The Finite Difference Time Domain method is gaining popularity as a means to simulate and solve room acoustical problems. In this paper, a new set of stencils is defined that approximate the wave equation with a high degree of accuracy and lower dispersion error. Compared to the previously presented optimal scheme, the Interpolated Wideband scheme, our schemes are computationally less demanding and more practical to implement. They use at least 8 times less memory for the same audio rate and are an order of magnitude faster, although the former has a higher valid bandwidth. Despite their larger computational expense per node update, it is shown that our schemes on the whole use less memory and computation time than the Standard Rectilinear stencil, particularly when GPU implementations are employed. Lastly, a new way of visualizing and comparing valid bandwidth is recommended.