We present a method of performing high-speed rotational anisotropy nonlinear optical harmonic generation experiments at rotational frequencies of several hertz by projecting the harmonic light reflected at different angles from a sample onto a stationary position-sensitive detector. The high rotational speed of the technique, 10 3 to 10 4 times larger than existing methods, permits precise measurements of the crystallographic and electronic symmetries of samples by averaging over low frequency laser-power, beampointing, and pulse-width fluctuations. We demonstrate the sensitivity of our technique by resolving the bulk fourfold rotational symmetry of GaAs about its [001] axis using second-harmonic generation.