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Born in Holland, Michigan, van Appledorn attended the Eastman School of Music in Rochester, New York, where she studied piano and theory with Bernard Rogers and Alan Hovhaness. She received her Bachelor of Music in 1948, her Masters of Music in 1950, and her Ph.D. in music theory from Eastman in 1966. She also completed post-doctoral studies in computer-synthesized sound at MIT in 1982. She was a member of the music faculty of Texas Tech University from 1950 until 2008. She was the Paul Whitfield Horn Professor of Music from 1989 to 2000.
She composed numerous works for various instrumental combinations and also composed computer music. She had work commissioned by the Music Teachers National Association and National Intercollegiate Bands.