Jónsi is a pseudonym of, at least, two Icelandic artists:

1) Jón Þór Birgisson is the lead singer and guitarist for Sigur Rós and half of Jónsi & Alex, known for his soft falsetto voice . He released his solo debut album, Go, on April 6, 2010.

Birgisson grew up in Iceland, raised by parents who weren't particularly musical; his early memories include playing The Beatles at double speed on his turntable and listening to and playing along with Iron Maiden records. You can hear him speak at length about his musical past and loves in a recent episode of "All Songs Considered," in which Birgisson plays guest DJ. His history as Sigur Ros' singer and guitarist spans 16 years, during which time the band has released five studio albums and coined a unique sound that has yet to be matched by any act since.

2) Jón Jósep Snæbjörnsson (b. 1 Jun '77), is a singer & member of Í Svörtum Fötum ("In black clothing"). He was Iceland's Eurovision Song Contest 2004 representative, finishing 19th. He has also competed at Söngvakeppni Sjónvarpsins 2007, which is a television show to pick Iceland's song for the Eurovision Song Contest with the song Segðu Mér.
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Artist biography from last.fm