@gailcalled Re: your post two above – muscle memory definitely comes into play. Knowing chord structures, keeping harmonies in mind (I play the clarinet, so my hands work on the same musical line at the same time – this may be different for pianists), and having a good ear for pitch is mostly background info my brain processes but doesn’t make me aware of at the time I’m playing the piece – though I’m sure the knowledge does help, I don’t base memorization strategies around those factors. Music theory class was cool because I got to examine those background processes in a more conscious way.
@Jeruba I think I usually notice when performers miss a note, because something sounds off for a split second. It’s like a blip, the auditory version of a tiny fly bumbling across your field of vision. Perhaps this is because I enjoy (and have worked on) a good sense of relative and absolute pitch.
@marmoset I feel like maybe you are interpreting the question differently than most of us – no one claims that instrumentalists learn pieces without using the sheet music initially. I suppose some must, but I have never met any, and this is not the way they train us. I and everyone I know learn off the sheet music, then memorize it. And it is considered…not better, but more professional, to memorize for performance. I was taught that it shows consideration for your audience because then they can see you properly and because you are more attuned to playing for them rather than simply playing perfectly. And in some cultures it is necessary – my Russian and Ukranian clarinet teachers were not allowed to perform with music in front of them, back when they were in school in their home countries.