My post was not clear, for which I apologise.

In Christopher Stone, 1906, "Sea Songs and Ballads," no. VIII, is the song "Cordial Advice," with the note "To the Tune of, 'I'll no more to Greenland sail,' &c." Thanks to Barry Finn for posting the song from Palmer, which is identical except for the odd spelling-grammatical difference.

I took the note of tune in Stone to mean that there was a previous song and tune, and that is what I was looking for.

Admiral Sir Cyprian Bridge, in an Appendix note, refers to the Bodleian Ballad referenced above by Malcolm Douglas, and says,

"This most likely refers to the practice of paying seamen by the lunar month, there being not much difference in the number of days (148) in six lunar months and that (151) in five calendar months, January to May inclusive. Till a very late date the crews of short voyage steamers were victualed for a lunar month only, though serving for a full calendar month. The song is founded on a genuine sailor's song; and seems to be but little altered."

This comment also led me to believe that there was a prior song or version. I saw a google entry that referred to Palmer's book, and seemed to indicate that it was "I'll No More ...."

I gather from Malcolm's note that if there was a previous song, as stated by Admiral Bridge, it may be lost as well as the tune.