"With the Stones, I get to do amazing work in the background and even there, in the silence, I have to keep a particular energy and a heightened sense of alertness because there is so much music going on around me.
"That's the reason the focus has to be total and you need to be there in case Mick [Jagger] or Keith [Richards] need something. I don't get a chance to relax and dream."
With Grand Baton - they've been performing together for about two years - it's a different rhythm and energy, dictated by the music they decide to play and the way the audiences, always smaller and more up close and personal, respond.
"The music dictates what the focus will be but the audience dictates the energy because every person needs a different kind of attention and has different musical needs. I am in synch with Grand Baton and tell a complete story but I live vicariously through the audience."
She says she sometimes has to pinch herself to make sure she's awake, because seeing her own name in lights still feels like a dream. Best known as the voice that has backed the Rolling Stones for 25 years, Fischer always wanted to be a backing vocalist.
She recalls listening to records as a child and trying to work out how many backing vocalists there were: "And I always thought the background was an interesting and fun place to be."
Fischer was raised in Fort Greene, Brooklyn. Her parents split when she was 14 and her mother died three years later, leaving her daughter and two younger sons in the care of extended family. Only 17, Fischer was already singing in clubs when The Crystals' Deedee Kennibrew asked her to tour with the all-girl group. It was the "big break" but Fischer, who learned to sing in the choir at the Evergreen Baptist Church, feared it might lead to a genuine break.
"I was scared to death," she recalls. "I couldn't see a thing! It was before I got contact lenses and I wasn't able to wear my glasses on stage so I was singing and hoping and praying that I wouldn't fall into the audience."
Fischer stayed on stage and, impressing with her vocal range and work ethic, has pretty much been there ever since. The Crystals' tour marked the start of her four decades long - and counting - career singing background on tour and in recording sessions for the likes of the Rolling Stones, Luther Vandross, Tina Turner, Chaka Khan and Nine Inch Nails.
In 1991, still touring with the Stones and Vandross, Fischer recorded a solo album which lead to the No. 1 R&B hit, How Can I Ease the Pain, and her very own Grammy Award for Best R&B Vocal Performance, Female. She shared the award with Patti LeBelle who won for Burnin'; Fischer had sung the backing vocals.
Ten years later, after a number of solo projects and in continual demand for her background vocals, Fischer thought her career would be winding down. Then she was asked to appear in the documentary film Twenty Feet from Stardom, celebrating the work of background vocalists.
"That film changed everything and it proved to be a beginning for me when I thought I was close to the end," she says. "I would show up between gigs, do the interviews and then go away and not think about it too much. Then, all of a sudden, there was this energy and all sorts of people asking when I would be doing my own thing, my own shows, so here I am!"
• The Wellington Jazz Festival runs across five days from June 8-12. Lisa Fischer & Grand Baton perform on Sunday, June 12 at the Opera House.