From what I understand at this point, the concepts of consonance and dissonance appear as an outcome of neurological processing resulting in to what degree we find a given audio input as pleasing. Another non-Boolean spectrum where we have degrees of pleasing (or non-pleasing) audio inputs.
I don't know that's something that's generally accepted.
That consonant and dissonant intervals align closely to physical phenomena - such as the overtone series and beating - would put a strong weight towards physical explanation, rather than a neurological one.
The concept of a critical band is well known, where frequencies are "close enough" that the ear can't distinguish between them. The psycho-acoustic phenomena of masking is when weaker harmonic signals that are "masked" by stronger, nearby harmonic signal and thus not heard. Audio compression algorithms take advantage of this by removing the weaker harmonic signals, thus reducing the signal complexity.
Similarly, it is hypothesized that different tones that lie in the same critical band are perceived as dissonant. The timbre of tones will come into play, as richer timbres with more overtones will share more critical bands.
In short, although it's been known the ratio has been a factor in how consonant an interval is likely to be heard, it's only relatively recently that we've identified a probably underlying physical explanation in the auditory systems. Critical bands provide this sort of explanation.
Obviously, hearing consonance in music instead of simple intervals is more complex.
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