Note: This is too much of a story to be meta, but not quite enough of a story to be a story, so . . . it is what it is. I hope you like it.
Once upon a time—a time when witches wore corsets and bustles under their robes, and tall pointed hats weren't just for school uniforms, and the Hogwarts Express hadn't been built yet, because steam trains were still suspiciously Muggle-ish affairs—there lived a boy named Claudius Chant. For as long as anyone could remember, all the women in Claudius' family had been witches, and all the men had been wizards, but Claudius wasn't. His sister told him so, when he tried to go for a ride on her broom and it turned to lifeless wood in his hand. "Squib!" she called him.
If you've heard stories like this before, you may think that eventually Claudius would discover that he could do magic, better and more special magic than anyone else. Claudius' parents certainly thought so. They took him to doctors as far away as Switzerland and Morocco. They hired tutors whose patented educational methods included making their pupils stand on their heads, or subsist on a diet of whole grains and raw vegetables. They even consulted Dr. Pawson, the brilliant young chair of Metamagical Studies at Cambridge. "Face it," said Dr. Pawson, "the boy's a squib."
Claudius' parents could not face it. Claudius was their only son, and it was inconceivable that one of the oldest pureblood families in England could come to such an ignoble end. But Claudius believed it. He stopped dreaming about being able to levitate and transfigure and brew potions, and started to dream of a world without magic, where he could make a name for himself with his wits and determination, and where no one would ever call him squib. When he was fourteen, he joined the Muggle navy as a ship's boy, and never returned to the wizarding world.
In time, Claudius got married and had three sons. Carl and Constantine could no more cast spells than their father, but the family talent reappeared in Cornelius, the youngest. In a way, Cornelius was the son most like his father. When he got his letter from Hogwarts, he too left his family behind and never looked back.
At Hogwarts, Cornelius met—and had a brief tempestuous romance with—beautiful, wealthy, Muggleborn Ophelia Argent. But Ophelia left him to elope with his best friend, Algol Black. Cornelius set out on a tour of the world, hoping to mend his broken heart in unfamiliar places where nothing could remind him of Ophelia or Algol.
Cornelius was visiting Japan when it entered World War Two. Murakami Miu, the headmistress of a local magic school, saved him from being detained with the Muggle foreigners caught in Japan when the hostilities started, and after the war he stayed on, teaching Divination and English. Generations of Japanese witches and wizards fondly remember Chant-sensei, his atrocious accent, his terrible luck with money, and the way his predictions always came out nearly correct.
The Argent-Black marriage caused a scandal in English wizarding society, and the divorce, less than a year later, caused a bigger one. Ophelia went to Paris to live with her brother, where the two of them became minor heroes in the war against Grindelwald, best known for their success in smuggling weapons to the Resistance.
Neither Cornelius nor Ophelia ever had children.
Meanwhile, the two elder Chant sons married quiet, respectable Muggle women and lived quiet, respectable Muggle lives. It caused no scandal in society, but only in the family, when Carl's daughter Caroline and Constantine's son Phillip decided to get married against everyone's advice.
Caroline and Philip had one daughter, Janet, whose story—or part of it—you may know.
The summer after Janet turned thirteen, a letter arrived at Caroline and Philip's house. It was delivered by owl, and addressed—to the consternation of the girl who had nearly got used to thinking of herself as Janet—to Romillia Chant. In light of her peculiar circumstances, it said, though contrary to general school policy, Romillia had been accepted as a third-year student at Hogwarts, starting in the fall term.