A wind power installation with a tower, an aerodynamic rotor, wherein the aerodynamic rotor can be operated with a variable rotor speed and has a number of rotor blades respectively with an adjustable rotor blade angle, a generator for generating an electrical output power, wherein for operating the wind power installation an operating characteristic, which indicates a relationship between the rotor speed and the output power, is specified and a controller, which sets the output power in a way corresponding to the operating characteristic in dependence on the rotor speed, is provided, wherein selectable as the operating characteristic is a reduced-tonality operating characteristic, which is designed such that an excitation of a system resonance of the wind power installation is reduced as compared with an optimum-power operating characteristic, without however excluding a speed that excites this system resonance.