“Interesting” is an understatement. For months now, advance copies of Gray’s debut CD have been passed from rock critics to DJs and other urban tastemakers. Sold-out shows at such hipster spots as the Bowery Bar in New York and the Viper Room in L.A. have only heightened the buzz. This week the album, “Macy Gray on How Life Is,” goes on sale. Andy Slater, the manager who brought us Fiona Apple and the Wallflowers, believes that Gray is ripe to win some of the crossover audience that went nuts over Lauryn Hill. Like Hill’s, “Macy’s point of view is vulnerable, sensitive and honest,” says Slater. “There’s no show-business artistry to her; that’s what draws people to her music.”

Nobody is more surprised at the ascension of Macy Gray than her family back home in Canton, Ohio. Call Gray’s mother, Laura McIntyre, and the first thing she says is, “If you don’t mind, I’ll call her Natalie. That’s her name.” Gray’s moniker is actually a misguided homage to a beloved neighbor. “Macy Gray was a man who used to come over and shoot pool with my husband,” her mother explains. “She was always extremely shy, and he would tell her, ‘You’re going to be something special one day.’ She said she took his name because she’d always liked Mr. Gray and was so sorry he’d died. I said, ‘No, Natalie, it’s his wife that died’.”

Gray, 29, grew up in a blue-collar African-American neighborhood. Her mother is an eighth-grade math teacher, her father a retired steelworker. It was the 1970s, and civil-rights optimism was going strong: all the grown-ups had jobs and the children were taught to aim high. At 14 Gray was sent to boarding school, and later she attended the film school at the University of Southern California, where she sang in a jazz band. A member of L.A.’s underground-music scene for eight years, Gray can go from the sweet plaintiveness of songs like “Why Didn’t You Call Me?” to the Prince-like sexiness of “Caligula.” Her multiethnic band includes Red Hot Chili Peppers alum Arrik Marshall and Funkadelic guitarist Blackbird McKnight. The lovely strings on track No. 7? Those were done by Beck’s dad, David Campbell. The diversity of Gray’s influences is “quintessential L.A.,’’ says Slater. “L.A.’s a horizontal city with one landscape. She incorporates all of it, from rock and soul to hip-hop, with even a little bit of a salsa groove.”

A single mother, Gray leaves her three kids with their grandmother while she’s on the road. The two older kids were both born in 1995, one in January, one in December. “I never figured that out,” her mother says. “I keep the children now. I just didn’t want her to have to worry, leaving them with babysitters.”

Prior to recording this album, Gray was the hostess of an after-hours club called the We Ours in a Hollywood coffee shop. Her musician guests, including the Roots and Tricky, had street cred to spare. The club’s popularity was due to “Macy’s influence,” says the coffee shop’s owner, Ron Harris. “She has a way of embracing people and nurturing them.” You only have to listen to the smoking grooves on her debut album to know that she’s taken the spirit of the We Ours with her. The more you listen to Macy Gray, the more she makes you feel at home.