||: I – VII – VI – V :||
This progression need not be included in a cycle, but occasionally it does. It is named the “lament” progression because in early classical music, this chord progression (almost always in minor) was used as the ground bass (a repeated bass pattern that formed be foundation for a set of variations, not unlike the cyclical progressions of pop/rock songs) for songs of lament. Examples include “Dido’s Lament” by Henry Purcell, from the opera Dido and Aeneas, and J.S. Bach’s “Crucifixus,” from his Mass in B Minor.
The opening of the verse in Muse’s “Thoughts of a Dying Atheist” is a prominent example from recent pop/rock music (it is followed by a circle-of-fifths progression).