Sensamagic chords
A sensamagic chord is an essentially tempered dyadic chord tempered by the sensamagic comma, 245/243.
The 9-odd-limit sensamagic chords are of pattern 1a, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. In this article, voicing with the perfect fifth is prioritized.
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.
The other sensamagic triads are
- 1–7/6–9/7, with steps 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 the following palindromes:
- 1–7/6–9/7–3/2, with steps 7/6, 10/9, 7/6, 4/3;
- 1–7/6–9/7–9/5 with steps 7/6, 10/9, 7/5, 10/9.
And the following inversely related pairs:
- 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.
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.
Equal temperaments with sensamagic chords include 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283, with 283edo giving the optimal patent val.