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The pleasurable urge to move to music ("groove") has been shown to be greatest for moderately complex musical rhythms. This is thought to occur because temporal predictions from the motor system reinforce our perception of the beat when there is a balance between expectation and surprise. The supplementary motor area (SMA) has been identified as the potential origin of these temporal predictions. Thus, to causally test the role of the SMA in the experience of groove, we used continuous theta burst stimulation (cTBS) to disrupt activity in this region or an active control site (V1). Nonmusicians listened to and rated musical clips that varied in rhythmic complexity and groove before and after stimulation. Following inhibitory stimulation over the left SMA, participants preferred moving to music with higher rhythmic complexity while after V1 stimulation, they preferred moving to music with lower rhythmic complexity. Pleasure ratings, however, were unaffected. These results suggest that the SMA weighs the precision of beat-based predictions generated by the dorsal auditory stream. Therefore, stimulating the SMA may have disinhibited the dorsal striatum or other nodes generating the beat-based predictions. In summary, these findings provide causal evidence that the SMA and V1 play critical roles in embodied rhythm processing.