This is from the second tetrad which is essentially concerned with the cultivation of the feeling of joy. Feelings link the body with the mind, and Buddhism is interested in the higher feelings which are associated with mind, that’s why the terminology is “calming mental fabrications:”
“Perceptions & feelings are mental; these are things tied up with the mind. That’s why perceptions & feelings are mental fabrications.”—MN 44
Calming feeling means developing a skill of tranquillization following the opposite activity of developing joy which is energetic, and corresponding to the two contrasting groups in the seven factors of awakening, investigation (insight) and serenity (SN 46.53). To progress further on the path it is necessary to be in command of skills to exert energy then calm it. It is required to go through the process of exerting the energy to develop joy to understand the experience of calming it. This is to maintain balance between serenity and insight to preserve wellbeing.
The key aspect of the second tetrad is developing joy which has ramifications for the entire practice, and follows the development from the first and second jhanas (feeling), to the equanimity of the third, and the awareness (mental) of the fourth (AN 5.28). This progession from body to feeling to mind parallels the first three tetrads and foundations.
How to develop joy in the body: