Stäblein, Monumenta monodica I, nr. 506; Schmid, Musica enchiriadis, p. 217

Transcription of the melody transmitted in Klosterneuburg 1000 is straightforward due to the two-line stave (f and c) and precise heighting of the neumes in relation to the other letters written between the two lines as part of the stave (d and a). Stäblein regularises the spelling of the text and records liquescences only in the accompanying commentary (Monumenta monodica I, p. 569). His edition is also neutral with respect to rhythm in so far as it presents noteheads without stems.

Schmid reproduces the relevant diagram from the version of the Musica Enchiriadis transmitted in the so-called Bamberg organum treatise. The diagram features Daseian signs aligned vertically, from which strings are extended and on which are placed the syllables of the first line of Gratuletur omnis; the vertical alignment of syllables indicates simultaneously sounding pitches. A transcription of the pitches indicated in the Bamberg organum treatise into modern notation using stemless noteheads is provided in Stäblein (Monumenta monodica I, 569).

The similarities between the three melodies given for Gratuletur omnis are strong for the opening half line (syllables 1-8). In the Naples and Klosterneuburg manuscripts this opening melodic contour is repeated for the first eight syllables of the third line and similar melodic contours are again traced. Elsewhere within the strophe correspondences in melodic contour are harder to identify.
Stäblein noted that the melody for Gratuletur omnis recorded in Klosterneuburg 1000, which was only ever transmitted East of the Rhine, is identical in its opening half-line to the upper voice of the polyphonic hymn recorded in the Bamberg manuscript. The neumed version of Gratletur omnis in Napoli IV. G. 68, which appears to have been unknown to Stäblein, is identical in its opening contour to the opening of the melody recorded in both the Bamberg and Klosterneuburg manuscripts. This might be taken to mean that the later medieval melody can be traced back as far as the first quarter of the tenth century, when it was used for both Gratuletur omnis and Alma vera at St. Gall. Although this proposal is attractive in its simplicity, it needs to be tempered by recognition of the differences between the early and later medieval melodies at all points other than the first halves of the first and third lines. A more cautious conclusion would be that an opening melodic contour was associated with this text and remained in circulation East of the Rhine from at least the tenth through to the fourteenth century. There is no evidence to suggest that two further melodies identified by Stäblein for Gratuletur omnis in later hymnals (one transmitted in Italian sources, no. 758, the other a widely disseminated melody more commonly associated with Pange lingua, no. 56) were in use before the eleventh century. In view of the paucity of hymn notations before the earliest notated hymnals at the beginning of the eleventh century, this lack of evidence cannot be taken as a sign of the primacy of the melody recorded in Napoli IV. G. 68. 

The Klosterneuburg manuscript assigns Gratuletur omnis to Lauds at Epiphany, a common position for this hymn in hymnals of the Middle Ages. A shorter neumed version of Gratuletur omnis is assigned to the Mass for Epiphany with the rubric «ante episcopum» in Roma 123; for a discussion of the implications of this rubric, see the entry for Gloriam Deo. The melody recorded for Gratuletur omnis in this shortened version of the text is the one that Stäblein identified as transmitted only in Italian sources. The probability that this Italian melody entered into transmission before the mid eleventh century is high given its survival in later Italian manuscripts (for an alignment of the neumes of Roma 123 with a later version of the Italian melody that can be transcribed into modern notation, see Sevestre, Du versus au conduit II, p. 98).