(Taken from Notes Made at the Conferences of Dom Prosper Guéranger)
The Gradual is followed by the Alleluia - or, if the season require it, by the Tract. The Alleluia is repeated after the manner of a Responsory; it is then followed by a Verse; which having been said, the Alleluia is sung a third time. This, by excellence, the chant of the praise of God, deserved to have a Place in the Mass. There is something so joyous, and, at the same time, so mysterious about it, that during penitential seasons, - that is, from Septuagesima to Easter, - it is not to be said.
During those Seasons, it is replaced by the Tract. The Tract takes up the attention of the Faithful during the time required for the several ceremonies, when the Deacon, after having asked the Priest’s blessing, goes in procession to the Ambo of the Gospel, and prepares to herald the Word of God. The Tract is composed, sometimes of an entire Psalm, or nearly so, - as we have for the first Sunday of Lent; but, generally, it gives only a few Verses. These Verses, which are sung to a rich and characteristic melody, follow each other without any refrain or repetition: and it is because of their being thus sung without any break, that they are called by this name of Tract. [Latin trahere -- to draw or pull]
On certain Solemnities, there is added to the Alleluia or Tract, what is called the Sequence, (Sequentia). It was added to the chant of the Mass long after the time of St. Gregory; the addition was made some time about the 9th century. It received the name of Sequence, that is to say, sequel, because it originally consisted of certain words adapted to the notes which form a sequel to the word Alleluia, and which were called Sequentia, even before the introduction of the Sequence.
It is called, also, the Prose (Prosa) because originally, it bore no resemblance either to the metrical hymns composed by ancient writers, nor to cadenced rhythms, which appeared later on. It was a real piece of prose, which was sung in the manner we have described, as a way of putting words to the pneuma of the Alleluia. By degrees, however, it partook of the character of a Hymn.
The Sequence thus added to the solemnity of the Liturgy; and, whilst it was being sung, the Bells were rung, as now, and the Organ was played. There was a Sequence for every Feast, and, therefore, for the Sundays during Advent. In the Roman Missal drawn up by order of St. Pius the Fifth, only four of the Sequences were retained. These four are, the Victimae Paschali [Easter Sunday], which is the most ancient of all, and was followed as the model of the rest; the Veni Sancte Spiritus [Pentecost Sunday], the Lauda Sion [Corpus Christi], and the Dies Irae [Requiem Masses]. Later on, there was added the Stabat Mater [Feast of the Seven Sorrows of the BVM]. The Monastic Missal has also the Laeta dies, for the feast of St. Benedict; it is a composition of the 16th century.