[dharma1]

I haven't tested this, but my intuition is that any musical sound with harmonic (as opposed to inharmonic) partials will sound like a single note, if the first fundamental is clearly the loudest, and the harmonics follow some kind of natural distribution in terms of loudness and temporal decay.

Two notes played in an octave would be quite distinct since you have a clear first fundamental for both notes, and the loudness/decay of the harmonics is slightly different between both notes