[krig]

That's basically the questions that music theory answers. As far as I understand things, it mostly relate to frequencies and harmonic resonance. The octaves are exact multiples of the same frequency (so a higher octave is 2x the frequency of the lower octave). The seven notes all fall out from that as well, but it is more complicated to explain and I don't know things well enough to break it down in a way that would be correct and make sense. But basically they resonate with each other.

As to why the human ear finds harmonic resonance pleasing is a more difficult question to answer. Why do we find order pleasing, and chaos frustrating? Speaking generally, the human brain functions as an advanced pattern seeking machine. What we do is take in chaotic and diverse information and make sense of it in some way, piecing individual facial features together into a specific face, and so on. Information that is ordered to begin with requires less work for the brain to process, so perhaps we find it pleasing because it is easy to sort and label mentally?

The intervals of black and white keys relate to the major scale. Basically, the major scale has the property of consisting of two whole steps, one half step, three whole steps and finally one half step. So the piano is constructed based on that scale.

Again, I can't explain it much better than that, but any book on the mathematics of music and signal processing / frequencies would have more information.

But yeah, the reason why you can't answer those questions is because you don't know music theory. That's where the answer to them is. It's not that they can't be answered.