The new piece is not all birdsong. When the viola breaks out with a mellow solo it's "just what I wanted to write," she smiles. "For an instrument that can lament rather well."
The cellist of the New York-based group is New Zealander, Richard Belcher. He has the last of a number of expressive solos, which allows him the sort of liberties not found in Haydn or Debussy.
Whitehead likes to give players "material that they can interpret more freely", a far cry from her highly structured scores of the 1960s and 70s. She dates her change of tactic to her struggles with cancer in the early 90s.
"I'd been filtering my music through complex, prefabricated structures," she explains. "Then, writing The Journey of Matuku Moana, I found myself stretching those structures and almost destroying them. I never went back."
Whitehead is naturally reticent, although her care and kindness towards fellow composers is legendary. However, when we talk of the Maori taonga puoro, played so evocatively by Horomona Horo in duet with flautist Luca Manghi in her Hineraukatauri on Manghi's new Atoll album Quays, you can feel a new enthusiasm.
"The issue of being a Maori composer has been far more important to me than being a woman composer," she says. "Everyone was going on about women composers and I couldn't quite see why it was an issue. The pull of the other was so much more important."
Whitehead's Maori-influenced music can be heard on the New Zealand String Quartet's 2008 album Puhake ki te rangi, with its fascinating accompanying DVD, as well as in her 1998 opera, Outrageous Fortune, in which Deborah Wai Kapohe's soul-searching lament almost achieves a fusion of waiata and Puccini.
For now, though, she is looking forward to hearing the new Enso commission when the quartet premieres it in Christchurch next week. "Until I've heard a piece played I don't know it," she confesses. "It's as if something in black and white becomes colour and three-dimensional. And then I need to hear it a second time to relearn it in sound."
What: Enso String Quartet
Where and when: Auckland Town Hall, October 29 at 8pm