The song also appeared in the second volume of George Thomson's "Select Collection ...." , published in 1801 after Burn's Death and was listed as "unknown" although Thomas knew exactly who wrote it (see Jim Carroll's previous post). Again it is to a different melody to today's tune which was set to Burns' lyrics after his death. The tune "Low down in the Broom" was known to Burns but not used by him for "My Love .."
I have studied Burns and Scotish music of this period and have never come across the line mentioned by McGrath of Harlow and even the word "instrument" doesn't really ring true to my ears.
I think the beauty and truth of Burns' line lies in " sweetly played in TUNE".