The rite gives two possible antiphons “(w)hile the gifts are being brought.”
From the sermon on the mount:
If you are bringing your gift to the altar, and there you remember that your neighbor has something against you, leave your gift in front of the altar; go at once and make peace with your neighbor, and then come back and offer your gift, alleluia.
Moses consecrated the altar to the Lord and offered sacrifices and burnt offerings; he made an evening sacrifice of sweet fragrance to the Lord God in the sight of the children of Israel.
No psalms given with these; just the antiphons.
As with the dedication of the Church in II, 73, the bishop kisses the altar after the gifts are prepared and Mass continues in the usual way (IV, 58). The prayer over the gifts (59) is different from the one used for the church dedication in II, 74. The preface is different as well (60).
Two communion antiphons are given in IV, 61 to be used with Psalm 128. One is the same as in II, 78, and this one, liftted from Psalm 84 in fact, differs:
Even the sparrow finds a home and the swallow a nest wherein she places her young: near to your altars, O Lord of Hosts, my King and my God.
The Mass concludes with a different Prayer after Communion (62), Blessing (63), and Dismissal (64).
The Mass for the Dedication of an Altar is not just a variant of the Mass for the Dedication of the Church. Its texts, mainly antiphons, psalms, and prayers, are a unique offering. The Church has foreseen an altar’s dedication as not just an important moment demanding the bishop’s attention, but a distinctive ritual when celebrated apart from the dedication of a building for worship.