[It appears that I typed in my addendum in the second message, but forgot to paste my file text. Now if I start to block this from the begining for copying we should be okay.]

Here's the tune from SMM. Wm. Stenhouse said Burns sent the tune with his song for SMM. John Glen, 'Early Scottish Melodies', said the tune was not known earlier (than 1792), and it might be by 'Major Logan, or some Ayreshire worthy.' He added that some prefer this tune to Humes.

X:1
T:Afton Water. (Written for this work by Robert Burns)
S:Scots Musical Museum, #386
Q:1/4=120
L:1/4
M:3/4
K:F
C|FA(G/F/)|(G/A/)B(A/G/)|FAG/F/|{F}E2C|FAG/F/|G/A/c(f/d/)|\
cB/A/ G/A/|F2||(c/d/)|e(f/e/) (d/c/)|cdf|eAG/F/|(FE)C|\
FAG//F/|(G/A/)cf/d/|cB/A/ G/A/|F2|]

PS: See the Scottish tune index on my website for a tune called "Pentland Hills". So far as I know there's no song for it.