We investigate the accuracy of the coherent potential approximation (CPA) for the optical absorption spectra of a one-dimensional Frenkel exciton system with nearest-neighbor interactions and a Gaussian distribution of fluctuations in the optical transition frequency (diagonal Gaussian disorder). Our earlier studies have established that the CPA gives highly accurate results for the integral of the density of states of this system. In this paper we compare the CPA results for the normalized optical absorption with the finite-array calculations of Schreiber and Toyozawa and Schreiber for the same model. It is found that the CPA results for the absorption are in good agreement with their findings. It is pointed out that an expansion of the density of states in terms of the eigenstates of the ideal (no disorder) array contains a term proportional to the normalized absorption. Since the density of states is accurately approximated by the CPA, the presence of this term explains the success of the CPA in reproducing the absorption spectra. Our findings support the use of the Gaussian disorder model to interpret the absorption spectra of one and quasi-one dimensional exciton systems. (C) 2014 Elsevier B.V. All rights reserved.