There's a refreshingly simple mechanic to all of this:
- all factors of two of a given frequency (AKA 'fundamental') within discriminable range are resolved as being 'equivalent' to it - this is the magical, almost inexplicable percept of sameness between octaves. What's actually 'the same' between these tones of such wildly varying pitch? Nothing, of course.. This paradox is resolved by realising that we assign this property of parity to maximally simple frequency relationships.
In other words, 'consonance' and 'dissonance' are but degrees of this equivalence, and difference from it - or inequivalence.
'Consonance' has a maximum value, peaking at maximum simplicity; 2f. In other words, we're processing frequency relationships in terms of their relative complexity.
And, specifically, we're measuring this complexity in terms of complexity of the network activity in the associated resolving nuclei - a 2f relationship resolves every other cycle. The next most simple relationship, the 'perfect fifth' or 3f, resolves every 3rd cycle (ie. three cycles of the higher freq for each single cycle of the lower one). And so on; 5f, 6f etc. etc.; as we get to progressively higher ratios, more and more neurons are corralled into resolving their temporal integration window, and they become less harmonious.
In short, if a freq ratio can be resolved as any factor of two between the two freqs, then they're maximally simple and thus assigned parity (octave equivalence). For 3f, less so. 4f is equivalent again (2 x 2f), but 5f is even more inequivalent (dissonant) than 3f.
The harmonic series can be produced in a number of different ways, but from this angle it seems pretty obvious we're using recursive subdivision by two - that is, take a string (or monochord), halve its length, and the ratio between the new note and the full chord length is one octave.
Halve that distance again (so now a quarter of the original) and the relationship of the new note to the original is a perfect fifth. Repeat again and we have another octave. Next we get a Third, then another octave, and so forth. Keep repeating and this simple function reproduces all intervals of the harmonic series.
A simple biological architecture that might accomplish such recursive subdivision would be recirculation of input signals through a feedback / feedforward network with a 2f modulation.
Miller et al have shown just such an effect between auditory cortex neurons and their thalmic afferents - although one can only speculate if this indeed affords us some kind of affinity for the series. What seems unequivocal however is this principle of maximal consonance correlating to maximal simplicity. Consonance has an elementary form, in this mysterious and perplexing sensation of parity between maximally-simple frequency ratios, and by which dissonance is, by default, defined in terms of relative complexity. Again, there is really nought but equivalence, and degrees of inequivalence in relation to it...
