A timepiece regulating mechanism with a magnetic escapement, including a transmission train, a magnetic escape wheel set, a resonator wheel set, and a return mechanism, said regulating mechanism including an energy storage mechanism delivering energy as an output torque via said transmission train, to said magnetic escape wheel set, forming a magnetic escapement mechanism with said resonator wheel set subjected to a return torque from said return mechanism, said magnetic escape wheel set cooperating with said resonator wheel set, either directly, or via a magnetic stop member of said regulating mechanism, said magnetic escapement mechanism being arranged to operate when said magnetic escape wheel set receives a torque higher than or equal to a maintenance torque specific to said magnetic escapement mechanism, wherein said transmission train includes a torque regulator arranged to deliver to said magnetic escape wheel set a constant torque comprised between 1.0 and 2.0 times said maintenance torque, said torque regulator including a fusee of continuously variable cross-section from which unwinds a chain wound by a drum driven by said energy storage mechanism, said magnetic escape wheel set including at least one magnetized or ferromagnetic track with an interior track portion and exterior track portion providing a period of travel between the interior track portion and the exterior track portion said stop member including at least one magnetized or ferromagnetic pole piece, and said pole piece being mobile in a transverse direction relative to the direction of travel of at least one element on a top surface of said track.