Humans and a few select insect and reptile species synchronise inter-individual behaviour without any time lag by predicting the time of future events rather than reacting to them. This is evident in music performance, dance, and drill. Although repetition of equal time intervals (i.e. isochrony) is the central principle for such prediction, this simple information is used in a flexible and complex way that accommodates both multiples, subdivisions, and gradual changes of intervals. The scope of this flexibility remains largely uncharted, and the underlying mechanisms are a matter for speculation. Here I report an auditory illusion that highlights some aspects of this behaviour and that provides a powerful tool for its future study. A sound pattern is described that affords multiple alternative and concurrent rates of recurrence (temporal levels). An algorithm that systematically controls time intervals and the relative loudness among these levels creates an illusion that the perceived rate speeds up or slows down infinitely. Human participants synchronised hand movements with their perceived rate of events, and exhibited a change in their movement rate that was several times larger than the physical change in the sound pattern. The illusion demonstrates the duality between the external signal and the internal predictive process, such that people's tendency to follow their own subjective pulse overrides the overall properties of the stimulus pattern. Furthermore, accurate synchronisation with sounds separated by more than 8 s demonstrate that multiple temporal levels are employed for facilitating temporal organisation and integration by the human brain. A number of applications of the illusion and the stimulus pattern are suggested.