Hey dlwalke,

This could be a deep topic to get into involving physics and the overtone series (and probably psychology), but I'll add some thoughts:

It also has to do with the context in which you hear these intervals.

For example, you might find (like I do) the Lydian mode to be a beautiful sound. But it also relies HEAVILY on that tritone interval. West Side Story, The Simpsons, E.T., Close Encounters, etc. Such beautiful otherworldly moments created with the tritone interval...

Also, that Major 7th note you mention is often heard at the TOP of the chord. So it's not so much of a clashing Minor 2nd interval, as it would be down an octave or two right next to the root. But that same interval could be totally clashing in another context.

A lot of it has to do with what we are expecting in the moment. If you have set up the expectation of hearing Dominant 7 chords and you play a Major 7 it will sound "wrong." You might find you can get pretty out-there as far as setting up expectations (making music out of dissonant intervals) and as long as you stick to those expectations or "rules" it can feel like they work together. Then if you add a consonant chord in the middle of it, that chord will sound wrong.

To go way outside, there is a popular book called 20th Century Harmony by Vincent Persichetti that sets up some vocabulary for creating music with dissonant intervals, but that's a matter of taste. VERY useful stuff if you get into film scoring.

This is a topic totally worth exploring, so that's great that you are interested in it. I love it when I see people asking these types of questions...

-Carl.