Many nervous systems contain rhythmically active subnetworks that interact despite oscillating at widely different frequencies. The stomatogastric nervous system of the crab Cancer borealis produces a rapid pyloric rhythm and a considerably slower gastric mill rhythm. We construct and analyze a conductance-based compartmental model to explore the activation of the gastric mill rhythm by the modulatory commissural neuron 1 (MCN1). This model demonstrates that the period of the MCN1-activated gastric mill rhythm, which was thought to be determined entirely by the interaction of neurons in the gastric mill network, can be strongly influenced by inhibitory synaptic input from the pacemaker neuron of the fast pyloric rhythm, the anterior burster (AB) neuron. Surprisingly, the change of the gastric mill period produced by the pyloric input to the gastric mill system can be many times larger than the period of the pyloric rhythm itself. This model illustrates several mechanisms by which a fast oscillatory neuron may control the frequency of a much slower oscillatory network. These findings suggest that it is possible to modify the slow rhythm either by direct modulation or indirectly by modulating the faster rhythm.