Spinocerebellar Ataxia (SCA) refers to a family of genetic diseases that cause progressive problems with gait and balance, as well as other debilitating symptoms. This is a randomized controlled pilot study to test a novel therapeutic intervention that uses noninvasive magnetic brain stimulation to improve functional outcomes in patients with SCA. The study will include quantitative evaluations of gait, balance, and brain physiology to examine possible objective end-points for a future, larger multi-site clinical trial. The investigators anticipate that patients receiving the real intervention will show a functional gain.