Then from holy Easter until Pentecost let the Alleluia be said without exception—with the psalms and with the responses. However, on all Sundays outside of Lent, let the canticles, Lauds, Prime, Terce, Sext, and None be said with Alleluia. Let Vespers be said with the antiphon; but let the responses never be said with Alleluia (except from Easter to Pentecost).
Saint Benedict devotes a whole chapter to this one word: Alleluia.
During Easter especially, the monks sing Alleluia like it was going out of style. We sing it during the opening prayers and during the psalm responses, in hymns and before the gospel, at all the hours of the Divine Office and even before we go to bed at night. There’s Alleluia all over the place. It’s like a big truck of Alleluia overturned in our driveway and we’ve been swimming in it ever since. “Of all the Christian mysteries,” says Saint Leo the Great, “we know that the paschal mystery is the most important.” So we respond with the Alleluia, which is our song of triumph and joy.
There is time, of course, for meditating on the sufferings of Our Lord. After all, Saint Paul instructs us always to keep our eyes fixed on Christ crucified. And to be sure, no Christian church—no Christian home—is complete without a crucifix. But adoration, thanksgiving, praise, and blessing are what it’s all about, and these, Saint John the evangelist tells us, will be dissolved into a single expression of religious devotion: “I heard what sounded like the loud voice of a great multitude in heaven saying: "Alleluia! Salvation, glory, and might belong to our God…then a second time: "Alleluia!” …then the twenty-four elders and the four living creatures fell down and worshiped God who sat on the throne, saying, "Amen. Alleluia." …and a voice coming from the throne said: "Praise our God, all you his servants, and you who revere him, small and great." And I heard something like the sound of a great multitude or the sound of rushing water or mighty peals of thunder, as they all said: "Alleluia!”
This is why Holy Mother Church repeats this word throughout her liturgy. She would have us all be living Alleluias—souls fundamentally ordered to God—obsessively, compulsively God-centered in everything we do. So the monks repeat this Alleluia again and again throughout the Easter season. Then we repeat it some more when it’s not the Easter season. We repeat it and repeat and repeat it until our whole life becomes a hymn of praise to the glory of the Father.