The septimal major third is an interval not occurring in most western music. It corresponds to the difference between the 7th and 9th harmonics, and is slightly wider than a major third. The septimal major third sounds more dissonant than the major or minor thirds.
In 31-ET, the septimal major third is made out of 11 scale steps, and is slightly out-of-tune, as it is slightly too narrow. This difference is subtle and may not be noticed by most people. However, it can make this interval a bit harder to sing or play in-tune.
The septimal major third implies a root one whole-step below the top note, or a septimal whole tone above the bottom note. However, this effect is rather weak. If the septimal major third is included as the bottom interval of a perfect fifth, the result will be a slightly dissonant-sounding major chord, with a clear bottom root implied by the fifth, overriding the septimal major third's tonal center. As the top interval of a septimal minor chord, the septimal major third's tonal center shines through more readily.
The 11-step interval in 31-ET is also a match to the 14:11 ratio of the harmonic series, which can be called the undecimal major third. This interval can be seen as the distance between the 11th harmonic, and the 7th harmonic an octave up. It can be constructed by stacking a 7:6 septimal minor third on top of a 12:11 neutral second.
The 11-step interval in 31-ET falls roughly halfway between these two intervals, which are only 17.57 cents apart. (For reference, minor thirds in 12-ET are flat by 15.64 cents). So, even with this interval falling in between the two true intervals in width, both are matched quite well.
Because the 14:11 ratio involves both the 7th (as the 14th) and 11th harmonics, harmonics which are well-incorporated into 31-ET, the interpretation of this interval as an undecimal major third may be harmonically useful in this tuning.
If this interval is interpreted or functions as an undecimal major third, it will have a different root, a septimal whole tone above the top note, or an undecimal tritone (11:8) below the bottom note. These relationships are a bit esoteric, and as this interval is harmonically weaker than the septimal major third, the 11-step interval will be unlikely to be interpreted in this way unless the overall harmonic context supports such an interpretation.
In 31-ET, stacking two 11-step intervals creates an un-ambiguous interpretation, equivalent to 9:7 stacked on top of 14:11, adding up to a neutral minor sixth, or the 18:11 ratio. Although this interpretation is unambiguous in 31-ET with these three notes alone, all involved intervals are quite harmonically weak, so the presence of a conflicting stronger interval can change the tonal center (and interpretation of the 11-step intervals).