Relative-sea-level (RSL) change influences surface processes and stratigraphic architecture of deltaic systems and has been studied extensively for decades. However, we still lack a quantitative framework to define how the magnitude and period of a RSL cycle influences deltaic morphodynamics and the resulting stratigraphy. One method for scaling the magnitude and period of RSL cycles is through comparison with the autogenic time and space scales that characterize individual deltaic systems. We explore this method using a suite of physical experiments that shared identical forcing conditions with the exception of sea level. This approach utilizes two nondimensional numbers that characterize the magnitude and period of RSL cycles. Magnitude is defined with respect to the maximum autogenic channel depth, while the period is defined with respect to the time required to deposit one channel depth of sediment, on average, everywhere in a basin. The experiments include: 1) a control experiment lacking RSL cycles, used to define autogenic scales, 2) a low-magnitude, long-period (LMLP) stage, and 3) a high-magnitude, short-period (HMSP) stage. We observe clear differences in the response of deltas to the forcing in each experiment. The RSL cycles in the HMSP stage induce allogenic surface processes and stratigraphic products with scales that exceed the stochastic variability found in the control stage. These include the generation of rough shorelines and long temporal gaps in the stratigraphy. In contrast, the imprint of LMLP cycles on surface processes and stratigraphy is found in properties that define the mean state of a system. These include the mean shoreline location and the timing and location of mass extraction from the transport system. This work demonstrates the effectiveness of defining the magnitude and period of RSL cycles through autogenic scales and provides insights for generation of forward stratigraphic models influenced by RSL change.