A Tom Lehrer classic. It’s called “The Irish Ballad.” And after the first line in the source you cited, place “rickety etc.” for that full Lehrer flavor.
Not unless it was a song other than this one, which (as the linked page, which includes sound, says) was a hit in 1939. Performing the tune was an orchestra headed by a man named Kay Kyser.
If it counts for anything, I know for a fact that my parents used a tape of Marine Corps running cadences to help put my infant/toddler sister to sleep. (It worked, BTW.)
I wannabe a Drill Instructor, I wanna cut off all of my hair,
I wannabe a Drill Instructor, I wanna earn that smokie bear!
I don’t recall my parents ever singing with me other than formal settings.
Heh. My dad used to sing that to me, but the end (his version, anyway) was:
And he died with a toothpick in his heel.
My mom would sing:
Oh Senor Don Gato was a cat
On a hiiiiigh red roof Don Gato sat
He was there to read a letter
Meow Meow Meow
Where the reading light was better
Meow Meow Meow
Twas a love note for Don Gato
…
I remember a bit more, but not the entire song. I sing it to my nephew these days, making up words as I go along.
Boy, I haven’t thought about this in nearly fifty years, but my mother used to sing Go Tell Aunt Rhodie to me.
According to this site, “This is a very popular children’s song in spite of its rather dark lyrics.” Good to know - looking at the lyrics, one would think my mother was some kind of sadist!
My mom used to sing this one to me:
*Alice, where art thou going?
Upstairs to take a bath.
Alice, you’re like a toothpick.
Your head is like a tack.
Alice stepped in the bathtub.
She slipped on the soooo-ooo-oooap.
Oh my goodnes, oh my soul!
There goes Alice down the hole!
Alice! Where art thou going?*
Nope, my Dad used to sing it to me. He also used to sing a song about a racehorse:
*Old Stewball was a racehorse
and I wish he were mine.
He never drank water,
he always drank wine
His bridle was silver
and his mane it was gold
and the worth of his saddle
has never been told…*
There was more, something about a fairground and betting, but I don’t remember it.
I met her on the mountain
There I took her life
Met her on the mountain
Stabbed her with my knife
This song would always put my kids to sleep when I sang it. I think it’s the soft repetitious melody. The lyrics are certainly dark enough.
Two other favorites I would sing to my kids were:
I am a roving gambler
I’ve gambled all around
Wherever I meet with a deck of cards
I lay my money down
Lay my money down, lay my money down
and
Frogg went a-courtin’ and he did go, un-huh
Frogg went a-courtin’ and he did go, un-huh
Frogg went a-courtin’ and he did go
To the Coconut Grove for the midnight show, un-huh un-huh un-huh
Thanks, Queen Tonya --I do remember more of the verses now–I never learned the bit about jail–but I remember the arms around me bit.
There must be a reason why so many of these are sad or mournful. Perhaps it’s the rythym? Or maybe, like fairy tales, kids are attracted to dark things–it’s grown ups who insist on sweetness and light. Fascinating.