The song is 'Ein ledig tag' ('A day off', 'A free day'). The setting is 26 September 1967, on a popular Swedish TV show, Hylands Hörna (although some versions of the videotape are date-stamped September 3).
It's a near virtuosic song, but Frida's pitch is perfect, and her expressive choices are beautiful. She's already a consummate professional, handling awkward questions at the beginning straightforwardly, firmly but lightly.
The segment reminds us of just how talented and, in Frida's case, feted the Abba boys and girls were as individuals. It's easy to imagine Frida fans from the '60s (and her teachers perhaps) originally tut-tutting that with Abba she was squandering her talent on pop music for kids, and that she was 'slumming it' by signing up with Benny and Bjorn in the 1970s.
Bonus Awesomeness: Frida sings a reworked Swedish version of 'Alice Blue Gown' in 1970. That vid. vaguely reminds one of Cremaster 1.
Wouldn't Frida have made a great Queen of Chain for Cremaster 5 had Ursula Andress not done it?!
And this is the best - ridiculously sunny day etc. - it ever looks. To get the full effect of this one you have to encounter it on a gloomy winter late afternoon when all of its thousands of slats and struts are sloshing water down at you as you walk past. Your life may be miserable but at least you don't have to work in that, at least you didn't design that.