Usually Free Verse, Occasional Use of Rhyming Couplets and a Sustained Rhyme Scheme
Man, oh man. Where to begin? Like much of his other poetry, "Four Quartets" uses Eliot's tone of high seriousness. But even less than "The Waste Land," this poem uses almost entirely free verse, relying on constant repetitions of key words—as opposed to any fancy meter or consistent rhyme scheme—to make its message seem circular, just like the model of time that the speaker is trying to communicate to us.
That's not to say that regular rhyme doesn't pop up in this poem. Section Four of "East Coker," for example, does fall into a very tight ABABBrhyme scheme, repeating that pattern a total of five times. Meter-wise, the five-line sections start out in a form called iambic tetrameter, but then shift to iambic pentameter in each fourth line, and iambic hexameter in each fifth line. Come again? It's not as complicated as it might sound. An iamb is a pair of syllables where the first is unstressed and the second stressed (if you say "allow" out loud, you'll hear what one sounds like in real life: "daDUM"). So, four of those in a line would be iambic tetrameter (tetra- meaning four), five is iambic pentameter, and six iambs in a line is—you guessed it—iambic hexameter. Just check out one example of this set-up:
The wounded surgeon plies the steel
That questions the distempered part;
Beneath the bleeding hands we feel
The sharp compassion of the healer's art
Resolving the enigma of the fever chart. (327-331)
This kind of sustained metric pattern and rhyme scheme is really rare in Eliot's poetry, which is all the more reason it sticks out to us as readers when we come across it in this poem. So what's it doing there? Well, it might just show that at this late point in Eliot's career, he's willing to explore new approaches in this work in order to get through to us.
The speaker's tight rhyming and meter is most obvious in Section Four of "East Coker," but if you look closely, you'll find that the fourth sections of all four poems are more structured than the others. In Section Four of "Burn Norton," you won't find a clear meter, but you'll see a complex rhyming of AABACDECDE, which is like a classic English ode in its last six lines, but not its first four (which should be ABAB). The speaker's choice here to write something like a classic ode, but not quite an English ode, shows how he has a certain level of attraction to classic artistic forms, but can't help but show these forms as being a little bit warped or broken, just as classic beauty might be warped in the modern age.
Just as there is a hidden pattern to the fourth sections in each of Eliot's "Four Quartets," so too might there be a hidden pattern in the world that we might not be noticing. This isn't to say we should go out and become conspiracy theorists. Rather, it seems that Eliot specifically would like you to look for spiritual patterns in the world.
All of "Four Quartets," in fact, gives the sense that the speaker is trying to find some way into our minds, striking at one place with a certain phrase, then repeating his point with different phrasing or a different image. In this case, he starts switching up his form to get at our hearts, though his message (the importance of humility and submission to higher principles) remains pretty much the same. Maybe Eliot's "submission" to traditional meter and rhyming might even suggest a certain humility on his own part.
You also find a strict rhyming scheme in part II of "Little Gidding" of AABBCCDD. This kind of rhyming is almost childishly simple for a man of Eliot's talent; but a big part of his message in this poem is humility, and he's no doubt showing it by abandoning his poetic complexity for grade-school forms of rhyme.