If you had perfect pitch (maybe relative pitch is enough) then couldn't you just make marks in each position on the fretboard where it sounds like a new full note, and then go back and listen for the half-notes and do the same thing?
But this is not exact!
Music harmonics are just about multiples. Ie one note rings at some frequency and another note that sounds nice with it rings at some multiple of it. Or they have some common factor. The twelve note system and the twelvth roots are just approximations for some of these harmonies. There's even very recent innovation like true temperament frets. But I don't think that works with all the different song keys and tunings... Maybe it's another reason why I should buy a guitar for every song key we have!