  We discover a pronounced dependence of the strength of the X-ray orbital
modulation and the hardness in Cyg X-1 in the hard state on its superorbital
phase. Our results can be well modelled as a combination of two effects: the
precession of the accretion disc (which causes the superorbital flux
modulation) and the orbital-phase dependent X-ray absorption in an accretion
bulge, located at the accretion disc edge close to the supergiant companion but
displaced from the line connecting the stars by about 25^o. Our findings are
supported by the distribution of the X-ray dips showing concentration towards
zero superorbital phase, which corresponds to the bulge passing through the
line of sight. We Fourier analyse our model, and find it explains the previous
finding of asymmetric beat (between the orbital and superorbital modulations)
frequencies in the observed power spectrum, provided the disc precession is
prograde. We find no statistically significant changes of the orbital
modulation with the superorbital phase in the 15-GHz radio data. This absence
is consistent with the radio being emitted by a jet in the system, in which
case the orbital modulation is caused by wind absorption far away from the
disc. We also find that both the X-ray and radio fluxes of Cyg X-1 in the hard
state on time scales >10^4-s have lognormal distributions, which complements a
previous finding of a lognormal flux distribution in the hard state on 1-s time
scales. We point out that the lognormal character of the flux distribution
requires that flux logarithms rather than fluxes themselves should be used for
averaging and error analysis. We also provide a correct formula for the
uncertainty of rms of a light curve for the case when the uncertainty is higher
than the measurement.
