True absolute pitch (AP), labeling of pitches with semitone precision without a reference, is classically studied using isolated tones. However, AP is acquired and has its function within complex dynamic musical contexts. Here we examined event-related brain responses and underlying cerebral sources to endings of short expressive string quartets, investigating a homogeneous population of young highly trained pianists with half of them possessing true-AP. The pieces ended regularly or contained harmonic transgressions at closure that participants appraised. Given the millisecond precision of ERP analyses, this experimental plan allowed examining whether AP alters music processing at an early perceptual, or later cognitive level, or both, and which cerebral sources underlie differences with non-AP musicians. We also investigated the impact of AP on general auditory cognition. Remarkably, harmonic transgression sensitivity did not differ between AP and non-AP participants, and differences for auditory cognition were only marginal. The key finding of this study is the involvement of a microstate peaking around 60 ms after musical closure, characterizing AP participants. Concurring sources were estimated in secondary auditory areas, comprising the planum temporale, all transgression conditions collapsed. These results suggest that AP is not a panacea to become a proficient musician, but a rare perceptual feature.