At age 12-13 he began studying the violin but soon switched to viola and at sixteen was accepted into the Royal Swedish Academy of Music.
During the 1940s Allgén belonged to the ’Monday Group’ (Måndagsgruppen) along with other radical modernist composers such as Karl-Birger Blomdahl, Sven-Erik Bäck and Hans Leygraf.
Lacking income, Allgén was forced to live on social benefits and refused to accept early retirement.
Allgén’s entire musical production was long alleged to be technically unplayable but recent consideration has shown this to be untrue.
The fire destroyed parts of his musical production, including his last composition Horror Vacui, written for the Stockholm Saxophone Quartet.