The air, "Miss Admiral Gordon's Strathspey", was the composition of William Marshall, a fiddle-player himself and an employee of the Duke of Gordon (I think he was the Butler). I think Burns met him at Castle Gordon during his Highland Tour of 1787; he certainly called him "the first composer of strathspeys of the age", i.e., the "best" (notwithstanding the fame of his older contemporary, Niel Gow). "Strathspey", incidentally, is the valley of the River Spey; there's a kind of dance-tune called a "Strathspey" which is in Reel Time but has a much more irregular rhythm, making use of cut and dotted quavers (i.e. the familiar "Scots Snap"). Most settings of the song in question have been made more regular, in keeping with European classical norms; the version in SMM is (obviously) as Burns knew the air, and the note-values for which he composed the words. The story goes that the air - which is very similar to "The Low Lands of Holland" - was Jean Armour's favourite, so Burns put the words given by wolfgang above to this "slow strathspey". The words just recently posted by Jim Dixon are by a clergyman (the name Gilfillan comes to mind?).   Incidentally, at the time of composing the song, Burns was building the house at Ellisland in Dumfriesshire where and Jean would live for a few years, but she was still living in Ayrshire (to the North-West). Finally, in the first measure, the word "row" should be pronounced to rhyme with "how", and the word "grow" pronounced not as in English English but as in Scots English, i.e., to rhyme with "how" again. Sometimes, these words are spelt with a final "e", "rowe" and "growe".