In this paper we take a connectionist machine learning approach to the problem of metre perception and melody learning in musical signals. We present a two-layered network consisting of a nonlinear oscillator network and a recurrent neural network. The oscillator network acts as an entrained resonant filter to the musical signal. It `perceives' metre by resonating nonlinearly to the inherent periodicities within the signal, creating a hierarchy of strong and weak periods. The neural network learns the long-term temporal structures present in this signal. We show that this network outperforms our previous approach of a single layer recurrent neural network in a melody and rhythm prediction task. We hypothesise that our system is enabled to make use of the relatively long temporal resonance in the oscillator network output, and therefore model more coherent long-term structures. A system such as this could be used in a multitude of analytic and generative scenarios, including live performance applications.