Biyatismic chords

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Biyatismic chords are essentially tempered dyadic chords tempered by the biyatisma, 121/120.

Biyatismic temperament contains many possibilities for essentially tempered dyadic chords including 2 triads and 8 tetrads in the 11-odd-limit of the 2.3.5.11 subgroup.

The two biyatismic triads are in inverse relationship:

  • 1-11/8-5/3 chord with steps of 11/8-11/9-6/5;
  • 1-6/5-16/11 chord with steps of 6/5-11/9-11/8.

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

  • 1-9/8-11/8-18/11 chord with steps of 9/8-11/9-6/5-11/9;
  • 1-5/4-11/8-11/6 chord with steps of 5/4-11/10-4/3-11/10.

The inversely related pairs of chords are

  • 1-11/9-11/8-18/11 chord with steps of 11/9-9/8-6/5-11/9 and 1-11/9-16/11-18/11 chord with steps of 11/9-6/5-9/8-11/9;
  • 1-11/8-5/3-11/6 chord with steps of 11/8-11/9-11/10-11/10 and 1-11/10-6/5-16/11 chord with steps of 11/10-11/10-11/9-11/8;
  • 1-5/4-3/2-11/6 chord with steps of 5/4-6/5-11/9-11/10 and 1-11/10-4/3-8/5 chord with steps of 11/10-11/9-6/5-5/4.

Equal temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46 and 53.

See also