There is an award for Original Music Score.
No.
None. The 70th Academy Awards took place in May 1998. Fiddler on the Roof was released in 1970 and therefore was ineligible for consideration in 1998.The film won three Academy Awards and two Golden Globes in 1971. It won Academy Awards for Best Original Score, Best Cinematography, and Best Sound. It also won Golden Globe's "Best Motion Picture (Musical or Comedy)" category, and "Best Performance by an Actor in a Motion Picture - Musical or Comedy" for Topol's acting.
Three new categories were introduced at the 1934 Academy Awards: Best Original Song, Best Original Score and Best Film Editing.
Five.
No. Jones, who has been nominated seven times for Academy Awards, served as the musical director of the 43rd Academy Awards ceremony on April 15, 1971. That night, he accepted the 1970 Oscar for Best Original or Adaptation Score on behalf of the winners who could not be there -- the Beatles, who won for their music in the documentary "Let It Be."
The 1961 musical swept the 1962 Academy Awards.
None. "Cars," a 2006 film by Disney/Pixar, received Academy Award nominations for Best Animated Feature and Best Original Song ("Our Town" by Randy Newman). It did not win in either category.
There is no horror category for Academy Awards consideration.
Golden Laurel Award in 1966 Musical Category.
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Neither Howard Hawks' 1932 original nor Brian De Palma's 1983 remake won Academy Awards.
"Annie" the musical has won several awards, including seven Tony Awards, including Best Musical, Best Original Score, and Best Book of a Musical. It also won a Grammy Award for Best Cast Show Album.