Gassormic chords: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Newer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled
4,516 edits
Created page with "'''Gassormic chords''' are essentially tempered dyadic chords tempered by the gassorma, 275/273. Gassormic temperament contains many possibilities for es..."
 
Xenllium (talk | contribs)
autopatrolled
4,516 edits
Add tetrads
Line 1: Line 1:
'''Gassormic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the gassorma, [[275/273]].
'''Gassormic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the gassorma, [[275/273]].


Gassormic temperament contains many possibilities for essentially tempered dyadic chords including six triads in the [[13-odd-limit]].
Gassormic temperament contains many possibilities for essentially tempered dyadic chords including 6 triads and 21 tetrads in the [[13-odd-limit]].


The inversely related pairs of triads are:  
The inversely related pairs of triads are:  
* 1-7/5-5/3 chord with steps of 7/5-13/11-6/5 and 1-6/5-10/7 chord with steps of 6/5-13/11-7/5
* 1-7/5-5/3 chord with steps of 7/5-13/11-6/5 and 1-6/5-10/7 chord with steps of 6/5-13/11-7/5;
* 1-14/11-5/3 chord with steps of 14/11-13/10-6/5 and 1-6/5-11/7 chord with steps of 6/5-13/10-14/11
* 1-14/11-5/3 chord with steps of 14/11-13/10-6/5 and 1-6/5-11/7 chord with steps of 6/5-13/10-14/11;
* 1-7/5-11/6 chord with steps of 7/5-13/10-12/11 and 1-12/11-10/7 chord with steps of 12/11-13/10-7/5
* 1-7/5-11/6 chord with steps of 7/5-13/10-12/11 and 1-12/11-10/7 chord with steps of 12/11-13/10-7/5.


Equal temperaments with gassormic chords include {{Vals| 4, 5, 10, 15, 22, 26, 29, 31, 41 and 53 }} ETs.
For tetrads, there are 3 palindromic chords and 9 pairs of chords in inverse relationship. The palindromic chords are
* 1-6/5-10/7-12/7 chord with steps of 6/5-13/11-6/5-7/6;
* 1-6/5-13/10-11/7 chord with steps of 6/5-13/12-6/5-14/11;
* 1-13/10-10/7-13/7 chord with steps of 13/10-12/11-13/10-14/13.
 
The inversely related pairs of chords are
* 1-13/11-10/7-12/7 chord with steps of 13/11-6/5-6/5-7/6 and 1-7/6-7/5-22/13 chord with steps of 7/6-6/5-6/5-13/11;
* 1-6/5-20/13-5/3 chord with steps of 6/5-14/11-13/12-6/5 and 1-6/5-13/10-5/3 chord with steps of 6/5-13/12-14/11-6/5;
* 1-12/11-10/7-13/7 chord with steps of 12/11-13/10-13/10-14/13 and 1-14/13-7/5-11/6 chord with steps of 14/13-13/10-13/10-12/11;
* 1-12/11-10/7-12/7 chord with steps of 12/11-13/10-6/5-7/6 and 1-7/6-7/5-11/6 chord with steps of 7/6-6/5-13/10-12/11;
* 1-6/5-10/7-11/7 chord with steps of 6/5-13/11-11/10-14/11 and 1-14/11-7/5-5/3 chord with steps of 14/11-11/10-13/11-6/5;
* 1-6/5-10/7-13/7 chord with steps of 6/5-13/11-13/10-14/13 and 1-14/13-7/5-5/3 chord with steps of 14/13-13/10-13/11-6/5;
* 1-12/11-10/7-11/7 chord with steps of 12/11-13/10-11/10-14/11 and 1-14/11-7/5-11/6 chord with steps of 14/11-11/10-13/10-12/11;
* 1-12/11-20/13-5/3 chord with steps of 12/11-7/5-13/12-6/5 and 1-6/5-13/10-11/6 chord with steps of 6/5-13/12-7/5-12/11;
* 1-7/5-5/3-11/6 chord with steps of 7/5-13/11-11/10-12/11 and 1-12/11-6/5-10/7 chord with steps of 12/11-11/10-13/11-7/5.
 
Equal temperaments with gassormic chords include {{Vals| 10, 15, 22, 26, 29, 31, 41 and 53 }} ETs.


[[Category:Chords]]
[[Category:Chords]]
[[Category:Dyadic]]
[[Category:Dyadic]]
[[Category:Triad]]
[[Category:Triad]]
[[Category:Tetrad]]
[[Category:Gassormic]]
[[Category:Gassormic]]

Revision as of 14:01, 8 February 2022

Gassormic chords are essentially tempered dyadic chords tempered by the gassorma, 275/273.

Gassormic temperament contains many possibilities for essentially tempered dyadic chords including 6 triads and 21 tetrads in the 13-odd-limit.

The inversely related pairs of triads are:

  • 1-7/5-5/3 chord with steps of 7/5-13/11-6/5 and 1-6/5-10/7 chord with steps of 6/5-13/11-7/5;
  • 1-14/11-5/3 chord with steps of 14/11-13/10-6/5 and 1-6/5-11/7 chord with steps of 6/5-13/10-14/11;
  • 1-7/5-11/6 chord with steps of 7/5-13/10-12/11 and 1-12/11-10/7 chord with steps of 12/11-13/10-7/5.

For tetrads, there are 3 palindromic chords and 9 pairs of chords in inverse relationship. The palindromic chords are

  • 1-6/5-10/7-12/7 chord with steps of 6/5-13/11-6/5-7/6;
  • 1-6/5-13/10-11/7 chord with steps of 6/5-13/12-6/5-14/11;
  • 1-13/10-10/7-13/7 chord with steps of 13/10-12/11-13/10-14/13.

The inversely related pairs of chords are

  • 1-13/11-10/7-12/7 chord with steps of 13/11-6/5-6/5-7/6 and 1-7/6-7/5-22/13 chord with steps of 7/6-6/5-6/5-13/11;
  • 1-6/5-20/13-5/3 chord with steps of 6/5-14/11-13/12-6/5 and 1-6/5-13/10-5/3 chord with steps of 6/5-13/12-14/11-6/5;
  • 1-12/11-10/7-13/7 chord with steps of 12/11-13/10-13/10-14/13 and 1-14/13-7/5-11/6 chord with steps of 14/13-13/10-13/10-12/11;
  • 1-12/11-10/7-12/7 chord with steps of 12/11-13/10-6/5-7/6 and 1-7/6-7/5-11/6 chord with steps of 7/6-6/5-13/10-12/11;
  • 1-6/5-10/7-11/7 chord with steps of 6/5-13/11-11/10-14/11 and 1-14/11-7/5-5/3 chord with steps of 14/11-11/10-13/11-6/5;
  • 1-6/5-10/7-13/7 chord with steps of 6/5-13/11-13/10-14/13 and 1-14/13-7/5-5/3 chord with steps of 14/13-13/10-13/11-6/5;
  • 1-12/11-10/7-11/7 chord with steps of 12/11-13/10-11/10-14/11 and 1-14/11-7/5-11/6 chord with steps of 14/11-11/10-13/10-12/11;
  • 1-12/11-20/13-5/3 chord with steps of 12/11-7/5-13/12-6/5 and 1-6/5-13/10-11/6 chord with steps of 6/5-13/12-7/5-12/11;
  • 1-7/5-5/3-11/6 chord with steps of 7/5-13/11-11/10-12/11 and 1-12/11-6/5-10/7 chord with steps of 12/11-11/10-13/11-7/5.

Equal temperaments with gassormic chords include 10, 15, 22, 26, 29, 31, 41 and 53 ETs.

Retrieved from "https://en.xen.wiki/index.php?title=Gassormic_chords&oldid=85558"