The Penitential Psalms or Psalms of Confession, so named in Cassiodorus's commentary of the 6th century AD, are the Psalms6, 32, 38, 51, 102, 130, and 143 (6, 31, 37, 50, 101, 129, and 142 in the Septuagint numbering).
Psalm 6 - Domine ne in furore tuo (Pro octava)
Psalm 32 - Beati quorum remissae sunt iniquitates
Psalm 38 - Domine ne in furore tuo (In rememorationem de sabbato)
Psalm 51 - Miserere mei Deus
Psalm 102 - Domine exaudi orationem meam et clamor meus ad te veniat
Perhaps the most famous musical setting of all seven is by Orlande de Lassus, with his Psalmi Davidis poenitentiales of 1584. There are also fine settings by Andrea Gabrieli and by Giovanni Croce. The Croce pieces are unique in being settings of Italian sonnet-form translations of the Psalms by Francesco Bembo. These were widely distributed; they were translated into English and published in London as Musica Sacra; and were even translated (back) into Latin and published in Nürnberg as Septem Psalmi poenitentiales. William Byrd set all seven Psalms in English versions for three voices in his Songs of Sundrie Natures (1589). Settings of individual penitential psalms have been written by many composers. Well-known settings of the Miserere (Psalm 51) include those by Gregorio Allegri and Josquin des Prez. Settings of the De profundis (Psalm 130) include two in the Renaissance by Josquin.