here is another point.
the math behind the 12 tones is actually not as cut and dried as it is considered to be.
there are two ways of calculating the length of the distance between tones, and the result is that we use an average of the two.
thus if you follow the octaves (i) up and up, and (ii) down and down, the more octaves you move away from the center, the less in tune (i) is with (ii)
i can't off hand remember all the details as it was some time ago when i studied the philosophy of music, (within the context of philosophy, not music) but i clearly remember how it fascinated me that music theory is just a little bit fuzzy when it comes to calculating it all PERFECTLY.
however if you only move a handful of octaves, the rounding error is so small, that it is just not noticable; except to the mathematician!
so perfect pitch is actually an illusion.
just as perfect pi cannot be calculated.
a source for this quote would be nice?
my searches for the shortest wavelength find so many different answers, i'm not sure who is correct. however, the logic is the same regardless.
(i recommend gargling with salt water for the cough)