From Jeffrey Kacirk's Forgotten English calendar, we learn of an old word: "ratt-rime." Formerly, "ratt-rime" was verse used in charming rats. Later it came to mean doggerel.
("Rime" here is broader than in modern usage and included chants and spells and suchlike.)
"Rhime them to death, as they do Irish rats / In drumming tunes." --Ben Jonson
Now, rats are pursued with guns and poisons and cats aplenty. Perhaps the Irish practice of drumming out the rats had to do with music and merry making?
One wonders what was their explanation for the effectiveness of the chanting? Did they think the rats became enchanted? Or did they simply accept the premise that rats could be charmed to death as given fact?