Inspired by theories of perception-action coupling and embodied music cognition, we investigated how rhythmic music perception impacts self-paced oscillatory movements. In a pilot study, we examined the kinematic parameters of self-paced oscillatory movements, walking and finger tapping using optical motion capture. In accordance with biomechanical constraints accounts of motion, we found that movements followed a hierarchical organization depending on the proximal/distal characteristic of the limb used. Based on these findings, we were interested in knowing how and when the perception of rhythmic music could resonate with the motor system in the context of these constrained oscillatory movements. In order to test this, we conducted an experiment where participants performed four different effector-specific movements (lower leg, whole arm and forearm oscillation and finger tapping) while rhythmic music was playing in the background. Musical stimuli consisted of computer-generated MIDI musical pieces with a 4/4 metrical structure. The musical tempo of each song increased from 60 BPM to 120 BPM by 6 BPM increments. A specific tempo was maintained for 20s before a 2s transition to the higher tempo. The task of the participant was to maintain a comfortable pace for the four movements (self-paced) while not paying attention to the music. No instruction on whether to synchronize with the music was given. Results showed that participants were distinctively influenced by the background music depending on the movement used with the tapping task being consistently the most influenced. Furthermore, eight strategies put in place by participants to cope with the task were unveiled. Despite not instructed to do so, participants also occasionally synchronized with music. Results are discussed in terms of the link between perception and action (i.e., motor/perceptual resonance). In general, our results give support to the notion that rhythmic music is processed in a motoric fashion.