A post at Via Negativa on John Ashbery and other things points to one by Reginald Shepherd on the degrees of difficulty in poetry, and a lot of the post works for other art forms as well.
Semantic difficulty can in turn be broken down into difficulty of explication and difficulty of interpretation. Some poems present both kinds of difficulty, some only one or the other. In the case of explicative difficulty, the reader cannot decipher the literal sense of the poem: “What is this poem saying?” One encounters this in Hart Crane’s “At Melville’s Tomb,” and he wrote an extensive explication of the poem for Harriet Monroe, then editor of Poetry. In the case of interpretive difficulty, one grasps what is being said on the literal level, but doesn’t know what it means, what it is meant to do. John Ashbery’s poems, usually syntactically and explicationally clear, often present this interpretive difficulty. To say that one doesn’t know what a poem means, if one understands its literal sense, is to say that one doesn’t know why it’s saying what it’s saying. The reader asks, “Why am I being told/shown this?”
It is semantic difficulty which readers are usually experiencing when they say, “I don’t understand this poem.”
In theater, this translates to the comment one hears in the lobby at intermission, “I wish they would put something in the program to tell us what this play is about.” It’s perfectly clear what, say, Waiting for Godot is “about,” what the story is: two hoboes hanging out by a withered tree expecting to meet someone who doesn’t show up. But the bemused audience member wants to know why he’s being told this particular story. (Of course, my perennial frustration is with audience members who, when presented with the fence of a difficult play, balk and refuse to jump it, even with the carrot of a program note suggesting an interpretation.)
And as well:
Formal difficulty is a particular case of what George Steiner, cited by Shetley, calls modal difficulty…. In the case of modal difficulty, a reader asks, “What makes this a poem?”
Some of the experimental work of the 1960s might fall into this category.