  The cubic $Ia\bar{3}$ (BC8) and tetragonal $P4_32_12$ (ST12) high pressure
modifications of Si and Ge are attractive candidates for applications in
optoelectronic, thermoelectric or plasmonic devices. Si$_x$Ge$_{1-x}$ alloys in
BC8/ST12 modifications could help overcome the indirect and narrow band gaps of
the pure phases and enable tailoring for specific use-cases. Such alloys have
experimentally been found to be stable at ambient conditions after release from
high pressure synthesis, however their fundamental properties are not known. In
this work, we employ {\it ab initio} calculations based on density functional
theory (DFT) to investigate the electronic properties of these compounds as a
function of composition $x$. We obtain the effective band structures of
intermediate alloys by constructing special quasi random structures (SQS) and
unfolding their band structure to the corresponding primitive cell.
Furthermore, we show that the indirect band gap of the ST12 Ge end-member can
be tuned to become direct at $x_\text{Si} \approx 0.16$. Finally, our
investigations also demonstrate that the BC8 modification, on the other hand,
is insensitive to compositional changes and is a narrow direct band gap
semiconductor only in the case of pure Si.
