Hi all,  As an electronics engineer, I would say that this should
be possible, although expensive.  It should be possible to construct
88 filters that analyze the audio signal from microphone and give an
output if that particular frequency is present.  To make that into MIDI
would or sheet music or piano rolls would just be a software exercise.
The modern way to do this is probably a fast DSP (digital signal
processor) to simulate the filters.

Problems I can see with this are the harmonics in a piano and also
other instruments, voice and singing.  Nevertheless, I am convinced
it is possible.

Kind regards,

Bernt Damm
Cape Town