Tarnowsky was born in Kiev. His mother was a singer who had studied in Italy, and his father was a jurist. Visiting musicians often visited the family home and Sergei showed an interest in the piano at an early age. At the age of eight he studied privately with Henryk Bobinski, a graduate of the Warsaw Conservatory. At age 19 he commenced studies with Anna Yesipova at the St. Petersburg Conservatory. The director of the Conservatory was Alexander Glazunov, whose stepdaughter Tarnowsky later married. On graduation, Tarnowsky received a gold medal and the Anton Rubinstein Prize.
He went to teach at Odessa, where he appeared as soloist under Vasily Safonov. Safonov was so impressed that he arranged for Tarnowsky to appear with the Berlin Philharmonic in a program of three works for piano and orchestra - concertos by Tchaikovsky and Rachmaninoff, and a Fantasy by Arensky. He then toured other European cities.
In between concert tours, Tarnowsky worked at the Mariinsky Theatre with Albert Coates. He then become piano professor at the Kiev Conservatory, where he taught Vladimir Horowitz and was his only teacher from the years 1914 to 1919 (Horowitz was 11 years old when he first entered Tarnowsky's class and 16 when he left to study with Felix Blumenfeld). His other students at Kiev included Alexander Uninsky, Vladimir Yampolsky and Anatole Kitain. Tarnowsky married Glazunov's stepdaughter in 1928 and they moved to Paris. They emigrated to the United States in 1930. In 1933 he joined the De Paul University School of Music in Chicago and appeared in concert with artists such as Nathan Milstein, William Primrose, Raya Garbousova and Maria Kurenko. He recorded an album of Tchaikovsky songs with Kurenko.
He married one of his pupils, Maxine Matlavish, and they settled in California, where from the 1940s until his death he was one of the most sought-after piano teachers. Among the many pianists he taught during his years in Southern California is the Cuban virtuoso Horacio Gutiérrez, who Tarnowsky claimed was the biggest pianistic talent he had encountered since Vladimir Horowitz.
Other students included Rebecca Anna Lou Melson, later to become the wife and widow of William Kapell (she is now known as Anna Lou Dehavenon) and Madeleine Stowe, who gave music up to become an actress when Tarnowsky died.
- Ancient Faces
- Liner notes from Vignettes of Old Russia, Genesis Records
- Schonberg, Harold C. (1992). Horowitz: his life and music. New York: Simon & Schuster.
Tarnowsky thought that Gutierrez was the most phenomenal pianistic talent he had encountered since the young Horowitz and he said exactly that in a testimonial letter to the young pianist