We compare the predictions of two solar models with the observed p-mode eigenfrequencies. The two models use the same input microphysics (nuclear reaction rates, opacity, and equation of state) and the same numerical evolutionary code, but differ in the treatment of turbulent convection. The first model employs the standard mixing-length theory of convection (MLT), while the second model employs a new model of turbulent convection (CM) whose primary goal was that of accounting for the whole spectrum of turbulent eddies so as to avoid the MLT approximation that such a wide spectrum be represented by a single, large eddy. With the suggestion that the mixing length, LAMBDA, be taken to be z, the distance to the nearest convective boundary, the new CM model has no free parameters, and yet it predicts a solar T(eff) to within 0.5%. The LAMBDA = z suggestion, within the context of the MLT, would yield T(eff) of by approximately 3% that forces the introduction of LAMBDA = alphaH(p), with alpha a free, adjustable parameter. The main result of this paper is that the p-mode eigenfrequencies calculated with the CM model show an overall improvement with respect to those calculated with the standard MLT model.