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 basis behind rhythmic tapping remains elusive. Here we found that the activity of hundreds of primate MPC neurons show a strong periodic pattern that becomes evident when their activity is projected into a lower dimensional state space. We show that different 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 beat-based timing, regardless of whether it is guided by an external metronome or is internally controlled and is not the result of repetitive motor commands. Furthermore, the increase in amplitude and variability of the neural trajectories accounted for the scalar property of interval timing. In addition, we found that the interval-dependent increments in the radius of periodic neural trajectories are the result of larger number of neurons engaged in the production of longer intervals. Our results support the notion that beat-based timing during rhythmic behaviors is encoded in the radial curvature of periodic MPC neural population trajectories.