Transcribing music from from .wav (or any other audio) to a .midi file is very possible and actually frequently made audio conversion. What such wav to mid conversion does, is that it converts the audio data and creates a file with musical instrumental data that can be replayed with any MIDI player.
Open WAV file Open MID fileA music composition and editing program
A music notation and transcription software
Tool for load your own WAV files into your Nord keyboard
A WAV to MIDI converter