Today's Piano Puzzler

This week's contestant is Mirabai Knight from New York, New York.  At first, I  thought I knew the hidden song right off, but then it went off into a different direction.  And in fact, the contestant had the same guess.  But then halfway through I figured it out right and got it.  And the contestant's guess on composer style was mine, too -- and wrong.  But close.  In fact, the correct answer was my first thought.  So...yep, I should have stuck with my instinct.  Especially since it quotes a well-known piece.