The majority of Irish session tunes use the notes found in either the D-major or G-major scale, even when the tonal center is E, A or B.
The note D is usually going to be either the 1st note of the D scale or the 5th note of the G scale. It’s not unusual for a tune to have D as its tonal center but be using the G scale (i.e. Tatter Jack Walsh, Rakish Paddy, Star Above the Garter). More on this later.
The note E is either the 2nd note of the D scale or the 6th of the G scale. Without going too far down the path of chords, which is a loose concept in Irish music, those two chord E-minor/D-major tunes like Cooley’s Reel and Swallowtail Jig can be thought of as using the II chord and the I chord of the D-scale, with the II chord (E-minor) being the “home” chord and the I chord (D-major) being the “away” chord. That’s better than thinking of the E-minor chord as the I chord and the D-major chord as some kind of flattened VII chord.
The note F# is either the 3rd note of the D scale or the 7th note of the G scale.
The note G is either the 4th note of the D scale or the 1st note of the G scale.
The note A is either the 5th note of the D scale or the 2nd note of the G scale. Those “two chord” A-minor/G-major tunes like Mist Covered Mountain and Congress Reel are using G-scale notes (A-Dorian), just like how those E-minor/D-major tunes are using D-scale notes (E-Dorian).
The note B is either the 6th note of the D scale or the 3rd note of the G scale. You occasionally have tunes like Musical Priest or Connaughtman’s Rambles that have B as the tonal center for portions of the melody, and/or modulate from B to D. That’s usually an indication that B is acting as the 6th note of the D scale.
The note C does not reside in the D scale, but it is the 4th note of the G scale. When you encounter a tune like Tatter Jack Walsh which resolves to D but has that prominent C-chord, you’re actually working within the G-scale. The D-major chord in Tatter Jack Walsh, even though it is the “home” chord, is acting as a V chord, while the C-major chord, even though it can be seen as the “away” chord, is functioning as a IV chord. These are characteristics of D-mixolydian, which is simply the G-major scale starting on its 5th note.
The note C# is the 7th note of the D scale. It does not exist in the G-major scale, proper. However, C# does seem to be one of those notes that can sometimes be used in place of a C-natural note in a modal tune at the discretion of the melody player. The presence of a C# in a tune like The High Reel is an indication that it is in A-mixolydian - the same notes as the D scale – meaning that the C# is serving as the 7th note of the D scale.
This is kind of a hard concept to describe, but it gets clearer the more you think about it. Basically, most tunes use either the D scale (resolving to either the 1st note D, the 2nd note E, the 5th note A or the 6th note B) or the G scale (resolving to either the 1st note G, the 2nd note A, the 5th note D or the 6th note E). It’s also worth noting that the tonal centers D, E and A show up in both the D and G scales, and that both scales use all the same notes except for C or C#.