> A lot of advanced digital synthesizers will carefully detune oscillators from each other so they aren't "perfectly in tune" in order to get thicker sounds

As noted in other comments, this also applies to singing and arbitrary pitch instruments, possibly at a subconscious level, and it has the opposite "mathematical" implication than you seem to think: any fixed tuning is a serious constraint that makes some chords sound wrong, and only being able to tune individual notes perfectly allows the introduction of aesthetically pleasing imperfections.