Neuroscientific and musicological approaches to music cognition indicate that listeners familiarized in the Western tonal tradition expect a musical phrase boundary at predictable time intervals. However, phrase boundary prediction processes in music remain untested. We analyzed event-related potentials (ERPs) and event-related induced power changes at the onset and offset of a boundary pause. We made comparisons with modified melodies, where the pause was omitted and filled by tones. The offset of the pause elicited a closure positive shift (CPS), indexing phrase boundary detection. The onset of the filling tones elicited significant increases in theta and beta powers. In addition, the P2 component was larger when the filling tones started than when they ended. The responses to boundary omission suggest that listeners expected to hear a boundary pause. Therefore, boundary prediction seems to coexist with boundary detection in music segmentation.