The Golden Ratio: (0.618X1X1.618) yields a 2/3 octave spread between the first standing wave of each dimension.
A common acoustic ratio of: (0.7937X1X1.2559) spreads the first standing wave of each dimension by about 1/3 octave.
There is a bit of easy math that predicts the low frequency performance of a room but most goes out the window when the space becomes more complex than a box.
I am interested in this project.
Barry.