[en] Iron based high temperature superconductors have several common features with superconducting cuprates, including the square lattice and the proximity to an antiferromagnetic phase. The magnetic excitation spectrum below T_c of $\mathrm{F}{\mathrm{e}}_{1.02}\mathrm{T}{\mathrm{e}}_{0.7}\mathrm{S}{\mathrm{e}}_{0.3}$ shows an hourglass-shaped dispersion with a resonance around the commensurate point . In a previous inelastic neutron scattering study, we showed that the hourglass-shaped dispersion is most likely a prerequisite for superconductivity, while the consequences are the opening of a gap and a shift of spectral weight. In this paper we follow the evolution of the hourglass shaped dispersion under applied pressure up to 12 kbar. Our results show that that the pressure-induced 37% increase of T_c is concomitant with a change in the magnetic excitation spectrum, with an increase of the hourglass energy by 38%. (paper)