Method for maintaining and regulating a timepiece resonator

A method for maintaining and regulating frequency of a timepiece resonator mechanism around a natural frequency of the resonator mechanism during operation of the resonator mechanism, the method comprising:

• imparting a periodic motion to the resonator mechanism by at least one regulator device,
• wherein the periodic motion imposes a periodic modulation of resonant frequency of the resonator mechanism, with a regulation frequency of the regulator device between 0.9 times and 1.1 times a value of an integer multiple of the natural frequency, the integer being greater than or equal to 2 and less than or equal to 10,
• wherein the periodic modulation of the resonant frequency of the resonator mechanism is imposed by a modulation of an active length of a spring comprised in the resonator mechanism, a modulation of a cross-section of the spring, a modulation of a modulus of an elasticity of an elastic return means, or a modulation of a shape of the elastic return means, and
• wherein the modulation of the modulus of the elasticity of the elastic return means is obtained by implementing a piezoelectric system, employing periodic localized heating, magnetostriction, or shaping memory components.