Abstract: The spiral includes turns of rectangular section, whose pitch p and/or thickness e can vary from the inside curve towards the outside curve, or whose winding can deviate from the line of a perfect spiral. The inside curve can also be extended by a self-locking washer for fixing the spiral on the balance arbour with no play. The spiral is manufactured by photolithography and galvanic growth, or by micro-machining an amorphous or crystalline material, such as a silicon wafer.

Abstract: Balance spring including, tangent to each other: a first inner coil at a first angle at the center and of decreasing section in a first ratio; a second coil at a second angle at the center and of constant section; a third coil at a third angle at the center and of increasing section in a third ratio; a fourth coil at a fourth angle at the center and of constant section; a fifth coil at a fifth angle at the center and of increasing section in a fifth ratio; a sixth outer coil at a sixth angle at the center and of increasing section in a sixth ratio. In a variant, a seventh more rigid segment deviates from this sixth coil. Movement including this balance spring. Watch including this movement.

Abstract: The coupled resonator comprises a first low frequency resonator, such as a balance spring (1) and a second higher frequency resonator, such as a tuning fork (2), the two resonators (1 and 2) including permanent mechanical coupling means. Application to the regulating system of a timepiece.

Abstract: The coupled resonator comprises a first low frequency resonator, such as a balance spring (1) and a second higher frequency resonator, such as a tuning fork (2), the two resonators (1 and 2) including permanent mechanical coupling means. Application to the regulating system of a timepiece.