The septimal minor third, also called the subminor third, is a musical interval not found in most western music. It corresponds to the difference between the 6th and 7th harmonics, and is wider than a whole tone and narrow than a regular minor third; in 31-ET this interval is one step wider than a septimal whole tone and one step narrower than a minor third.
The septimal minor third is a fairly consonant interval, although its relative dissonance or consonance depends on context.
To understand the notation on the right, note that in 31-ET the septimal minor third is one step (represented by a semisharp or semiflat) smaller than a regular minor third, and two steps (represented by a normal sharp or flat) wider than a whole tone.
Because it matches the 7:6 ratio in the harmonic series, the septimal minor third implies a root a perfect fifth below the bottom note of the interval, or a septimal whole tone above the top note.
The septimal minor third is an interesting interval in that it is tends to sound alien or unfamiliar to most people only exposed to Western music, yet it can be a key component of chords that are more consonant than other, similar chords from 12-ET.
The septimal minor third functions surprisingly differently from the regular minor third when it is the bottom interval of a minor triad. The familiar western minor chord does not occur in the harmonic series, but a minor chord involving the septimal intervals does, as the ratios 6:7:9. The septimal minor chord thus tends to sound much more consonant than the regular minor chord, even though the septimal thirds are usually perceived as more dissonant when they are encountered in isolation.
Stacking the septimal whole tone on top of the septimal minor third produces a perfect fourth. The three-note chord produced in this fashion also tends to be much more consonant than any chords in 12-ET produced by adding a note in between the notes of a perfect fourth.
There are also numerous tone clusters involving this interval. Because the 13th harmonic is poorly matched in 13-ET, tone clusters made my adding a third note in between the notes of a septimal minor third tends to create a very dissonant sound. (I.e. a 12:13:14 ratio cannot be closely matched). However, a neutral second under a septimal minor third provides a decent match to the 11:12:14 ratios, creating a relatively more consonant tone cluster. Stacking a diatonic semitone on top of the interval produces a major third and also provides a good match to the 12:14:15 ratios.
Most other tone clusters involving this interval sound very dissonant and have ambiguous or weak roots or tonal centers.
The septimal minor third can often be used to produce large chords, such as seventh chords, that sound more consonant than any similar chords possible in 12-ET, such as by stacking it on top of a major triad or a septimal minor triad.