The windings of high-field accelerator magnets are usually made of Rutherford-type superconducting cables. The magnetic field distribution along the axis of such magnets exhibits a periodic modulation with a wavelength equal to the twist pitch length of the cable used in the winding. This effect, resulting from quasipersistent currents, was investigated with a Hall probe array inserted inside the aperture of the LHC superconducting dipoles, both in short models and full-scale prototypes. The amplitude and the time dependence of this periodic field oscillation have been studied as a function of the magnet current history. The origin and, the impact on the LHC dipole stability of the nonuniform current redistribution producing such a field modulation are discussed.