Ok, maybe explain like I'm 4. I've tried to get it before and I just don't. I'm OK at math, I'm a database engineer so I understand logic and relationships OK as well. I just don't get why some relationships (between notes) would "sound good" to (all? Most?) brains while some just "sound bad." Are our brains that predictable, is it cultural training... can someone help me out? Thanks!

Ok, maybe explain like I'm 4. I've tried to get it before and I just don't. I'm OK at math, I'm a database engineer so I understand logic and relationships OK as well. I just don't get why some relationships (between notes) would "sound good" to (all? Most?) brains while some just "sound bad." Are our brains that predictable, is it cultural training... can someone help

I'm not sure what you mean by "relationships (between notes)". Are you talking about intervals, entire compositions, or fragments of compositions? If you mean entire compositions or fragments of compositions then the answer is far too involved to answer in a box. If you mean intervals, then presumably by sounding "good" you mean consonant. There have been various theories about the consonance and dissonance since antiquity, many of them exuding more than a whiff of numerology. In the nineteenth-century Helmholz proposed his beat theory of consonance and dissonance, subsequently debunked. In the 1960's Plomp and Levelt proposed their critical band theory of musical theory of consonance. The critical band is real enough and does explain why the same interval can sound muddy in a low register and diffuse in a high register, but its application to consonance and dissonance has also been debunked.

I'm personally satisfied to note that in general consonant intervals involve simpler mathematical proportions than dissonant intervals. It's not that dissonant intervals sound "bad"; it's that they sound more complex (because mathematically they are more complex), and it's simplistic to classify intervals binarily; there is a continuum, a gradation. Perception of consonance is also greatly affected by timbre and musical context.

When I've expounded this, my personal theory of consonance and dissonance, before I've been asked to define "proportion complexity" mathematically. Obviously, this can't be done, but it isn't necessary because consonance and dissonance can't be defined with anything analogous to mathematical precision either. Nevertheless, it's indisputable that a 2:1 proportion is simpler than a 6:5 proportion, just as it's indisputable that it's easier for the ear to apprehend an octave than a minor sixth. If you don't believe me, compare tapping two-against-one with tapping six-against-five, bearing in mind that since a pitch is merely a gestalt perception of oscillation, so is an interval merely a gestalt perception of a rhythm.

Whoops! Re: "Nevertheless, it's indisputable that a 2:1 proportion is simpler than a 6:5 proportion, just as it's indisputable that it's easier for the ear to apprehend an octave than a minor sixth [sic]." That should be "Nevertheless, it's indisputable that a 2:1 proportion is simpler than a 6:5 proportion, just as it's indisputable that it's easier for the ear to apprehend an octave than a minor third."

You won't get it until you have freely exposed yourself to a variety of music in an open-minded fashion. Attend concerts and make notes about what you like. Seek out more of what you like. Your musicial palette will expand, and that's how it goes. There are no shortcuts, and experience takes time.