First-principles band structure calcns. were performed for the ternary alk.-earth silicon nitride BaSi7N10 using the d. functional theory (DFT) within the pseudo-potential (PP) method. The calcns. show that both the coordination no. of nitrogen by silicon (N[x]) as well as the way of sharing SiN4 tetrahedra (corner vs. edge) influence the local electronic structure of these atoms. The top of the valence band is dominated by the 2p states of the N atoms, while the N 2p states are positioned lower in energy. It is also noted that edge-sharing N atoms show N character. The conduction band is detd. by Ba 6s states. The compd. is calcd. to be a wide band gap semiconductor with an indirect energy gap of about 3.8 eV. The direct energy gap is predicted to be about 4.0 eV, in agreement with the exptl. value of 4-4.5 eV.