I built a reproduction of Albert Michelson’s harmonic analysis machine with the help of Bowdoin’s physics department machine shop. This machine is an analog, mechanical computer that synthesizes and analyzes fourier series. The computations this machine does are ubiquitous and essential to modern technology. The math takes ~hours by hand, ~minutes with this machine, and ~milliseconds with modern electronics. It is beautiful to run, and it is an exceptionally good tool for understanding Fourier series.