A tetralogy (from Greek τετρα- tetra-, "four" and -λογία -logia, "discourse") is a compound work that is made up of four distinct works. The name comes from the Attic theater, in which a tetralogy was a group of three tragedies followed by a satyr play, all by one author, to be played in one sitting at the Dionysia as part of a competition.
In the early modern period of literature, Shakespeare drafted a pair of tetralogies, the first consisting of the three Henry VI plays and Richard III, and the second, what we now call a prequel because it is set earlier, consisting of Richard II, the two Henry IV plays, and Henry V.
As an alternative to "tetralogy", "quartet" is sometimes used, particularly for series of four books. The term "quadrilogy", using the Latin prefix quadri- instead of the Greek, and first recorded in 1865, has also been used for marketing the Alien movies.
I have always had a romantic idea that the writer or the artist was, as Coleridge and Virginia Woolf said, androgynous. The whole of The Virgin in the Garden quartet is about the desirability of an androgynous mind... JN & JF: I notice that the quartet which begins with The Virgin in the Garden is sometimes called The Frederica Quartet. ASB: My paperback publisher, you will be glad to hear, is going to make it a boxed set, and it's just going to be called The Quartet. It isn't Frederica's book--though she's the sort of person who would muscle in and try to take it!