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Perhaps this illusion is the result of an acoustic rather than physiological or cognitive phenomena.

Record a sound from a musical instrument - something with a well defined harmonic signature -  and edit the recording to remove the fundamental.  
Play the recording through a speaker, in an ordinary room (not an anechoic chamber) and  re-record it and examine the recording.
Does the fundamental re-appear (at reduced amplitude) in the new recording?

Has anyone tried this?