I first learned Josephine Begley’s Hornpipe many years ago from Terry Bingham’s album, on which he calls this tune “Mairtin O’Connor’s”. I only found out in February 2021 that this tune was in fact a composition of Frankie Gavin. It is the great flute and concertina player from Laois Tommy Fitzharris who provided me with this information, as he recorded the tune for an online concert.
Here’s a link to the online concert by Tommy Fitzharris with Brian Mooney, starting when they play “Josephine Begley’s Hornpipe” : https://youtu.be/HDMKAj7Zj3Q?t=524
Terry Bingham recorded “Mick Carr’s” before this tune.
FA|BABd ezdB|AFEF DEFG|ABcA dABF|E2ED E2FA|
BA (3Bcd e2dB|AFEF DEFG|ABcA dABF|E2ED E2FA||
|:BABd g2f2|edBc d2df|efed BA (3Bcd|edfd edBd|
g2 (3fgf efdB|AFEF DEFG|ABcA dABF|1E2ED E2FA:|2E2DF E4||