The atomic structures of magnesium silicate melts are key to understanding processes related to the evolution of the Earth's mantle and represent precursors to the formation of most igneous rocks. Magnesium silicate compositions also represent a major component of many glass ceramics, and depending on their composition can span the entire fragility range of glass formation. The silica rich enstatite (MgSiO(3)) composition is a good glass former, whereas the forsterite (Mg(2)SiO(4)) composition is at the limit of glass formation. Here, the structure of MgSiO(3) and Mg(2)SiO(4) composition glasses obtained from levitated liquids have been modeled using Reverse Monte Carlo fits to diffraction data and by density functional theory. A ring statistics analysis suggests that the lower glass forming ability of the Mg(2)SiO(4) glass is associated with a topologically ordered and very narrow ring distribution. The MgO(x) polyhedra have a variety of irregular shapes in MgSiO(3) and Mg(2)SiO(4) glasses and a cavity analysis demonstrates that both glasses have almost no free volume due to a large contribution from edge sharing of MgO(x)-MgO(x) polyhedra. It is found that while the atomic volume of Mg cations in the glasses increases compared to that of the crystalline phases, the number of Mg-O contacts is reduced, although the effective chemical interaction of Mg(2+) remains similar. This unusual structure-property relation of Mg(2)SiO(4) glass demonstrates that by using containerless processing it may be possible to synthesize new families of dense glasses and glass ceramics with zero porosity.