A fiber-optic measurement device (10) includes a SAGNAC ring interferometer (20) having a proper frequency fp. The aim is to improve response time while maintaining high precision across the measurement range. Biasing elements (130) are used to produce: a first biasing phase-differential modulation component Δφb1(t) (34) which is periodic in time-slots, having levels +π and −π, at a first biasing modulation frequency fb1 such that fb1=(2k1+1) fp, k1 being a natural number; and a second periodic biasing phase-differential modulation component Δφb2(t) (35), having extreme amplitudes +π/a and −π/a, a being a non-zero real number such that |a|>1, at a second biasing modulation frequency fb2 such that fb2=(2k2+1) fp, k2 being a non-zero natural number such that k2>k1. A gyrometer including such a measurement device and a navigation or inertial-stabilization system including at least one such gyrometer are also described.