Tønnesen was born February 27, 1955, in Oslo. His parents were both scientific researchers, but he showed early talent on the violin, and after studying at Oslo's Veivet Music School, he took first prize at a contest in Lausanne, Switzerland, at age 16. That won him admission to the conservatory in Bern, where he studied with Max Rostal. Tønnesen also attended summer classes in Trondheim, Norway, and he and a group of like-minded young players continued their work in a university seminar at the Folkeuniversitetet in Friundervisningen. The Norwegian Chamber Orchestra (in Norwegian, Det Norske Kammerorkester or DNK) grew out of these interactions and made its debut in 1977 with Tønnesen as leader. He then became artistic director, sharing that position for many years with British violinist Iona Brown and continuing in the role after her death. The Norwegian Chamber Orchestra, with Tønnesen at the helm, almost immediately began to attract the attention of recording companies; its first album, of Baroque flute concertos, appeared on BIS in 1978. It has recorded for Simax, Virgin, Naim, Chandos, and many other labels, moving to Lawo Classics in 2017 for a recording of Leos Janacek's two string quartets, arranged for string orchestra.
Tønnesen became the face of the orchestra. He specialized in works like Vivaldi's Four Seasons that demand a charismatic violin soloist, and his appeal easily made the transition to recordings. Independently of the Norwegian Chamber Orchestra, Tønnesen has recorded for ECM, Simax, BIS, and other labels, issuing a pair of recordings on BIS in 2017 with a new group, Camerata Nordica, devoted to "mad songs" of Biber and Telemann and to chamber orchestra works of Mozart.
A composer as well as a violinist and leader, Tønnesen has written music for stage productions performed at the Nye Theater in Oslo. ~ James Manheim, Rovi