Abstract Beat perception is central to music cognition. The motor system is involved in beat perception, even in the absence of movement, yet current frameworks for modeling beat perception do not strongly engage with the motor system’s neurocomputational properties. We believe fundamental progress on modeling beat perception requires a synthesis between cognitive science and motor neuroscience, yielding predictions to guide research. Success on this front would be a landmark in the study of how “embodied cognition” is implemented in brain activity. We illustrate this approach by proposing specific roles for two key motor brain structures (the supplementary motor area, and the dorsal striatum of the basal ganglia) in covert beat maintenance, building on current research on their role in actual movement. Highlights ⍰ Components of the brain’s motor system are activated by the perception of a musical beat, even in the absence of movement, and may play an important role in beat-based temporal prediction. ⍰ Two key brain regions involved in movement, the supplementary motor area and dorsal striatum, have neurocomputational properties that lend themselves to beat perception. ⍰ In supplementary motor area, neural firing rates represent the phase of cyclic sensorimotor processes. ⍰ Supplementary motor area’s involvement in perceptual suppression of self-generated sounds suggests that it could play a broader role in informing auditory expectations. ⍰ Dorsal striatum plays a central role in initiating and sequencing units of movement, and may serve similar functions in structuring beat-based temporal anticipation.