The disclosed embodiments relate to a memory system that generates a multiplied timing signal from a reference timing signal. During operation, the system receives a reference timing signal. Next, the system produces a multiplied timing signal from the reference timing signal by generating a burst comprising multiple timing events for each timing event in the reference timing signal, wherein consecutive timing events in each burst of timing events are separated by a bit time. Then, as the reference clock frequency changes, the interval between bursts of timing events changes while the bit time remains substantially constant.