Representation of time during time interval reproduction and rhythmic timing. A, Top, Time interval production task. Monkeys were required to estimate a sample interval demarcated by Ready and Set, and reproduce that interval by a delayed motor response (Go). Sample intervals were drawn from one of two prior distributions: Short or Long. Bottom, A schematic showing the curved neural trajectory during the Ready-Set epoch for the Short prior condition. Linear readout of time intervals from the curved neural trajectory (left) generates biased internal estimates of the sample interval (middle) and reduces variability near the extrema of the prior distribution (right). B, Top, Synchronization task. Monkeys were required to tap (circles) synchronously three intervals (SO1-SO3) to an external metronome (arrows). The interstimulus interval was either Short or Long. Bottom, Neural trajectories during the synchronization task. The trajectory starts from a tapping manifold (black line), completes a cycle during every intertap interval, and returns to the tapping manifold. The tapping manifold is invariant across durations and serial order elements of the task. The metronome's tempo modulates the amplitude of the trajectories and the serial order element as the third axes in the state population.