A room acoustic diffuser exploits interference, by reflecting waves out-of-phase with the specular energy, making it possible to diminish specular energy. This is achieved by using a diffuser based on a ternary sequence, which nominally has reflection coefficients of 0, -1 and +1. A method for obtaining the design sequence for Quaternary diffusers is also disclosed. Also, design methods for forming the sequences into arrays, and forming hemispherical diffusers are explained.