Timepiece comprising a mechanical oscillator wherein the medium frequency is synchronised on that of a reference electronic oscillator

A timepiece, comprising:

• a mechanical movement which comprises
• an indicator mechanism of at least one time data item,
• a mechanical resonator configured to oscillate along an oscillation axis about a neutral position corresponding to the minimum potential energy state thereof,
• a maintenance device of the mechanical resonator forming therewith a mechanical oscillator that is arranged to time a running of the indicator mechanism, and
• an auxiliary oscillator forming a reference time base and determining a set-point frequency F0C for the mechanical resonator, an inverse of said set-point frequency defining a set-point period T0C;
• and
• a synchronization device configured to slave a medium frequency of the mechanical oscillator on said set-point frequency, the synchronization device comprising an electromagnetic braking device of the mechanical resonator, said electromagnetic braking device being formed of a coil and at least one permanent magnet, which are arranged such that, within a usable operating range of the mechanical oscillator, an induced voltage is generated between two terminals of the coil in each alternation of said oscillation, the synchronization device being configured to momentarily reduce an impedance between the two terminals of the coil, wherein the electromagnetic braking device is arranged such that the induced voltage is generated in the coil substantially continuously for any oscillation of the mechanical resonator within the usable operating range of the mechanical oscillator,
• wherein the synchronization device is further configured to reduce the impedance between the two terminals of the coil during distinct time intervals TP such that starts of any two successive time intervals Tp, among said distinct time intervals Tp, exhibit therebetween a time distance DT equal to a positive whole number N multiplied by half of the set-point period T0C for the mechanical oscillator, such that a mathematical relation DT=N·T0C/2 is satisfied, and
• the synchronization device is further configured to determine, with the reference time base, a start of each of the distinct time intervals so as to fulfil the mathematical relation between the time distance DT and the set-point period T0C.