Gassormic chords: Difference between revisions

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'''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 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.


The inversely related pairs of triads 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.


Equal temperaments with gassormic chords include {{Vals| 4, 5, 10, 15, 22, 26, 29, 31, 41 and 53 }} ETs.
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.


[[Category:Chords]]
The inversely related pairs of chords are
[[Category:Dyadic]]
* 1–13/10–11/7–11/6 with steps of 13/10, 6/5, 7/6, 12/11, and its inverse
[[Category:Triad]]
* 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 {{Optimal ET sequence| 10, 15, 22, 26, 29, 31, 41 and 53 }}.
 
[[Category:13-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[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.

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