Sensamagic chords

A sensamagic chord is an essentially tempered dyadic chord tempered by the sensamagic comma, 245/243.

The sensamagic triad is a sensamagic chord with three notes when reduced to the octave.

One of the sensamagic triads in close position consists of two supermajor thirds, approximately 9/7, and a minor third, approximately 6/5, which closes at the octave because the sensamagic comma, 245/243, is tempered out:

• 1-9/7-5/3 with steps of 9/7-9/7-6/5.

Sensamagic triad

The other sensamagic triads are

• 1-7/6-9/7, with steps of 7/6-10/9-14/9, and its inversion 1-7/6-9/5, with steps 7/6-14/9-10/9.

For sensamagic tetrads there are

• 1-7/6-9/7-3/2, with steps 7/6-10/9-7/6-4/3;
• 1-7/6-3/2-9/5 with steps 7/6-9/7-6/5-10/9 and its inversion 1-9/7-3/2-5/3 with steps 9/7-7/6-10/9-6/5;
• 1-7/6-7/5-9/5 with steps 7/6-6/5-9/7-10/9 and its inversion 1-7/6-9/7-5/3 with steps 7/6-10/9-9/7-6/5; and
• 1-7/6-9/7-9/5 with steps 7/6-10/9-7/5-10/9.

For pentads there are

• 1-7/6-9/7-3/2-5/3 with steps 7/6-10/9-7/6-10/9-6/5 and its inversion, 1-7/6-9/7-3/2-9/5 with steps 7/6-10/9-7/6-6/5-10/9.

The 9-odd-limit sensamagic chords number triads: 3, tetrads: 6, pentads: 2, for a total of 11.

Equal temperaments with sensamagic chords include 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283, with 283edo giving the optimal patent val.