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Many types of user would find it valuable to search collections of music via queries representing music fragments, but such searching requires a reliable technique for identifying whether a provided fragment occurs within a piece of music. The problem of matching fragments to music is made difficult by the psychology of music perception, because literal matching may have litile relation to perceived melodic similarity, and by the interactions between the multiple parts of typical pieces of music. In this paper we analyse the propeties of music, music perception, and music database users, and use the analysis to propose alternative techniques for extracting monophonic melodies from polyphonic music; we believe that such melodies can subsequently be used for matching of queries to data. We report on experiments with music listeners, which rank our proposed techniques for extracting melodies.