Pitch is one of the most fundamental percepts in the auditory system and can be extracted using either spectral or temporal information in an acoustic signal. Although pitch perception has been extensively studied in human subjects, it is far less clear how nonhuman primates perceive pitch. We have addressed this question in a series of behavioral studies in which marmosets, a vocal nonhuman primate species, were trained to discriminate complex harmonic tones differing in either spectral (fundamental frequency [f0]) or temporal envelope (repetition rate) cues. We found that marmosets used temporal envelope information to discriminate pitch for acoustic stimuli with higher-order harmonics and lower f0 values and spectral information for acoustic stimuli with lower-order harmonics and higher f0 values. We further measured frequency resolution in marmosets using a psychophysical task in which pure tone thresholds were measured as a function of notched noise masker bandwidth. Results show that only the first four harmonics are resolved at low f0 values and up to 16 harmonics are resolved at higher f0 values. Resolvability in marmosets is different from that in humans, where the first five to nine harmonics are consistently resolved across most f0 values, and is likely the result of a smaller marmoset cochlea. In sum, these results show that marmosets use two mechanisms to extract pitch (harmonic templates [spectral] for resolved harmonics, and envelope extraction [temporal] for unresolved harmonics) and that species differences in stimulus resolvability need to be taken into account when investigating and comparing mechanisms of pitch perception across animals.