Gassormic chords

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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.

For triads, there are 3 pairs of chords in inverse relationship. The inversely related pairs of chords 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.