In this article, we identify and analyze the periodicity of violent and property crimes committed in Tshwane, South Africa, from 2001 to 2006. This is done using Fourier analysis, an advanced explorative mathematical technique commonly used in the physical sciences to detect the presence of a frequency or periodicity in a large time-series data set. The use of this technique in criminology is in its infancy, and in this study, Fourier analysis is used to identify periodic moments in time at which the risk of being a victim of violent and property crime in the city of Tshwane is heightened. Results indicated that violent crime peaks roughly every 7 and 75 days over the 5-year study period, with a marginal peak every 150 days. Property crimes peak every 75 days and every 150 days. Periodic peaks of crime observed in this study are explained using the central tenets of routine activities theory. Fourier analysis is an underused, powerful data-driven mathematical tool that should be added to the methodological arsenal available to criminologists when analyzing the temporal dimension of crime.