The folk song trio Þrjú á palli (Three on a Platform) first performed in public when they took part in the production of the play Þið munið hann Jörund (You Remember Jörundur) in 1970. Playwright, author, lyricist and member of parliament Jónas Árnason had written lyrics to Irish, Scottish and English folk songs for the play and decided that he wanted a minstrel trio to perform the songs. He asked Troels Bendtsen, who had played with the Savanna trio for years, to form such a group and Troels got Edda Þórarinsdóttir and Helgi Einarsson to join him. The play was a success and Þrjú á palli performed night after night and sang to an appreciative audience. The trio was then sent to London to record the music from the play in the Marquee Studios and the album Eitt sumar á landinu bláa (One Summer On the Blue Island) was released in March 1970. The album sold well and soon the trio started to play concerts outside the theatre, to much acclaim.

In August 1970 the band recorded the album Við höldum til hafs á ný (We Sail Again) but now they had as many as twenty musicians to back them up. The songs were Irish and Scottish folk songs, to which Jónas Árnason wrote catchy lyrics. In early 1971, Helgi was replaced by Halldór Kristinsson . They trio decided to make a two year plan which entailed that they were going to dedicate themselves to music, release another record of English folks songs to Jónas’s lyrics and then turn to Icelandic folk songs. Soon they were recording their next album which was simply called Þriðja Platan (The Third Album). In July 1971, they performed at several folk concerts in Sweden and later that year they returned to record an album of traditional Christmas carols.

In 1974, Þrjú á Palli released the album Folk Songs From Iceland, featuring ambitious arrangement of Icelandic folk songs.  The trio was one of several Icelandics groups to perform at the Alternitive Music Festival in Stockholm in March 1975 and in the summer of 1975 they collaborated once again with lyricist Jónas Árnason, this time on an album of children’s songs.  That same year, the trio performed at a nordic folk festival at the Garden State Art Center in New Jersey.  In 1976, Þrjú á palli, released their final album, Tekið í blökkina, recorded while Edda recovered from head injuries sustained in an accident.  The album was a collection of sea shanties and the lyrics were once again written by Jónas Árnason.  Þrjú á palli last performed together at a concert in honour of Jónas Árnason on his 70th birthday in 1998.