The brain's analyses of speech and music share a range of neural resources and mechanisms. Music displays a temporal structure of complexity similar to that of speech, unfolds over comparable timescales, and elicits cognitive demands in tasks involving comprehension and attention. During speech processing, synchronized neural activity of the cerebral cortex in the delta and theta frequency bands tracks the envelope of a speech signal, and this neural activity is modulated by high-level cortical functions such as speech comprehension and attention. It remains unclear, however, whether the cortex also responds to the natural rhythmic structure of music and how the response, if present, is influenced by higher cognitive processes. Here we employ electroencephalography to show that the cortex responds to the beat of music and that this steady-state response reflects musical comprehension and attention. We show that the cortical response to the beat is weaker when subjects listen to a familiar tune than when they listen to an unfamiliar, non-sensical musical piece. Furthermore, we show that in a task of intermodal attention there is a larger neural response at the beat frequency when subjects attend to a musical stimulus than when they ignore the auditory signal and instead focus on a visual one. Our findings may be applied in clinical assessments of auditory processing and music cognition as well as in the construction of auditory brain-machine interfaces.