Perhaps it's not quite analogous to music theory, but what you're describing in the first paragraph would be referred to as the formal elements of art or simply the elements of art.

Analysis of these elements (form, line, space, color, and texture) is usually a part of the sort of art criticism you'd find in academic studio art, art history, or even just the New York Times art section.

The visual design field has a similar, extended set of elements for describing the formal elements of a design piece.

In both art and design, works are usually considered effective if they use the formal elements of art/design to support what you refer to as the semantics of the subject. That's a broad generalization, but you see it in practice a lot, so it seems like a fair thing to say.

Academic art history is starting to feel the influence of machine learning and computer vision precisely because computers can be trained to recognize the formal elements of art and associate their use with movements and historical periods. There are way more detailed articles than this one, but this will get you started if you're interested in this sort of thing:

https://www.technologyreview.com/s/537366/the-machine-vision...

The problem is that you'll hit a wall when it comes to understanding "what makes art." You can do all the theory you want, and people do, of course. You can analyze all that has ever been done, and come up with rules for describing and even generating music and art. But there is no guarantee that these will allow you to predict what makes future art. Just like with financial markets, in art, what happened in the past is not a good predictor of the future. That is the mistake that "art theorists" tend to make, have made for decades and decades, and are carrying over rather simplistically to statistical analysis via machine learning.

This is particularly challenging in art (as compared e.g. to financial markets) because much of what defines new art is specifically what makes it different from what has come before it. That is to say, art, by its nature, will always beat any rules you try to design, because that is what it does, indeed, what is must do.

The proof is in the pudding: that machine learning systems can be designed to learn the statistical trends in a body of works and then generate similar art, done since at least the 80s if not earlier, evokes the very definition of the detractive term "cookie cutter art." "Good" art then, by contradiction, is exactly that art that does not fit into such a model -- plus "something".

Surely it is that "something" we'd like to find, but I am afraid that using rule- or statistically-based analysis to help curators sort through art, even with the prescribed notion that this should help them find "diamonds in the rough", it will generate an echo chamber in which the next diamond, which by definition is quite different from diamonds that came before it, to remain undiscovered, buried in a pile of sorted spam.

It is for this reason that I believe that despite the advances in machine learning, nothing will ever replace the past-time of "crate digging" for finding gems. The DJs job will never completely die.

... I will add: That is not to say that tools for automatically understanding and measuring aspects of a photo or piece of music are not useful for artists as a way of judging their own work and making decisions. But it is exactly those artists that will look at the "goodness indicator" drop one notch while they make a change, and say, "I'm fine with that", who will produce the next important work.