Neural oscillations have been proposed as a mechanism for structure building in language and music. In music, this idea is appealing because of the intuitive mapping between perceptual and neural rhythms. The strongest evidence has come from studies in which participants listened to isochronous sequences of identical tones and were asked to imagine hearing them in binary (march) or ternary meter (waltz). The critical finding was that in addition to increased signal at the frequency corresponding to the tone rate there was increased signal at the imagined meter frequencies. While it is striking that meter tracking was observed without any acoustic cues in the input, rhythm perception was confounded with rhythm imagery involving active generation of rhythmic structure. We conducted two electroencephalography experiments with musicians and non-musicians, teasing apart the effects of rhythm perception and rhythm generation. Evidence for meter-related neural oscillations was only observed in situations where rhythmic structure was actively generated, either via rhythm imagery or in the form of overt behavior (tapping). Thus, our data suggest that mere rhythm perception is not sufficient to elicit oscillations at the meter frequency and that they are instead driven by the active generation of rhythm. This undermines the proposal that neural oscillations constitute a basic structure building mechanism in rhythm perception and raises questions about the role of oscillations in language processing.