Diagram 21: 3-Couple Triangular Set.
At the start of the third repeat following the most usual progression, 231, or of the second repeat following the less usual progression, 312.
Note that the numbered Places of the Dancers in the Full set (the Places in which they started the dance) are shown as 1 2 3, i.e., in Times New Roman font in the upper left part of the Dancer's symbol; their numbered Places in the Active set (the Places in which they started the Repeat) are shown as 1 2 3, i.e., in Helvetica font in the lower right part.
Square set is a completely natural name for the Circular set for 4 Couples since it is easy to visualize the square formed by extending the lines joining the Positions of the Man and the Lady of each Couple. On that basis, it was logical to name the Circular set for 3 Couples as the Triangular set. However, with no markers for the points, A B C, visualizing the equilateral triangle, ABC, formed by extending the lines joining the Positions of the Man and the Lady of each Couple in the Triangular set is strongly counter-intuitive (even mathematicians have difficulty with alignment at 60o rather than a right angle!). If only the Square set had been called an Octagonal set, i.e, the shape of the polygon formed by joining the Positions of the adjacent Dancers, the Triangular set would much more fortunately have been called a Hexagonal set, as shown shaded in Diagram 21.
Given that most Scottish Country Dancers have so much difficulty in positioning themselves correctly in this Set format, while Making up they should all Take hands in a neat circle; they should then move round as necessary so that the Top couple are aligned Across the set, as they would be in a 4-Couple Square set. When not required to Face Partner, every Dancer in a Triangular set should take care to Face the Opposite Dancer. It is most important that the "Side" Couples should never align themselves as though they were 2nd and 4th couples of a Square set.
Each Dancer should maintain the correct shape of the Triangular set by checking his/her Position whenever back to one of the Starting Places. Some dances, such as The Wind on Loch Fyne, use Figures particularly suitable for Circular sets and so the Triangular set format can readily be maintained, throughout; others, such as Indian River Strathspey, use Figures which have to be distorted from their use in Longwise and Square sets, making the Triangular set format more difficult to maintain.