Adults habitually adopt a special vocal register when talking to children. Current evidence suggests that the acoustic properties characterizing infant-directed speech change over development, in response to changes in infant vocal behavior, but the factors driving these changes remain largely unknown. The goal of this study is to elucidate developmental progressions in the acoustic structure of infant-directed speech over the first two years of life, and to determine the origin of these changes in infant vocal response. Samples of adult- and infant-directed speech and infant vocalizations were extracted from audio recordings of 10 typically developing infants and 10 infants later diagnosed with autism and their mothers, collected from 0 to 24 months using LENA technology. Multitaper analysis was used to determine the time-varying harmonic structure of each utterance, deriving indices summarizing differences in source and filter properties between infant- and adult-directed speech. In typical development, transitions were found towards the end of the first year of life from baby talk, emphasizing prosodic properties, towards mature child-directed register, emphasizing resonance dynamics. In autism, caregivers persisted in baby talk or shifted into adult-directed register, concurrent with disruptions of vocal contingency, which may be stimulating the transition.