In its Constitution on the Sacred Liturgy, the Second Vatican Council (1962-1964) required that official sacred chant books for the Church be published with care:
§117. The typical edition of the books of Gregorian chant is to be completed; and a more critical edition is to be prepared of those books already published since the restoration by St. Pius X. It is desirable also that an edition be prepared containing simpler melodies, for use in small churches.
One edition containing simpler melodies was released as the Graduale Simplex in 1967. Since then, use of Simplex antiphons in the U.S. has been limited, but at least one scholar has written that the Simplex did exert a considerable effect on the Alleluia before the Gospel. Prior to the new Missal of 1970, Alleluias were sizable melismatic chants. When usage of the Graduale Romanum declined, it appears the Simplex substitution of a triple Alleluia was adopted widely as the new default. Use of the actual melodies was not.
Whatever the faults of the overall approach of the Simplex, the use of a triple Alleluia throughout the liturgical year, and the lack of apparent rationale for their seasonal/festal distribution, the Alleluias in the Simplex are good examples of modal melody. They also have interesting rhythmic variety if one pays careful attention to groups of two and three. Some are somber, some haunting. All the triple Alleluias in the Simplex are available for study in PDF.
The 1955 encyclical is here:
It is the duty of all those to whom Christ the Lord has entrusted the task of guarding and dispensing the Church’s riches to preserve this precious treasure of Gregorian chant diligently and to impart it generously to the Christian people…. And if in Catholic churches throughout the entire world Gregorian chant sounds forth without corruption or diminution, the chant itself, like the sacred Roman liturgy, will have a characteristic of universality, so that the faithful, wherever they may be, will hear music that is familiar to them and a part of their own home. In this way they may experience, with much spiritual consolation, the wonderful unity of the Church. This is one of the most important reasons why the Church so greatly desires that the Gregorian chant traditionally associated with the Latin words of the sacred liturgy be used.