To define the structural aspect of "Get Up and Bar the Door" and how it relates to the ballad's tone, it is important to define what a ballad is.
A ballad is a form of verse, often a narrative set to music.
The form appeared during the medieval period (1066-1485) in England and Ireland. Most were tragic in nature (e.g., "Bonny Barbara Allan"), with themes such as:
...disappointed love, jealousy, revenge, sudden disaster...
There were some exceptions—in ballads about "deeds of adventure or daring;" still others, like "Get Up and Bar the Door," reflected the humorous subject matter "of everyday life of the common folk" that in this case tells the timeless tale of the battle of the sexes—husband vs. wife—as to who gets "the last word." This is sometimes referred to as "domestic humor."
In general, ballads are considered "popular, traditional, or folk," and these forms of verse were passed down for many years via the oral tradition, or "word-of-mouth." It was not until the 18th Century that collections of these ballads were written down, with many variations of the same ballads depending upon where (geographically) they were collected.
The ballad probably derives its name from medieval French dance songs or "ballares"...
Interestingly, "ballare" means "to dance or to shake," which may come from its rhythm or that it may have been sung. It is written generally in "ballad stanza." A "stanza" is also known as a quatrain (which is a four-line stanza—like "poetic paragraphs"). Their rhythm or meter is generally "iambic" (with stressed and unstressed syllables which alternate). In terms of the number of syllables per line, they followed the "ballad meter:"
...tetrameter (eight syllables) and iambic trimeter (six syllables)
In other words, one line had eight syllables, and the next line consisted of six syllables. One syllable would be stressed; the next, not. The rhyme occurs at the end of the second and fourth line of each stanza.
In "Get Up and Bar the Door," the structure is made up of a straightforward narrative of a event—told in a "dramatic fashion." Little attention is given to characterization or description, or introductory information. The story develops through dialogue. Hints are given— which the audience uses to "read between the lines"—rather than the delivery of direct details.
In the beginning, we learn that it is near a holiday (Martinmas). We can infer then, that this is a busy time requiring a great deal of preparation. It occurs in the fall, so we are not surprised with:
The wind sae cauld blew south and north,
And blew into the floor...
However, the ballad completely surrounds the husband's demand that the "goodwife"...
“Gae out and bar the door.”
This line introduces not only the title of the ballad, but the conflict of the tale as well. In that she is very busy, the wife believes her husband is fit enough to fulfill this task himself—and round and about they go, each refusing to back down and close the door.
The structure of this ballad, specifically the rhythm—which is lilting, like a swaying back and forth—supports the movement of the spouses as the power struggle between them (tone) also moves back and forth (under comic circumstances), until the husband speaks, the woman is vindicated, and her man must get up and close the door—based on their "agreement."
Adventures in English Literature. Orlando: Harcourt Brace Jovanovich, 1985.