Attention is not constant but rather fluctuates over time and these attentional fluctuations may prioritize the processing of certain events over others. In music listening, the pleasurable urge to move to music (termed ‘groove’ by music psychologists) offers a particularly convenient case study of oscillatory attention because it engenders synchronous and oscillatory movements which also vary predictably with stimulus complexity. In this study, we simultaneously recorded pupillometry and scalp electroencephalography (EEG) from participants while they listened to drumbeats of varying complexity that they rated in terms of groove afterwards. Using the intertrial phase coherence of the beat frequency, we found that while subjects were listening, their pupil activity became entrained to the beat of the drumbeats and this entrained attention persisted in the EEG even as subjects imagined the drumbeats continuing through subsequent silent periods. This entrainment in both the pupillometry and EEG worsened with increasing rhythmic complexity, indicating poorer sensory precision as the beat became more obscured. Additionally, sustained pupil dilations revealed the expected, inverted U-shaped relationship between rhythmic complexity and groove ratings. Taken together, this work bridges oscillatory attention to rhythmic complexity in relation to musical groove.