Most theories of motor cortex have assumed that neural activity represents movement parameters. This view derives from an analogous approach to primary visual cortex, where neural activity represents patterns of light. Yet it is unclear how well that analogy holds. Single-neuron responses in motor cortex appear strikingly complex, and there is marked disagreement regarding which movement parameters are represented. A better analogy might be with other motor systems, where a common principle is rhythmic neural activity. We found that motor cortex responses during reaching contain a brief but strong oscillatory component, something quite unexpected for a non-periodic behavior. Oscillation amplitude and phase followed naturally from the preparatory state, suggesting a mechanistic role for preparatory neural activity. These results demonstrate unexpected yet surprisingly simple structure in the population response. That underlying structure explains many of the confusing features of individual-neuron responses.