A thriambus (also spelled thriamb, thriambas, or thriambos; Greek θρίαμβος) is a hymn to Dionysus, sung in processions in his honour, and at the same time an epithet of the god himself, according to Diodorus (4.5.2): Thriambus is a name that has been given him, they say, because he was the first of those of whom we have a record to have celebrated a triumph (thriambos) upon entering his native land after his campaign, this having been done when he returned from India with great booty.
Arrian traces the custom to Alexander the Great when he states (Anabasis 6b.28): Certain authors have said (though to me the statement seems incredible) that Alexander led his forces through Carmania lying extended with his Companions upon two covered waggons joined together, the flute being played to him; and that the soldiers followed him wearing garlands and sporting.
They say that he did this in imitation of the Bacchic revelry of Dionysus, because a story was told about that deity, that after subduing the Indians he traversed the greater part of Asia in this manner and received the appellation of Thriambus, and that for the same reason the processions in honour of victories after war were called thriambi.
An old hypothesis is that the word is borrowed from Phrygian or Pelasgian, and literally means "Dreischritt", i. e., "three-step", compare iamb and dithyramb, but H. S. Versnel rejects this etymology and suggests instead a derivation from a cultic exclamation.
[1] From the time of Roman Greece (2nd century BC), the Greek term increasingly narrows to a translation of Latin triumphus.