A perfect fifth is just 150% (3/2) the frequency of the root, just as an octave is 200% (2/1). "What sounds good" is in a certain sense based on the harmonic series, and in that sense it is equivalent to what makes sense mathematically.

A problem is that if you stack perfect fifths to get 12 notes then they won't sound in tune with each other across different keys. It's this issue which forms the crux of the linked post.