The developmental trajectory of nervous system dynamics shows hierarchical structure on time scales spanning ten orders of magnitude from milliseconds to years. Analyzing and characterizing this structure poses significant signal processing challenges. In the context of birdsong development, we have previously proposed that an effective way to do this is to use the dynamic spectrum or spectrogram, a classical signal processing tool, computed at multiple time scales in a nested fashion. Temporal structure on the millisecond timescale is normally captured using a short time Fourier analysis, and structure on the second timescale using song spectrograms. Here we use the dynamic spectrum on time series of song features to study the development of rhythm in juvenile zebra finch. The method is able to detect rhythmic structure in juvenile song in contrast to previous characterizations of such song as unstructured. We show that the method can be used to examine song development, the accuracy with which rhythm is imitated, and the variability of rhythms across different renditions of a song. We hope that this technique will provide a standard, automated method for measuring and characterizing song rhythm.