To me, Falconer's "sort of song" suggests more than a sing-out, less than a fully developed melody.

Think of vendors' street cries: "sort of" songs.

Something with three or four distinguishable notes perhaps. "Little Sally Rackett" may be a little more primitive melodically than the related "Cheer'ly Man." Maybe an abbreviated "LSR" with a "Cheer-i-lee Man" chorus?

Sheer conjecture is fun even when groundless.