With the growth in digital representations of music, and of music stored in these representations, it is increasingly attractive to search collections of music. One mode of search is by similarity, but, for music, similarity search presents several difficulties: in particular, deciding what part of the music is likely to be perceived as the theme by a listener, and deciding whether two pieces of music with different sequences of notes represent the same theme. In this paper we propose a three-stage framework for matching pieces of music. We use the framework to compare a range of techniques for determining whether two pieces of music are similar, by experimentally testing their ability to retrieve different transcriptions of the same piece of music from a large collection of MIDI files. These experiments show that different comparison techniques differ widely in their effectiveness; and