They gave themselves a usefully loose concept. They would become Sgt. Pepper’s Lonely Hearts Club Band, setting aside all outside expectations of the Beatles and treating the album as a performance complete with canned audience reaction: a theatrical, distancing device.

While the Beatles had traveled the world, only “Within You Without You” flaunted the exotic. Mostly, Sgt. Pepper’s band was almost provincially British: wandering London in “A Day in the Life,” telescoping an entire middle-class English life (complete with prospective grandchildren) above a music-hall bounce in “When I’m 64.” Stalwart British brass answered the rowdy distorted guitar in “Sgt. Pepper’s Lonely Hearts Club Band”; “She’s Leaving Home” is a stately waltz set to a harp and parlor orchestra that might have accompanied high tea. One of the Beatles’ paths forward led through an expanded embrace of the past.

They rejected any generation gap. The album cover set the 1967 Beatles, with their mustaches and shiny mock band uniforms, alongside their suited, mop-topped pop-star wax statues — so recent, yet so distant — and cultural figures like Karlheinz Stockhausen, Sonny Liston and W. C. Fields, a rightful claim to adult significance. But the LP was also packaged with cardboard cutouts — a mustache, military stripes — like something for children. While the Summer of Love nurtured hippie dreams of creating a new world, the Beatles reminded listeners of how entrenched the old one was, and how comforting.

But at the same time, “Sgt. Pepper” gazed forward in sound and sense. The Beatles and their producer, George Martin, concocted eerie, unforgettable sounds from hand-played instruments and analog tape tricks; “Strawberry Fields,” which miraculously interweaves two arrangements of the song in two keys, remains a marvel of internal disorientation. And despite all the vintage references, “Sgt. Pepper” situated its songs in the present: sometimes a rushed, workaday world and sometimes a mind-altered escape. The album’s magnificent, sobering finale, “A Day in the Life,” understood — and anticipated — the ethical and emotional ambiguities of a world perceived through mass media, even back when the news media was just newspapers, radio and television.

“Sgt. Pepper” had an immediate, short-lived bandwagon effect, as some late-1960s bands sought to figure out how to make those strange Beatles sounds, and others got more studio time and backup musicians than they needed. Artistic pretensions also notched up. And the pendulum started its long-term swings: progressive rock and corporate rock would be swatted back by punk and disco, hair metal would be blasted by grunge and hip-hop. The studio artifice that “Sgt. Pepper” daringly flaunted has long since become commonplace.

Yet while “Sgt. Pepper” has been both praised and blamed for raising the technical and conceptual ante on rock, its best aspect was much harder to propagate. That was its impulsiveness, its lighthearted daring, its willingness to try the odd sound and the unexpected idea. Listening to “Sgt. Pepper” now, what comes through most immediately is not the pressure the Beatles put on themselves or the musicianly challenges they surmounted. It’s the sheer improbability of the whole enterprise, still guaranteed to raise a smile 50 years on.