For a long time, this was seen as a rule, that in order to be a tragedy the protagonist must have a certain social standing. This can be seen in Hardy's choice to make Michael Henchard, the protagonist of his novel, the mayor of Casterbridge. He has the highest social standing of the town. .
Also, nineteenth century interpretation said that Aristotle defined a tragedy as a certain structure. A Greek tragedy is constructed in odes and episodes. Episodes are sections that move the plot along, while odes are the ancient Greek equivalent of a song-and-dance number: a Greek chorus sang and danced, expressing the emotions in the play with song and dance, in lyrical, beautiful language. In The Mayor of Casterbridge, Hardy's descriptions are his odes. They do not advance the plot, but rather are full of lyrical language and convey an emotion, as in the following passage: .
"The door was studded, and the keystone of the arch was a mask. Originally the mask had exhibited a comic leer, as could still be discerned; but generations of Casterbridge boys had thrown stones at the mask, aiming at its open mouth; and the blows thereon had chipped off the lips and jaws as if they had been eaten away by disease . . . by the alley it had been possible to come unseen from all sorts of quarters in the town - the old play-house, the old bull-stake, the old cock-pit, the pool wherein nameless infants had been used to disappear. High-Place Hall could boast of its conveniences undoubtedly" (Chap. XXI). .
This is Hardy's chorus; the narrator's lyrical language conveys a mood of ugliness and forboding, and no event of the plot is described. .
Classical plot structure is linear, events happening one after the other. Classical tragedies fill you in on a situation, then somebody brings a piece of news, so the terms of the event keep shifting. This can be seen in The Mayor of Casterbridge when new characters are introduced who completely change the situation the narrator has set up.