Over my thirty years of teaching, I have had parents approach me and say, usually with pride, "my child plays by ear." When the child sits down to play for me, I find out he/she is NOT playing by ear, but by test.
What is the difference?
When you play by ear, you should be able to go to the instrument, and on your first try, be able to play either exactly or reasonably close to accurately what you have just heard or memorized. Mozart reputedly could do this from a young age. This requires a good musical memory, and the ability to recognize pitch and patterns without trying them out repeatedly on the instrument.
When you play by test, which many students who claim to play by ear are actually doing, you go to the instrument and play different notes until you find the one you want, then go to the next note and try several until you find the one you want, and so on. Like hunt and peck on a typewriter (remember those?) It can be a slow and painful process in trying to learn or play back a piece of music you have heard. After a measure or two, the ear and memory can get tired, you lose your place, get confused, and then need to stop and try again later.
Can you improve your playing be ear? Yes. In lessons, play back games with your teacher can improve the musical memory you need and the correlation between what you are hearing and the key or fret or position that will produce that sound. Starting with short patterns and building over time in to longer patterns will improve your ability to play by ear, and less by test. This skill is learned more easily by children, especially young children, than by adults, but anyone can improve their musical ear skills if they are willing to give it a try!
Next post, what is the difference between learning by ear or by rote?