We report on the analysis of hard-state power spectral density function (PSD) of GX 339-4 down to the soft X-ray band, where the disc significantly contributes to the total emission. At any luminosity probed, the disc in the hard state is intrinsically more variable than in the soft state. However, the fast decrease of disc variability as a function of luminosity, combined with the increase of disc intensity, causes a net drop of fractional variability at high luminosities and low energies, which reminds the well-known behaviour of disc-dominated energy bands in the soft state. The peak frequency of the high-frequency Lorentzian (likely corresponding to the high-frequency break seen in active galactic nuclei, AGN) scales with luminosity, but we do not find evidence for a linear scaling. In addition, we observe that this characteristic frequency is energy dependent. We find that the normalization of the PSD at the peak of the high-frequency Lorentzian decreases with luminosity at all energies, though in the soft band this trend is steeper. Together with the frequency shift, this yields quasi-constant high-frequency (5-20 Hz) fractional rms at high energies, with less than 10 per cent scatter. This reinforces previous claims suggesting that the high-frequency PSD solely scales with black hole mass. On the other hand, this constancy breaks down in the soft band (where the scatter increases to ˜30 per cent). This is a consequence of the additional contribution from the disc component, and resembles the behaviour of optical variability in AGN.