In earlier work by March and Matthai [Phil. Mag. Lett. 84 335 (2004)], the energy gaps E_g of the diamond-type semiconductors C, Si, Ge and α-Sn were shown to correlate well with the mean interelectronic separation r_s of the 4 valence electrons per atom. Furthermore for the III-V analogues such as GaAs and InSb, it was demonstrated that a useful extension could be effected by introducing additionally the electronegativity difference between the constituent atoms. Here, we consider available experimental data, and their interpretation, for such energy gaps, as a function of pressure. The intensity of the X-ray forbidden reflections will also be discussed under pressure.