We performed mutual tapping experiments between two humans to investigate the conditions required for synchronized motion. A transition from an alternative mode to a synchronization mode was discovered under the same conditions as when a subject changed from a reactive mode to an anticipation mode in single tapping experiments. The experimental results suggest that the cycle time for each tapping motion is tuned by a proportional control that is based on synchronization errors and cycle time errors. As the tapping frequency increases, a mathematical model based on feedback control in the sensory-motor closed loop predicts a discrete transition of the mode as the gain factors of the proportional control decrease. The conditions for synchronization are shown as a consequence of the coupled dynamics based on the next feedback loop in the sensory-motor system.