Her aunt, the singer M. Hortik, and her mother's cousin, the famous Russian pianist, music teacher and composer Samuil Feinberg, played a crucial part in her life and upbringing.
Despite her lifelong desire to become a singer and the lessons she took with M. Hortik, Davydova’s vocal talent remained unappreciated for a long time.
While studying piano at the Conservatory she took lessons with the legendary voice coach Dora Belyavskaya, who expressed her doubt that Davydova would ever become a professional singer.
Denisov, recognising Davydova was originally trained as a pianist, was impressed by her abilities as a singer: "perhaps her voice was not really so large, but her internal musicality and her understanding of everything that she performed always astonished."
Furthermore, her accuracy and ability to sight-read were ideal qualities for performing avant-garde music: "if she memorized something, then even if all the instruments around her made mistakes, she would still sing exactly perfectly.
She was the first to introduce Soviet listeners to vocal works of the contemporary Western composers: Charles Ives, Béla Bartók, Luciano Berio, Anton Webern, John Cage, and Paul Hindemith.