There are many websites which claim to teach you to play piano by ear. But, the real question is; does it work? Can you truly learn to play the piano strictly by ear? While I believe it is possible, I believe that this method has its limitations.
First of all, learning to play by ear generally means that you need to be able to hear pitch and gage the quality of chords with your ear. In other words you would need to be able to distinguish the difference between major and minor chords, dominant and diminished etc. The only problem is most people do not possess an ear capable of such distinctions.
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