Ainismic chords: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Xenwolf (talk | contribs)
m typo?
"Inversion" here customarily refers to the inverse of a chord. What was dubbed "inversion" was actually "rotation"
Line 2: Line 2:


The known ainic triads are:  
The known ainic triads are:  
* 1-17/16-13/11 with steps 17/16-10/9-22/13, and its inversions
* 1-17/16-13/11 with steps 17/16-10/9-22/13, and its inversion, 1-10/9-13/11 with steps 10/9-17/16-22/13.
* 1-10/9-13/11 with steps 10/9-17/16-22/13, and its inversions
* 1-18/17-5/4 with steps 18/17-13/11-8/5, and its inversion, 1-13/11-5/4 with steps 13/11-18/17-8/5.
* 1-18/17-5/4 with steps 18/17-13/11-8/5, and its inversions
* 1-13/11-17/12 with steps 13/11-6/5-24/17, and its inversion, 1-6/5-17/12 with steps 6/5-13/11-24/17.
* 1-13/11-5/4 with steps 13/11-18/17-8/5, and its inversions
* 1-12/11-17/12 with steps 12/11-13/10-24/17, and its inversion, 1-13/10-17/12 with steps 13/10-12/11-24/17.
* 1-13/11-17/12 with steps 13/11-6/5-24/17, and its inversions
* 1-11/9-24/17 with steps 11/9-15/13-17/12, and its inversion, 1-15/13-24/17 with steps 15/13-11/9-17/12.
* 1-6/5-17/12 with steps 6/5-13/11-24/17, and its inversions
* 1-6/5-17/13 with steps 6/5-12/11-26/17 and its inversion, 1-12/11-17/13 with steps 12/11-6/5-26/17.
* 1-12/11-17/12 with steps 12/11-13/10-24/17 and its inversions
* 1-5/4-26/17 with steps 5/4-11/9-17/13, dubbed the "ainic major triad".
* 1-13/10-17/12 with steps 13/10-12/11-24/17 and its inversions
* 1-11/9-26/17 with steps 11/9-5/4-17/13, dubbed the "ainic neutral triad".
* 1-11/9-24/17 with steps 11/9-15/13-17/12, and its inversions
* 1-11/8-26/17 with steps 11/8-10/9-17/13, dubbed the "ainic suspended demisharp four chord".
* 1-15/13-24/17 with steps 15/13-11/9-17/12, and its inversions
* 1-10/9-26/17 with steps 10/9-11/8-17/13, dubbed the "ainic suspended two chord".
* 1-6/5-17/13 with steps 6/5-12/11-26/17 and its inversions
* 1-12/11-17/13 with steps 12/11-6/5-26/17 and its inversions
* 1-5/4-26/17 with steps 5/4-11/9-17/13, and its inversions; dubbed the "ainic major triad"
* 1-11/9-26/17 with steps 11/9-5/4-17/13, and its inversions; dubbed the "ainic neutral triad"
* 1-11/8-26/17 with steps 11/8-10/9-17/13, and its inversions; dubbed the "ainic suspended demisharp four chord"
* 1-10/9-26/17 with steps 10/9-11/8-17/13, and its inversions; dubbed the "ainic suspended two chord"


The known ainic tetrads are:
The known ainic tetrads are:
* 1-12/11-17/12-3/2 with steps 12/11-13/10-18/17-4/3 and their inversions
* 1-12/11-17/12-3/2 with steps 12/11-13/10-18/17-4/3, and its inversion, 1-12/11-15/13-3/2 with steps 12/11-18/17-13/10-4/3.
* 1-12/11-15/13-3/2 with steps 12/11-18/17-13/10-4/3 and their inversions
* 1-13/10-17/12-3/2 with steps 13/10-12/11-18/17-4/3, and its inversion, 1-13/10-11/8-3/2 with steps 13/10-18/17-12/11-4/3.
* 1-13/10-17/12-3/2 with steps 13/10-12/11-18/17-4/3 and their inversions
* 1-18/17-15/13-3/2 with steps 18/17-12/11-13/10-4/3, and its inversion, 1-18/17-11/8-3/2 with steps 18/17-13/10-12/11-4/3.
* 1-13/10-11/8-3/2 with steps 13/10-18/17-12/11-4/3 and their inversions
* 1-15/13-24/17-3/2 with steps 15/13-11/9-17/16-4/3, and its inversion, 1-17/16-13/10-3/2 with steps 17/16-11/9-15/13-4/3.
* 1-18/17-15/13-3/2 with steps 18/17-12/11-13/10-4/3 and their inversions
* 1-18/17-11/8-3/2 with steps 18/17-13/10-12/11-4/3 and their inversions
* 1-15/13-24/17-3/2 with steps 15/13-11/9-17/16-4/3 and their inversions
* 1-17/16-13/10-3/2 with steps 17/16-11/9-15/13-4/3 and their inversions


[[Category:17-limit]]
[[Category:17-odd-limit]]
[[Category:Chords]]
[[Category:Essentially tempered chords]]
[[Category:Dyadic]]
[[Category:Dyadic]]
[[Category:Ainos]]
[[Category:Triad]]
[[Category:todo]]
[[Category:Tetrad]]
[[Category:Ainic]]

Revision as of 02:58, 5 February 2022

An ainic chord is an essentially tempered dyadic chord tempered by 936/935, the ainos comma. Assuming we stick to the 17-odd-limit, sixteen ainic triads and eight ainic tetrads are known, however, other triads and tetrads, as well as pentads and so forth, are likely to exist. However, if we are willing to go as high as the 39-odd-limit, many more options become available.

The known ainic triads are:

  • 1-17/16-13/11 with steps 17/16-10/9-22/13, and its inversion, 1-10/9-13/11 with steps 10/9-17/16-22/13.
  • 1-18/17-5/4 with steps 18/17-13/11-8/5, and its inversion, 1-13/11-5/4 with steps 13/11-18/17-8/5.
  • 1-13/11-17/12 with steps 13/11-6/5-24/17, and its inversion, 1-6/5-17/12 with steps 6/5-13/11-24/17.
  • 1-12/11-17/12 with steps 12/11-13/10-24/17, and its inversion, 1-13/10-17/12 with steps 13/10-12/11-24/17.
  • 1-11/9-24/17 with steps 11/9-15/13-17/12, and its inversion, 1-15/13-24/17 with steps 15/13-11/9-17/12.
  • 1-6/5-17/13 with steps 6/5-12/11-26/17 and its inversion, 1-12/11-17/13 with steps 12/11-6/5-26/17.
  • 1-5/4-26/17 with steps 5/4-11/9-17/13, dubbed the "ainic major triad".
  • 1-11/9-26/17 with steps 11/9-5/4-17/13, dubbed the "ainic neutral triad".
  • 1-11/8-26/17 with steps 11/8-10/9-17/13, dubbed the "ainic suspended demisharp four chord".
  • 1-10/9-26/17 with steps 10/9-11/8-17/13, dubbed the "ainic suspended two chord".

The known ainic tetrads are:

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