Many people think of dancing to music only as stepping on the beat, but there is much more to it. Dancing with cadencia, for example, is also a part of the equation. Cadencia refers to the swing of the body in correspondence with the rhythm and speed of the music. In other words, dancing to music involves not only timing the steps, but timing the swings of the body also. Cadencia is one of the key techniques in tango that is essential to the dance but often being overlooked.
Imagine, now, that your leg does not start from the hip but from the chest, that is, imagine everything below your chest is your leg. The chest is where you and your partner connect in the embrace. It can serve as a fixed point to swing everything below it as a whole. That way, not only the line of your leg looks long, but your whole body looks tall and elegant also.
For the body to swing elegantly it must remain long and straight. A curly ribbon cannot swing well, neither can a soft spaghetti body. You need to keep your body tall and tenacious so it can swing like a pendulum with weight at the bottom.
The swing is in the horizontal direction. Many students fail to do cadencia because there is a lack of horizontal motion and they only focus on the vertical action of stepping down on the beat. In order to do cadencia you need to generate enough speed. (See Cadencia and the Flow of Tango.) The foot must land on the beat, but the horizontal motion of the body continues due to the inertia, carrying the body to pass over the center of gravity until the other foot lands on the next beat. Cadencia is the lilting motion of the body between two steps. It feels like the fish in the water being pushed by the waves, or the water hits the beach, then retreats, and hit the beach again, then retreats.
The following example illustrates this technique: