Beginners may think of dancing to music only as stepping on the beat, but there are 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 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.
The swing is in the horizontal direction. Some students fail to do cadencia because there is a lack of horizontal motion and they only focus on the vertical action of stepping down. To do cadencia you need to generate enough speed by pushing or pulling the woman's torso to accelerate the horizontal motion of her body, which will bring her hip and leg to swing. The leg must land on the beat, but the horizontal motion of the body continues due to the inertia, causing her other leg to swing along and land on the next beat. Cadencia is the lilting motion of the body between two steps. (See Cadencia and the Flow of Tango.)
In short, cadencia is a two-part process. The first part is using the chest as the fixed point to swing the torso, hip and leg. You must keep the body tall and tenacious, so everything below the chest can swing like a pendulum until the foot lands on the floor. The second part is letting the body surge by the inertia, using the foot as the fixed point. You must keep the body tall and straight as it surges forward or backward, so it looks elegant. Cadencia is usually done to and fro alternately in the opposite directions. It feels like riding back and forth on a swing.
The following example illustrates this technique: