In its strictest sense, traditional music is linear, purely melodic and generally not harmonised. Most of the dance music (jigs, reels, hornpipes, slides, etc.) is in simple binary form, each part being a repeated 8-bar phrase (AABB).
This framework allows for endless variations of rhythm, phrasing, and melody. It is really up to the individual. Dynamic variation and the use of vibrato are rare. Slower unmetered airs in general derive from song melodies.
The Connaught Heifers, a two-part reel in binary form
Colonel Frazier, here, a four-part reel
Paddie Glackin & Robbie Hannan
Glackin on fiddle and Hannan on uilleann pipes perform The Glen Road to Carrick, a two part reel in binary form