see Daniel Green's comments on literary formalism, in his posts of Dec. 12 and 13.
The aesthetic sense : free intellectual capability to absorb information (facts, ideas, arguments, opinions, sensations), and then to encompass same within a sense of form, order, beauty. A formal (and holistic) response to beauty in works of art.
I might have more to say about "form" after I finish this interesting book on Dante by Christian Moev. He describes the subtleties of Aristotle's central concepts - ie. the relation between form (as the substantial reality of things in the hierarchy of nature or "chain of being") and the intellect (the free power of the soul to apprehend real things).
(This sounds awfully vague, I know.)
When you know the form of something, you grasp its identity. Matter, strictly speaking, doesn't exist : it's the potentiality of form. & form fulfills potentiality in acts of creative intellect (the Prime Mover for Nature; the human intellect for art).
But what is it to say that something has (primarily) an aesthetic form? Maybe Aristotle would say something like this : an aesthetic form is an object structured in such a way as to reflect the sense of beauty which resides in the (complementary) inner form of the soul.