We used a quasi-spherical cavity as an acoustic and microwave resonator to measure the thermodynamic temperatures, T, of the triple points of equilibrium hydrogen, neon, argon and mercury and to measure the difference T - T-90, in the range 7 K to 273 K. (T-90 is the temperature on the International Temperature Scale of 1990 (ITS-90).) In the range 7 K to 24.5 K, our preliminary values of T - T-90 agree with recent results from dielectric-constant gas thermometry and achieve uncertainties that are comparable to or smaller than those achievable using the interpolating constant volume gas thermometer as currently defined on the ITS-90. In the range 90 K to 273 K, the present results for T - T90 obtained using a helium-filled, copper-walled, quasi-spherical cavity agree with earlier results obtained using argon-filled, steel-walled or aluminium-walled, spherical cavities. The agreement confirms our understanding of both acoustic and microwave cavity resonators and demonstrates that resonators function as primary thermometers spanning wide temperature ranges. The mutually consistent acoustic thermometry data from several laboratories imply that the values of (T-T-90)/T-90 are 5 times larger than the uncertainty of T/T-90 near 150 K and near 400 K. They also imply that the derivative dT/dT(90) is too large by approximately 10(-4) near 273.16 K and that dT/dT(90) has a discontinuity of 4 x 10(-5) at 273.16 K.