The Tartans offered by The Wales Tartan Centre are not asymmetrical as much as not true Tartans. To be a Tartan the thread count should be the same horizontally and vertically. Some of these Tartans are symmetrical horizontally, some are not, but the vertical is totally different. It gives them a noticeable vertical element.
I will make my wife a hostess skirt from the Williams Tartan and I love the look and colors, but I knew it was not a "true" Tartan going in.