From the Wikipedia :- "Deck the Halls" (original English title: "Deck the Hall") is a traditional Yuletide and New Years' carol. The "fa-la-la" refrains were probably originally played on the harp. The tune is Welsh dating back to the sixteenth century, and belongs to a winter carol, Nos Galan.
The tune is that of an old Welsh air, first found in a musical manuscript by Welsh harpist John Parry Ddall (c. 17101782), but undoubtedly much older than that. The composition is still popular as a dance tune in Wales, and was published in the 1784 and 1794 editions of the harpist Edward Jones's Musical and Poetical Relics of the Welsh Bards. Poet John Ceiriog Hughes wrote the first published lyrics for the piece in Welsh, titling it "Nos Galan" ("New Year's Eve"). A middle verse was later added by folk singers. In the eighteenth century the tune spread widely, with Mozart using it in a piano and violin concerto and, later, Haydn in the song "New Year's Night.
Originally, carols were dances and not songs. The accompanying tune would have been used as a setting for any verses of appropriate metre. Singers would compete with each other, verse for verse known as canu penillion dull y De ("singing verses in the southern style"). The church actively opposed these folk dances. Consequently, tunes originally used to accompany carols became separated from the original dances, but were still referred to as "carols". The popular English lyrics for this carol are not a translation from the Welsh."
The above version ( together with many other tracks ) is performed by Dr J.Marshall Bevil on the Welsh traditional instrument - the crwth. Linked below is a three part interview with Dr Bevil about the instrument:-