Ainismic chords: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Aura (talk | contribs)
autopatrolled, emailconfirmed
5,920 edits
No edit summary
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
Update the article
 
(25 intermediate revisions by 3 users not shown)
Line 1: Line 1:
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 and two ainic tetrads are known, however, other triads and tetrads, as well as pentads and so forth are likely to exist.  The known ainic triads are 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; 1-5/4-24/17 with steps 5/4-44/39-17/12 and its inversions; 1-17/13-3/2 with steps 17/13-55/48-4/3 and its inversions; 1-11/9-24/17 with steps 11/9-15/13-17/12 and its inversions; and 1-16/13-128/85 with steps 16/13-11/9-85/64 and their inversions.  Known ainic tetrads are the result of combining intervals seen in triads, for instance, 1-16/13-128/85-16/9 with steps 16/13-11/9-13/11-9/8 and its inversions; and 1-5/4-24/17-5/3 with steps 5/4-44/39-13/11-6/5 and its inversions.
'''Ainismic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by [[936/935]], the ainisma.  


[[Category:17-limit]]
Ainismic chords are numerous, including 22 triads and 99 tetrads as 2.3.5.11.13.17 subgroup [[17-odd-limit]] essentially tempered chords.
[[Category:Chords]]
 
[[Category:Dyadic]]
For triads, there are eleven pairs of chords in inverse relationship:
[[Category:Ainic]]
* 1-5/4-26/17 with steps of 5/4-11/9-17/13 (ainismic major triad), and its inversion
[[Category:todo]]
* 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 {{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.

Retrieved from "https://en.xen.wiki/index.php?title=Ainismic_chords&oldid=128748"