One kind of prosodic structure that apparently underlies both music and some examples of speech production is meter. Yet detailed measurements of the timing of both music and speech show that the nested periodicities that define metrical structure can be quite noisy in time. What kind of system could produce or perceive such variable metrical timing patterns? And what would it take to be able to store and reproduce particular metrical patterns from long-term memory? We have developed a network of coupled oscillators that both produces and perceives patterns of pulses that conform to particular meters. In addition, beginning with an initial state with no biases, it can learn to prefer the particular meter that it has been previously exposed to.