Pitch is an auditory percept critical to the perception of music and speech, and for these harmonic sounds, pitch is closely related to the repetition rate of the acoustic wave. This paper reports a test of the assumption that non-human primates and especially rhesus monkeys perceive the pitch of these harmonic sounds much as humans do. A new procedure was developed to train macaques to discriminate the pitch of harmonic sounds and thereby demonstrate that the lower limit for pitch perception in macaques is close to 30 Hz, as it is in humans. Moreover, when the phases of successive harmonics are alternated to cause a pseudo-doubling of the repetition rate, the lower pitch boundary in macaques decreases substantially, as it does in humans. The results suggest that both species use neural firing times to discriminate pitch, at least for sounds with relatively low repetition rates.