Investigators will recruit 20 patients with genetically-confirmed SCA to use a novel approach - noninvasive transcranial magnetic stimulation (TMS) - to improve balance, gait, and posture in patients with SCA. Half will be randomly assigned to a real intervention, and half to a sham (control) intervention. The TMS intervention will consist of 20 stimulation sessions over a four week period. At baseline and follow-up, patients will undergo comprehensive assessments including several SCA rating scales, along with sophisticated tests of balance (ie. walking, standing, and muscle coordination). Patients will also complete a series of neurophysiologic tests to evaluate the function of the cerebellum and its connections before and after the intervention.