Sigmund has continuously released albums since 1975. These are the standard original covers for his Norwegian albums, both solo albums and collaborations. Re-editions or foreign editions may have different artwork.
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- 2023 – Kjenslevev
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- 2021 – In Concert
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- 2020 – The sound of Telemark
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- 2019 – Songs for harmonica
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- 2018 – Bønn for drømmen
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- 2016 – Concerto
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- 2015 – Tradition
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- 2014 – Harmonica Hits
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- 2012 – Classical Harmonica
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- 2010 – harmOrgan (with Iver Kleive)
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- 2007 – Grieg Album
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- 2005 – PhilHarmonica
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- 2004 – Here, There and Everywhere
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- 2003 – Over the Rainbow
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- 2001 – Vi på Langedrag
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- 2000 – Innunder jul (with Iver Kleive)
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- 1998 – Harmonica Album
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- 1996 – I godt lag (2CD compilation)
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- 1995 – Til Telemark
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- 1993 – Siesta
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- 1991 – Nattønsker (compilation)
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- 1990 – Nordisk natt
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- 1988 – Aria
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- 1988 – Sigmund Groven (compilation)
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- 1986 – Marit og trollstenen (with Ove Røsbak)
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- 1985 – Colour slides
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- 1983 – Songar utan ord (with Henning Sommerro)
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- 1981 – Lævandes dikt (with Ove Røsbak and Iver Kleive)
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- 1981 – Kom sol på alle mine berg (with Geirr Lystrup)
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- 1981 – Musikken inni oss (with Arve Tellefsen)
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- 1979 – Motlys
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- 1977 – Musikk for en lang natt (with Ketil Bjørnstad)
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- 1976 – Music for two Harmonicas (with Tommy Reilly)
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- 1975 – Så spiller vi harmonica
Many of the CDs are available to buy from Grappa (worldwide shipping possible).