Some critics have guessed that the Duke had his last wife incarcerated in a convent. Others think he had her murdered. The latter seems far more likely, since he could hardly be planning to marry the Count's daughter if he still had a living wife. In fact, these lines should prove that the young woman is dead:
Oh sir, she smiled, no doubt,
Whene'er I passed her; but who passed without
Much the same smile? This grew; I gave commands;
Then all smiles stopped together. There she stands
As if alive.
Throughout this dramatic monologue the Duke reveals himself as such a cold-blooded, insensitive monster that his visitor finally jumps out of his chair and starts to run downstairs without saying "Thank you" or "Goodbye" or offering any excuse for his flight.
Will't please you rise? We'll meet
The company below, then.
. . . . . . . . . . . . . . . . . . . . . . . . . .
Nay, we'll go
Together down, sir.
The Duke is so insensitive that he cannot understand the bad impression he has made on this man who has come upstairs with him to discuss the matter of a dowry. In referring to the beautiful young woman in the painting as "My last duchess," the Duke shows that he never really regarded her as a human being but as a piece of property. He is also implying that the Count's beautiful daughter whom he plans to wed will be "his next duchess." He probably feels that wives are replaceable if for any reason they become unsatisfactory, and that a person with his "nine-hundred,years-old name" can get all the wives he wants, as if from an assembly line. He resembles England's King Henry VIII in this respect--or even the murderous Sulltan in The Arabian Nights.
In referring to the painting as his "last duchess," the Duke does not seem to distinguish between the real woman and the painting. He undoubtedly values the painting by Fra Pandolf much more than he ever valued the lovely girl who posed for it. He cannot even realize his bad taste in showing the picture of a dead wife to the man representing the father of his next wife.
Not all of Browning's dramatic monologues were rhymed, but "My Last Duchess" is in rhymed couplets. This fact can be easily overlooked because the rhymes are so ungainly and the lines so ragged and staggered that the reader may not even want to recognize the intentionally grotesque poetry as such. Browning's purpose in using rhyming but unclosed couplets must have been to further emphasize the Duke's mental deformity. The Duke himself acknowledges that he has no skill in expressing himself.
Even had you skill
In speech--(which I have not)--to make your will
Quite clear to such an one, and say, "Just this
Or that in you disgusts me, here you miss,
Or there exceed the mark"--and if she let
Herself be lessoned so, nor plainly set
Her wits to yours, forsooth, and made excuse,
--E'en then would be some stooping, and I choose
Never to stoop.
(Notice the rhymes: skill/will, this/miss, let/set, excuse/choose)
The Duke has brought this visitor upstairs ostensibly to show him part of his art collection but actually to discuss the dowry he expects with the Count's daughter. The visitor is obviously a gentleman, rather than a mere servant, but he is representing the Count. When he jumps up and starts to run downstairs to where the other visitors are gathered, including presumably the Count himself, the reader hopes the horrified man intends to advise the Count to spare his daughter from the fate of marrying a greedy, heartless Bluebeard.