Mistuning one partial of a complex harmonic tone makes that partial easier to hear as a tone separate from the complex. At the same time, two pitch shifts may be observed. First, the low pitch of the complex is shifted in the direction of the mistuning, as if it were "pulled" by the partial. Second, the mistuning of the partial is perceptually exaggerated, as if the pitch of the partial were "pushed" away from the harmonic series defined by the complex. This paper shows how the latter effect can emerge within a hypothetical neural circuit. The circuit involves a gating neuron fed by three pathways, one direct and excitatory and the other two delayed and inhibitory. The neuron responds to any excitatory input spike unless it is accompanied by an inhibitory input spike on either delayed input, thus acting as a kind of "anticoincidence counter". The first delay is fixed and tuned to the period of the background harmonic complex. Its purpose is to weaken correlates of in-tune components and allow the mistuned partial to stand out. The second delay is variable and used to estimate the period of the mistuned partial, by searching for a minimum output as a function of delay. With an appropriate choice of parameters, the estimate is subject to shifts that are of the same sign as the mistuning and that peak at about 4\% mistuning and decrease beyond, as observed experimentally.