Consonance and dissonance are basic phenomena in the perception of chords that can be discriminated very early in sensory processing. Musical expertise has been shown to facilitate neural processing of various musical stimuli, but it is unclear whether this applies to detecting consonance and dissonance. Our study aimed to determine if sensitivity to increasing levels of dissonance differs between musicians and nonmusicians, using a combination of neural (electroencephalographic mismatch negativity, MMN) and behavioral measurements (conscious discrimination). Furthermore, we wanted to see if focusing attention to the sounds modulated the neural processing. We used chords comprised of either highly consonant or highly dissonant intervals and further manipulated the degree of dissonance to create two levels of dissonant chords. Both groups discriminated dissonant chords from consonant ones neurally and behaviorally. The magnitude of the MMN differed only marginally between the more dissonant and the less dissonant chords. The musicians outperformed the nonmusicians in the behavioral task. As the dissonant chords elicited MMN responses for both groups, sensory dissonance seems to be discriminated in an early sensory level, irrespective of musical expertise, and the facilitating effects of musicianship for this discrimination may arise in later stages of auditory processing, appearing only in the behavioral auditory task.