Sergey was born in Odessa, in a wealthy Russian-Jewish family, the son of 1st guild merchant, composer, and pianist Adolf Barjansky (c. 1850 – 1900 Odessa, Russian Empire) and Maria Clara Weisstein (1861 Tarnopol, Galicia (Eastern Europe), Austria-Hungary – 1927 Vienne, Austria).

Serge's father, who studied piano and composition with Ignaz Amadeus Tedesco,[2] Carl Reinecke, and Salomon Jadassohn, was a composer of classical music for solo piano and chamber music ensembles in the Romantic tradition.

While following his doctorate in mathematics from the Imperial Novorossiya University in his home town, Serge studied the cello at the Royal Conservatory of Music of Leipzig with Julius Klengel[3] (1859-1933), famous cellist of the Leipzig Gewandhaus Orchestra.

Serge's debut was on 17 February 1906 in Leipzig, performing the concertos for cello by Karl Davydov and Édouard Lalo.

[1] He later wrote about this period "The war, the Russian revolution, twenty years of life lost in Turkey where musical activity was impossible, and where one had to struggle to obtain the means of bare existence, all combined to retard my work.