The perceived pitch of a complex harmonic sound changes if the partial tones of the sound are frequency shifted by a fixed amount. Simple mathematical rules are expected to govern perceived pitch, but these rules are violated in psychoacoustic experiments. Cognitive cortical processes are commonly held responsible for this discrepancy. Here, we demonstrate that this need not be the case. We show that human pitch perception can be reproduced with a biophysically motivated mesoscopic model of the cochlea, by fully recovering published psychoacoustical pitch-shift data and related physiological measurements from the cat cochlear nucleus. Our study suggests that perceived pitch can be attributed to combination tones in the presence of a cochlear fluid.