"Farm Implements and Rutabagas in a Landscape" is a sestina with no regular rhythm. If you take away one thing from this poem, it's that you should never give the Sea Hag keys to your apartment. If you take away two things, it's that you should never give the Sea Hag keys to your apartment and that the poem is a sestina.
The key to the sestina is the number six. The prefix "sest-" means "six," just like "sext-" as in sextet. The poem has six words that must be repeated at the end of the line in each stanza, except for the seventh stanza, which has three lines instead of six. Thus, it always has 39 lines. In this poem, the six words are: thunder, apartment, country, pleasant, scratched, spinach. The chart below assigns each of these words a "number" and then shows the order in which they appear at the end of successive lines in each stanza. In the last stanza, the two words enclosed in each set of parentheses appear together in one line.
Stanza I. ABCDEF
Stanza II. FAEBDC
Stanza III. CFDABE
Stanza IV. ECBFAD
Stanza V. DEACFB
Stanza VI. BDFECA
Stanza VII. (ECA) or (ACE)
There's no reason you need to look at the specific order of words except maybe to marvel at how complicated it is and then say, "Huh. Neat!" Notice that the last word of the last line of each six-line stanza is the same as the last word of the first line of each stanza. The secret of a good sestina is for the poet to use these words over and over again while drawing as little attention as possible to the structure. "Farm Implements and Rutabagas in a Landscape" pulls off this feat brilliantly, particularly as some of the words are so silly, like "scratched" and "spinach." Unless you were really paying attention the first time you read the poem, you might not have caught that these words were being repeated over and over again. That's really hard to do.
The first poet we know of to use the sestina was a 12th century French man named Arnaut Daniel. He belonged to a school of poetry that started around Southern France and spread through Europe during the late Middle Ages. The troubadours wrote complex songs about lords and ladies and all that good medieval stuff, and they competed to see who could write the most daring poems.
But, honestly, it doesn't matter how complicated the form is and how well the poet pulls it off if the poem is no good or boring to read. We don't love this poem because it's a sestina; we love it because it's hilarious, original, and totally fun to read aloud.
The poem has no regular rhythm, and Ashbery writes in prose-like sentences that flow right over the line breaks into the next line, which is a technique called enjambment. The sentence connecting the fourth and fifth stanzas is an example of enjambment:
At this own astonished becoming, rupturing the pleasant
Arpeggio of our years. (24-25)
Ashbery's lines are also pretty long, which helps to mask the sestina form even more.