The first experimental insight into the nature of the liquid-solid interface occurred with the pioneering experiments of Turnbull, which simultaneously demonstrated both that metals could be deeply undercooled (and therefore had relatively large barriers to nucleation) and that the inferred interfacial free energy γ was linearly proportional to the enthalpy of fusion [D. Turnbull, J. Appl. Phys. 21, 1022 (1950)]. By an atomistic simulation of a model face-centered cubic system via adiabatic free energy dynamics, we extend Turnbull's result to the realm of high pressure and demonstrate that the interfacial free energy, evaluated along the melting curve, remains linear with the bulk enthalpy of fusion, even up to 100 GPa. This linear dependence of γ on pressure is shown to be a consequence of the entropy dominating the free energy of the interface in conjunction with the fact that the entropy of fusion does not vary greatly along the melting curve for simple monoatomic metals. Based on this observation, it appears that large undercoolings in liquid metals can be achieved even at very high pressure. Therefore, nucleation rates at high pressure are expected to be non-negligible, resulting in observable solidification kinetics.