If you were to mention the term ‘formal analysis’ to an art historian today, you’d probably be told it’s passé. No one really tries to objectively compare one painting against another using formal concepts anymore. However, formal analysis—or the concepts that it identified—does still present some interesting ideas, especially for photographers.
Swiss art historian Heinrich Wölfflin was a key figure in formal methodology. He devised a system that compared opposing artistic concepts so that they could be applied to paintings and used to analyse them. In particular, Wölfflin was interested in trying to characterise Renaissance and Baroque art.
One pair of comparators used by Wölflinn was closed form against open form. While I’m doubtful you’re set on recreating Renaissance or Baroque pictures, knowing what the terms mean, and how they can be applied to your photos and make your audience feel about them, is useful.