We have studied the rapid X-ray time variability in 149 pointed observations with the Rossi X-Ray Timing Explorer (RXTE)'s Proportional Counter Array of the atoll source 4U 1636–53 in the banana state and, for the first time with RXTE, in the island state. We compare the frequencies of the variability components of 4U 1636–53 with those in other atoll and Z sources and find that 4U 1636–53 follows the universal scheme of correlations previously found for other atoll sources at (sometimes much) lower luminosities. Our results on the hectohertz QPO suggest that the mechanism that sets its frequency differs from that for the other components, while the amplitude-setting mechanism is common. A previously proposed interpretation of the narrow low-frequency QPO frequencies in different sources in terms of harmonic mode switching is not supported by our data or by previous data on other sources, and the frequency range that this QPO covers is found to be unrelated to spin, angular momentum, or luminosity.