Å Jänta å Jag is a song tune that is an essential part of the Swedish national culture. It was composed around the beginning of the 20th century, and was already recorded in 1904.
The composer was Fredrik August Dahlgren, from the province of Värmland. It has become a standard dance tune and song dance in every corner of Swden since then.
Considered a “gammaldans (old-time dance” tune, it is seldom played nowadays by fiddlers except at Midsommar and Christmas festivities. But EVERYONE in Sweden knows it, and it is most often either sung or played on accordion.
On YouTube there are scores of recordings, almost all of them either song or accordion. There are also some recordings there of regional dance variations of the tune.
Here is a video of a youth group with fiddles and accordions playing it for the dance called hambo.
And to the left is a video of me playing it alone.