Brillouin and Raman scattering experiments on methanol through its glass transition under pressure are reported. The Brillouin scattering data were analyzed using viscoelastic theory and a fit to the Vinet equation of state. The variation in the linewidth of the longitudinal acoustic mode with pressure shows a broad maximum centered around 3 GPa. The pressure evolution of the relaxation time in the GHz range is obtained, and the Raman data are analyzed in terms of the Boson peak and its associated relaxation time in the THz range. The pressure evolution of these two relaxation processes extends previous determinations of relaxations at lower frequency based on dielectric measurements in supercooled methanol. The relaxation processes in glass-forming methanol have now been investigated over a wide frequency range and their evolution followed over a large variation of density.