This paper reports the results of ultrasonic measurements of the second-order elastic constants of a single-crystal specimen of almandine-spessartine garnet as a function of pressure and temperature. The density of the sample, &rgr;0=4.2396¿0.0016 g/cm3, is consistent with the composition (Fe0.52, Mn0.46, Ca0.01)3Al2Si3O12 as determined by microprobe analysis. The pertinent results, Ks=1763.3¿2.3 kbar, (∂Ks/∂P) &tgr;=4.590.16, and (∂Ks/∂T) p =-0.172¿0.005 kbar/¿C, where KS is the adiabatic bulk modulus, are related systematically to other garnet results published by previous investigators. In addition to the foregoing conventional ultrasonic data we have obtained a measurement of the higher-order property (∂2Ks/∂T∂P) of 0.9¿0.6¿10-3 ¿C 1. The magnitude of this parameter suggests that it could significantly effect seismic velocity and density equations of state which are used commonly to model the earth's mantle. Assuming that the second-order elastic constants Cij of garnets are related linearly to the molar fraction of their constituent end-members, the present data have been combined with the work of previous investigators in order to derive the elastic properties throughout the garnet solid solutions series. The relevant results for Ks from the least squares analysis for the various end members are as follows (in kilobars); pyrope, 1658¿13; almandine, 1801¿7; spessartine, 1723¿10; grossular, 1705¿13. These data provide the basis for calculating the elastic wave velocities for any (Mg, Fe, Mn, Ca)3Al2Si3O12 garnet.