If such a thing as an unsung singer can actually exist, it's probably fair to say Annie Ross is one of the greatest unsung singers of our time. With a career spanning 60 years, Ross remains an enigma on Scotland's shores. That's despite the fact that she is to all intents and purposes Scottish herself.

Now a naturalised US citizen, Ross was born in London to Scottish Vaudevillian parents, almost immediately after their performance in an afternoon matinee. If there's truth in the saying that showbiz is in the blood, Ross is as close to the source as you can get. She is part of a great theatre dynasty and the sister of the late Jimmy Logan, but, on the outbreak of war, ended up on the other side of the Atlantic. She was raised on the west coast by her aunt Ella.

At 13, she made her film debut opposite Judy Garland in Presenting Lily Mars, singing Loch Lomond. While it was an auspicious start, it provided few clues to what lay ahead. She went on to become one of the greatest jazz singers of the "cool era" and the finest proponent, by a mile, of the style that became known as vocalese. For the uninitiated, this is essentially a style of jazz singing where lyrics are written for melodies that were originally part of an all-instrumental composition or improvisation. It's different from scatting, which uses improvised nonsense syllables (bap ba doo dweeba da habba da bop da dop). Vocalese uses lyrics, either improvised or set to pre-existing instrumental solos.

Her time with Lambert, Hendricks and Ross - a vocal trio that epitomised east-coast cool - from1957 until 1962 was perhaps the pinnacle of her career. The albums they recorded together are neglected these days but sell for premium prices on-line. If you can find them, by hook, crook or download, tracks such as Twisted and Jackie are essential.

When I speak to Ross by phone at her home in Manhattan, she tells me about the genesis of Jackie, an idiosyncratic tune which kicks off "I sat one night/Right in the middle of a glass of Coca-Cola".

"I was living in a flat in New York," she says. "I shared it with a mouse. He'd come and hang out with me. It kinda freaked me out, so I wrote a song about him. The song very much reflects the nonsensical lyrics we sometimes used at the time."

The trio's most popular song, Twisted, featuring Ross's lyrics set to a Wardell Gray melody, was featured in Woody Allen's 1997 film Deconstructing Harry, and has been covered by many, most famously by Joni Mitchell.While singing with the trio, Ross recorded solo albums, most notably 1958's Sings a Song With Mulligan!, which also features Chet Baker. It epitomises the sound of a brief period in jazz history when vocals were integrated to the band sound. You only have to listen to her on Bernstein's I Feel Pretty to appreciate her charm. In 1962 Ross left the group and was replaced by vocalist Yolande Bavan. The renamed Lambert, Hendricks and Bavan made three live albums before disbanding in 1964. Any hopes of a reunion of the original trio ended with Lambert's death in a car accident in 1966.

When I ask her who she rates amongst modern singers, my question is answered by an eloquent silence. She is more forthcoming on some of her contemporaries, however, citing Ella Fitzgerald, Billie Holiday, Carmen McRae and Nancy Wilson as influences.

As for her own career, she is happy to let that speak for itself. However, Daniel Halperin's sleeve notes to that album with Mulligan offer a fine thumbnail of the woman she was at the time. He wrote: "Anything you want to know about Annie Ross can be heard in her singing, save for the possibly related facts that she cooks divine pork chops and apple slice, is incapable of arriving anywhere on time, can go through desperate bouts of feeling utterly unsure of herself, loves London, particularly the churchyard of St Anne's, Soho, comes from a family of Scottish music-hall troupers, smokes rasping French Gitanne cigarettes, adores black Wedgwood, was born in 1930 and is always looking for recipes that include deployment of garlic."

Her recording career has been sporadic in the past 45 years, save for a few live recordings and a handful of well-crafted studio outings, but she has stayed in the limelight with sterling film performances. Her appearance in Robert Altman's Short Cuts in 1993, as a jazz singer, is perhaps the most memorable, but she also had roles in Superman III and Throw Momma From A Train.

In the early 1970s Annie Ross did a lot of "behind the scenes" filmwork, particularly dubbing. In 1973, she voiced Liv Ullmann in Bergman's Scenes from the Marriage.

"To my delight," she laughs, "Bergman told me that if Liv spoke English, she'd sound like me."

Another little-known Ross fact is that she provided the vocals for Britt Ekland's erotically charged performance of Willow's Song in The Wicker Man.

"I was living in London and doing some dubbing work. The chance came along to perform the vocals to accompany Britt's performance and I did it as a job." The film, however, has gone on to become a cult and Ross is justly proud of her part.

Lately, Ross has been finding fresh acclaim with a weekly performance at The Metropolitan Room in New York. It's been a long-standing gig and it was there her forthcoming live CD, to be released later this year, was recorded. She says: "It's a wonderful room and I've been playing with a great band." Some members of that band will be with her when she makes her first appearance since 1994 at the Glasgow International Jazz Festival, including the legendary cornet player and regular visitor to Scotland, Warren Vache, and Tardo Hammer on piano. Although she is a rare performer on these shores, she is frequent visitor and often stays with family in Helensburgh, where, she says, she enjoys the food, particularly from the local butcher. "I love changeable weather, she says. "I love the seasons, which is why I like coming to Scotland and why I live in New York. I find the weather on the west coast of America just too bland."

When I ask her what we can expect to hear on the night, she says it will reflect the set she performs in New York and on the forthcoming CD. "I'm really looking forward to returning to Glasgow to perform, it's been a while. I plan to sing some songs by Johnny Mercer, Rodgers and Hart, some Lambert, Hendricks and Ross material, which will be tough on my own, as well as some of my own songs."