There follows a double Alleluia, without gradual ... since on the day of judgement, there will be joy for the Lord’s Resurrection and our own... the Alleluia is doubled because that rejoicing will be everlasting; so one Alleluia is sung to signify the rejoicing, the second to signify that it lasts forever... one Alleluia is sung for the (newly) baptized, namely “Praise the Lord, o children”, and the other for the Resurrection, namely, “This is the day.”
Allelúja, allelúja. Ps 117 Haec dies, quam fecit Dóminus: exsultémus et lætémur in ea. (This is the day the Lord has made; let us be glad and rejoice in it.)Allelúja Ps 112 Laudáte, púeri, Dóminum, laudáte nomen Dómini. (Praise the Lord, o children: praise ye the name of the Lord. - This is also the Alleluia sung at the Mass of the Holy Innocents when it falls on a Sunday or is celebrated as a patronal feast.)
Excerpts from William Durandus’ Rationale Divinorum Officiorum, VI, 95
The Communion is: “All ye who have been baptized in Christ have put on Christ, alleluia.” On this day, the station is at the church of blessed John in the Lateran, for there on the preceding Saturday the children were baptized, and on the eighth day, in the Law (of Moses) they were circumcised. Therefore rightly in this day so they come together thin that same place, so that this may be done spiritually among the baptized, which is said in the Epistle (1 Pet. 2, 1-10), ‘Laying aside all malice, and all guile... as newborn babes (desire the rational milk without guile, etc.),’ lest death enter in by the windows of the five senses.” (Durandus is here following a tradition of the Fathers by which the rite of circumcision under the Old Law symbolizes the cutting off of the senses from all incitement to sin.)