VLF wave growth and emission triggering in the magnetosphere are known to depend on the coherence of the input signal. In these experiments the input signal may take the form of a constant frequency pulse (1 s duration) or a linearly chirped pulse (also 1 s duration) with a frequency ramp (1000 Hz/s) of either positive or negative slope. When a frequency ramp of 1000 Hz/s is approximated by a contiguous sequence of short, constant frequency steps, the growth behavior is unchanged for step durations less than 25 ms. For a step duration of 25 ms, the behavior more nearly resembles that of a pure ramp, but some evidence of individual step growth can be seen. For step durations of 50 ms and 100 ms, growth is relatively small and is confined to each individual step, with little coupling between steps. Rising ramps generally show more growth than falling ramps of similar step size and average slope, confirming earlier observations. An equivalent ''sawtooth'' frequency variation with an average slope of zero and a step size of 25 ms behaves much like a constant frequency pulse. An interpretation of the response to step size can be found in the theory of second-order resonance, where the spatial rates of change of the electron gyrofrequency and the Doppler-shifted wave frequency are equal. This theory also accounts for the previously observed ''dot-dash'' anomaly, where a long constant frequency pulse shows much more growth and emission triggering than a short pulse. ¿ American Geophysical Union 1993