Being able to "play piano by ear" is one of the most misunderstood concepts of learning to play piano as a beginner. Here's how piano pros "hear" melodies and intervals easily, and how you can do the same thing.
PianoGenius.com

The good news is that your ear is already somewhat trained, even if you can't play music at all yet. I'll prove it to you in the first few minutes. :-)

To clarify: There's something called "perfect pitch", also called "absolute pitch" that is extremely rare. I don't have it, you don't have it, hardly anybody has it.

However, you CAN develop "RELATIVE PITCH", and all that means is recognizing what a note is relative to another note. That's what I'm talking about in this video. You already have relative pitch to some degree, and the better you can get at it the easier it will be to learn new songs quickly.

I've got a lot more of this type of training on PianoGenius.com, so hop on over there if you're looking for more. :-) Thanks for watching, and please post whatever comments and questions you may have!
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Tim Gross Bio:
Tim Gross currently tours nationwide with Grammy award-winning artist Rick Springfield and has performed and/or recorded with Robin Zander (Cheap Trick), Terri Nunn (Berlin), Tommy Tutone, Check Negron (Three Dog Night), Greg Kihn, John Waite, Sammy Hagar, Mickey Thomas (Starship), Kevin Cronin (REO Speedwagon), George Thorogood, and others.