In this note we plan to show how the evenness and oddness of the spatial dimensions influence the general properties of wave propagation.The solution of the inhomogeneous wave equation will be given by a multiple integral; one of the integrations is to be performed in a complex time-plane. The singularities of the integrand in this plane have an alternating character depending on the evenness or oddness of the spatial dimensions. If the space is odd-dimensional, the singularities are poles; if it is even-dimensional, the singularities are branch points. This, then, will alter profoundly the properties of the solution.