in Irish music, "harp tune of a sportive and animated character" [OED], 1790, of unknown origin, evidently not a native Irish word; some suggest ultimate derivation from Latin plangere "to strike, beat" (see plague (n.)). See also [Katrin Thier, "Of Picts and Penguins -- Celtic Languages in the New Edition of the OED," in "The Celtic Languages in Contact," 2007.
Examples from the Web for planxty
She was in her mood of Planxty Kelly and Garryowen all the way.
She rose on the morning of her marriage day with his favourite Planxty Kelly at her lips, a natural bubble of the notes.
So, they up and axed him, in the civilest way they could, if he'd favor them with a planxty on his pipes.Bits of Blarney
R. Shelton Mackenzie