When Sally Beamish was commissioned to write a concerto for the Rascher Saxophone Quartet - which will receive its world premiere performance in Glasgow on Friday - her creative imagination automatically switched on to her long-standing interest in jazz. This private passion has found voice in several of her works, most famously the superb saxophone concerto she wrote for John Harle, entitled The Imagined Sound of Sun on Stone.

More recently, she has been absorbed by the playing and the sound world of saxophonist Branford Marsalis. In fact, when she learned that Marsalis was playing her Sun on Stone concerto at the North Sea Jazz Festival in Rotterdam, she took off for the Dutch city to visit him.

It was a crucial meeting of minds. They expressed interest in working together. Beamish was writing her third viola concerto, for Lawrence Power, the leading UK viola player, and she confesses that her inspiration throughout the composition of the concerto was fired by Marsalis's playing. Consequently, she has decided to transcribe the beautiful viola concerto, entitled Under the Wing of the Rock, for Marsalis to play on sax.

So she went into an early discussion with the Rascher Saxophone Quartet bristling with her jazz credentials. One can only imagine her mental reaction when they stonewalled the discussion in a single sentence: "We don't do jazz."

It wasn't the first time she'd had such an experience. When James Crabb, the best accordionist in the world, asked her for an accordion concerto, the request was accompanied by a proscription: "No tangos, please."

The Rascher players, who have commissioned more than 100 new pieces for their line-up, appeared then to compound their response by requesting that Beamish's new concerto should be for just four saxes and string orchestra - no flutes, oboes, clarinets, trumpets, or trombones. "They wanted it to be portable," says Beamish, unfazed by the apparent limitation, which was actually a shrewd move on the part of the Raschers. (Portability equals a potential for more opportunities for more performances.) So Beamish set aside the jazz concept and turned her inspiration towards the sound world of four wind instruments and strings. At some stage in the creative process, she had a "eureka!" moment. "It just suddenly popped into my head: this is a Brandenburg."

Bach's six Brandenburg Concertos have been central to Beamish's musical career. "I've known them all my life, they have been a huge part of my life, and I've played them on harpsichord, viola and violin. It's Brandenburg Four, really, from which I've taken exactly the model with a group of wind soloists and a string ripieno section. And it's that feel, with the recorders (or flutes) and the strings, that has inspired me."

Beamish aficionados will recognise that this influence from an earlier model is a highly unusual step for one of Britain's finest and most original composers to adopt. "That's the case. I've not done this before; not as directly." She has worked previously with early music as her raw material, though with that she tended to take fragments and deconstruct them. "This is different. Here I'm more taking the structure, using it as a base and building my own sound world on that."

So there is a baroque look to the new Chamber Concerto, which is a three-way co-commission between the Scottish, Stuttgart and Norbotten Chamber Orchestras. It lasts about 20 minutes and is in three movements (fast, slow, fast). And the baroque inspiration seeps into the interior of the music, which uses all the standard devices of the period: the patterns, the sequences, the imitations and the fugal writing in the finale. There is also, for keen ears to find, a direct quote from Brandenburg Six, including a walking bass line.

But Beamish being Beamish, there is more to it than that. The composer has had a few brushes recently with period instrument playing and the whole language and style of baroque ornamentation, figuration and performance finds its way into the new concerto. She has also sensed other connections. "There's something very baroque-like about the ornamentation of pibroch; and Scottish fiddle playing isn't a million miles away from baroque music."

For anyone wanting to track these influences in her new piece, Beamish, as well as indicating the instrumentation and general feel of the music, points directly towards the slow movement, which might sound to some like a lament. "That movement is actually Scottish, but it's crossing the border between the Scottish and baroque schools; the ornamentation makes a link."

The tough call for the composer was writing for a sax quartet. She has plenty of experience writing for solo saxophone, but had none writing for soprano, alto, tenor and baritone saxes as a group, and even less experience in how to balance such a group with an orchestra comprised exclusively of strings.

"It was difficult to get a grip on the actual characters of the four saxes. In a string quartet, the instruments are very different from each other. It's the same with saxes, but I didn't know them from the inside, so I had to learn all that and discover the world of each saxophone. And as for the balancing the quartet with the strings, it features territory I've never covered before. I had no idea how that was going to work."

She'll find out at the world premiere on Friday in Glasgow; as long as she manages to get to it. Beamish is one of the country's busiest composers, and has two world premieres on consecutive nights this week. Tomorrow night, she'll be in Stavanger for the first performance, by the Stavanger Symphony Orchestra, of another new orchestral piece, A Cage of Doves, commissioned to mark the city's period as European City of Culture. She'll then hotfoot it back to Scotland and the City Hall to hear conductor Garry Walker, the SCO and the Raschers unveil her Chamber Concerto.

It all coincides with a period of extraordinary fertility in the career of this remarkable woman whose fifth CD (featuring the incredible Tabea Zimmermann playing the heartfelt Second Viola Concerto) is just out; whose musical, Shennachie - which didn't win Cameron Mackintosh's Highland Quest competition - has just been awarded American money to develop it for possible performance in the States; who had a short story on Radio 4 last year; who was short-listed in a competition for a radio drama about music; and who, almost 18 years after moving to Scotland and becoming one of the country's leading and most prolific composers, finally has been taken on by a publishing house which has decided to publish everything she has written, generating a profound and fairly radical impact on her life. Team Beamish now exists to support and further her music and her career.

At times it has been a bit of a struggle, but Sally Beamish has won through. "I am so happy now. I just love my life. I like the way it's all evolved. It's tailor-made for me. It's been a slightly circuitous route getting here, but I feel well looked-after."