We propose a decomposition of the neurocognitive mechanisms that might underlie interval-based timing and rhythmic entrainment. Next to reviewing the concepts central to the definition of rhythmic entrainment, we discuss recent studies that suggest rhythmic entrainment to be specific to humans and a selected group of bird species, but, surprisingly, is not obvious in non-human primates. On the basis of these studies we propose the gradual audiomotor evolution hypothesis that suggests that humans fully share interval-based timing with other primates, but only partially share the ability of rhythmic entrainment (or beat-based timing). This hypothesis accommodates the fact that non-human primates (i.e., macaques) performance is comparable to humans in single interval tasks (such as interval reproduction, categorization, and interception), but show differences in multiple interval tasks (such as rhythmic entrainment, synchronization, and continuation). Furthermore, it is in line with the observation that macaques can, apparently, synchronize in the visual domain, but show less sensitivity in the auditory domain. And finally, while macaques are sensitive to interval-based timing and rhythmic grouping, the absence of a strong coupling between the auditory and motor system of non-human primates might be the reason why macaques cannot rhythmically entrain in the way humans do.