We study properties of the superorbital modulation of the X-ray emission of Cyg X-1. We find that it has had a stable period of ∼300 d in soft and hard X-rays and in radio since 2005 until at least 2010, which is about double the previously seen period. This new period, seen in the hard spectral state only, is detected not only in the light curves but also in soft X-ray hardness ratios and in the amplitude of the orbital modulation. On the other hand, the spectral slope in hard X-rays, ≳20 keV, averaged over superorbital bins is constant, and the soft and hard X-rays and the radio emission change in phase. This shows that the superorbital variability consists of changing the normalization of an intrinsic spectrum of a constant shape and of changes of the absorbing column density with the phase. The maximum column density is achieved at the superorbital minimum. The amplitude changes are likely to be caused by a changing viewing angle of an anisotropic emitter, most likely a precessing accretion disc. The constant shape of the intrinsic spectrum shows that this modulation is not caused by a changing accretion rate. The modulated absorbing column density shows the presence of a bulge at the disc edge, as proposed previously. We also find the change of the superorbital period from ∼150 to ∼300 d to be associated with almost unchanged average X-ray fluxes, making the period change difficult to explain in the framework of disc-irradiation models. Finally, we find no correlation of the X-ray and radio properties with the reported detections in the GeV and TeV γ-ray range.