  Superconducting MgB$\_2$ shows an E$\_{2g}$ zone center phonon, as measured
by Raman spectroscopy, that is very broad in energy and temperature dependent.
The Raman shift and lifetime show large differences with the values elsewhere
in the Brillouin Zone measured by Inelastic X-ray Scattering (IXS), where its
dispersion can be accounted for by standard harmonic phonon theory, adding only
a moderate electron-phonon coupling. Here we show that the effects rapidly
disappear when electron-phonon coupling is switched off by Al substitution on
the Mg sites. Moreover, using IXS with very high wave-vector resolution in
MgB$\_2$, we can follow the dispersion connecting the Raman and the IXS signal,
in agreement with a theory using only electron-phonon coupling but without
strong anharmonic terms. The observation is important in order to understand
the effects of electron-phonon coupling on zone center phonons modes in
MgB$\_2$, but also in all metals characterized by a small Fermi velocity in a
particular direction, typical for layered compounds.
