Although in the OF the Alleluia is widey regarded as a processional chant to accompany the Book of the Gospels from altar to ambo, as expressed in GR and GS it is a meditation before the Gospel, see GIRM :When the deacon or the priest arrives at the ambo with the book of gospels, he shouldn’t have to wait too long until the chant is finished.
Although the Deacon moves during it, he should time it to fit the chant.37. Finally, among other formulas:
a) Some constitute an independent rite or act, such as the Gloria in excelsis (Glory to God in the highest), the Responsorial Psalm, the Alleluia and Verse before the Gospel, the Sanctus (Holy, Holy, Holy), the Memorial Acclamation, and the chant after Communion;
While I think it is correct that it is not intended as a processional chant, I think it is less of a mediation and more of an acclamation (like the Sanctus).as expressed in GR and GS it is a meditation before the Gospel,
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