This paper outlines a cognitive and comparative perspective on human rhythmic cognition that emphasizes a key distinction between pulse perception and meter perception. Pulse perception involves the extraction of a regular pulse or “tactus” from a stream of events. Meter perception involves grouping of events into hierarchical trees with differing levels of “strength”, or perceptual prominence. I argue that metrically-structured rhythms are required to either perform or move appropriately to music (e.g., to dance). Rhythms, from this metrical perspective, constitute “trees in time.” Rhythmic syntax represents a neglected form of musical syntax, and warrants more thorough neuroscientific investigation. The recent literature on animal entrainment clearly demonstrates the capacity to extract the pulse from rhythmic music, and to entrain periodic movements to this pulse, in several parrot species and a California sea lion, and a more limited ability to do so in one chimpanzee. However, the ability of these or other species to infer hierarchical rhythmic trees remains, for the most part, unexplored (with some apparent negative results from macaques). The results from this animal comparative research, combined with new methods to explore rhythmic cognition neurally, provide exciting new routes for understanding not just rhythmic cognition, but hierarchical cognition more generally, from a biological and neural perspective.