The Gradual. From: http://www.newadvent.org/cathen/06715a.htm
(Latin Graduale, from gradus, a step)
The Gradual … is the oldest and most important of the four chants that make up the choir's part of the Proper of the Mass. Whereas the three others (Introit, Offertory, and Communion) were introduced later, to fill up the time while something was being done, the Gradual (with its supplement, the Tract or Alleluia) represents the singing of psalms alternating with readings from the Bible, a custom that is as old as these readings themselves. Like them, the psalms at this place are an inheritance from the service of the Synagogue. Copied from that service, alternate readings and psalms filled up a great part of the first half of the Liturgy in every part of the Christian world from the beginning. Originally whole psalms were sung. In the "Apostolic Constitutions" they are chanted after the lessons from the Old Testament: "The readings by the two (lectors) being finished, let another one sing the hymns of David and the people sing the last words after him" (ta aposticha hypopsalleto, II, 57).
This use of whole psalms went on till the fifth century. St. Augustine says: "We have heard first the lesson from the Apostle. Then we sang a psalm. After that the lesson of the gospel showed us the ten lepers healed." (Serm. clxxvi, 1). These psalms were an essential part of the Liturgy, quite as much as the lessons. "They are sung for their own sake; meanwhile the celebrants and assistants have nothing to do but to listen to them" (Duchesne, "Origines du Culte chrétien", 2nd ed., Paris, 1898, p. 161). They were sung in the form of a psalmus responsorius, that is to say, the whole text was chanted by one person — a reader appointed for this purpose. [For some time before St. Gregory I, to sing these psalms was a privilege of deacons at Rome. It was suppressed by him in 595 (Ibid.).] The people answered each clause or verse by some acclamation. In the "Apostolic Constitutions" (above) they repeat his last modulations. Another way was to sing some ejaculation each time. An obvious model of this was Psalm 135 with its refrain: "quoniam in æternum misericordia eius"; from which we conclude that the Jews too knew the principle of the responsory psalm. We still have a classical example of it in the Invitatorium of Matins (and the same Psalm 94 in the third Nocturn of the Epiphany). It appears that originally, while the number of biblical lessons was still indefinite, one psalm was sung after each. When three lessons became the normal custom (a Prophecy, Epistle, and Gospel) they were separated by two psalms. During the fifth century (Duchesne, op. cit., p. 160) the lessons at Rome were reduced to two; but the psalms still remain two, although both are now joined together between the Epistle and Gospel, as we shall see. Meanwhile, as in the case of many parts of the Liturgy, the psalms were curtailed, till only fragments of them were left. This process, applied to the first of the two, produced our Gradual; the second became the Alleluia or Tract.