One kind of prosodic structure that apparently underlies both music and language is meter. Yet detailed measurements of both music and speech show that the nested periodicities that define metrical structure are noisy in some sense. What kind of system could produce or perceive such variable metrical timing? And what would it take to store particular metrical patterns in the long-term memory of the system? We have developed a network of coupled oscillators that both produces and perceives metrical patterns of pulses. In addition, beginning with an initial state with no biases, it learns to prefer 3-beat patterns (like waltzes) over 2-beat patterns. Models of this general class could learn to entrain to musical patterns. And given a way to process speech to extract appropriate pulses, the model should be applicable to metrical structure in speech as well.