After the performance of his First String Quartet at the Frankfurt Festival of the International Society for Contemporary Music (ISCM) on 30 June 1927 was met with critical acclaim, Mosolov shifted his focus to composition. He was appointed secretary of the Russian section of the ISCM in 1927 and 1928.
In 1928 and 1929, Mosolov was commissioned by the Bolshoi Theater to compose a futurist imagination of what Moscow would be like in 2117 for a speculative ballet called The Four Moscows. Leonid Polovinkin, Anatoly Alexandrov, and Dmitri Shostakovich were also involved, each to compose Moscow in 1568, 1818, and 1918 respectively, but nothing ever came of the project.