The production of speech and music are two human behaviors that involve complex hierarchical structures with implications for timing. Timing constraints may arise from a human proclivity to form ‘self-organized’ metrical structures for perceived and produced event sequences, especially those that involve repetition. To test whether the propensity to organize events in time arises even for simple motor behaviors, we developed a novel experimental tapping paradigm investigating whether participants use the beat structure of a tapped pattern to determine the interval between repetitions. Participants listened to target patterns of 3, 4, or 5 events, occurring at one of four periodic rates, and tapped out the pattern 11 times, creating 10 inter-pattern intervals (IPIs), which participants chose freely. The ratio between mean IPI and mean inter-tap interval (ITI) was used to measure the beat-relatedness of the overall timing pattern; the closer this ratio is to an integer, the more likely the participant was timing the IPI to match a multiple of the target pattern beat. Results show that a beat-based strategy contributes prominently, although not universally, to IPI duration. Moreover, participants preferred interval cycles with even numbers of beats, especially cycles with four beats. Finally, the IPI/ITI ratio was affected by rate, with more beats of silence for the IPI at faster rates. These findings support the idea that people can generate a larger global timing structure when engaging in the repetition of simple periodic motor patterns, and use that structure to govern the timing of those motor events.