Why does music move us? We have a natural tendency to move to music and perhaps this can be explained through timing theories, but our understanding of the neural mechanisms underlying timing in music remains limited, particularly for the timing of sequences. Temporal sequences can be represented relative to a recurrent beat (beat-based or relative timing), or as a series of absolute durations (non-beat-based or absolute timing). Neuroimaging and neuropsychological work suggest the involvement of the basal ganglia, supplementary motor area (SMA), the premotor cortices, and the cerebellum in both beat- and non-beat-based rhythms, however, evidence for causal roles remains limited, particularly in healthy adults. Here we examined how beat-based timing and non-beat-based sequence timing were affected by changes in the excitability of the SMA using transcranial direct current stimulation (tDCS). Anodal and cathodal tDCS were used to increase and decrease cortical excitability, respectively. All 36 participants completed a true stimulation session (2mA) and a sham stimulation session. During both sessions, participants reproduced rhythms with different metric types: beat-inducing rhythms, and non-beat-inducing rhythms. The strength of the beat in a rhythm was a significant factor in the accuracy of rhythm reproduction ability, supporting the beat-based timing model. However, altering the excitability of the SMA did not influence rhythm reproduction accuracy. We discuss our study's limitations and further directions in order to evaluate the SMA causal role in the temporal and beat perception abilities required to reproduce auditory rhythms.