The model [N. Todd, ``A theory of the principal monaural pathway I. Pitch and time perception,'' J. Acoust. Soc. Am. 99, 2491(A) (1996)] proposes also to account for the psychophysics of time by the interaction of a ``sensory memory,'' in the form of the collective response of cortical bandpass cells, and a ``long-term memory,'' which is the result of learning in a cortical neural network. Since the time constants of the cortical cells are relatively long, their response to an inferior collicular (ICC) input lasts long after the ICC input has ceased (and hence the form of the sensory memory above). The cortical amplitude modulation response is roughly a Laplace transform of the ICC response envelope, and so is highly dependent on envelope duration. The cortical response thus captures both the pitch and durational properties of the tone. It is shown how this model is able to provide an account of two fundamental aspects of auditory temporal processing: (1) the psychophysical law for time interval discrimination and (2) the psychophysical law for AM detection. The model is further applied to the problem of the ``filled interval illusion,'' which hitherto has evaded a convincing explanation.