Geddes was born in Maryhill, Glasgow in 1941; his father, Jack, was a fireman stationed in Belgium during the war and was a joiner to trade.
A scholarship enabled him to study with Niels Viggo Bentzon at the Royal Danish Conservatoire in Copenhagen.
He lectured at many American universities and European academies, and was composer-in-residence in Hamburg, Berlin and Bremen.
In Postlude for Strings, the players in the orchestra leave the stage one by one (as in Haydn's Farewell Symphony).
His style was an encounter between post-war modernism and Scottish traditions... there was always a web of vivid allusion, formal dexterity and a sense of humour that could break through the dark clouds of serious symphonic thought.