Harmonic intervals are interesting but they are also misunderstood. Humans are able to distinguish out of tune notes down to a value of about 1%. To get more accurate tuning we tend to listen for beating (a kind of amplitude modulation) instead. This means we can tolerate tuning systems other than just intonation. Another thing to consider - the missing fundamental phenomenon suggests that the ear/brain is actually doing something like autocorrelation. This makes more sense than the idea that we have a template for the harmonic series wired in our brains. Finally auto correlation works for chords too, not just intervals. Every chord has a fundamental period of repetition - shorter periods are widely ranked as more consonant. There are lots of grand music theories that fixate on the harmonic series. The maths is fun, but it can get in the way of more effective alternatives for organising sounds.