Harmony and Unconsciousness

I don't know much about music, though I'm reasonably good at listening to it. I've read that it was Pythagoras that found that sounds created by strings with lengths that are integer multiples of each other sound good together. I was wondering what the mechanism was for this. Some scientists use this discovery as a cornerstone in the development of science. There was the music of the spheres and all, which turned out to be untrue. But then there was quantum mechanics and so forth, which now seems to reflect this beauty in nature. This is all well and good, but what I was wondering is, what is it about these integer multiples that makes them sound better? 

So then it occurred to me that the hairs in our inner ears must vibrate like musical strings. It's just that they receive the sounds instead of creating them. Now these "strings" are much shorter than the musical strings, but I'd bet they still vibrate at the frequencies of the sounds they encounter. So, there must be some kind of  spectrum analyzer inside us, which allows our brains to get a frequency spectrum. Then our brains sort out the spectrum, and one simple way to make sense of it all is to sort the different peaks in terms of integer multiples. This would be one of the simplest ways of sorting things out, and maybe that's why sounds composed of integer multiples sound better, because the analysis is simpler. Anyway, I guess this is obvious on some level, but it just occurred to me. So, although the time domain generally seems more intuitive to most of us, we have some part of us, mostly unconscious, that is pretty familiar with the frequency domain too.