Just a couple of notes while you're waiting for real help:

The full editor/title, etc. is listed as: "Theodoric Petri, ed., Piae Cantiones Ecclesiasticæ Et Scholasticae Et Scholasticae Vetervm Episcoporum. (Gyphisuualdiæ: Augustinum Ferberum, 1582)." https://www.hymnsandcarolsofchristmas.com/Hymns_and_Carols/NonEnglish/gaudete_gaudete_christus_est_nat.htm


Google translate (lamentably awkward for translations, but available...)says Piae means "Patriotic" and I assume Cantiones are "songs". Ecclesiasticæ would be Ecclesiasticals. Vetervm = veterum = "old". Episcoporum translates as "Bishops". Scholastiæ appears to mean "scholarly" or scholars?

It would appear just the full title helps with some of your queries, but I'm sure some of our Latin scholars will appear soon to set us straight. ;)