James Muir Mathieson (24 January 1911 – 2 August 1975) was a British conductor and composer. Mathieson was almost always described as a "Musical Director" because he worked in films.

Mathieson was born in Stirling, Scotland in 1911. After attending Stirling High School, he went to the Royal College of Music in London. In the 1930s he was head of the music department for Alexander Korda at Denham Film Studios.

During his wartime service with the Ministry of Information, Mathieson is credited with commissioning film scores from Arthur Bliss, William Walton, Ralph Vaughan Williams and Malcolm Arnold. He composed the music for the films This Happy Breed (1944), Hide and Seek (1963), and Woman of Straw (1964).

Jointly with the composer of the score for the 1953 film Genevieve - the harmonica player Larry Adler - Mathieson was nominated for an Academy Award, in his capacity as Musical Director. Under fierce pressure from the House Un-American Activities Committee, the composer's name was reluctantly omitted from the list of nominees. Mathieson's name as Musical Director (not as composer) went forward. Many years later, Adler's name as composer was restored to the list by the Academy.

Mathieson was also musical director on films with scores composed by others, most notably on Alfred Hitchcock's Vertigo in 1958, where he conducted Bernard Herrmann's score, later releasing an album of the music with the Sinfonia of London.

In the year of Vertigo alone he is credited with musical directorship of 28 films. Overall he is said to have conducted the music for over a thousand British films. His daughter, Fiona Mathieson, became an actress.

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