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Early life and education 
Kolisch was born in Klamm, Schottwien, Lower Austria and raised in Vienna. His father (also named Rudolf Kolisch) was a prominent physician and a Dozent at the University. Due to a childhood injury to the middle finger of his left hand, Kolisch, who had already begun to play the violin, relearned the instrument with the functions of the hands reversed. Following service in World War I, Kolisch attended both the University and the Musikakademie, where he studied violin with Ottokar Ševčik, composition with Franz Schreker and conducting with Franz Schalk, intending at first to make a career as a conductor. One of his two sisters was Gertrud Schoenberg.
In 1919 he began studying composition with Arnold Schoenberg, who later became his brother-in-law (1924). He put Kolisch to work in the "Society for Private Musical Performances in Vienna" (Verein für musikalische Privataufführungen in Wien). This led to the creation of a string quartet ("Wiener Streichquartett") to perform both Schoenberg's music and the classical string quartet repertoire in a manner that would take into account the principles of Schoenberg's teaching. Schoenberg directed many rehearsals of this quartet. By 1927 the ensemble had become known as the Kolisch Quartet. Numerous works were written for this ensemble by composers including Alban Berg, Anton Webern, Schoenberg, and Béla Bartók.
Stranded in New York by the entrance of the United States into World War II, Kolisch at first tried to keep the Quartet together. When this failed, he took a position on the faculty of The New School, lecturing on "Musical Performance: The Realization of Musical Meaning". With Otto Klemperer, he co-founded a chamber orchestra at the school, with which he gave the first U.S. performances of Bartók's Music for Strings, Percussion and Celesta, Igor Stravinsky's l'Histoire du Soldat and Schoenberg's Chamber Symphony No. 1. During this time he prepared the ensemble and participated in the recording of Schoenberg's Pierrot lunaire, conducted by the composer. He researched and wrote an article, "Tempo and Character in Beethoven's Music" which was presented to the New York chapter of the American Musicological Society and later published in two installments in the magazine Musical Quarterly.
In 1944 Kolisch was invited to the University of Wisconsin–Madison to become the new leader of the Pro Arte String Quartet (recorded as the first "Quartet in Residence" at any U.S. university). He was also granted a full Professorship. In the 1950s he began to tour in Europe again as a recitalist. He became a member of the faculty at the Internationale Ferienkurse für Neue Musik in Darmstadt, Germany, along with his close friends and long-time associates Eduard Steuermann and Theodor Adorno. Except for one year (1956) spent in Darmstadt, he remained active in Madison until reaching the mandatory retirement age in 1966.
At that time he was invited by Gunther Schuller to become head of the Chamber Music department at the New England Conservatory in Boston. He remained on the faculty until the end of his life. During the summers of 1974 through 1977, he also taught chamber music performance at the annual Schoenberg Seminars in Mödling, Austria near Vienna.
Marriage and family 
Kolisch was married in the 1930s to Josefa Rosanska (b. 1904, d. 1986), a concert pianist; the marriage ended in divorce. In the early 1940s he married Lorna Freedman (b. 1917, d. 2006), a professional violinist and violist.
Legacy and honors 
- The papers of Rudolf Kolisch are held in the Manuscript Department of the Houghton Library at Harvard University.