In our daily lives, auditory stream segregation allows us to differentiate concurrent sound sources and to make sense of the scene we are experiencing. However, a combination of segregation and the concurrent integration of auditory streams is necessary in order to analyze the relationship between streams and thus perceive a coherent auditory scene. The present functional magnetic resonance imaging study investigates the relative role and neural underpinnings of these listening strategies in multi-part musical stimuli. We compare a real human performance of a piano duet and a synthetic stimulus of the same duet in a prioritized integrative attention paradigm that required the simultaneous segregation and integration of auditory streams. In so doing, we manipulate the degree to which the attended part of the duet led either structurally (attend melody vs. attend accompaniment) or temporally (asynchronies vs. no asynchronies between parts), and thus the relative contributions of integration and segregation used to make an assessment of the leader-follower relationship. We show that perceptually the relationship between parts is biased towards the conventional structural hierarchy in western music in which the melody generally dominates (leads) the accompaniment. Moreover, the assessment varies as a function of both cognitive load, as shown through difficulty ratings and the interaction of the temporal and the structural relationship factors. Neurally, we see that the temporal relationship between parts, as one important cue for stream segregation, revealed distinct neural activity in the planum temporale. By contrast, integration used when listening to both the temporally separated performance stimulus and the temporally fused synthetic stimulus resulted in activation of the intraparietal sulcus. These results support the hypothesis that the planum temporale and IPS are key structures underlying the mechanisms of segregation and integration of auditory streams, respectively.