A mechanical oscillator, formed of a mechanical resonator and a device for maintaining oscillation, and an auxiliary oscillator forming a reference time base including a synchronisation device arranged to slave the medium frequency of the mechanical oscillator on that of the auxiliary oscillator. The synchronisation device includes an electromagnetic braking device which is formed of a coil and at least one permanent magnet and arranged such that an induced voltage is generated between the terminals of the coil in each alternation of the oscillation of the mechanical resonator. The synchronisation device is arranged to be able to reduce momentarily the impedance between the terminals of the coil during distinct time intervals, any two successive time intervals exhibiting between the respective starts thereof a time distance substantially equal to a positive whole number multiplied by half of a set-point period for the mechanical oscillator.