A common but none the less remarkable human faculty is the ability to recognize and reproduce familiar pieces of music. No two performances of a given piece will ever be acoustically identical, but a listener can perceive, in both, the same rhythmic and tonal relationships, and can judge whether a particular note or phrase was played out of time or out of tune. The problem considered in this lecture is that of describing the conceptual structures by which we represent Western classical music and the processes by which these structures are created. Some new hypotheses about the perception of rhythm and tonality have been cast in the form of a computer program which will transcribe a live keyboard performance of a classical melody into the equivalent of standard musical notation.