Who is the duke addressing his remarks about the duchess?

The Duke is the speaker of the poem, and tells us he is entertaining an emissary who has come to negotiate the Duke’s marriage (he has recently been widowed) to the daughter of another powerful family. As he shows the visitor through his palace, he stops before a portrait of the late Duchess, apparently a young and lovely girl. The Duke begins reminiscing about the portrait sessions, then about the Duchess herself.