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Mary Elizabeth, I'd appreciate if you would qualify what you mean by 'seriously beloved.' Are you using the term 'seriously' to connote that ABBA's popularity is rooted in some sort of deep 'seriousness' of their work or the respect afforded it, or are you using the term hyperbolically, like a valley girl saying 'I SERIOUSLY love this new neon headband'?
I'll grant that ABBA deserves as much respect as Madonna or any number of other major pop success stories for their ability to craft highly professional, listenable, and enduring pop tunes, and though they don't suit my personal taste or aesthetic, I don't mind shaking a leg to 'Take a Chance on Me' or crooning along with 'Fernando' if it happens to pop up on the radio when I'm traveling.
But comparing the Beatles to ABBA is like comparing Bob Dylan to Tin Pan Alley. ABBA, from its inception, was making commercial dance music. While the Beatles started out with a similar goal, they ended up going a lot further with the pop form, which is why my brow furrowed when I read the comparison in the title for your piece.
It's silly for people to let their fur stand up over pop music assessments, but there does seem to be a useful distinction here. The Beatles--at least, from 'Revolver' on--led a vanguard of artistic and intellectual experimentation with pop music forms and had an influence that stretched far beyond the realm of pop. ABBA, it seems to me, was always and forever a commercial hit machine with no artistic goals other than to make catchy tunes that would get people dancing and feeling good.
Making people dance is an absolutely valid purpose for pop music (we'd probably all be better off if fewer groups were trying so hard to be taken 'seriously'), and while I don't revere ABBA or, say, the Bee-Gees or the Doobie Brothers or Madonna or Michael Jackson the way I do the Beatles and the Who or even U2 and Radiohead, I dig their tunes and recognize them as 'classics' of a sort. But I don't have any problem comparing 'Dancing Queen' to, say, Kool & the Gang's 'Celebration' or Lionel Richie's 'All Night Long,' and I don't hear anyone trying to compare those dudes to the Beatles. It would be fairer to compare ABBA even to Elvis rather than the Beatles--the King, after all, despite his phenomenal originality and influence, was always a tightly controlled pop product whose music was primarily meant to be danced to.