There is not currently any widely accepted or empirically successful theory of art. There have been many high-profile attempts to explain the value and/or appeal of art over the centuries, but none that have proven able to anticipate or even keep up with the evolution of art. In more recent years some sociological and statistical surveys have been able to identify some general wide trends, but not with much underlying philosophical backing. For example:
Netflix uses datamining on a massive scale to produce reasonably accurate predictions of what movies a given viewer will like, based on their viewing history.
The original study that gave birth to "The Mozart Effect" theory suggested modest gains in spatial reasoning based on exposure to classical music.
A more recent study suggests that creating a hit song is a combination of talent and luck.
The basic problem that no one has succeeding in solving is that we all have individual tastes --there is no one universal piece of art that all people in all times and places love (although some come close) --and yet it doesn't seem as though it can be completely random and unpredictable. Most of us agree that there can be actually better and worse pieces of art, but not necessarily what those are. (I've actually been personally working over the last 20 years on a theory of the kind you're seeking, but since it's original research, I won't include it here.)