Recent temporal models of pitch and amplitude modulation perception converge on a relatively realistic implementation of cochlear processing followed by a temporal analysis of periodicity. However, for modulation perception, a modulation filterbank is applied whereas for pitch perception, autocorrelation is applied. Considering the large overlap in pitch and modulation perception, this is not parsimonious. Two experiments are presented to investigate the interaction between carrier periodicity, which produces strong pitch sensations, and envelope periodicity using broadband stimuli. Results show that in the presence of carrier periodicity, detection of amplitude modulation is impaired throughout the tested range (8-1000 Hz). On the contrary, detection of carrier periodicity in the presence of an additional amplitude modulation is impaired only for very low frequencies below the pitch range (<33 Hz). Predictions of a generic implementation of a modulation-filterbank model and an autocorrelation model are compared to the data. Both models were too insensitive to high-frequency envelope or carrier periodicity and to infra-pitch carrier periodicity. Additionally, both models simulated modulation detection quite well but underestimated the detrimental effect of carrier periodicity on modulation detection. It is suggested that a hybrid model consisting of bandpass envelope filters with a ripple in their passband may provide a functionally successful and physiologically plausible basis for a unified model of auditory periodicity extraction.