[4] Like his younger brother Julius (1910–2005), a violinist and concertmaster, he studied piano from the age of 17 at the Royal Danish Conservatory under Rudolph Simonsen and Emilius Bangert.
[4][5] As a pianist, Koppel premiered in 1930 at a concert where he included Carl Nielsen's Opus 40, "Theme with Variations", which was enthusiastically acclaimed as "never having been played so beautifully as this evening".
[4] In addition to Nielsen's music, Koppel's repertoire included romantic pieces, especially those by Mozart and Brahms.
He also frequently played more modern music from a variety of composers, including the concertos of Bartok, Hans Werner Henze and Darius Milhaud and pieces by Stravinsky and Arnold Schoenberg.
During the German occupation of Denmark in the Second World War, Koppel, together with his wife and two small children, had to move to Sweden.
His Tre Davidssalmer (1950) was inspired by an episode he witnessed during the war when a group of Jews locked inside a German truck began to sing slowly and softly.
His only opera Macbeth, performed at the Royal Danish Theatre in 1970, was less successful, receiving mixed reviews.