[Nils Jacob Holt Hanssen]

For another, there are intervals that we hear as consonant but which do not correspond to particularly simple ratios. The most striking example is the (12 tone equally tempered) minor third – indeed, one of the component intervals of the major triad – where the ratio of the two pitches is the fourth root of 2: a number which is not close to any rational number as simple as 6/5 or 7/6, and yet which produces an interval which is more familiar and natural to us (or at least to me!) than the just minor third (ratio 6:5) and certainly than the septimal minor third (7:6).

Good point! I didn’t really investigate other intervals than those in a major chord 😊.

Any chord, anyfrequency sound can become “dissonant” in the “right” context.

Thus the perfect fifth (3:2), though it has a high chance of becoming a harmonious interval, is not guaranteed to, just as the minor third is not prohibited.

Can you mention any specific context that you’re thinking of here? Where, for instance, a perfect fifth would sound dissonant? Sure, if you play a C + G and then add a G# (minor second) on top, then you’ll get dissonance, obviously. But then it’s not a perfect fifth anymore. Or rather, it’s more than a perfect fifth. Or are you thinking of less straightforward, more subtle combinations with other chords or intervals?

And I still believe that there is always some purely physical/physiological/neurological factors at play when people perceive certain frequency combinations, like a minor second, as grating. Even in cultures where, because of musical traditions and conditioning, that interval may not be regarded as unpleasant, I would think they still can perceive its, um… gratiness.