There are a few tunes - see Bronson.

One that Bronson didn't include was this parody:

  X:1
  T:The Corbie and the Crow
  S:Edinburgh University Library Mic.M.605 (William Macmath MSS)
  Z:Jack Campin, Valentines Day 2000
  M:C
  L:1/4
  K:F
  C|A>G Ac|A>G Ac|d>c cA |c2 z||
  A|G>F GA|G>F GA|cf  A>G|F3  |]

The corbie wi' his roupie throat ca'd frae the leafless tree,
"Come ow'r the loch! Come ow'r the loch! Come ow'r the loch tae me!"

The crow pit up her sooty heid, looked frae her nest whaur she lay,
And gied a fluff wi her rusty wings, and cried "Whaur tae, whaur tae?"

"To pyke a deid man lying there, ahint yon mickle stane".
"Is he fat, is he fat, is he fat, is he fat? If no we'll let him alane".

"He's frae merry England come to steal oor sheep and kill oor deer".
"I'll come, I'll come, for an Englishman is aye the best o' cheer".

"We'll breakfast on his bonnie breest and on his back we'll dine,
For the lave hae gane to their countrie and ne'er come back sin-syne".