Penitential Psalms
Cyclopedia of Biblical, Theological and Ecclesiastical Literature [1]
These are usually reckoned seven. They are so called because they are regarded as specially expressive of sorrow for sin, and accepted by Christian devotion as forms of prayer suitable for the repentant sinner. They are Psalms 6, 32, 39, 51, 102, 130,, 143 according to the A.V., which correspond with 6, 31, 37, 50, 101, 129, and 142 of the Vulgate. These Psalms have been set apart from a very early period, and are referred to as such by Origen (Hom. ii in Leviticum). Pope Innocent III ordered that they should be recited in Lent. They have a special place in the Roman Breviary, and more than one of the popes attached an indulgence to the recital of them. The most deeply penitential, and the most frequent in use, both public and private, is the 51st Psalm, or the Miserere (50th in the Vulgate.)
The Nuttall Encyclopedia [2]
s a name given from very early times to Psalms vi., xxxii., xxxviii., li., cii., cxxx., which are specially expressive of sorrow for sin. The name belonged originally to the fifty-first Psalm, which was recited at the close of daily morning service in the primitive Church.