Gassormic chords: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Xenllium (talk | contribs)
autopatrolled
4,516 edits
mNo edit summary
m Cleanup
 
(6 intermediate revisions by 2 users not shown)
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 6 triads and 21 tetrads in the [[13-odd-limit]].
Gassormic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the [[13-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.


For triads, there are 3 pairs of chords in inverse relationship. The inversely related pairs of chords are:  
For triads, there are three pairs of chords in inverse relationship:  
* 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 with steps of 7/5, 13/11, 6/5, and its inverse
* 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;
* 1–6/5–10/7 with steps of 6/5, 13/11, 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.
* 1–14/11–5/3 with steps of 14/11, 13/10, 6/5, and its inverse
* 1–6/5–11/7 with steps of 6/5, 13/10, 14/11;
* 1–7/5–11/6 with steps of 7/5, 13/10, 12/11, and its inverse
* 1–12/11–10/7 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:
For tetrads, there are three palindromic chords and six 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;
* 1–6/5–10/7–12/7 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;
* 1–6/5–13/10–11/7 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.
* 1–13/10–10/7–13/7 with steps of 13/10, 12/11, 13/10, 14/13.


The inversely related pairs of chords are:
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;
* 1–13/10–11/7–11/6 with steps of 13/10, 6/5, 7/6, 12/11, and its inverse
* 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;
* 1–7/6–7/5–11/6 with steps of 7/6, 6/5, 13/10, 12/11;
* 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;
* 1–6/5–10/7–11/7 with steps of 6/5, 13/11, 11/10, 14/11, and its inverse
* 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;
* 1–14/11–7/5–5/3 with steps of 14/11, 11/10, 13/11, 6/5;
* 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;
* 1–13/10–11/7–13/7 with steps of 13/10, 6/5, 13/11, 14/13, and its inverse
* 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;
* 1–13/10–7/5–5/3 with steps of 13/10, 14/13, 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;
* 1–11/10–6/5–11/7 with steps of 11/10, 12/11, 13/10, 14/11, and its inverse
* 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;
* 1–11/10–7/5–11/6 with steps of 11/10, 14/11, 13/10, 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.
* 1–7/5–20/13–5/3 with steps of 7/5, 12/11, 13/12, 6/5, and its inverse
* 1–6/5–13/10–10/7 with steps of 6/5, 13/12, 12/11, 7/5;
* 1–7/5–5/3–11/6 with steps of 7/5, 13/11, 11/10, 12/11, and its inverse
* 1–12/11–6/5–10/7 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 }}.
For pentads, there are three pairs of chords in inverse relationship:
* 1–11/10–13/10–7/5–11/6 with steps of 11/10, 13/11, 14/13, 13/10, 12/11, and its inverse
* 1–13/10–7/5–5/3–11/6 with steps of 13/10, 14/13, 13/11, 11/10, 12/11;
* 1–6/5–13/10–10/7–11/7 with steps of 6/5, 13/12, 12/11, 11/10, 14/11, and its inverse
* 1–13/12–13/10–5/3–11/6 with steps of 13/12, 6/5, 14/11, 11/10, 12/11;
* 1–7/6–7/5–5/3–11/6 with steps of 7/6, 6/5, 13/11, 11/10, 12/11, and its inverse
* 1–7/6–14/11–7/5–5/3 with steps of 7/6, 12/11, 11/10, 13/11, 6/5.


Equal temperaments with gassormic chords include {{Optimal ET sequence| 10, 15, 22, 26, 29, 31, 41 and 53 }}.
[[Category:13-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Dyadic]]
[[Category:Triads]]
[[Category:Triad]]
[[Category:Tetrads]]
[[Category:Tetrad]]
[[Category:Pentads]]
[[Category:Gassormic]]
[[Category:Gassormic]]

Latest revision as of 13:50, 19 March 2025

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

Gassormic chords are of pattern 2 in the 13-odd-limit, meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.

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

  • 1–7/5–5/3 with steps of 7/5, 13/11, 6/5, and its inverse
  • 1–6/5–10/7 with steps of 6/5, 13/11, 7/5;
  • 1–14/11–5/3 with steps of 14/11, 13/10, 6/5, and its inverse
  • 1–6/5–11/7 with steps of 6/5, 13/10, 14/11;
  • 1–7/5–11/6 with steps of 7/5, 13/10, 12/11, and its inverse
  • 1–12/11–10/7 with steps of 12/11, 13/10, 7/5.

For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are

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

The inversely related pairs of chords are

  • 1–13/10–11/7–11/6 with steps of 13/10, 6/5, 7/6, 12/11, and its inverse
  • 1–7/6–7/5–11/6 with steps of 7/6, 6/5, 13/10, 12/11;
  • 1–6/5–10/7–11/7 with steps of 6/5, 13/11, 11/10, 14/11, and its inverse
  • 1–14/11–7/5–5/3 with steps of 14/11, 11/10, 13/11, 6/5;
  • 1–13/10–11/7–13/7 with steps of 13/10, 6/5, 13/11, 14/13, and its inverse
  • 1–13/10–7/5–5/3 with steps of 13/10, 14/13, 13/11, 6/5;
  • 1–11/10–6/5–11/7 with steps of 11/10, 12/11, 13/10, 14/11, and its inverse
  • 1–11/10–7/5–11/6 with steps of 11/10, 14/11, 13/10, 12/11;
  • 1–7/5–20/13–5/3 with steps of 7/5, 12/11, 13/12, 6/5, and its inverse
  • 1–6/5–13/10–10/7 with steps of 6/5, 13/12, 12/11, 7/5;
  • 1–7/5–5/3–11/6 with steps of 7/5, 13/11, 11/10, 12/11, and its inverse
  • 1–12/11–6/5–10/7 with steps of 12/11, 11/10, 13/11, 7/5.

For pentads, there are three pairs of chords in inverse relationship:

  • 1–11/10–13/10–7/5–11/6 with steps of 11/10, 13/11, 14/13, 13/10, 12/11, and its inverse
  • 1–13/10–7/5–5/3–11/6 with steps of 13/10, 14/13, 13/11, 11/10, 12/11;
  • 1–6/5–13/10–10/7–11/7 with steps of 6/5, 13/12, 12/11, 11/10, 14/11, and its inverse
  • 1–13/12–13/10–5/3–11/6 with steps of 13/12, 6/5, 14/11, 11/10, 12/11;
  • 1–7/6–7/5–5/3–11/6 with steps of 7/6, 6/5, 13/11, 11/10, 12/11, and its inverse
  • 1–7/6–14/11–7/5–5/3 with steps of 7/6, 12/11, 11/10, 13/11, 6/5.

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

Retrieved from "https://en.xen.wiki/index.php?title=Gassormic_chords&oldid=187134"