“Mamma Mia!” is a joyful experience but consider this sad nugget: The characters in this jukebox musical exist in a world where there is no Abba.

Like Maria von Trapp or Ado Annie trilling Rodgers and Hammerstein, the songs are simply part of their way of expressing themselves, so these poor folks never got to hear Abba’s “Waterloo” blasting from a radio or “Knowing Me, Knowing You” as part of a Spotify playlist labeled “Songs That Make Me Instantly Happy.” If you think about it, which the almost 100 percent idea-free show would prefer you not do, it could almost make you sad.

In eight touring-company visits to the Twin Cities, two movies and now an Ordway production, “Mamma Mia!” is a convincing argument for these songs’ greatness. The truncated cover versions in some jukebox musicals — I’m looking at you, “Motown” — just make you wish you were listening to recordings of the timeless originals. But that’s not the case with “Mamma Mia!,” which reveals that Abba’s hits are about the impeccable, synthy production as much as the vocals.

That sound is faithfully duplicated at the Ordway under conductor Raymond Berg, whose “orchestra” of nine features four keyboards, but the songs are enriched by a cast of big-voiced, Broadway-style belters.

Christine Sherrill’s “The Winner Takes It All,” for instance, is the show’s 11 o’clock number, a powerful blast of heartache that feels like it was created for the show, not plucked from “ABBA Gold” and sandwiched in. Erin K. Schwab and Aloysius Gigl turn “Take a Chance on Me” into a winning character number and “Dancing Queen” showcases steps that include the Cabbage Patch and Ann Michels’ expert Moonwalk.

The large chorus is an asset in most of those songs, filling out Abba’s wall of sound, but director Martha Banta makes peculiar use of it in the second act. That’s when “Mamma Mia!” shifts to more intimate scenes, so the chorus members aren’t around, but, weirdly, while a couple are singing a confessional number in the bedroom, we hear dozens of disembodied voices accompanying them. For four straight songs, including “S.O.S.,” we’re left to wonder: Where are those voices coming from? And why are they trying to drown out the stars?

Earlier, I used the word “characters” and that was a mistake. There are no actual characters in “Mamma Mia!,” in which a young woman invites three strangers to her wedding at her mother’s inn in Greece so she can discern which of them is her “sperm donor.” Throughout the show, various people behave in various ways that don’t make sense until we get to one of those finales where it’s best to take a gulp of our Acropolis cocktails (ouzu, lemonade and grenadine) while the show “explains” everything and pairs everyone up randomly. To be fair, this practice goes back at least as far as Shakespeare.

Abba may not be in Shakespeare’s league, quite, but “Mamma Mia!” assures us that the group’s songs will survive. Their ingenious catchiness often is used by one person in the show to cheer up another — or, in a series of three encores at the end of the show, to hand-deliver that good cheer directly to the audience. Whatever their lyrics happen to be saying, Abba’s songs are about hope and joy, and that is something that will never go out of style.