Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Serious, Cataclysmic, Hopeful
In keeping with the other plays in the Oresteia trilogy, The Eumenides maintains a pretty capital-S Serious tone throughout. This is in keeping with the fact that these plays are intended as tragedies, as well as with the weightiness of the themes involved—your standard-order hodge-podge of murder, revenge, justice, fate, and so on.
But in this play, things actually go beyond "serious." Things get so over-the-top and ridiculous, that we have decided only an over-the-top and ridiculous word can capture it; we've picked "cataclysmic."
Why so over-the-top? Well, this mainly represents the perspective of the Furies, who think the world is absolutely coming to an end when the matter (a) gets put to trial, and (b) when Orestes gets acquitted. In fact, they think this represents nothing less than a cosmic struggle between the old gods (including themselves) and the order they established, and the younger generation of gods (like Apollo and Athena), whom they view as crazy teenage troublemakers:
(Chorus of Furies): "You younger gods! The ancient laws—
you have ridden them down! You have taken them out of my hands for yourselves!
I am dishonoured, wretch that I am; my heavy rancour releases on this land—woe to it!—
a poison, a poison from my heart to requite my grief,
dripping from below the earth, intolerable. From this
a canker destroying leaves, destroying offspring—O Justice [Justice]!—
will sweep over and strike the land
with a blight killing men." (779-787)
Jeepers, right? These Furies are, well, furious.
Now, you tell us, does the world end in this play or not? It doesn't, right? (In these generational conflicts, it never does.) After such a potential tragedy is passed, anything would seem pretty hopeful, right? Actually, though, the hopefulness at the end of the play isn't just in contrast to the fear of disaster in the middle. There is actually a genuine sense of forward-looking social progress, as the Furies adapt themselves into the "Kindly Ones" ("Eumenides") in charge of rewarding the good as well as punishing the wicked:
(Chorus of Furies): "I pray too that faction, insatiable for harm,
never clamours for this city,
nor the dust drinks its people's black blood
from counter-killings in rage,
in retribution,
the city's ruin its eager pursuit;
may they reciprocate joys,
resolved on sharing friendship,
and show hate with a single mind:
for this remedies much among men." (976-987)
Yeah, these Furies go from talking about destroying offspring and killing men to… friendship. This is a surprising end to the absolute darkness of the trilogy, which makes it seem all the more amazing.