"Corbie" means "crow" in Scots, but "crow" usually means "rook".

It's "three crows sat upon a wall", completely different song. "Three Ravens" is the one that's the same family as "Twa Corbies".

An entirely unrelated tune:

  X:362
  T:Da Corbie an' da Craw
  B:Ringing Strings, Tom Anderson (Lerwick 1983)
  Z:Nigel Gatherer
  L:1/4
  M:4/4
  K:D
  B|A2FD E2=c2|EFGE =CDEC|DDFD   E2 =c2|EFGE   [G,3D3]:|
  F|AddA d2 df|efec  d2FA|A,dd>c d2  eg|f>de>c  d2  AF |
    Addc d2 df|efec  d2FA|dB=cA  B2  Gc|E>FG>E [G,3D3]|]

I just remembered the author of that parody - the Rev. Alexander "Jupiter" Carlyle of Inveresk, who was something like the chaplain of the Scottish Enlightenment.