We examine various computational accounts of aspects of music understanding. These accounts involve programs which can notate melodies based on pitch and duration information. It is argued that this task involves significant musical intelligence. In particular, it requires an understanding of basic metric and harmonic relations implicit in the melody. We deal only with single-voice, tonal melodies. While the task is a limited one, and the programs give only partial solutions to this task, we argue that this represents a first step towards a computational realization of significant aspects of musical intelligence.