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Humans can easily distinguish many sounds in the environment, but speech and music are uniquely important. Previous studies, mostly using functional magnetic resonance imaging, have identified separate regions of the brain that respond selectively for speech and music. Yet there is little evidence that brain responses are larger and more temporally precise for human-specific sounds like speech and music, as has been found for responses to species-specific sounds in other animals. We recorded EEG as healthy, adult subjects listened to various types of two-second-long natural sounds. By classifying each sound based on the EEG response, we found that speech, music, and impact sounds were classified better than other natural sounds. But unlike impact sounds, the classification accuracy for speech and music dropped for synthesized sounds that have identical frequency and modulation statistics based on a subcortical model, indicating a selectivity for higher-order features in these sounds. Lastly, the trends in average power and phase consistency of the two-second EEG responses to each sound replicated the patterns of speech and music selectivity observed with classification accuracy. Together with the classification results, this suggests that the brain produces temporally individualized responses to speech and music sounds that are stronger than the responses to other natural sounds. In addition to highlighting the importance of speech and music for the human brain, the techniques used here could be a cost-effective and efficient way to study the human brain’s selectivity for speech and music in other populations. Significance Statement In other species, ecologically important sounds such as vocalizations generate larger responses in the auditory cortex than other types of natural sounds, but it is unclear if this is true for humans. We recorded EEG as subjects listened to various natural sounds. Classification analysis based on the EEG responses as well as analysis of the average power of the EEG responses showed increased activation in the brain to speech and music sounds compared to other natural sounds. This study demonstrates the human brain’s selectivity to speech and music sounds and suggests a cost-effective and efficient way to study the brain’s selectivity for speech and music in other populations.