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Thank you Jno & Tigger, it is not Kellermann's Anthem but you set me on the track to find the correct answer. That was adapted for Dirty Dancing from:
"Annie Lisle" is an 1857 ballad by Boston, Massachusetts songwriter H. S. Thompson, first published by Moulton & Clark of Newburyport, Massachusetts, and later by Oliver Ditson & Co.[1] It is about the death of a young maiden, by what some have speculated to be tuberculosis, although the lyric does not explicitly mention tuberculosis, or "consumption" as it was called then. The song might have slipped into obscurity had the tune not been adopted by countless colleges, universities, and high schools worldwide as their respective alma mater songs"
I knew it wasn't just from DD because I have heard it in other films (most notably 'The Last Picture Show' which was on today, probably because of the death of Chloris Leachman.