Pitch perception - why is the missing fundamental not directly detected in the cochlea?
The basilar membrane in the inner ear (cochlea) is a place-dependent Fourier transformer (Fig. 1). This means that there is an orderly tonotopic map projected on the basilar membrane (BM). Traveling waves imposed on the BM via the ossicle chain and the oval window start of at the base and travel all the way to the apex. Along the way the resonance frequency of the BM gradually decreases, as the BM gets wider and more flexible (like piano strings). 

Now, if a certain frequency is missing, the BM is not moving at that frequency location, and hence the hair cells do not become activated, and the neurons with that specific characteristic are not activated either. How on earth can you still hear that frequency?  

It is the harmonic structure that determines our perception of pitch, rather than the lowest harmonic alone. Our brains are sensitive to the frequency difference from one harmonic to the next and base the "real" pitch of the tone on that difference. This is referred to as the "difference tone". When you hear two pure tones, the ear and brain subtract one frequency from the other, and you "hear" a tone with a frequency of this difference (source: National Taiwan University).


Fig. 1. Frequency tuning in the cochlea. source: New York University