Nancy Rogers and Michael Buchler,
Square Dance Moves and Twelve-Tone Operators

Figure 14. Animation of "swing through," iterated twice.

 Dancers holding right hands rotate 180 degrees clockwise (described in square dancing terms as "swing half by the right"). Dancers holding left hands rotate 180 degrees counterclockwise (described in square dancing terms as "swing half by the left"). Notice that this maneuver only affects the dancers in the center because the dancers on the ends are not holding anyone by the left hand. The result is that dancers who begin on the ends of the ocean wave rotate twice while dancers who begin in the middle of the ocean wave rotate only once.

 STn = Swing through iterated n times. For any wave of length n: STn = original wave [ T0 ] STn/2 retrogrades the initial wave [ R(T0) ] Example: ST0 = < 0, 1, 2, 3 > ST1 = < 1, 3, 0, 2 > ST2 = < 3, 2, 1, 0 > ST3 = < 2, 0, 3, 1 > ST4 = < 0, 1, 2, 3 > = ST0
 We might be tempted to view "swing through" as a combination of Lewinesque contextually-defined functions FLIPENDS followed by FLIPMIDDLE. However, this would not be altogether accurate. Callers occasionally navigate the dancers into a sort of inverted position called a "left-handed wave," in which the outer dancers touch left hands and the inner dancers touch right hands. Because of the way it is defined, "swing through" called from this formation would entail FLIPMIDDLE followed by FLIPENDS. From a left-handed ocean wave, the most common call is a "left swing through," defined as "swing half by the left and half by the right." "Left swing through" could, of course, also be called from a standard righted-handed ocean wave, but this is exceedingly rare.