Aristotle on Greek tragedy
In his work On the Art of Poetry*, Aristotle commented extensively on Greek tragedy. Some of the words and concepts he employed have become a basic part of any critic's vocabulary. He sums up his description of tragedy thus:
Tragedy, then, is a representation of an action that is worth serious attention, complete in itself, and of some amplitude; in language enriched by a variety of artistic devices appropriate to the several parts of the play; presented in the form of action, not narration; by means of pity and fear* bringing about the purgation [catharsis] of such emotions.
Did Shakespeare know of Aristotle's precepts?
As usual, there is no clear answer. One of Shakespeare's earliest plays, The Comedy of Errors, follows accurately the precepts of those who interpreted Aristotle in the Renaissance, keeping to the so-called "unities" of time and place, unlike most of the popular drama of the period. And Hamlet appears to be referring to the concept of hamartia (sometimes rather simplistically called a "fatal flaw") as he discusses the state of the King and the Kingdom.
A page with more Greek critical terms.
Aristotle's Poetics are available from Perseus.
Footnotes
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Aristotelian Authority
On the Art of Poetry comments at length on the different forms of poetry, and discusses Greek tragedy in particular. Aristotle is supposed to have written on comedy, but the work has not survived.
In the Renaissance, Aristotle's authority was such that his critical precepts were followed and admired by scholars. English playwrights of the renaissance, even those who were educated in the universities, however, followed native traditions in the theatre, a choice which earned them the scorn of later critics.
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Pity and fear
Pity alone is not enough to make a play a tragedy. The kind of drama that depends solely on its capacity to provoke pity are likely to be "tear-jerkers." Pathos requires humour, irony, or something more disturbing, which we may call fear (Sidney called it "admiration"), to prevent it from lapsing into sentimentality.
Fear alone is similarly inadequate. An average suspense-thriller may hold attention, but if we know the ending or have seen it already we rapidly become aware that the thriller is simply melodramatic.
Melodrama is to tragedy what farce is to comedy: the plot is all-important, and the characters tend to be stereotyped, fitting into prearranged roles (goodies and baddies).