Douglas Durant, a close friend of Ms. Rittmann's, said the cause of death was respiratory failure.
Born Gertrud Rittmann in Mannheim, Germany, in 1908, Trude Rittmann immigrated to the United States in 1937, where she was engaged by Lincoln Kirstein as concert accompanist and pianist for George Balanchine's American Ballet Caravan, the precursor to New York City Ballet. During her years as musical director for the troupe, she worked closely with composers such as Aaron Copland, Elliott Carter, Virgil Thomson, Leonard Bernstein and Marc Blitzstein.
In 1941 Ms. Rittmann became a concert accompanist for choreographer Agnes de Mille, who invited her to be dance arranger for the 1943 Broadway musical One Touch of Venus, choreographed by de Mille and composed by Kurt Weill.
Over the next three decades Rittmann would be credited with the dance and/or vocal arrangements for more than 50 Broadway musicals, including Finian's Rainbow, Peter Pan, Fanny, Brigadoon, Paint Your Wagon, My Fair Lady, Camelot, Gigi, Bloomer Girl, On a Clear Day You Can See Forever, Two by Two, Miss Liberty, Gentlemen Prefer Blondes and Rodgers & Hammerstein's Carousel, Allegro, South Pacific, The King and I (creating the innovative percussion score to the ballet, "The Small House of Uncle Thomas," according to the Rodgers & Hammerstein Organization) and The Sound of Music (creating the rapturous choral arrangements)
She also arranged the ballet music in the film of "The King and I," and contributed arrangements for lesser-known musicals, including Hot Spot, Christine, At the Grand and more, and composed ballet music for Look Ma, I'm Dancin'!, Juno and provided "musical continuity" to such shows as Wish You Were Here and All American. As a composer, Ms. Rittmann provided music for television programs as well as several original ballets.
She is survived by her nephew, Peter Krebs, of Wigton Cumbria, England.