Human rhythmic movements spontaneously synchronize with auditory rhythms at various frequency ratios. The emergence of more complex relationships—for instance, frequency ratios of 1:2 and 1:3—is enhanced by adding a congruent accentuation pattern (binary for 1:2 and ternary for 1:3), resulting in a 1:1 movement–accentuation relationship. However, this benefit of accentuation on movement synchronization appears to be stronger for the ternary pattern than for the binary pattern. Here, we investigated whether this difference in accent-induced movement synchronization may be related to a difference in the neural tracking of these accentuation profiles. Accented and control unaccented auditory sequences were presented to participants who concurrently produced finger taps at their preferred frequency, and spontaneous movement synchronization was measured. EEG was recorded during passive listening to each auditory sequence. The results revealed that enhanced movement synchronization with ternary accentuation was accompanied by enhanced neural tracking of this pattern. Larger EEG responses at the accentuation frequency were found for the ternary pattern compared with the binary pattern. Moreover, the amplitude of accent-induced EEG responses was positively correlated with the magnitude of accent-induced movement synchronization across participants. Altogether, these findings show that the dynamics of spontaneous auditory–motor synchronization is strongly driven by the multi-time-scale sensory processing of auditory rhythms, highlighting the importance of considering neural responses to rhythmic sequences for understanding and enhancing synchronization performance.