Trilogy (3)
Tetralogy (4)
Pentalogy (5)
These would come after five...
Hexalogy (6)
Heptalogy (7)
Octalogy (8)
Ennealogy (9)
Decalogy (10)
NOTE:
ology can mean an account or narration. Replacing the above with quad, septa, and quinti is just making nonce words.
Quintilogy is not a real word.
AnswerA quadrilogy, meaning part 4 of 4.The word 'quadrilogy' doesn't exist and was invented by the movie industry.The correct word is 'tetralogy'.
This does not appear to be recognised as a system but rather as an informal convention, and does not have an agreed name. However, the word "trilogy" is derived from the Greek "trilogia", simply meaning 'three stories' ("ology" or "logos", translating as 'written work'). It is used in reference to works of three distinct parts. Higher numbers of distinct-but-related works may be named by combining the Greek number with "-logy". The proper labelling convention for a work of four distinct parts, therefore, is actually "tetralogy" ("tetra" means four) rather than "quadrilogy". The word 'quad' is Latin, not Greek. Higher numbers are easily constructed: 5 = pentalogy 6 = hexalogy 7 = heptalogy 8 = octalogy 9 = ennealogy 10 = decalogy 11 = hendecalogy / undecalogy 12 = dodecalogy 13 = triskaidecalogy / tridecology 14 = tetrakaidecalogy / tetradecology 15 = pendedecalogy 16 = hexdecalogy 17 = heptdecalogy 18 = octdecalogy 19 = enneadecalogy 20 = icosalogy ...and so on. Of course, it would seem impractical to use this convention for such high numbers when a work of many parts would be more simply and easily referred to as a "series". However, being informal, there's no particular reason not to be utterly absurd: 100 = hecatology 1000 = chilialogy