Final answer:
The only complete satyr play known to exist is Cyclops by Euripides. Satyr plays are a form of tragicomedy from Greek theatre, contrasting with the serious dramatic tone seen in tragedies by contemporaries such as Aeschylus and Sophocles. Roman theatre, influenced by Greek traditions, had its variations and contributions, setting the stage for later dramaturgical developments.
Step-by-step explanation:
The complete satyr play mentioned is known as Cyclops by Euripides. In the context of the theatre, a satyr play is a form of tragicomedy featuring the lecherous and wine-loving satyrs. Satyr plays were often presented as the afterpiece to a set of three tragedies at the Athenian festivals. Euripides, unlike his contemporaries such as Aeschylus and Sophocles, is known for structuring the narratives of his plays on the misfortunes of a known lineage, illuminating the concept of hamartia—the character's great error or frailty leading to their downfall. This style confirms that the best tragedies, according to Aristotle's Poetics, revolve around the legends and myths of well-known families.
Euripides’ Cyclops is an exception among his plays for its satirical tone and the burlesque revelry of its characters, differing significantly from the serious dramatic tone of tragedies like Oedipus Rex or the Oresteia. Additionally, the legacy of Greek theatre influenced Roman performances, yet with differences such as the use of Roman attire in fabula togata, and notable Roman playwrights like Seneca. Roman theatre introduced developments like the focus on emotional drives in tragic protagonists and the use of supernatural elements, which influenced later tragedians, including Renaissance writers.