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.

I am with you.

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?

Your comment reminds me that I wanted to elaborate on what I am imagining re: how "cheerly" and "sally brown oh ho" possibly refer to more or less the same chant.

My proposal is that instead of connecting the "sally brown" in these references to later "Sally Brown" chanties (i.e. about the "bright mulatto," etc.), it may just be part of "Cheer'ly." The name of "Sally Brown" may have functioned just like "Sally Racket," "Polly Riddle," etc. Compare to Hugill's "Oh Sally Racket, hi o! -- cheerly man!"

The found phrases "Sally Brown, oh, ho," and "Oh Sally Brown, Sally Brown, oh!" are, arguably, appreciably distinct from the sort of "way hey roll and go" or "spend my money on Sally Brown" that we'd expect to find in the Sally Brown chantey form.

However, in time, Marryat's windlass song "Oh! Sally Brown," which has the "bright mulatto" theme and which has a similarly primitive and yet wholly distinct form from Cheer'ly kind of messes up that theory!