Just a note on the tune as it is used in English Traditional music...
There are several collected versions associated with Cotswold Morris
dancing, mistly in the major key but at least one in the minor. Cotswold
Morris is the variant you are most likely to see with dances wearing bells
on the ankles, waving hankies or clashing sticks and was actually danced
over a wide area north of the Thames from Gloucestershire to Hertfordshire.
The tune is sometimes known as Nelson's Praise and is associated with a solo
jig (think of a manic solo set dance with hand movements). Many of the tunes
used in this form of dance, which reached it's apogee in the mid-C19 before
dying down and being revived, were taken from ballad operas or other popular
songs of the day and I suspect that this is why this tune was so popular.
Shield's Arethusa has been cited and no doubt someone conciously selected
this air for the song Nelson's Praise thus increasing it's popularity. But
it was (and still is) more often called Princess Royal so I suspect it was
either well known in this area before Nelson' Praise was written or was
known from the many Irish navigators building the canals and then the
railways through the area.
The tune as played for Morris dancing is still recognisably the same as the
tune attributed to Carolan.