The adiabatic bulk (KS) and shear (G) moduli of a polycrystalline majorite-garnet solid solution with composition (Na0.92Mg2.08)(Mg0.02Al1.06Si0.92)Si3O12 were measured at ambient conditions by Brillouin spectroscopy. KS and G were found to be 171.6 (3.5) GPa and 103.5 (2.0) GPa, respectively. Assuming a linear dependence of the elastic moduli on composition for the Mg2Si2O6 (enstatite-majorite, En-Mj) -- NaAlSi2O6 (jadeite-majorite, Jd-Mj) join, the calculated KS and G of the fictive Jd-Mj end-member are 178 and 125 GPa, respectively. At ambient conditions, the shear velocity change associated with the pyroxene to majorite transition increases dramatically with increasing Na content in the system. In contrast, there is virtually no shear velocity increase associated with the pyroxene to majorite transition in MgSiO3. If this relationship holds at high pressures and temperatures, it suggests that for mineral assemblages containing an abundance of large radius cations such as Ca and Na, the pyroxene→garnet reaction will produce higher shear velocity gradients than assemblages that are relatively deficient in these elements. Such chemical effects could play a significant role in explaining high seismic velocity gradients in the transition zone.