Took a while for me to absorb it, but there are two tunes: "Sherburne," by Daniel Read, and "Sherborne," a tune from Mendelssohn-Bartholdy (haven't found the source composition).

Both are used for "While (Whilst) Shepherds...," along with "Christmas" from "Siroe" by Handel, a tune arranged by Methfessel (Academy Song Book, Levermore), "Seraph" by Fink, a rearrangement of the Fink version by Sir Arthur Sullivan,- and I am sure, others.

Sorry for my confusion of two different tunes.

"Sherborne" may be heard at Cyberhymnal, attached to the Saxton hymn, "See the Gold Upon the Hills." Sherborne midi


Sorry for the confusion