The processing of temporal structure has been widely investigated, but evidence on how the brain processes temporal and nontemporal structures simultaneously is sparse. Using event-related potentials (ERPs), we examined how the brain responds to temporal (metric) and nontemporal (harmonic) structures in music simultaneously, and whether these processes are impacted by musical expertise. Fifteen musicians and 15 nonmusicians rated the degree of completeness of musical sequences with or without violations in metric or harmonic structures. In the single violation conditions, the ERP results showed that both musicians and nonmusicians exhibited an early right anterior negativity (ERAN) as well as an N5 to temporal violations (“when”), and only an N5-like response to nontemporal violations (“what”), which were consistent with the behavioral results. In the double violation condition, however, only the ERP results, but not the behavioral results, revealed a significant interaction between temporal and nontemporal violations at a later integrative stage, as manifested by an enlarged N5 effect compared to the single violation conditions. These findings provide the first evidence that the human brain uses different neural mechanisms in processing metric and harmonic structures in music, which may shed light on how the brain generates predictions for “what” and “when” events in the natural environment.