The major piece of the Byzantine Divine Liturgy of this day is the Grand Entrance sung at the offertory of the mass (and again at the communion):
Τοῦ Δείπνου σου τοῦ μυστικοῦ, σήμερον Υἱὲ Θεοῦ, κοινωνόν με παράλαβε· οὐ μὴ γὰρ τοῖς ἐχθροῖς σου τὸ Μυστήριον εἴπω, οὐ φίλημά σοι δώσω, καθάπερ ὁ Ἰούδας, ἀλλ' ὡς ὁ Λῃστὴς ὁμολογῶ σοι. Μνήσθητί μου Κύριε, ὅταν ἔλθῃς ἐν τῇ Βασιλείᾳ σου. Aλληλούια, αλληλούια, αλληλούια.
Of Thy mystical Supper, thou receivest me today, Son of God, as a partaker. For I will not reveal this mystery to Thy enemies; I will not I give Thee a kiss as did Judas; but as the thief, confessing to Thee: remember me, O Lord, in Thy kingdom.
The same piece have been translated since a very ancient time in the Ambrosian mass of today, and used (without the triple Alleluia, and μυστικοῦ translated by mirabili, wondrous) at the same place:
Cœnæ tuæ mirábili hódie, Fílius Dei, sócium me áccipis. Non enim inimícis tuis mystérium dicam: non tibi dabo ósculum, sicúti et Judas: sed sicut latro confiténdo te. Meménto mei, Dómine, in regno tuo.
Do not be misled by the title of this piece in the Ambrosian liturgy: the Antiphona post Evangelium is sung in fact at the beginning of the offertory.
Here is its music:
In Russian Byzantine parishes, one of the finest musical settings used for this piece is that made by Alexei Lvov (1799 † 1870), who succeeded his father as Maestro of the Imperial Chapel in St Petersburg in 1837:
In fact, "Of Thy mystical Supper" is not the only offertory of the Byzantine rite which has been used in the West.
During the Great Entrance (that is the offertory of the mass), the Byzantine rite uses only four pieces of singing during the year.
Probably the most ancient of these four offertories is that used at the liturgy of the Holy Saturday, borrowed from the ancient and venerable Liturgy of St James:
Let all mortal flesh be silent, and stand with fear and trembling, and meditate nothing earthly within itself. For the King of kings and Lord of lords, Christ our God, comes forward to be sacrificed, and to be given for food to the faithful. And the bands of angels go before Him with every power and dominion, the many-eyed cherubim, and the six-winged seraphim, covering their faces, and crying aloud the hymn, Alleluia, Alleluia, Alleluia.
According to some scholars, this piece might have been known or used in the Gallican rites after the Byzantine legation of 567, when the Emperor of Constantinople gave a part of the True Cross to the French Queen saint Radegund, for her monastery of Poitiers.
On Maundy Thursday, the Great Entrance sung is, as we have seen, "Of Thy wondrous Supper", used also by the Ambrosian rite.
The rest of the year, except the liturgies of the Presanctified, the Great Entrance is the very famous Cherubic hymn, added to the Divine Liturgy by the Emperor Justin II (565 - 578):
We who mystically represent the Cherubim, and who sing to the Life-Giving Trinity the thrice-holy hymn, let us now lay aside all earthly cares that we may receive the King of all, escorted invisibly by the angelic orders. Alleluia, Alleluia, Alleluia.
During the Middle Ages, this piece was also sung in latin at the offertory of the Roman Mass at the Royal Abbey of Saint-Denis, the royal necropolis of French kings.
In those holiest days, please don't forget to pray also for the unity of the Church, like our Lord Himself who prayed today for they all shall be one.