The elastic properties of two single crystals of majoritic garnet (Mg3.24Al1.53Si3.23O12 and Mg3.01Fe0.17Al1.68Si3.15O12), have been measured using simultaneously single-crystal X-ray diffraction and Brillouin spectroscopy in an externally heated diamond anvil cell with Ne as pressure transmitting medium at conditions up to ∼30 GPa and ∼600 K. This combination of techniques makes it possible to use the bulk modulus and unit-cell volume at each condition to calculate the absolute pressure, independently of secondary pressure calibrants. Substitution of the majorite component into pyrope garnet lowers both the bulk (Ks) and shear modulus (G). The substitution of Fe was found to cause a small but resolvable increase in Ks that was accompanied by a decrease in ∂Ks/∂P, the first pressure derivative of the bulk modulus. Fe substitution had no influence on either the shear modulus or its pressure derivative. The obtained elasticity data were used to derive a thermo-elastic model to describe Vs and Vp of complex garnet solid solutions. Using further elasticity data from the literature and thermodynamic models for mantle phase relations, velocities for mafic, harzburgitic and lherzolitic bulk compositions at the base of Earth's transition zone were calculated. The results show that Vs predicted by seismic reference models are faster than those calculated for all three types of lithologies along a typical mantle adiabat within the bottom 150 km of the transition zone. The anomalously fast seismic shear velocities might be explained if laterally extensive sections of subducted harzburgite-rich slabs pile up at the base of the transition zone and lower average mantle temperatures within this depth range.