Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
High Tragic, Playful
Since Walcott has taken Homer's Iliad as a model for his work and deals with some of the greatest struggles in history, it's no surprise that he also adopts the serious tone generally reserved for epic tragedy. But Walcott's narrative, though it contains tons of super tragic episodes, can't fairly be called a tragedy.
See, in the end, Achille triumphs over history and nature, while characters like Ma Kilman and Seven Seas tell us that healing is on its way. Plus, though the narrator visits the pit of hell, he doesn't fall in. So we have good reason to hope. Because Walcott walks the line between euphoria and despair, we get some playful punning and wry commentary. His general tone is so composed, though, that you'll be startled when comedy crops up—making sure it packs a real punch, and reinvigorating you despite whatever terrible thing the poem examines next.