Actually, you
can change the pitch of recorded audio, but it's not a simple thing to do.
The simplest way to do it is to speed up or slow down the playback, but this has the undesired effect of shortening or lengthening the duration of each sound-- not just the duration of each note, but the attack/decay/sustain/release times, the transitions between the various overtones in the note, etc.
Many modern DAWs have the ability to automatically identify the transients in an audio track-- the moments when the amplitude or pitch changes significantly-- and let you shift the pitch of the track up or down while maintaining the positions of the transients. But I believe it works best when the pitch is shifted just a little bit; larger shifts tend to introduce odd qualities to the sound that make it sound artificial or "chipmunky."
EDIT -- I was still composing my message when Ian posted his, and I didn't intend to parrot him.