“The Pale Blue Eye” is one of those movie titles that’s evocative yet teasingly vague — it makes the film sound like a Western based on a song by Lou Reed. Actually, the movie is based on Louis Bayard’s 2006 novel, which uses an 1830s military setting and murder mystery to frame a kind of origin story of Edgar Allan Poe. At West Point, which in the early 19th century is basically a fort in the woods overlooking the Hudson River, a cadet suffers a violent death. He is cut down from a noose hanging from a tree branch (his feet were touching the ground), but it’s what happens after he dies that counts: Someone has made a vertical incision in his chest and removed his heart.

Christian Bale plays Augustus Landor, the haunted eccentric detective who is brought in by the West Point brass to solve the crime. But as written and directed by Scott Cooper (“Hostiles,” “Crazy Heart”), this is really the story of two men — a painstakingly dour, restrained, slow-moving art-film buddy movie. Early on in his investigation, Landor meets Cadet Fourth Classman E.A. Poe, who has a predilection for detecting things that syncs up with his own. There are many photographs and paintings of Edgar Allen Poe, and Harry Melling, the veteran of the “Harry Potter” films who plays him, matches up with them in an uncanny way. He’s small, with a square pale face framed by severely parted hair and eyes so burning with intelligence that they look a little crossed.

His speech, however, is designed to reassure. Poe, orphaned at a young age, grew up in a troubled foster home in Richmond, VA, and in “The Pale Blue Eye” he speaks in the flowery style of an effete Southern dandy. He’s a geek who styles himself as an aesthete-aristocrat, and he establishes his credentials as an early-American crime profiler — a kind of Benoit Blanc in training — when he tells Landor that whoever killed the cadet and cut out his heart was a poet. The heart, you see, is a symbol. (It certainly was for Poe.) To remove it from a body is to act out a meaning.  

Landor and Poe both like to drink, and that’s about poetry too — about their need to stimulate themselves to see beyond the everyday. By now, though, you may wish the film were up to something more than taking homicide tropes that would be routine in a modern setting and plopping them into a high-toned wintry landscape of “literary” Americana. I’ve seen one period serial-killer movie that’s enthralling, and that’s “From Hell” (2001), the Jack the Ripper drama by the Hughes brothers, starring Johnny Depp as a London detective with hallucinatory visions (he favors absinthe); he’s a character very much like Melling’s Poe. But “From Hell,” though it’s a movie few remember, had energy and intrigue and gave off a slashing demonic charge. “The Pale Blue Eye” wants to get into the 19th-century darkness, but it’s suffocatingly somber and static. The film showcases its two investigators in an ostensibly enigmatic dance-of-the-seven-frontier-high-collars way, but for much of the movie we’re a step ahead of them. (I rarely puzzle out thrillers, and the solution to this one struck me early on.)

There are Satanic rites! There are glowering officers played by the likes of Timothy Spall. And there is Lea (Lucy Boynton), the rosy sister of a cadet who later comes under suspicion. Poe develops a crush on her, but in matters of the heart — or at least intact ones — he proves to be rather ineffectual. He’s like a polite mad scientist hovering around Landor as a sidekick, and despite the gloom-inflected atmosphere there is little here that actually feeds our fascination with Poe and the macabre mystique he became famous for.

It’s Bale, recessive behind a thick groomed beard, who remains at the center. His Landor is a rogue baptized in loss — a widower, with a daughter who died as well. His misery emerges in the solution to the crime, as each investigator learns who the other really is. Yet by then, whatever pinpricks of allure they once offered have passed into disinterest.