A major scale on tenor banjo
Three sharps, and the key of a good share of the big reels. Two full octaves fit in first position, starting on the second fret of the low G string.
Hear the scale, played on the banjo voice
The notes
Every note above sits in first position on a GDAE-tuned tenor banjo: nothing higher than fret 6, and each note has one home. Learn the scale as a shape and your fingers know where every note of every A major tune lives before you have heard it.
The chords that go with it
This is the connection that makes session playing make sense. The backer's chords are built from the same 7 notes as the scale, so when the guitar holds A, anything you play from the A major scale fits. Melody players who seem to improvise freely are doing exactly this: decorating the tune with notes that never leave its own scale. Shapes for every chord here are on the tenor banjo chord page.
Tunes in A major
257 of the 2701 tunes on this site are recorded in A. A dozen to start on, in alphabetical order - every one has free GDAE tab, playback and the ABC source.
Questions about A major
A, B, C#, D, E, F#, G#, A. On a GDAE-tuned tenor banjo the whole scale sits in first position, between the open strings and fret 6.
A, D, E carry most tunes in A major, with F#m, E7 as passing and turnaround chords. Two or three chords are enough: Irish accompaniment stays out of the tune's way.
In an Irish session the chord follows the tune, not the other way round. If the tune is in A major, every note of the scale above fits over its chords, including A and D and E. That is how melody players improvise variations without reading anything: they stay inside the tune's own scale.
This site's collection has 257 tunes recorded in A out of 2701 in total, each with free GDAE tab. The corpus is O'Neill's 1903 and 1907 collections plus Kerr's Merry Melodies, so the balance reflects the tradition as it was written down.