(Mostly) Blank Verse
Robert Browning was known as a dramatic monologist. That would be someone who specializes in dramatic monologues. To take a deep dive into this form, we know of a course that can help. For now, though, we'll just note that these poems tend to be longer in length and are told from the perspective of a speaker who is an invented or historical character, not the poet him- or herself.
That's why we like to warn you never to confuse the speaker and the poet. Even if you see first-person point of view in a poem, it may just be a character speaking. That's certainly the case with "The Bishop Orders His Tomb."
One look at the poem, in fact, lets us know that we're in for a dramatic monologue. Notice that there are no stanza breaks to interrupt the flow of the bishop's speech. He just keeps rambling on without a break. And, much like natural human speech, there really isn't much rhyming here, either. Instead, we get a free-flowing stream of words coming our way.
If you listen closely, though, you'll notice a pattern starting to emerge among some of these lines. Check out this example:
What's done is done, and she is dead beside,
Dead long ago, and I am Bishop since, (6-7)
When you read those lines out loud (go ahead, nobody's looking), you start to hear a pattern emerge in the lines' rhythm. It should sound like this: daDUM, daDUM, daDUM, daDUM, daDUM.
That, folks, is the sound of iambic pentameter. An iamb is just a two-syllable pair in which the first syllable is unstressed and the second is stressed. Stick five of those suckers into one line and you have one of the most common meters in English poetry: iambic pentameter (penta- means five, by the way).
So we do see a pattern in the rhythm of the lines, but, as we noted, they don't seem to be joined closer by any sort of rhyme scheme. In the poetry biz, unrhymed iambic pentameter goes by the special name of blank verse. This was a form that a lot of poets used, in fact, to imitate the flow of normal human speech (we're looking at you, Shakespeare). By that token, it's a pretty appropriate choice for a dramatic monologue.
But Browning was smart enough to know that regular speech isn't always in lockstep with a preordained pattern. That's why we have an irregularity in the poem's iambic pentameter, like
Nephews—sons mine… ah God, I know not! Well— (3)
It's a rare holdout to the predominant blank verse that's going on here, but as such it serves to remind us that we're listening to someone's speech pattern—and what a speech it is.