31 equal temperament

More generally, it is a regular diatonic tuning in which the tempered perfect fifth is equal to 696.77 cents, as shown in Figure 1.

Huygens not only realized this, he went farther and noted that 31 EDO provides an excellent approximation of septimal, or 7 limit harmony.

The composer Joel Mandelbaum (born 1932) used this tuning system specifically because of its good matches to the 7th and 11th partials in the harmonic series.

It has the necessary property that a chain of its four fifths is equivalent to its major third (the syntonic comma 81:80 is tempered out), which also means that it contains a "meantone" that falls between the sizes of 10:9 and 9:8 as the combination of one of each of its chromatic and diatonic semitones.

Chords not discussed there include the neutral thirds triad (Playⓘ), which might be written C–E–G, C–D–G or C–F–G, and the Orwell tetrad, which is C–E–F–B.

31 EDO on the regular diatonic tuning continuum at p5 = 696.77 cents [ 1 ]
19 limit just intonation intervals approximated in 31 EDO
Circle of fifths in 31 equal temperament
I–IV–V–I chord progression in 31 tone equal temperament. [ 1 ] Whereas in 12 EDO B ♮ is 11 steps, in 31 EDO B ♮ is 28 steps.
C subminor, C minor, C major, C supermajor (topped by A ♭ ) in 31 EDO
C seventh and G minor, twice in 31 EDO , then twice in 12 EDO