A Melodic Addition

Folio 230r contains a curious musical addition that has not yet been identified. This folio relates part of the mass for the Finding of the Cross (May 3). The beginning of the alleluia verse "Dulce lignum dulces" has been covered by a slip of parchment bearing a textless melody that is notated on a four-line staff with an F clef. Underneath the parchment, the original melody is a setting of the word "Alleluya." (Click on the image to the left once to view its metadata, and again on that page to view a high-quality version.)

What to make of the addition? It seems unlikely that it is related to "Dulce lignum dulces": the alleluia verse is in mode 8, while the added melody is squarely in mode 1 or 2 (note the 5-step descent from A to D on the pasteover). It is also possible, though unlikely, that it was intended as a cadence for the communion chant for the Feast of Philip and Jacob, "Tanto tempore," which lies on the first half of the leaf. Without more context, it is difficult to situate this melodic addition.