Burns contributed largely to the work, and Stephen Clarke prepared the arrangements of most of the airs. ["The volumes of the Musical museum, as originally published, were 'Humbly dedicated to the Catch Club, instituted at Edinburgh June 1771.' On the completion of the sixth and last volume, in 1803, Johnson substituted a new set of title-pages, dedicating the work 'To the Society of Antiquaries of Scotland.'"--Laing's pref., to 1839 ed., v. 1, p. ii, foot-note]. (National Library of Scotland)
"The first volume was published in 1787 and included three songs by Burns. He contributed 40 songs to volume 2, and would end up responsible for about a third of the 600 songs in the whole collection as well as making a considerable editorial contribution. The final volume was published in 1803.
As well as collecting old songs, Burns wrote new words to old tunes, and many of the songs now attributed to Burns have older roots. Songs in the collection include Auld Lang Syne, Lord Ronald, my Son (better known as Lord Randal) and My love is like a Red, Red Rose. Burns' songs include The Battle of Sherramuir, Scots Wha Hae, Green Grow the Rashes, Flow Gently Sweet Afton, Ye Banks and Braes of Bonnie Doon, Ae Fond Kiss, The Winter it is Past, Comin' Thro the Rye and John Anderson, My Jo.
The collection became popular internationally, and songs and tunes were arranged by composers such as Joseph Haydn and Ludwig van Beethoven." (Wikipedia)