Gassormic chords: Difference between revisions

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For triads, there are three pairs of chords in inverse relationship:  
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;
* 1-7/5-5/3 with steps of 7/5-13/11-6/5, and its inverse  
* 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;
* 1-6/5-10/7 with steps of 6/5-13/11-7/5;
* 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.
* 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:
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  
* 1-13/10-11/7-11/6 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;
* 1-13/10-11/7-11/6 with steps of 13/10-6/5-7/6-12/11, and its inverse  
* 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;
* 1-7/6-7/5-11/6 with steps of 7/6-6/5-13/10-12/11;
* 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;
* 1-6/5-10/7-11/7 with steps of 6/5-13/11-11/10-14/11, and its inverse  
* 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;
* 1-14/11-7/5-5/3 with steps of 14/11-11/10-13/11-6/5;
* 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;
* 1-13/10-11/7-13/7 with steps of 13/10-6/5-13/11-14/13, and its inverse  
* 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.
* 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:
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;
* 1-11/10-13/10-7/5-11/6 with steps of 11/10-13/11-14/13-13/10-12/11, and its inverse  
* 1-6/5-13/10-10/7-11/7 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;
* 1-13/10-7/5-5/3-11/6 with steps of 13/10-14/13-13/11-11/10-12/11;
* 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.
* 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 }}.
Equal temperaments with gassormic chords include {{Optimal ET sequence| 10, 15, 22, 26, 29, 31, 41 and 53 }}.

Revision as of 02:52, 25 November 2023

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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