The pitch of vocalizations is a key communication feature aiding recognition of individuals and separating sound sources in complex acoustic environments. The neural representation of the pitch of periodic sounds is well defined. However, many natural sounds, like complex vocalizations, contain rich, aperiodic or not strictly periodic frequency content and/or include high‐frequency components, but still evoke a strong sense of pitch. Indeed, such sounds are the rule, not the exception but the cortical mechanisms for encoding pitch of such sounds are unknown. We investigated how neurons in the high‐frequency representation of primary auditory cortex (A1) of marmosets encoded changes in pitch of four natural vocalizations, two centred around a dominant frequency similar to the neuron's best sensitivity and two around a much lower dominant frequency. Pitch was varied over a fine range that can be used by marmosets to differentiate individuals. The responses of most high‐frequency A1 neurons were sensitive to pitch changes in all four vocalizations, with a smaller proportion of the neurons showing pitch‐insensitive responses. Classically defined excitatory drive, from the neuron's monaural frequency response area, predicted responses to changes in vocalization pitch in <30% of neurons suggesting most pitch tuning observed is not simple frequency‐level response. Moreover, 39% of A1 neurons showed call‐invariant tuning of pitch. These results suggest that distributed activity across A1 can represent the pitch of natural sounds over a fine, functionally relevant range, and exhibits pitch tuning for vocalizations within and outside the classical neural tuning area.