The ability to detect and rapidly process harmonic sounds, which in nature are typical of animal vocalizations and speech, can be critical for communication among conspecifics and for survival. Single-unit studies have reported neurons in auditory cortex sensitive to specific combinations of frequencies (e.g., harmonics), theorized to rapidly abstract or filter for specific structures of incoming sounds, where large ensembles of such neurons may constitute spectral templates. We studied the contribution of harmonic structure to activation of putative spectral templates in human auditory cortex by using a wide variety of animal vocalizations, as well as artificially constructed iterated rippled noises (IRNs). Both the IRNs and vocalization sounds were quantitatively characterized by calculating a global harmonics-to-noise ratio (HNR). Using functional MRI, we identified HNR-sensitive regions when presenting either artificial IRNs and/or recordings of natural animal vocalizations. This activation included regions situated between functionally defined primary auditory cortices and regions preferential for processing human nonverbal vocalizations or speech sounds. These results demonstrate that the HNR of sound reflects an important second-order acoustic signal attribute that parametrically activates distinct pathways of human auditory cortex. Thus, these results provide novel support for the presence of spectral templates, which may subserve a major role in the hierarchical processing of vocalizations as a distinct category of behaviorally relevant sound.