As regards to one-ness, I'd be curious to know what proportion of people don't hear the relationship. Cause I guess I'd call not hearing octaves on a piano something like tone deaf, but maybe it's more learned and less innate than I think.
http://www.brainmusic.org/MBB91%20Webpage/Evolution_Zentner....
Restricting your notes to octave intervals makes dissonance impossible, assuming you're using timbres made with vibrating strings or columns of air, or simulations of them.
We attached certain names to certain frequencies in western culture and made rules about 'proper music'. It is quite fascinating how culturally influenced we are on what is beautiful sound. Other cultures will have different frequencies and composition rules they consider good or artistic. Seven different D notes is how you say 7 unique frequencies, not one.