"I thought, you know, this is the height of arrogance, to think that I could sing this score, because I'd heard the great Bernadette Peters.
"But like everything that's wonderful - every play that has many, many lives, they can expand the shape of the people who are going to make it."
In short: There are a lot of ways to sing Sondheim, or any score, and get it right.
Once upon a time, actors in movie musicals had to meet certain standards of vocal beauty - or have their voices dubbed by singers who did. Audrey Hepburn was game to do her own singing in Funny Face but was dubbed by Marni Nixon in My Fair Lady; Nixon also became the singing voice of Deborah Kerr in The King and I and of Natalie Wood in West Side Story.
Today, however, actors who aren't known for singing are routinely performing their own parts: Johnny Depp in Sweeney Todd, Richard Gere in Chicago, Russell Crowe in Les Miserables. And this opens up a whole range of questions among the increasingly voice-oriented audience about what it means to be able to sing, and what we expect from a singing voice, and whether the singing of an actor who hasn't specialised in song - from Marlon Brando in Guys and Dolls to Crowe in Les Mis - ruins the show, or makes it more authentic.
The Into the Woods cast falls across the spectrum of vocal experience. There are non-singers such as Emily Blunt, who plays the baker's wife, and Depp, who took a critical drubbing (unfairly, I thought) for his performance as Todd and who's back here as the wolf. But Tracey Ullmann, who had a full-on recording career for a while, plays Jack's mother (as in Jack and the Beanstalk), and Cinderella is played by Anna Kendrick, who has been singing on stage and screen since age 12, when she played the role of Frederika in A Little Night Music at the New York City Opera under Paul Gemignani (who is the musical director of this movie).
When your work schedule is full, it's hard to put in the time to learn new roles. Acknowledging this, Disney Studios took the highly unusual step of setting aside six weeks of rehearsal time, with the full cast and musical staff, before filming even began. By the time they were done, the cast felt ready to perform the piece onstage.
Streep didn't work privately with a coach. "I didn't want to inflict that on anyone," she said, laughing. Instead, she practised herself, drawing on resources and exercises learned when she was studying at the Yale School of Drama.
Streep, who listens to music continually as part of her preparation for a role, didn't have a particular vocal model for this one. "I just listened to myself," she said. "And I was very interested to find my voice, because I hadn't sung out of the character of, I don't know, in Ironweed or Mamma Mia!, a sort of pop voice - I was using different voices for different things. But I wanted to locate, especially in Stay With Me" - the witch's signature song, the plea of a mother to the daughter she can't let go - "sort of the centre of what I would sound like. Because there are so many layers of the witch that it just didn't seem necessary for her to have any voice other than mine."
Streep has had singing particularly in her sights of late. The death of Mike Nichols may have put an end to filming Master Class, which would have allowed Streep to play Maria Callas, lionised in the popular imagination, for better or worse, as the greatest singer of all.
She is, however, going ahead with a project involving one of the worst: the eccentric patron Florence Foster Jenkins, who early in the 20th century used to rent out Carnegie Hall for concerts that became cult favourites among people who went, without her fully realising it, to laugh. Her recordings remain extremely popular, particularly at parties.
After spending time trying to sing well, how do you prepare to sing badly? "If you listen to those recordings," Streep said, "she was almost good, and then there was a point when she was off. And that is what makes it funny. It was almost there. It doesn't start out badly. It starts out hopefully.
"I think I'm going to try to be as good as I can, and then - we'll see."
• Into the Woods opens in New Zealand on Thursday.
- Washington Post-Bloomberg