The coherent-potential approximation (CPA) is used to study the electronic structure of amorphous Ge(Si). These studies are carried out within a tight-binding model which includes all interactions between the s and p valence states associated with nearest-neighboring atoms. Results are presented which show how randomness in the system not related to any particular defects can asymmetrically introduce states into the model gap. The effects of vacancies are also studied both by employing the simple CPA as well as a cluster generalization of it that we develop in this work. We also consider how self-trapping effects and Coulomb electron-electron interactions are expected to alter our results.