[pierrec]

Both statements are true. We have a strong tendency for integer ratios in harmony, and just intonation often sounds out of tune.

Integer ratios are the base upon which harmony is built. Temperament is a subtle modification that sounds very close to integer ratios, but allows more complex harmonic structures where dissonance is evenly spread out across all the relationships between tones.

[IsTom]

Seventh and eleventh harmonics are way off. If ratios were the fundamental thing Bohlen–Pierce would be about as pleasant as 12TET to people.

[pierrec]

Way off what? Complex ratios are likely to be heard as out-of-tune simple ratios, that's why they sound off. A concept sometimes called tolerance in music cognition. Note that by "complexity" and "simplicity" I'm referring to harmonic distance here.