Tina Turner pulled off the most unlikely, the most surprising and stunning and deserved comeback in rock history with 1984’s “Private Dancer.”

At 45, Tina was old in 1984, and the rock and pop field was crowded with young talent. Michael Jackson’s “Thriller” spent the first three and half months of the year in the No. 1 spot. Behind Jackson, fresh stars rushed in with landmark releases — Madonna’s “Like A Virgin,” Prince’s “Purple Rain,” Wham!’s “Make It Big.” Just into their 30s, Bruce Springsteen and Lionel Richie were the older stars.

But with “Private Dancer,” Tina overcame age, and half a dozen more industry stigmas. A quarter of a century into her career, she defied critical incredulity — four different production teams on one album (gasp!). She did this by letting her voice and attitude bind a set of tunes that shouldn’t work together on an album.

Three of the record’s singles dominated radio and the charts with distinctive sounds. The first breakout, “What’s Love Got to Do with It,” hit No. 1, won three Grammys, and embodied ’80s Top 40 while contradicting it — the music is all Billy Ocean; the words and vocals shattered but defiant and totally un-bubblegum. In the title track, she predicts the sophisti-pop of Sade (another new face in 1984) with a slinky French Riviera groove and lyrics about the exploitation of women. Then there’s “You Better Be Good to Me” — the era’s “Respect,” complete with epic hook, righteous crescendo, and earned bravado.

The rest of the album is just as diverse as the singles: en vogue styles, old fashion rhythm & blues, and big rock ‘n’ roll.

There’s stuff that winks at new wave (“Show Some Respect”) and stuff that wallows the jagged edges of the synth genre (Bowie cover “1984”). There’s stuff that shows off her r&b credibility with both retro and contemporary approaches. Classic Memphis soul nugget “I Can’t Stand the Rain” has neon “Miami Vice” vibes; the Beatles’ “Help!” reborn into a broken, gospel-like ballad that could be from 1965.

“Private Dancer” emerged during an era when the line between rock and pop was blurry, see “Beat It,” “Purple Rain,” “Dancing in the Dark.” And Tina charged into that era wanting to be a rock star. Around the release of the record, Tina Turner told her manager, “My dream is to be the first Black rock ‘n’ roll singer to pack places like the Stones.”

She released that dream by headlining stadiums around the world. But she never limited herself to just rock, and that’s obvious on “Private Dancer.”

You can find the magic rock, pop, and r&b of “Private Dancer” in a bunch of different reissue formats recently released to celebrate the album’s 40th anniversary — (5CD/Blu-ray package, double CD, LP Pearl vinyl, and LP picture disc). All of them are worthy. Feel free to dig deep into Tina with one of the deluxe packages, but make sure you at least explore the stunning original LP.