The Morgan Library :
"O Can Ye Labor Lea, Young Man"
pdf of Johnson & Co., 1792
& mp3
http://www.themorgan.org/collection/Auld-Lang-Syne/6
(mudcat TUNE FILE: AULDLANG @displaysong.cfm?songid=374)

&
The Morgan Library :
"Auld Lang Syne"
pdf of Johnson & Co., 1796
& mp3
http://www.themorgan.org/collection/Auld-Lang-Syne/7
(mudcat TUNE FILE: AULDLNG2 @displaysong.cfm?songid=374)


The Burns tune sung in the programme at 3:30 & 13:20 are surely the same
but did they mean as "the third tune" the Tannahill version, which they didn't play?
It sounds only slightly different to me. Like they're turning a harmony for Burns' original tune into their melody?
Someone with a better ear might say.

this is an easier Tannahill Youtube file
https://www.youtube.com/watch?v=7RjzQTP7eFU