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Room Setup, Page 8      

The Golden Trapagon

By George Cardas

The Golden Cuboid (Diagram H) is the best "rectangular" shape for a listening room. If, however, you have full architectural freedom, a Golden Trapagon (Diagram I) is by far the favored shape. A Golden Trapagon has a Golden rectangle for the front wall behind the speakers, and the room progresses to a larger (by Golden Ratio in area) Golden rectangle back wall behind the listener.

For example, if the wall behind the speakers is 10 feet x 16 feet, the room would then be 26 feet long and the wall behind the listener would be 13 feet x 21 feet. Ideally, the rear portion of this room would vent into an attic space filled with fiberglass insulation.

The trick to a Golden Trapagon shaped room is it eliminates the problem of parallel walls and the slap and sharp nodes associated with them. The "sound" of this room is a decaying hologram of the original, not a slap. This decay is exponential, or higher, at all frequencies. The relationship between the height and the width of the room, at any point, is Golden Ratio. The cross-section area at the rear of the room is 1.618 times the cross-section of the front. In the example above, the ceiling height would be 12.72 feet.

The ratio of front height or width, to rear height or width, is 1.272 to 1. 1.272 is the square root of 1.618 or Golden Ratio. The progression of size at the ends of the room is a area relationship. The sound confronts the entire surface of the end walls at the same time, rather than progressively as with height and width. It is like tuning a guitar to a major chord, the side walls become the strings and the end walls are the bridge and tailpiece.