Wow, great thread. If you're a guitarist play something in A. Now capo 2 and play the same thing in G. Capo 4 and play it in F. Capo 5 and play it in E. The music will sound hugely different in each situation...but it's still in A.I'm not sure my ear would REALLY hear the difference on a piano played in F or F# (not the pitch..which I WOULD hear...but the "feel". I think most keyboardists would hear it instantly.
Rick