D..W..

Yes, there is a science to why things sound good in music.
It's called Music Theory.
Certain bunches of notes sounding good can be explained in theory. As for all music being made with the same notes- You have 12 notes, and then you have the same note repeated an octave higher. So technically there are endless different notes (as none sound exactly the same), but we label them by what sounds the closest (albeit higher or lower). And if you use a chromatic tuner, you'll notice that one octave is equivalent to twice the frequency. (for example, open E on a bass is 42-i think- and open E on a guitar is 84-Again, i think. The numbers may not be exactly correct but the point is there, the octave is twice that of the octave before it). Also, we only have those twelve notes because of how tuning works. (This part gets more science then theory, we just take being in tune as a given factor when applying music theory) When you tune your guitar, you usually are tuning it with the reference point being A=440Hz. Therefore B,C,D and so on are in relation to that. I have heard of people with interesting reasons as to why 440Hz is bad and tune to 432Hz instead (you can adjust most chromatic tuners). But then try jamming with those guys- you'll sound like crap (i.e. out of tune) because you're tuned differently. Although his sounds good with his own guitar and to anyone else tuned to 432Hz, you can't make notes in between A and Bb sound good with notes that are directly at A, or Bb or whatever note you want. They will always sound off (ever played an out-of-tune guitar? You know what I mean). Why they sound off, I can't say, I just know that they do. (If that makes no sense, let me know, I'm not sure if it does or not.) In a sense it's just irreparably dissonant (to the point where it's just bad, not dissonant as in diminished chords, which can in fact sound good), which is why use half-steps and never quarter and eighth steps when talking about notes.
That's the theory portion of the answer.

The science behind your smaller frets thing would be actual science, but less in terms of why things sound good, and the physical science of making the right note come out of a string.
I'm I don't know for certain what would happen if you did that, although if you spoke to a good luthier he could probably tell exactly what it would do. I'm relatively sure, however, that you would need to put thinner strings on it and have a higher tuned instrument (like mandolins, ukuleles etc. Pretty small frets, pretty high notes). However, there a 1/2 and 3/4 size guitars out there, which I have never come up with a reasonable explanation for why they sound the same as a normal guitar (anyone know? I'm pretty curious about that lol). That's more of a physical thing then a sound thing.

It sounds like you might be going a bit too fast if you don't get it. Look for Josh Urban's series 'the crusades' for a decent beginner theory guide. It's here on UG, just give it a search. It starts at the beginning and I highly recommend reading each piece ALL THE WAY THROUGH, no matter how much you think you don't need to. He analyzes a few songs and does in fact explain why. And well, he's kinda funny too, which makes the 40 or so pages of reading enjoyable. (Try copying and pasting to your computer, printing and reading bit by bit if you don't want to read 40 pages off a screen). I would start there (read all 13 of them. By the end you get to some relatively complicated stuff, but it's good stuff to know, and he explains everything you need to understand that stuff).

Also, theory helps you more if you actually really get it. Musictheory.net has some good stuff but it never really helped me much, it just never seemed to go detailed enough.