Timepiece comprising a timepiece movement fitted with a tourbillon comprising a carriage (6,6A,106) arranged rotating about a main axis, a barrel arranged to accumulate mechanical energy and a geartrain kinematically linking the tourbillon carriage to the barrel, the tourbillon bearing a mechanical resonator (14,14B,114), formed of a balance (16,16A,116) and a balance-spring, and an escapement device; the oscillation frequency (Fo) of the mechanical resonator being substantially equal to or greater than six Hertz (Fo >= 6 Hz) and the escapement device being a magnetic escapement that comprises an escape wheel set (20,20B,20C, 120) formed of an escape pinion and at least one magnetic structure (26,40,26C, 126), which has a general annular shape centred on an axis of rotation of the escape wheel set, this magnetic escapement further comprising a magnetic element or a plurality of magnetic elements (32,33, 32B, 32C,33C, 102,103), this magnetic element or each magnetic element being arranged so as to have an oscillating movement that is synchronous with the oscillation of the mechanical resonator and that has a radial component different to zero relative to said axis of rotation, said magnetic element being coupled with said at least one magnetic structure or each magnetic element of said plurality of magnetic elements being coupled, at least momentarily periodically, with said at least one magnetic structure such that the escape wheel set rotates by a predetermined angular period at each oscillation period of the balance; the magnetic escapement being arranged so as to have, in normal timepiece movement operation, alternately energy accumulation phases, from a conversion of mechanical energy supplied by the barrel into magnetic potential energy in the magnetic escapement, and transfer phases of energy accumulated in the magnetic escapement to the magnetic resonator; the magnetic escapement being arranged such that: - during each energy accumulation phase, said at least one magnetic structure is subjected to a magnetic force torque, relative to said axis of rotation, having an opposite direction to that of a drive torque, applied by the barrel via the tourbillon carriage to the escape wheel set, and an intensity less than that of this drive torque, such that the escape wheel set rotates by a certain angle to enable the accumulation of a certain magnetic potential energy in the magnetic escapement; - during each transfer phase of energy, said magnetic element or each magnetic element of a set of magnetic elements, that of the plurality of magnetic elements was coupled with said at least one magnetic structure during a preceding energy accumulation phase, is subjected to a radial magnetic force, relative to said axis of rotation, during an alternation of the oscillating movement thereof and in the direction of the radial component of this oscillating movement during this alternation, such that the magnetic escapement then converts into mechanical energy magnetic potential energy accumulated in the preceding energy accumulation phase to be able to maintain the oscillation of the mechanical resonator. - during each energy accumulation phase, said at least one magnetic structure is subjected to a magnetic force torque, relative to said axis of rotation, having an opposite direction to that of a drive torque, applied by the barrel via the tourbillon carriage to the escape wheel set, and an intensity less than that of this drive torque, such that the escape wheel set rotates by a certain angle to enable the accumulation of a certain magnetic potential energy in the magnetic escapement; - during each transfer phase of energy, said magnetic element or each magnetic element of a set of magnetic elements, that of the plurality of magnetic elements was coupled with said at least one magnetic structure during a preceding energy accumulation phase, is subjected to a radial magnetic force, relative to said axis of rotation, during an alternation of the oscillating movement thereof and in the direction of the radial component of this oscillating movement during this alternation, such that the magnetic escapement then converts into mechanical energy magnetic potential energy accumulated in the preceding energy accumulation phase to be able to maintain the oscillation of the mechanical resonator.