I have, however, always noticed that classically trained players seem to have a difficulty improvising and playing by ear. I played with a violin player who was trying to play fiddle. He would always ask me where he could find sheet music to the songs we were playing. He could/would not learn any songs on his own. Just for kicks I created sheet music for a couple of western swing songs we do. He played them perfectly the first time. But could not memorize them without the music. Strangest thing ever, so obviously I had to let him go.