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" (). This led to the creation of a string quartet ("") 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==