The Foxtrot Basic is comprised of two walks, and a "chasse." A chasse is a series of two or three steps, where the feet close on the second step. In this case, we only use two steps.
Generally speaking, the Foxtrot Basic is danced with the leader dancing forward, and the follower dancing backwards, but on occasion it can be useful for the direction to reverse, resulting in the Back Basic.
The Left Hesitation Turn is a very useful figure for navigating the dance floor. Like the basic, it is comprised of two walks and a chasse, but unlike the basic, the second walk reverses the direction of travel. The chasse can then either not turn at all, or turn up to 3/8 of a turn to the left, thus giving the dancers a new path to travel. Alternatively, the Left Hesitation Turn can be repeated until you end up in the same alignment you started with, thus simply adding variety to your dance.
Progressive Quarter Turns is a more slightly more advanced figure that combines a forward Basic that turns a quarter to the right, and a back Basic that turns a quarter to the left. The end result is a sort of zig-zag action down the line of dance.
Promenade is a dance position where both partners are facing and dancing in the same direction. In this case, the basic figure is danced in promenade position, which means that both partners walk forward, and instead of the chasse being a side step, the chasse becomes a forward action.
There are a couple of ways of dancing an underarm turn to right from promenade position in Foxtrot, but I find this to be one of the better versions for beginners. For the lead, the basic structure of the step is the same as dancing the Basic in Promenade, but they do need to deal with leading the follow's underarm turn while dancing their part. The follow, on the other hand, has very different foot positions. That being said, the underlying structure is still that of two walks and a chasse, but the walks are rotating to the right.
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