Consonance is a musical concept describing the stability of a chord or harmony. Consonance is a subjective notion, and varies culturally, although there are certain well-established trends of harmonies or intervals that are considered consonant across various types of music. The opposite of consonance is dissonance.
In general, intervals corresponding to ratios between smaller numbers in the harmonic series are more likely to be perceived as more consonant, and intervals corresponding to larger numbers are more likely to be perceived as dissonance. As Western culture developed, the perception of consonance broadened, and intervals like thirds which were at one point considered dissonant came to be considered consonant.
The 31-ET tuning opens up new possibilities for consonance. Because it matches both the 7th and 11th harmonics, there are a number of new potentially consonant intervals in 31-ET that are not found in 12-ET:
The potential for consonance in 31-ET is also greatly enhanced by the fact that two of the main consonant intervals in western music, the major and minor third, are much more in-tune in this system. This gives these intervals a purer, more stable sound, which paves the way for new contrasts and harmonic nuances between the highly consonant major and minor thirds, and the slightly more dissonant consonances involving higher harmonics.
Here are a few examples of chords in 31-ET that utilize the new intervals and produce consonances not possible in 12-ET: