Duke Ellington’s “Cottontail” is primarily known as a virtuoso showcase for the amazing tenor saxophone of Ben Webster. Yet my favorite moment in the piece occurs just after that legendary solo: In what classical musicians would call a “tutti” passage, all the brass players reunite to play a vigorous, ascending series of phrases (derived from the chords to the bridge of Gershwin’s “I Got Rhythm”).

The pure sound of the number alone is inspiring enough, but in the “soundie” (I will explain in a minute) for “Cottontail,” we are shown a group of jitterbug dancers; at the moment when that phrase occurs, three girls fly into a series of gravity defying somersaults, transforming into superhuman projectiles that flash across the screen in perfect rhythm.

I saw that scene for the first time some 30 years ago, and ever since then, I have watched it hundreds of times, nearly as often as I have played Ellington’s classic 1940 recording. More important, every time I hear the song, whether played by Ellington or someone else, in concert or on a recording, I replay that image in my head, of those nine dancers moving to the swinging majesty of the Maestro’s masterpiece.

This moment is the opening salvo of “The Soundies: A Musical History,” a 76-minute documentary making its premiere Thursday on PBS, hosted by the singer and pop music authority Michael Feinstein. As Mr. Feinstein and Mark Cantor (the world’s premiere historian on the subject) explain, the soundies were a series of three-minute films made by the Mills Novelty Company between 1940 and 1947 — about 1,865 in all. The soundies were made to be exhibited in “Panoram” machines, innovative audio-video jukeboxes in which 16 mm film was projected through a series of mirrors onto a screen roughly the size of a TV set or computer monitor for a dime a throw.

During the war years, as Panoram machines were installed in bars, roadhouses, diners, and other public establishments, the soundies were so popular that studious had trouble turning them out fast enough: Three studios were set up, in New York, Hollywood, and Chicago, with the objective of producing eight of these three-minute filmettes a week. Performers would record the audio portions first, then lip-synch to them on camera a few days later.

The Mills Novelty Company didn’t have access the biggest names, such as Bing Crosby, Benny Goodman, or Tommy Dorsey — except among the black community, where it could get top talent like Ellington, Cab Calloway, Count Basie, and a young Nat King Cole (shown singing “The Frim Fram Sauce” while seated at a table in a restaurant, trying to get the attention of a waiter and, in a surreal move, interacting with himself on a panoram screen).

As the jazz historian Dan Morgenstern explains in the film, the soundies catered to every taste, from romantic crooners such as Buddy Clark, to country acts such as Merle Travis, to comedy musicians like Spike Jones and Mel Blanc, to all manner of swinging big bands, and vocal groups and dance acts. Nothing beats the amazing combination of the Ellington band and the famous swing dance troupe, Whitey’s Lindy Hoppers. At the opposite end of the spectrum is the Martins, a marvelous vocal group led by future songwriter Hugh Martin, whose lovely harmonies are misdirected into a novelty instrumental by Raymond Scott; in the background, a bizarre ménage à trois involving a drunk, an obese woman, and a duck makes things even stranger.

Contemporary documentarians and video producers inevitably compare the soundies phenomenon to MTV, and PBS’s show does the same. The idea is to make them seem more relevant to a modern audience, but with MTV having largely abandoned the music video in favor of lowbrow reality shows in recent years, the producers should instead have noted that soundies were the YouTube of the 1940s. (Naturally, hundreds of soundies are currently available for viewing on youtube.com.)

Likewise, it’s an obvious tactic to get some contemporary musical figure to talk about the performers in the soundies — and it makes perfect sense to have Mr. Feinstein and Wynton Marsalis here as talking heads. But why do the producers think the 60-year-old smooth jazz keyboardist George Duke and the lead singer of a group called Wall of Voodoo, Stan Ridgeway, will appeal to the younger demographic — why not John Pizzarelli or Diana Krall? In fact, the producers sabotage “Cottontail” by cutting to Mr. Duke at the climax, just so he can say the name “Duke Ellington” three times, as if it were “Beetlejuice.” It would have made more sense to have Jay-Z tell us that Cab Calloway was the original rapper.

Yet this cheesiness is part and parcel of the soundies tradition: PBS’s program features excellent segments dedicated to the use of jingoistic flag-waving visuals, the copious amounts of cheesecake and soft-core porn (there are feasts for any eyes that appreciate women in uniform, such as Lois Collier and the Glamourettes), and black performers surrounded by iconography that isn’t so much politically incorrect as blatantly racist (e.g. the great dancer Dorothy Dandridge doing the jig in the jungle in Hottentot drag while a bespectacled cannibal stirs a pot with his trombone). We also see the magnificent Louis Armstrong and his orchestra togged out in respectable dinner jackets in front of a giant shoeshine stand — there’s no shortage of watermelon, dice, and burnt cork faces.

But of course, there are also soundies featuring the marvelous Nat King Cole Trio, with a beautifully shot close up of his hands working their musical magic; the frenetic energy of Louis Jordan and his Tympany Five; and Claude Thornhill’s forward-thinking orchestra, complete with French horns. And there’s a segment for old movie buffs with a very young Cyd Charrisse and Yvonne DeCarlo, as well as Doris Day before she had her teeth fixed and Walter Liberace before he ditched his first name.

But the best moments are when the editors wisely intercut new interviews of surviving soundies performers — like Kay Starr, Les Paul, the conductor Van Alexander, the pianist Irving Fields, and the singer Ginny Mancini of the Mel-Tones — with vintage soundies footage from 60 years ago. Surprisingly, no behind-the-scenes personnel are interviewed or even mentioned — not even James Roosevelt, the president’s son, who was one of the original partners in the venture.

“The Soundies” has its faults, but it’s a worthwhile effort, helping us to understand what this incredible music looked like to the generation that created it.

wfriedwald@nysun.com