/11-26/15.
 
For tetrads, there are three palindromic chords and forty-eight pairs of chords in inverse relationship. The palindromic chords are:
* 1-12/11-6/5-17/13 with steps of 12/11-11/10-12/11-26/17;
* 1-13/11-17/12-5/3 with steps of 13/11-6/5-20/17-6/5;
* 1-12/11-17/12-17/11 with steps of 12/11-13/10-12/11-22/17.
 
Inversely related pairs of tetrads include:
* 1-12/11-17/12-3/2 with steps of 12/11-13/10-18/17-4/3, and its inversion
* 1-12/11-15/13-3/2 with steps of 12/11-18/17-13/10-4/3;
* 1-13/10-17/12-3/2 with steps of 13/10-12/11-18/17-4/3, and its inversion
* 1-13/10-11/8-3/2 with steps of 13/10-18/17-12/11-4/3;
* 1-18/17-11/8-3/2 with steps of 18/17-13/10-12/11-4/3, and its inversion
* 1-18/17-15/13-3/2 with steps of 18/17-12/11-13/10-4/3;
* 1-15/13-24/17-3/2 with steps of 15/13-11/9-17/16-4/3, and its inversion
* 1-17/16-13/10-3/2 with steps of 17/16-11/9-15/13-4/3.
 
Equal temperaments with ainismic chords include {{Optimal ET sequence|22, 24, 26, 31, 34, 46, 53, 65, 72, 87, 96, 111, 137, 145, 159, 183, 217 and 270}}.
 
[[Category:17-odd-limit]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Ainismic]]

Latest revision as of 12:24, 9 December 2023

Ainismic chords are essentially tempered chords tempered by 936/935, the ainisma.

Ainismic chords are numerous, including 22 triads and 99 tetrads as 2.3.5.11.13.17 subgroup 17-odd-limit essentially tempered chords.

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

  • 1-5/4-26/17 with steps of 5/4-11/9-17/13 (ainismic major triad), and its inversion
  • 1-11/9-26/17 with steps of 11/9-5/4-17/13 (ainismic neutral triad);
  • 1-11/8-26/17 with steps of 11/8-10/9-17/13 (ainismic suspended demisharp four), and its inversion
  • 1-10/9-26/17 with steps of 10/9-11/8-17/13 (ainismic suspended two);
  • 1-6/5-17/12 with steps of 6/5-13/11-24/17, and its inversion
  • 1-13/11-17/12 with steps of 13/11-6/5-24/17;
  • 1-13/10-17/12 with steps of 13/10-12/11-24/17, and its inversion
  • 1-12/11-17/12 with steps of 12/11-13/10-24/17;
  • 1-11/9-24/17 with steps of 11/9-15/13-17/12, and its inversion
  • 1-15/13-24/17 with steps of 15/13-11/9-17/12;
  • 1-13/10-11/8 with steps of 13/10-18/17-16/11, and its inversion
  • 1-18/17-11/8 with steps of 18/17-13/10-16/11;
  • 1-6/5-17/13 with steps of 6/5-12/11-26/17, and its inversion
  • 1-12/11-17/13 with steps of 12/11-6/5-26/17;
  • 1-11/9-13/10 with steps of 11/9-17/16-20/13, and its inversion
  • 1-17/16-13/10 with steps of 17/16-11/9-20/13;
  • 1-13/11-5/4 with steps of 13/11-18/17-8/5, and its inversion
  • 1-18/17-5/4 with steps of 18/17-13/11-8/5;
  • 1-10/9-13/11 with steps of 10/9-17/16-22/13, and its inversion
  • 1-17/16-13/11 with steps of 17/16-10/9-22/13;
  • 1-12/11-15/13 with steps of 12/11-18/17-26/15, and its inversion
  • 1-18/17-15/13 with steps of 18/17-12/11-26/15.

For tetrads, there are three palindromic chords and forty-eight pairs of chords in inverse relationship. The palindromic chords are:

  • 1-12/11-6/5-17/13 with steps of 12/11-11/10-12/11-26/17;
  • 1-13/11-17/12-5/3 with steps of 13/11-6/5-20/17-6/5;
  • 1-12/11-17/12-17/11 with steps of 12/11-13/10-12/11-22/17.

Inversely related pairs of tetrads include:

  • 1-12/11-17/12-3/2 with steps of 12/11-13/10-18/17-4/3, and its inversion
  • 1-12/11-15/13-3/2 with steps of 12/11-18/17-13/10-4/3;
  • 1-13/10-17/12-3/2 with steps of 13/10-12/11-18/17-4/3, and its inversion
  • 1-13/10-11/8-3/2 with steps of 13/10-18/17-12/11-4/3;
  • 1-18/17-11/8-3/2 with steps of 18/17-13/10-12/11-4/3, and its inversion
  • 1-18/17-15/13-3/2 with steps of 18/17-12/11-13/10-4/3;
  • 1-15/13-24/17-3/2 with steps of 15/13-11/9-17/16-4/3, and its inversion
  • 1-17/16-13/10-3/2 with steps of 17/16-11/9-15/13-4/3.

Equal temperaments with ainismic chords include 22, 24, 26, 31, 34, 46, 53, 65, 72, 87, 96, 111, 137, 145, 159, 183, 217 and 270.

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