Rasmussen studied in Norway, then returned to Tórshavn in the Faroes as a music teacher and jazz pianist. From 1990 to 1995 he studied musical composition at the Royal Danish Academy of Music in Copenhagen under Ib Nørholm and electronic music under Ivar Frounberg. In 1992 he received grants from the Leonie Sonning Foundation and the Danish Composer's Society.
He also became familiar with spectral music, which has its roots at the IRCAM in Paris, and the work of composers such as Tristan Murail. Rasmussen has produced a number of works combining electronic and acoustic instruments, some produced in co-operation with DIEM (the Danish Institute for Electro-Acoustic Music).
In 1997, he was awarded a three-year grant from the Danish State Arts Foundation.
In 2002, he won the Nordic Council Music Prize for his Symphony no. 1 - "Oceanic Days", which, in the NOMUS committee description: "derives its inspiration from Faroese nature and from age-old Faroese hymns, from which Rasmussen has created a work of comprehensive dimensions. It radiates a natural artistic integrity, combining tightness and structure with lyric feeling."
In 2004, he was visiting composer at the prestigious Korsholm Festival in Finland, while in 2010, he received the Faroese Cultural Prize from the Faroese Department of Culture. In 2013, he participated in the residency and concert series Other Minds in San Francisco.
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Rasmussen’s music always has a natural complexity, combining his jazz background with a rich tradition of Faroese folk music and electroacoustic and spectral music. He transforms folk music themes using spectral and serial techniques, using intervals in the original melody to generate rhythmic segments and harmonic overtone spectra to determine the melodic and timbral material; the result is an abstraction from Faroese traditional music, even though none of the original melodies can be discerned in the finished composition. He also draws much inspiration from the Faroese author and artist William Heinesen (1900-1991), using both the text and the mood of Heinesen's poetry in his music.
The result is highly evocative, beautiful, and not difficult to listen to. The power and complexity of his music often reflects nature, shimmering with energy and movement.
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His works include:
Orchestral works:
1990: Grave - In memoriam Karsten Hoydal for string orchestra + percussion (11 or 22 strings: 3.3.2.2.1) (09'00)
1995: Vox Humana, the song of the sea - for orchestra and tape for 3.3.3.3/4.3.3.1/timpani/2 percussion/harp/strings (22'00)
Rasmussen - Symphony No 1; Saxophone Concerto, Danish National Symphony Orchestra, Hannu Lintu (Conductor), Jeanette Balland (saxophone) - Da Capo, May 2005
Sunleif Rasmussen - Surrounded: Arktis (The Arctic), Mozaik / Miniature, Tilegnelse (Dedication), Trauer und Freude, Helene Gjerris (mezzo-soprano), Caput Ensemble, Guthmundur Oli Gunnarsson, Guthni Franzson - BIS Records
Cantus borealis: Wind Music from Faroe Islands includes Rasmussen: Cantus Borealis for wind quintet, Reykjavík Wind Quintet - BIS Records
Landid for Soprano And Symphony Orchestra, Gerandisdagur I Havn For Soprano And String Orchestra, Grave In Memoriam Karsten Hoydal For String Orchestra, Clarinet And Percussion, Klarinettkonsert Concerto For Clarinet And Orchestra - The Orchard, May 2000
Skærur Vindur includes Sig mær, hví er foldin føgur, Kvøldvísa um summarmála, Syngjandi grót, Sóljurnar og náttin, Blátt, Fyrsti sálmur Dávids, Vár, Skærur vindur and Tid, Ild, Baglæns - The Orchard, April 2000