Personally, I don't find 31-TET compelling since it gives worse ratios for perfect fifths 3/2 (1.495 instead of 1.498) and thus perfect fourths 4/3 (1.337 inste

Personally, I don't find 31-TET compelling since it gives worse ratios for perfect fifths 3/2 (1.495 instead of 1.498) and thus perfect fourths 4/3 (1.337 instead of 1.335). Anyway, back to 12-TET. Here's a useful formatting: 1.00 C = 1/1 unison, [diminished second] 1.06 C#/Db (augmented unison), minor second 1.12 D ~ 9/8 major second, [diminished third] 1.19 D#/Eb ~ 6/5 (augmented second), minor third 1.26 E ~ 5/4 major third, [diminished fourth] 1.33 F ~ 4/3 perfect fourth, [augmented third] 1.41 F#/Gb !!!!! satanic tritone (augmented fourth, diminished fifth) 1.50 G ~ 3/2 perfect fifth, [diminished sixth] 1.59 G#/Ab ~ 8/5 (augmented fifth), minor sixth 1.69 A ~ 5/3 major sixth, [diminished seventh] 1.78 A#/Bb ~16/9 (augmented sixth), minor seventh 1.89 B major seventh, [diminished octave] 2.00 C = 2/1 octave, [augmented seventh] Note that intervals are named based on the natural version (i.e. considering only letter half), then modified for the accidentals (sharps and flats). The names in (parentheses) are somewhat less likely to be used of each pair (That is, C to D# is an augmented second, but C to Eb is the minor third and much more common). The names in [brackets] would also refer to the same interval ratio but require either a double accidental on one end, or a sharp and flat in different directions, neither of which I wrote out here. "Doubly/triply/quadruply diminished/augmented" are also possible prefixes but increasingly rare; I don't think further is possible when you're limited to double accidentals.