It seems like some chord arrangement are natural (they were developed independently in different parts of the world and maybe be specifically well tuned to how our ears work) but pretty much everything else is cultural though sometimes you need to dig really deep to find the source of those cultural roots. Some are informed by animals but even those have mostly transitioned to cultural learnings - instruments associated with birds, horses, dogs may have some basis in their call but at this point they're mostly spread by cultural learnings.
There's so much variability in tonal systems, I don't think we can make any kind of claim about "natural".
Western Europeans are used to an 8 tone system that's been even tempered. Move away from that at all and it sounds weird to most people. Even what most people think of as classical would sound odd to them in their original un-tempered forms with contemporaneous instruments.
Hell, most people don't know what to make of minor chords, let alone something like pentatonic systems or even more "weird" to us tonal systems.
Professor Greenburg discusses this in "How to Understand Great Music" (if I remember right), which is in many libraries (It's a Teaching Company production, which are university courses on DVD). He's a fantastic presenter, very honest and direct about how music has developed.
Yea, temperament. Even though we use the same 8-note system that was used during the "classical" period, the distance (in frequency) between certain pitches isn't the same as then, because we now (generally) use even-tempering.
Re:move away
Move away from today's temperament in pop music (or even how classical is played with modern instruments) and most people would probably be confused because of these slight frequency changes.
I've heard classical played with historically accurate temperament using instruments adjusted to try to reflect the sounds of the time - very different.
Check out prof Greenburg - pretty sure he does it in one of his lecture series.