There is something a bit odd about this tune--though it is seems to be in a Dorian mode, the melody for the most part, moves in chord arpeggios, which is kind of unusual for modal music(chords and harmonies were not really used until modes were replaced by major/minor keys)--The melody notes start with an Em chord--b-e-g-b,then D major A-D-F#-A), before it finally moves scalewise B-C#-D-E", with "Early in the" being an inverted D6 chord leading to the final E--Unusual element for a tune that is claimed to be (in the link above) an medieval Irish Air--