The use of the number three is quite prevalent in the Church. There is, most obviously, our Triune God: Father, Son, and Holy Spirit. There are the three theological virtues: faith, hope, and love. There is the Communion of Saints: the Church Militant, the Church Suffering, and the Church Triumphant. There is the Holy Family: Jesus, Mary, and Joseph. There are the three temptations of Christ after His Baptism. There is the scene of the Transfiguration with Jesus, Moses, and Elijah being seen by Peter, James, and John (with this specific group of Apostles figuring prominently in other scenes). There is both Peter's triple denial of Jesus and his triple forgiveness. There were the three crosses on Calvary. And then there is something about "on the third day"....
It is prevalent during the Mass. It is heard in the Confiteor ("...through my fault, through my fault, through my most grievous fault.") and the prayer that follows. The Kyrie in the Extraordinary Form is a three-fold repetition. The Preface Dialogue has three parts. The beginning of the Sanctus praises our thrice-holy God. The end of any Eucharistic Prayer begins, "Through Him, and with Him, and in Him...", with a triple "Amen" sung at times in reply. The Agnus Dei is obvious. And when used, the Solemn Blessing at the end has three petitions.
It even has places in the Sacred Triduum. During the Good Friday liturgy, the cross used for veneration pauses three times on its way to the sanctuary. It is the same with the Paschal candle at the Easter Vigil. From there, the minimum number of readings before the Epistle and Gospel is three, with the account of the crossing of the Red Sea (the third of the seven) being mandatory. The Alleluia returns from its hiatus with a three-fold recitation. And the Church receives new members with Her three rites of initiation: Baptism, Confirmation, and Holy Communion.
And during the Vigil, there is one more example. It comes at the singing of the Exsultet. The opening three lines use the same melodic pattern. This unites the three expressions of joy found in the text:
Exsultet/Exult--the exultation of the angels in Heaven.Gaudeat/Be glad--the gladness of the earth. (Notice the connection to the 3rd. Sunday of Advent, which is also known as Gaudete Sunday.)Laetatur/Rejoice--the rejoicing of the Church. (Notice the connection to the 4th. Sunday of Lent, which is also known as Laetare Sunday.)
So may our joy at this most awesome, marvelous, and wonderful event--the Resurrection of our Lord and Savior Jesus Christ--may be united, complete, and limitless.
May those who have the privilege to chant this bring out this joy.