Chad Gadya tune

Most Jews are familiar with the music for chad gadya, a song sung at the end of the Passover seder.  After having seen the classic movie Moby Dick, I now wonder if the tune was of very recent origin.  The scene depicts 1841.  The song is a pub song, sung by the whalers about a courtesan in Amsterdam.  The words they sing are:

In Amsterdam, there lived a maid
Mark well what I do say
In Amsterdam, there lived a maid
who was the mistress of her trade
I'll go no more a-roving with you fair maid

and OMG, this is from about 7 minutes into the iconic film.

http://www.youtube.com/watch?v=iuOGkY2dNOg

That tune sounds awfully familiar and I did not hang around pubs much in 1841.