[5] In 1918–19 Jelinek studied with Arnold Schoenberg at Eugenie Schwarzwald's School in Vienna,[6] and privately with Alban Berg.
In 1920 he started the study with Franz Schmidt at the Vienna Academy of Music.
In order to support himself as a self-employed composer in Vienna, he appeared as a pianist in bars and cinemas and composed popular music under the pseudonym Hanns Elin.
[7][8][9] Among his pupils were: Petr Kotík, Gunnar Sonstevold, Maj Sønstevold, Igor Štuhec, Erich Urbanner, Junsang Bahk, Anne-Marie Ørbeck, Gregory Rose, Dawid Engela and Heinz Karl Gruber.
Khosrow Sinai, future Iranian filmmaker, and Alireza Mashayekhi, one of the most important representatives of new music in Persia (Iran), studied under Jelinek[10] for a while.