This paper is divided into three sections. The first section is theoretical; it extends Dynamic Attending Theory (Jones, M. R. Psychological Review 83 (1976) 323; Jones, M. R. Perception and Psychophysics 41(6) (1987) 631; Jones, M. R. Psychomusicology 9(2) (1990) 193; Jones, M. R., & Boltz, M. Psychological Review 96(3) (1989) 459) to developmental questions concerning tempo and time hierarchies. Generally Dynamic Attending Theory proposes that, when listening to a complex auditory sequence, listeners spontaneously focus on events occurring at an intermediate rate (the referent level), and they then may shift attention to events occurring over longer or shorter time spans, that is at lower (faster) or higher (slower) hierarchical levels (focal attending). The second section of the paper is experimental. It examines maturational changes of three dynamic attending activities involving referent period and level, attunement, and focal attending. Tasks involve both motor tapping (including spontaneous motor tempo and synchronization with simple sequences and music) and tempo discrimination. We compare performances by 4-, 6-, 8-, and 10-year-old children and adults, with or without musical training. Results indicate three changes with increased age and musical training: (1) a slowing of the mean spontaneous tapping rate (a reflection of the referent period) and mean synchronization rate (a reflection of the referent level), (2) enhanced ability to synchronize tapping and discriminate tempo (improved attunement), and (3) an enlarged range of tapping rates towards slower rates and higher hierarchical levels (improved focal attending). A final section considers results in light of the theory proposed here. It is suggested that growth trends can be expressed in terms of listeners' engagement of slower attending oscillators with age and experience, accompanied by the passage from the initial use of a single oscillator towards the coupling of multiple oscillators.