A “change of rein” is a change in the direction of travel in an arena. For instance, if you are travelling clockwise in the arena, you must make a change of rein to end up travelling counterclockwise. A “change of diagonal” is a rider’s change from posting on one diagonal—that is, rising at the trot when the horse’s outside foreleg swings forward and sitting when the outside forefoot hits the ground—to posting on the opposite diagonal when travelling the other direction. Regarding the change of diagonal for hunter-seat equitation riders, if you go to http://www.newrider.com/Library/Riding_Tips/changerein.html, you’ll find some numbered diagrams that will help you understand the following explanation:
Fig.1—Across the Long Diagonal-–If you are already posting the trot and the change of rein calls for a posting trot with a lengthening of stride, you don’t change the diagonal in the center of the ring (which would be X in a dressage arena), but should wait until you reach the end of the line and change diagonals just before you bend the horse in the new direction (Note: The rider of the black horse would change diagonals at M, while the rider of the brown horse, travelling the other direction, would change diagonals at K). If, however, the test does not call for a lengthening of stride, but simply asks you to change rein across the diagonal, then you can change your diagonal at X or can wait until the end of the line and change your diagonal just before you bend the horse. Changing the diagonal at X is considered the more elementary of the two choices, allowing the rider to change diagonals, then change the bend; whereas changing at the end of the line combines getting a new diagonal and changing the bend at the same time.
Fig. 3—A Half-Turn and a Half-Turn in Reverse—The top diagram shows a half turn, which is a half-circle, then a return to the track on a diagonal line. In this case, the rider stays on the same diagonal throughout the half-circle and the diagonal line, then changes diagonals as he bends the horse back onto the track on the long side of the arena. In the bottom diagram, the horse is performing a half turn in reverse, in which it leaves the track on a diagonal line, then performs a half-circle to return to the track. In this case, the rider stays on the original diagonal until the end of the diagonal line, then changes diagonals as he changes the bend to commence the half-circle.
Fig. 6—Serpentine—These are three good examples of serpentines, except that they are all based on an odd number of loops, which would make you end up travelling the same direction that you started. In order to change rein through a serpentine, you must have an even number of loops—2,4, etc. The rider’s change of diagonal occurs as his shoulder crosses the centerline of the ring—about where the black horse is shown in the second of the three diagrams.
Fig. 9—Change of rein through a circle—The change of rein through a circle involves making a two-loop serpentine in the middle of a circle. In this case, the rider changes diagonals as he changes the bend from the first loop of the serpentine to the second loop.
Figs. 12 & 13—Although the turn on the forehand, turn on the haunches, and leg yield are sometimes used in equitation classes, the change of diagonals does not apply. The turn on the forehand and turn on the haunches are performed at the walk, and the leg yield back to the track is performed at the sitting trot.