As revealed in this dramatic monlogue, the Duke prizes the painting of his wife, but what is the Duke’s approach to art?

The Duke prizes the portrait of his wife exactly because it is a work of art. He did not prize his wife - he had her murdered. But now she is a work of art, like the the bronze statue of Neptune taming the sea horse (how ironic!!!) she is valued and loved.(He could not tame her!!!)

The Duke only loves things that he can control, like art or the artists who rely on his patronage. In life he was unable to command her complete attention. She was too ready to rank the gift of his noble name with those things given by others. She smiled at everyone, now she only smiles at his behest when he draws the curtain aside to control who she smiles at.

The language reflects this as well as the narrative. When he speaks about art or artists the tone is controlled but when he begins to talk about the Duchess when she was alive, the lines run on (enjambment) as if out of control and the pauses (caeasura) indicate a further loss of control.

In short the Duke loves art because it is under his control.