Like a lot of poets, and a lot of poems, Yeats doesn't restrict himself to a single meter in "The Wild Swans at Coole" (now what would be the fun in that?). In fact, he uses at least three different kinds of rhythm to deliver his lines. Let's explore them, shall we?
First, there's iambic pentameter, the most well-known poetic meter. If you've read anything by Shakespeare, you've probably read iambic pentameter. So, how does it work? Well, it's basically a meter that contains five ("pent-" is Greek for five) iambs (which is a unit of rhythm that contains an unstressed syllable followed by a stressed syllable, sounding like this: da DUM). Let's look at line 17 to see how this works in the poem:
The bell-beat of their wings above my head,
Rhythmically, this sounds like da DUM da DUM da DUM da DUM da DUM. And, that, Shmoopers, is the beat of a nice, neat iambic pentameter line.
What do we do, however, with a line like this?
Mirrors a still sky (3)
There are five syllables in this line, so there's no easy way to scan it. It is, essentially, however, a line of trimeter (meaning three feet, or units of rhythm). The line contains a trochee (which is a syllable pair where the first is stressed, the second unstressed), then an iamb, and then—for the heck of it—one more stressed syllable. To put that in terms of conventional poetry: it's just funky!
For an example of yet a third rhythmic pattern, let's look at line 27:
Among what rushes will they build,
This is an example of iambic tetrameter (which is a line that contains four iambs). You should hear the same beat as an iambic pentameter line, only it's one da DUM short.
As you can see, the meter of the poem varies a lot. The question is, "Why?" Was Yeats just a bad poet who couldn't keep a beat? Um… no. Was he getting paid by the rhythmic pattern? Um… double-no. Nope, we think that this choppy metrical form is actually quite appropriate for a poem that describes a speaker's weariness at aging. Much like the rhythm itself, the speaker's thoughts are uneven and unsustained. He's tired, weary, and we think that this grab bag of rhythms is a great way to add to the halting, uncertain nature of the speaker's persona in the poem. If he was bouncing along lock step in iambic pentameter, it would tend to undercut the disturbance that he's communicating to us, right?
Despite the metrical free-for-all, there is still quite a bit of form to the poem. It's divided into five stanza, and each stanza contains six lines (nice and neat right?). Furthermore, each stanza has the following rhyme scheme: ABCBDD, where the matching letters indicate a rhymed pair. So, the last word of line 2 (B) would rhyme with the last word of line 4 (also B). This means that, in each stanza, the second and fourth lines rhyme, and the final two lines rhyme. (The first and third lines have no rhyming partner. Sorry, guys.)
As well, the last two lines of each stanza also rhyme (DD). This pairing is known as a couplet. Now, those last two dudes are significant because, without them, these stanzas would be following a pretty classic rhyme scheme associated with the ballad. As it is, though, Yeats is putting his own spin on things in a formal sense. He tacks on a rhyming couplet and creates a new kind of form, one that would have been in keeping with his artistic philosophy (for more on that, check out the "Calling Card" section).
The upshot of this form is that our ears are still treated to a regular sense of rhyme. But why so much rhyming in such a rhythmically choppy poem? Well, again, we have to consider what's going on the in poem. The speaker is appreciating the beauty of his surroundings, even as he's depressed by his own aging state. Still, that doesn't diminish the majesty of the swans or nature in general. So, we have this disturbed rhythmic flow that's nevertheless surrounded by a pleasing rhyme structure. In this way, the rhyme scheme imitates the symmetrical beauty of nature, even if—deep down (and on a rhythmic level)—the speaker is bummed out about his own situation.