The big mystery in the origin story is why Ms. Streisand passed on what, in hindsight, seems like a golden creative opportunity. Back then she was feeling “musically restless,” as she put it in a recent email, and was looking for ways to test herself. Yet Ms. Streisand had qualms about the Legrand/Bergman idea, then referred to as “Life Cycle of a Woman.”

“I don’t think Michel, Marilyn and Alan had fully mapped out their concept yet, except for the basic ‘womb to tomb’ idea,” Ms. Streisand said, adding that in 1973 they recorded five songs intended for the projects, which she released on various albums since. (Among them were “Between Yesterday and Tomorrow,” the new recording’s poignant title track, and the tender lullaby “Mother and Child,” in which the singer plays both roles and essentially duets with herself.)

“The only two songs I didn’t relate to musically or lyrically, at the time,” she added, “were about birth and death. They didn’t want to change them, and then we all became involved in other projects, so the idea lost momentum.”

And there was another, more practical impediment.

“I remember one of the things that made the project slightly complicated was that I’d decided to record standing in the middle of the studio surrounded by the orchestra,” Ms. Streisand said. “It’s thrilling being enveloped by the music, as opposed to standing in an isolated vocal booth with the musicians playing on the other side of the glass. However, it made the record very difficult to mix — because if we wanted to raise or lower my vocal level, it raised or lowered all the music around it!”

Ms. Dessay admitted in a phone interview from France that Ms. Streisand’s decision not to record the full oratorio made things easier. “She didn’t make it her own, which freed me to be the inspiration for the cycle’s completion,” she said. “The inclusion of birth and death speaks to me, and I really wanted to perform that.”