Undertow, there is a reason for the phi ratio. This is much more than just 'math', which I find most people irrationally shy away from. I am not going to give a history / math lesson, tempting as it might be, but the phi ratio is one of those 'perfect' numbers and in addition to some interesting properties, was also known to the ancients who prized it.
But, in short, for audio purposes, a phi shaped room, or speaker enclosure for that matter has few or no standing waves. Or, more exactly, a frequency which is an even wavelength into more than 1 dimension. Again, multiple bounces count...like any 2 walls across from each other. or any 3 walls, kind of imagine a ball bouncing around. You'll get the picture! Dead give aways for potential problems are rooms with even multiples of dimensions, like the OP's 9 and 18 foot dimensions. The worst room? probably some kind of cubic shape.
But, in short, for audio purposes, a phi shaped room, or speaker enclosure for that matter has few or no standing waves. Or, more exactly, a frequency which is an even wavelength into more than 1 dimension. Again, multiple bounces count...like any 2 walls across from each other. or any 3 walls, kind of imagine a ball bouncing around. You'll get the picture! Dead give aways for potential problems are rooms with even multiples of dimensions, like the OP's 9 and 18 foot dimensions. The worst room? probably some kind of cubic shape.