What is a Musical?

My wife and I recently went to a performance of a play characterized in the program as a "rock concert musical." The description seemed apt, given that the first of the play's two acts consisted almost entirely of musical numbers. However, appearances can be deceiving. We spoke with the theatre's artistic director during intermission. He quite firmly informed me the play was not a musical.

This perspective baffled me. It did lead me to consider the useful question of defining what a musical is. I don't have any bright ideas on the subject, but I'm curious about what others think on this topic. You're welcome to offer your comments.