Is there a way to define dissonance such that it can be quantifiable?

1. How do you quantify dissonance?
2. How is math able to predict the consonance or dissonance of musical pitches?

How do you quantify dissonance?

To compute a measure of dissonance one should take into account harmonics, i.e. compute all the pairwise contributions to the measureand sum them up (not too hard to do). For chords of more than two pitches you just sum up all the pairwise contributions to the measure, fundamentals and harmonics.

How is math able to predict the consonance or dissonance of musical pitches?

In sixth century BC, Pythagoras discovered the mathematical foundation of musical consonance and dissonance. When auditory frequencies in small-integer ratios are combined, the result is a harmonious perception. ... This result indicates a link between consonance and the dynamical features of the signal.