The Duke is a pompous, critical, controlling man, who believes that he should have power over his wife now that she is dead, just as he wanted to have when she was alive. Note that in lines 9-10 he says, "since none puts by/The curtain I have drawn for you, but I," indicating that he is the only person who is allowed to show visitors the painting of his "last Duchess." On the other hand, the Duchess is a cheerful, thoughtful woman who appreciates those around her as well as her surroundings. The Duke is annoyed by his wife because she seems to value his "nine-hundred-years-old name" (ancient family line) just as much as she values a small gift of flowers or her own "white mule."