The equilibrium properties of a single band tight binding model Hamiltonian are calculated within the framework of a generalized quasi‐crystalline approximation. Three particle correlation functions are treated explicitly and the qualitative features of the electronic density of states are found to depend on the form of the short range order in the system. For example, in a close packed solid the spectrum is essentially structureless while in the case of a tetrahedrally coordinated system the density of states exhibits two well defined peaks. The latter statement is in accord with the results of recent cluster calculations and has implications for both the electronic and vibrational spectra of amorphous semiconductors.