Note that these names are modern ones for tune types. They don't necessarily work on old tunes. "The Reel of Harden", c 1755, is in 9/8 time. "Carrickfregus - An Irish Reel" is "Haste to the wedding", a double jig (6/8). In R. Bride's 24 Country Dances for 1770, "The Wild Irishman (Nora Keeshta)", has timing altered slightly in the first strain and eighth notes grouped as triplets in the second, so it is in 2/4 time rather the than normal 6/8. The well-known "The Dusty Miller" has been published in 3/2, 3/4, 6/4, and 9/8 time.
[A crude definition is: strathspey = slow reel]