Acoustic wave velocities for synthetic polycrystalline almandine [Fe₃Al₂(SiO₄)₃] grossular [Ca₃Al₂(SiO₄)₃] and CMNF [0.2 NaAlSi₁₂O₆ + 0.3 Mg₂Si₁₂O₆ + 0.4 CaMgSi₁₂O₆ + 0.1 Fe₂Si₁₂O₆] garnet were measured up 8 GPa and temperatures up to 1000K by ultrasonic interferometry technique, in conjunction with energy-dispersive synchrotron X-ray diffraction in a cubic anvil DIA-type apparatus (D-DIA). Travel times of compressional (P) and shear (S) waves and X-ray diffraction data were collected after heating and cooling at high pressures to minimize effect of non-hydrostatic stress on the measurements. Elastic bulk (K_S) and shear (G) moduli data obtained at the end of the cooling cycles were fitted to functions of Eulerian strain to third order, yielding pressure derivatives of the elastic moduli (∂K_S/∂P)_T = 4.3 (1); (∂G/∂P)_T = 1.13 (3) for almandine, (∂K_S/∂P)_T = 4.4 (2); (∂G/∂P)_T = 1.28 (5) for grossular and (∂K_S/∂P)_T = 4.4 (4); (∂G/∂P)_T = 1.36 (6) for the CMNF garnet. Both (∂K_S/∂P)_T and (∂G/∂P)_T are identical within mutual experimental uncertainties for all three garnet compositions. Moreover, the new pressure derivatives of the elastic moduli are also equal within experimental uncertainties, to those of end-member pyrope garnet Py₁₀₀ (Gwanmesia et al., 2006), and of Py₆₀Mj₄₀ and Py₅₀Mj₅₀ (Gwanmesia et al., 2009), from previous ultrasonic studies, thus indicating that the effect on the pressure derivatives of the elastic moduli due to cation (Ca, Na, Fe) substitutions in the garnet structure, observed in this study is minimal or insignificant. Furthermore, these derivatives are also similar to those of other major mantle phases.