He became a student of the Royal Conservatoire in The Hague in 1921. He studied violin with André Spoor, piano with Van Beijnum and composition with Johan Wagenaar. After a year (1928-29) at the Berlin Hochschule für Musik under Paul Juon and Curt Sachs – with a scholarship from the Reich – he returned to Wagenaar (1929-30).
Polytonality and atonality did not suit him. After graduating from Wagenaar, in the thirties he worked on his own style, which manifested itself in his Second Symphony (Sinfonia piccola) from 1940 and the songs on poems by Rilke. Orthel was principal study teacher in piano at the Royal Conservatoire from 1941 and principal study teacher in composition at the Amsterdam Conservatoire from 1949. In 1970, he retired from both positions. In the following years he wrote about forty compositions. He was interested in philosophy, cultural history and literature. Orthel was a pianist and composer as well as a pedagogue. He performed as a piano soloist with orchestra, played chamber music and accompanied singers, especially the soprano Ank Reinders, in his own songs. He was chairman of the Department of Composers of the Royal Dutch Performing Arts Association (1947-69) and of the board of the Dr. Johan Wagenaarstichting (1957-72).