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LUKE DILLON. Irish, Planxty (3/4 time). D Major. Standard tuning (fiddle). AB. Composed by Turlough O'Carolan  (1670-1738). The air was first published in Dublin by John & William Neale, perhaps the foremost music publishers in the city at the time. It appeared in thie c. 1726 volume entitled 'A Collection of the Most Celebrated Irish Tunes proper for the violin, German flute and hautboy (p. 20). John Mullholland, a later publisher who lived in Belfast, printed an almost identical version in his 1810 collection. However, both versions, maintains O'Sullivan (1958) are misnoted in places--primarily in the opening measures of each strain and in the ending cadence.
O'Sullivan belives that the subject of the title is Luke Dillon of Clonbrock, near Mount Bellew, County Galway. He married Honora, daughter of Sir John Burke (4th Baronet of Glinsk), and sister of Sir Festus Burke, the subject of another of Carolan's airs.
Source for notated version: John & William Neale's A Collection of the Most Celebrated Irish Tunes proper for the violin, German flute and hautboy (Dublin, c. 1724) [O'Sullivan].
Printed sources: Complete Collection of Carolan's Irish Tunes, 1985; No. 39, p. 45. John & William Neal (A Collection of the Most Celebrated Irish Tunes), 1724; p. 20. O'Sullivan (Carolan: The Life, Times and Music of an Irish Harper), 1958; p. 123.
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Hear a guitar version played by Mike Lydiat on youtube 
X:1 T:Luke Dillon M:3/4 L:1/8 N:this is O'Sullivan's correction to the first measures K:D D2F2A2|ABAFED|F2A2 Bc|d4