Neurons in diverse brain areas can respond to the interruption of a regular stimulus pattern by firing bursts of spikes. Here we describe a simple model, which permits such responses to periodic stimuli over a substantial frequency range. Focusing on the omitted stimulus response (OSR) in isolated retinas subjected to periodic patterns of dark flashes, we develop a biophysically-realistic model which accounts for resonances in ON bipolar cells. The bipolar cell terminal contains an LRC oscillator whose inductance is modulated by a transient calcium concentration, thus adjusting its resonant frequency to approximately match that of the stimulus. The model reproduces ganglion cell outputs, which sum the ON and OFF bipolar pathways, and it responds to omitted flashes with approximately constant latencies, as observed experimentally.