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Near JI Alignment / 31
31:53:58 in 31-edo.
When you isolate it from the rest of the 31 chordmass in the uppermid area it really shines :D
less effective when adding voices. This combination sounds so concordant and very JI.
It loses a lot of it's concordance when you add a perfect fifth or add a lower rooted octave because it's "primordial" object its aligning next to is these higher prime relationships which don't have a 3/2 till a bit higher and don't have octaves below them any sooner.
It's the R - ‡6 - 7
The result is a concordance which emerges in the mid - high range when isolated as a 3-note triad. This inversion and formation of it onto /31 gives the best concordance because of both harmonic height vs voicing. Basically if rooted on 29, now you have a pinched interval 29:31 so naturally the overall discordance will increase relative to a wider spacing of like 31:53.
Voicing onto 53 will give the most "compact" expression but also a much higher suggestion of harmonic
Voicing it off the /31 and respecting that vertical is a really nice hidden object in 31.
31:53:58
0: 1/1 0.0
1: 53/31 928.4
2: 58/31 1084.5
3: 2/1 1200.0
31-edo
0: 1/1 0.0
1: 24\31 929.0
2: 28\31 1083.8
.6c error and .7c error across the whole triad.
Interesting to me because it gives a different interpretation of the Major 7th inside of 31edo, instead of looking at it as a somewhat damaged 15/8, this rendering places it in the spectrum as a 58th above /31 (a much closer approximation ~.7 c)
This interpretation doesn’t extend to saying - view 31edo maj7 as 1/1 - 5/4 - 53/31 because of the way verticality works. Interval composites become creepingly more complex.
#harmony #microtonality #musictheory #chords