“The American Epic Sessions,” a two-hour music documentary that premiered Tuesday night on PBS, is all about stunt casting. And that’s not even a reference to the artists who come through Jack White’s and T Bone Burnett’s studio to cut a track or two for the doc, a list that includes Elton John, Beck, Alabama Shakes, Nas, Rhiannon Giddens, the Avett Brothers, and one last teaming of Willie Nelson and the late Merle Haggard.

No, the ultimate star of this show is a meticulously reconstructed recording machine from the 1920s that seems to have talismanic qualities on those who enter its orbit even 80 years after it was last in use. This antiquated, cleaned up piece of studio equipment is so fetishistically photographed, it relegates the 19 musical acts that drop by for an old-school session to supporting players. Fortunately, it’s a stunt that pays off, in pristine contemporary recordings of (mostly) old blues and country songs you can scarcely believe went directly through a cutting stylus direct to disc, not as a series of X’s and O’s.

The climax of the two hours comes when Nelson’s and Haggard’s bus rolls up (without any visible smoke wafting out, believe it or not) and everyone’s two favorite outlaw in-laws stroll out to cut two songs with Burnett and White. In “The Only Man Wilder Than Me,” a song Haggard and Nelson wrote just prior to getting off the bus, apparently; you can see them in the run-up to the one-take recording still working on the distribution of lyrics. Funnily enough, it’s Hag who takes the line “I never did time,” which, in his case, famously counts as pure fiction.

With everyone else who participated in this time-travel experiment picking songs from the 19th century through the 1940s, Haggard and Jones are one of just two acts who wrote a new song to record on the ancient machine. The other is Elton John, who improvises a fresh tune from a lyric he was just given by longtime lyricist Bernie Taupin, with White sitting in for a guitar solo. Taupin has the best line about the mammoth recording device of yore that’s been squeezed into the tiny studio, quipping that he “thought it was an espresso machine.” (Well, steampunk does transcend generations and centuries.)

It’s Jack White in particular whose sense of wonder about the ancient recorder is infectious for the full two-hour length of the doc. He’s so in love with the physicality of music — not just the playing of it, but every last nuts-and-bolts aspect of the analog experience — that he kind of makes you want to run your hands over the lathes and pulleys, too. The machine itself, which took 10 years to reconstruct, is fairy Rube Goldberg-esque in its inventiveness. For one thing, it’s driven by a 105-pound weight that slowly drops to the ground during the (maximum) three minutes it takes to record a tune. At one point, just as Los Lobos have entered the studio and are ready to go, the cord holding the weight snaps in two. That sends the ever resourceful White off to a nearby upholstery shop to sew it back together himself while the Lobos cool their heels back at the studio. (“Where I know you?” asks the woman who runs the repair shop. “I don’t know. Maybe we went to school together!” answers the typically suited-up White.)

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Some of the acts who are interviewed to go along with their performances marvel at the contemporary-seeming nature of the material they’re recreating, as with the hip-hop artist Nas, who gets to repeatedly sing the word that just got Bill Maher in hot water, covering an adultery-themed Memphis Jug Band tune from 1928 that he calls “basically a street rap record.”

But it’s to the show’s credit that it acknowledges a more complicated history of some of this material. Blues-soul legend Bettye LaVette, prior to being seen recording “Tain’t Nobody’s Business,” talks about how, when she first started recording in the early ‘60s, she avoided anything that smacked of the blues she’d grown up with, because the hypersexualization of so many of the songs was “one of the things that made whites look down on the music” and, in harking back to the slaves’ lack of any privacy in their romantic lives, seemed “Uncle Tom-ish” to her, though she ultimately found a different perspective.

For this particular show, LaVette’s qualms aside, it’s all about romance. “This is a very romantic way of recording,” says white. “You can’t fix this later. Any mistakes that happen are going to be there in the finished record. Which is a great place to be. It’s a scary place to be for some people, too,” he adds, almost as a dare — can you, young whippersnapper, take the one-take Jack White challenge?

But director Bernard MacMahon, who championed this project for the better part of this century, makes the best case for this beautiful monstrosity of a machine representing the pre-homogeneity democratization of American music (a point that was made at greater length in a preceding three-part documentary about the original 1920s recordings themselves). “Most of the people making the records had never heard records themselves,” MacMahon points out. “Radio hadn’t come through rural American, so if you were living in Avalon, Mississippi, you hadn’t really heard anything outside your local town. So you can see all the strands of what make up American culture before it starts mingling together.”

Most of the artists who are seen doing one song in the documentary actually cut two while they were in the studio with Burnett and White, which you can find in a two-disc, deluxe version of the “American Epic Sessions” soundtrack coming out Friday. On the PBS show itself, only one number from each act is shown — except for Willie and Merle, who are not only portrayed cutting their own song but also a cover of Bob Wills’ “Old Fashioned Love,” with Haggard playing the fiddle on this one instead of a guitar solo.

That final bonus track from Willie and Merle is fitting: A year and a half after he passed away, we’re still desperate for Haggard to stick around and do time with us.