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Revealing and understanding the microscopic origins of the macroscopic properties of aluminosilicate glasses is important for the design of new glasses with optimized properties. In this work, we study the composition-structure-property relationships in 20 MgO/CaO sodium aluminosilicate glasses upon Al2O3-for-SiO2 and MgO-for-CaO substitutions. We find that some properties (density, molar volume, Young's modulus, and shear modulus) are linear through the investigated range of Al2O3 compositions, while others (refractive index, coefficient of thermal expansion, Vickers hardness, isokom temperatures, and liquid fragility index) exhibit a change in the slope around the composition with [Al2O3] = [Na2O], which is especially pronounced for the glasses containing MgO. We discuss these phenomena based on structural information obtained by NMR spectroscopy and topological considerations.