To constrain the effect of composition and temperature on the elasticity of glasses and super-cooled liquids, acoustic velocities of samples in the pseudoternary system anorthite-diopside-forsterite (An-Di-Fo) were measured by Brillouin spectroscopy. Both the longitudinal and shear wave velocities were measured in the glassy state and into the region of super-cooled liquids. The glass transformation temperatures (Tg) inferred from the Brillouin measurements are equal to those obtained by earlier viscosity and thermal expansion measurements on the same samples, within the limits of experimental uncertainties. The variation of the elastic properties with temperature is approximately linear, both for the glassy state (below Tg) and in the super-cooled liquid state (above Tg). The temperature derivative of vibrational contributions to Young's (E), bulk (KS), and shear (G) modulus is approximately 6--12 times greater for super-cooled liquids than for glasses. In the glassy state the elastic moduli and their temperature derivatives are described by ideal mixing of molar properties of oxides. The pronounced variations with composition in the elastic and anelastic properties above the glass transformation can be related to changes in configurational contributions. The configurational contribution for chemically complex glasses (mixtures of the An-Di-Fo end-members) does not affect the overall compressibility at lower temperatures, whereas at higher temperatures they dominate the temperature derivatives of the moduli. In the super-cooled liquid state the temperature dependence of the vibrational elastic moduli for simple end-member compositions (An, Di) is much higher than for complex compositions. On the other hand, the configurational contribution to compressibility is higher for complex compositions than extrapolated from end-member compositions. Therefore the density and elastic properties of complex melts in the basaltic anorthite-diopside-forsterite-system cannot be easily approximated from the behavior of pure anorthite or diopside samples. Our results indicate that with increasing temperature, configurations with a higher bond strength were preferentially occupied. Isothermal relaxation times, varying between ≈0.01 and ≈1 s at 950¿C, show a minimum for intermediate anorthite-diopside-compositions and are related to the maximum in configurational entropy.