It's impossible to get rid of, even the harmonics of a note change with a different instrument (even 2 different guitars). The harmonics that sound make up the note sounds, like a group of pitches make one singular fundamental pitch. If you got rid of all the harmonics and only heard the fundamental, it would be like looking a picture in only the color white.
I really just seem to be another over-analyzed theory to try to give perfect stability to music. If it helps some that's kool, but music is about hearing not science. You could easily go through life just playing the chord progression I - vi - IV - V7 because it works and science allows it. Why can't you play a chord progression like i - vi(hd) - ii(hd) - V7 (hd - half-diminished). Alot of theories will say this won't work or whatever, but it sounds awesome! Isn't that the point, what sounds good not what theory say you can or can not do??
"My whole life is a dark room...ONE BIG DARK ROOM" - a.f.i.