There are many ways to judge a documentary, but a solid one is this question: Could this movie be an article? A great documentary shouldn’t merely be informative, or even tell a good story; it should also be a movie, harnessing every tool at the filmmaker’s disposal. In making “Soundtrack to a Coup d’Etat,” director Johan Grimonprez used every instrument cinema affords. His documentary is rhythmic and propulsive, with reverberating sound and images juxtaposed against one another to lend more meaning. The result, in a word, is marvelous.

It’s also demanding, a full dissertation crammed into one feature film, complete with citations and footnotes. (Literally.) You can’t zone out during this film. But that doesn’t mean it’s dry or academic. “Soundtrack to a Coup d’Etat” is a furious and elliptical film, a piece of true history structured like a spider web and drenched in real urgency. The story at its center is the rise to power and eventual CIA-led assassination of Patrice Lumumba, the first prime minister of Congo, who was elected in May 1960, shortly before his country gained its independence from Belgium. Congo, a country rich with natural resources that were vital, among other things, to Western countries’ weapons of war, had been colonized by Belgium since the late 19th century.

Or is that the story? “Soundtrack” entwines a number of threads, all of which are knotted into one another, though the links aren’t always clear till the movie’s thunderous conclusion. Soviet premier Nikita Khrushchev visits the United States and addresses the United Nations, denouncing American racism and demanding an end to colonialism. Black jazz musicians, such as Louis Armstrong, Nina Simone, Duke Ellington and Dizzy Gillespie, are sent to perform around the world as “ambassadors” of American goodwill and freedom, yet segregation is still the law back home. Leaders of African and Asian countries, newly admitted to the United Nations, form a voting bloc that could threaten the influence of world powers like the United States and the Soviet Union. Leaders of newly independent African nations speak of forming a United States of Africa. And while President Dwight Eisenhower calls for no foreign interference into African politics, the CIA has other plans.

“Soundtrack” largely centers on events of 1960, depending almost entirely upon archival footage as well as the memoirs and writings of leaders and operatives from the time. Text — beautifully designed text, in fact, the work of designer Hans Lettany — provides historical context and voices from the moment, underscored by on-screen citations (right down to the page number). But Grimonprez swirls the timeline a bit, jumping backward and forward just enough that the links between events — Armstrong’s visit to Congo just as Lumumba is under house arrest and CIA agents arrive in the country, for instance — start to emerge.

But what really makes “Soundtrack” work is, well, its soundtrack. The film returns over and over to Max Roach and Abbey Lincoln performing their 1960 album “We Insist! Freedom Now Suite.” These famed jazz musicians and many more provide a kind of score, a gorgeous, buoyant, anxious momentum. We watch them play and talk about their music, their hopes for their travels. Yet it’s probably no accident that this film’s title echoes the lauded 2010 documentary “Soundtrack for a Revolution,” which explores the power of Black activists, and in particular their music, in the Civil Rights Movement.

This film, though, treads less optimistic territory. One of its major threads is the CIA’s use of unwitting Black musicians to not just spread soft power abroad during the Cold War but also, potentially, provide a smoke screen for the agency’s more covert dealings. Archival footage and audio of interviews with agents, in some cases many years later, underline the point: Art was art, but it was also a useful tool for machinations the artists quite publicly opposed.

That is the paradox at the core of argument that “Soundtrack to a Coup d’Etat” makes: Power takes many forms, some of which are invisible to the naked eye, and what you can’t see can be the most consequential. Telling such a story requires the multisensory detail cinema provides. Layering a voice telling us one thing over an image showing us another, all while jazz plays and texts appears, can feel a bit like audiovisual overload. Provoking a bit of confusion is the point. Covert power relies on misdirection, and it is only by looking back that we can sometimes make sense of what happened.

That’s why “Soundtrack” lands on a coda. Each of these historical threads, in some way, led to the Feb. 15, 1961, demonstration at the United Nations protesting Lumumba’s assassination, organized by a group called the Cultural Association of Women of African Heritage and led by Lincoln, Rosa Guy and Maya Angelou. But the story didn’t end there. “Soundtrack” makes an explicit connection between what happened in Congo in 1960 and ongoing conflict today. These events occurred a while ago, but they’re not really history, “Soundtrack” argues. The past, one might say, is never dead. It’s not even past.