Tenenbaum studied music at the Kiev Conservatory and obtained a master's degree. She performed with the Kiev Chamber Orchestra and the Kiev Philharmonic from 1979. She was also a soloist and concertmaster with the chamber orchestra Perpetuum Mobile, an ensemble supported by the Ukrainian Union of Composers. Several Russian and Ukrainian composers wrote works for her which she premiered. Dmitri Klebanov composed for her pieces such as a viola concerto and Japanese Silhouettes for soprano, viola d'amore and a mixed ensemble of thirteen players. In 1990, she emigrated to the United States. She has been the concertmaster of the chamber orchestra Philharmonia Virtuosi, founded and conducted by Richard Kapp, from 1993. From 1992, she was the concertmaster for choral concerts of the community chorus The Master Singers of Westchester in the Bedford Presbyterian Church, including Bach's Mass in B minor in 2003 and Mozart's Great Mass in C minor in 2007. She has been on the faculty of the Killington Music Festival, and has lectured at the Metropolitan Museum of Art and the Smithsonian Institution.
Recording
Tenenbaum recorded among others Bach's sonatas and partitas, Locatelli's Art of the Violin, Mozart's violin concertos, and Beethoven's Violin Concerto. She recorded Vivaldi's concerto for four violins in B-flat, RV 553, with her husband Alexander playing 2nd violin. She is known for also playing salon repertory, such as works for violin and piano recorded as Songs Without Words with pianist Kapp, by composers such as Fritz Kreisler and Henryk Wieniawski. A reviewer compared her to Jascha Heifetz and noted: In 1995, she recorded music she played on the Queen Elizabeth 2 with pianist Anton Nel, titled "Tea Time on the QE2". She recorded a viola recital, again with Kapp, of transcriptions and original pieces, Chausson's Pièce pour alto et piano, Op. 39, and Henri Vieuxtemps' Caprice from Hommage à Paganini, Op. 9. A reviewer described her playing of two Hungarian Dances "spontaneous and uninhibited, dramatic with an exciting touch of recklessness". In 1997, she recorded Klebanov's viola concerto and Japanese Silhouettes, a "unique combination of song cycle and viola d'amore concerto", with soprano Natalia Biorro and Kapp conducting the Philharmonia Virtuosi.