In auditory cortex, temporal information within a sound is represented by two complementary neural codes: a temporal representation based on stimulus-locked firing and a rate representation, where discharge rate co-varies with the timing between acoustic events but lacks a stimulus-synchronized response. Using a computational neuronal model, we find that stimulus-locked responses are generated when sound-evoked excitation is combined with strong, delayed inhibition. In contrast to this, a non-synchronized rate representation is generated when the net excitation evoked by the sound is weak, which occurs when excitation is coincident and balanced with inhibition. Using single-unit recordings from awake marmosets (Callithrix jacchus), we validate several model predictions, including differences in the temporal fidelity, discharge rates and temporal dynamics of stimulus-evoked responses between neurons with rate and temporal representations. Together these data suggest that feedforward inhibition provides a parsimonious explanation of the neural coding dichotomy observed in auditory cortex.