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In cognitive science, the sensation of "groove" has been defined as the pleasurable urge to move to music. When listeners rate rhythmic stimuli on derived pleasure and urge to move, ratings on these dimensions are highly correlated. However, recent behavioural and brain imaging work has shown that these two components may be separable. To examine this potential separability, our study investigates the sensation of groove in people with specific musical anhedonia. Individuals with musical anhedonia have a blunted ability to derive pleasure from music but can still derive pleasure from other domains (e.g., sex and food). People with musical anhedonia were identified as those with scores in the lower 10% of scores on the Barcelona Musical Reward Questionnaire, but who had no deficits in music perception, no symptoms of depression, average levels of physical and social anhedonia, and sensitivity to punishment and reward. We predicted that if the two components of groove are separable, individuals with musical anhedonia would experience lower levels of derived pleasure but have comparable ratings of wanting to move compared to controls. Groove responses were measured in an online study (N = 148) using a set of experimenter-generated musical stimuli varying in rhythmic and harmonic complexity, which were validated in several previous studies. Surprisingly, we found no significant differences in groove response between individuals with musical anhedonia (n = 17) and a matched control group (n = 17). Mediation analyses for the anhedonia sample found that wanting to move ratings fully mediated the effect of rhythmic and harmonic complexity on pleasure ratings. Taken together, these results indicate that the urge to move may compensate for the blunted pleasure sensation in those with musical anhedonia. More generally, these results suggest that the urge to move is a primary source of pleasure in the groove response.