Primitive MgO-SiO2 liquids dominate the early history of the Earth and Terrestrial planets. The structures of these liquids and structure-dependent properties, such as viscosity and diffusion, are considered important in the evolution of these planets, however, MgO-SiO2 liquids are refractory and do not form glasses easily and it is difficult to measure the structure of these liquids. Container-less synthesis techniques have been used to produce glasses that range in composition from 50 to 33% SiO2, corresponding to the compositions of two important mantle minerals: enstatite and forsterite. The structure of these glasses has been determined using combined neutron and high-energy diffraction and show changes in the short-range order as a function of composition. These changes include a jump in Mg-O coordination number at the limit to the formation of the silicate network in forsterite composition glass. These results imply a similar change in the structure of the liquid. Accordingly, the structures of forsterite and enstatite liquids have been determined using high-energy X-rays and a specialized sample environment, a containerless levitator. The main qualitative structural differences between MgSiO3 and Mg2SiO4 glasses are also observed in the melt. Liquid MgSiO3 is interpreted as forming a relatively 'strong' network of SiO4 tetrahedra, whereas the Mg2SiO4 liquid is "fragile" and dominated MgOn (n = 4, 5, 6) polyhedra and highly mobile oxygen ions. The results differ significantly from previously reported X-ray diffraction data for liquid MgSiO3.