Avidom was born Mendel Mahler-Kalkstein in Stanislaviv, Austria-Hungary, in 1908. This put him in Poland after World War I. He emigrated to Mandate Palestine in 1925 and, soon after, went to study at the American University of Beirut (from 1926 to 1928). After further studies at the Paris Conservatory (from 1928 to 1931), he moved to Tel Aviv, where he taught music theory.