Much current work in musical cognition is based on the notion of grammar, but there are problems in using this as a basis for modeling the process of listening as one of parsing. Not only are there unresolved issues in modeling listeners’ abilities to accommodate a multiplicity of musical styles, including novel styles, but also problems occur in modeling the recognition of recurrent patterns in a suitably flexible way. Discovery and learning are found to have a crucial role in the listening process, and so should be at the heart of a listening model. Learning models from other domains of cognitive science offer a potential basis for such models. This is illustrated through a model, based on Thagard and Holyoak's PI (“Processes of Induction”) system to learn the concept of beat by exposure to a metrical sequence of taps. Possibilities for the development of more sophisticated musical models along similar lines are explored.