The amplitude in periodic neural state trajectories underlies the tempo of rhythmic tapping

Our motor commands can be exquisitely timed according to the demands of the environment, and the ability to generate rhythms of different tempos is a hallmark of musical cognition. Yet, the neuronal underpinnings behind rhythmic tapping remain elusive. Here, we found that the activity of hundreds of primate medial premotor cortices (MPCs; pre-supplementary motor area [preSMA] and supplementary motor area [SMA]) neurons show a strong periodic pattern that becomes evident when their responses are projected into a state space using dimensionality reduction analysis. We show that different tapping tempos are encoded by circular trajectories that travelled at a constant speed but with different radii, and that this neuronal code is highly resilient to the number of participating neurons. Crucially, the changes in the amplitude of the oscillatory dynamics in neuronal state space are a signature of duration encoding during rhythmic timing, regardless of whether it is guided by an external metronome or is internally controlled and is not the result of repetitive motor commands. This dynamic state signal predicted the duration of the rhythmically produced intervals on a trial-by-trial basis. Furthermore, the increase in variability of the neural trajectories accounted for the scalar property, a hallmark feature of temporal processing across tasks and species. Finally, we found that the interval-dependent increments in the radius of periodic neural trajectories are the result of a larger number of neurons engaged in the production of longer intervals. Our results support the notion that rhythmic timing during tapping behaviors is encoded in the radial curvature of periodic MPC neural population trajectories.Beat-based timing depends on the amplitude of periodic neural population dynamics and on the number of engaged neurons in primate medial premotor areas.Author summary: The ability to extract the regular pulse in music and to respond in synchrony to this pulse is called beat synchronization and is a natural human behavior exhibited during dancing and musical ensemble playing. A part of the brain called the medial premotor cortex has been associated with rhythmic entrainment, and yet the neural basis of this complex behavior is still far from known. In this work, we recorded the neuronal activity from the medial premotor cortices of macaques trained to tap rhythmically to the frequency of a metronome. Using principal component analysis, we projected the time-varying activity of hundreds of neurons into a low-dimensional space. The projected activity of the neural population generated a circular trajectory for every interval produced in the sequence, which travelled at a constant speed but with different radii for different tapping tempos. In addition, the increase in amplitude and variability of the neural trajectories accounted for the scalar property of timing, a generalized feature of temporal processing across tasks and species and which defines a linear relationship between the variability of temporal performance and interval duration.