Steve, that's both old and old. As a kid, kids considered it cheap. But it's not circular, it's diminishing. There's also cumulative (counting) and infinate.

Still.

I've been collecting what I call Circular songs for some years. They're interesting to me because there's also a religious element to them. They often depict the circle of life as opposed to the cycle of life. That is (eg) reincarnation as opposed to the cycle of birth, etc, etc, death over generations. In Judaism, a hierarchical element is more common - starting at the lowest and working upwards towards God (of course) as in Chadgadyo. The well-suggested term, ourobarian is just Circular, of course but derives from "tail-eating." That is, the Greek for Milkey Way as a dragon in a circle eating its tail. A nice circle!

I got the notion on being in UK and first hearing "The Tree in the Hole" in it's English form, actually called "The Everlasting Circle." The difference being that the US dropped the slightly sexy verses that complete the Circle.

It's clearly a pagan folk/religious concept. I don't mean a hymn or anything, just a folk song in tune with accepted precepts but contrary to my own Jewish ones.



Here's a few others I thought of and the 1993 r.m.f and later Ballad-L discussions added:
(some are more short dialogues/recitations than songs)

Where have all the flowers gone?
Hole in the Bucket
and Les Barker's parody, I Have a Bodhran
Found a Peanut
The Bear Went Over the Mountain
Jonathan (Antonio/Wally), tell us a story
May name iss Yon Yonsen
Why is the Fourth of July
On Ilkley Moor Baht Hat (Seems Joe Hickerson wrote the last two
   verses that close the circle.)
Michael Finnigan
Around the corner, And under the tree
John Jacob Jingleheimer Smith
You remind me of a man (a fav of mine - Not trad of course, Cary Grant
   in the movie "The Bachelor and the Bobby Soxer" to teen aged
   Shirley Temple (her older sister was Myrna Loy?),
That's life! / What's life?
How Fights Start in Saloons, by Rudy Valle - "'E was the greatest man
   that England ever knew"