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Do you have any advice on how to learn to play by ear? I can play piano well, but figuring out a song from a recording is very difficult for me.
Without talent, you must practice. Take a song you don't know how to play, and start to figure it out from a recording. Once you've mastered that song, pick another one. There's no secret to any of this. I've have no natural talent for music, but I put in the hours. When I was 16, I was cut from my high school musical for my inability to sing back a note played on the piano. I took voice lessons, got a few chorus rol…
It would be helpful to do some songs that you can get the full score for, so you can do concrete validation of your correctness. However, be sure that they are the full, true score; grab a Guitar book of Beatles songs, for instance, and they're likely to be simplified in a way that won't help on this task.