Her mother, a violinist, taught her to read and write music at the age of four – "probably just to see what would happen," she says. "I couldn't read or write words yet, so in a way music was my first language." She drew little pictures on the staves, little flowers or faces, and her mum would play them back to show how the picture notation might sound.
The experiment seems to have worked because today Beamish is one of the UK's busiest, and best, classical composers. I've come to meet her at home in the Stirlingshire village of Gartmore, where she's lived for 20-odd years since leaving London. The broad, sleepy main street has a pub, a village hall, a community-run shop and wide, open views south to the Campsies.
At the bottom of Beamish's garden is a dirt track winding off into the fields. Her composing hut (her commute to work consists of stepping down a mossy garden path) is stacked full of scores, reference books and a keyboard. "No doorbell or dishwasher or hoovering," she smiles.
The house itself is cosy and stylish. Beamish shows me some of her artwork, miniature nudes in muted pen and ink that find a classy balance between sleek and ambiguous. There's a landscape, too: a serene loch scene in the Trossachs. I hadn't realised she painted at all, let alone so well.
"I always wanted to make my own stuff," she says. "I've made my own clothes, written stories, painted. When I started learning piano I wrote myself a little exercise book." That was at the age of five. Surely such an early fixation with craft must have contributed to the vivid imagination she brings to her scores nowadays? She allows a typically modest "maybe... my music was tied in with visual things from the start, and that has definitely stayed with me."
Beamish's latest work, to be given its premiere by Red Note Ensemble later this month, incorporates that affinity for visual expression. The Intoxicating Rose Garden uses dance and animation as well as music set to poems by the 14th-century Persian mystic Hafez. Beamish's starting point was a book of "shape poems" by the contemporary Iranian artist Jila Peacock, in which beautiful ink calligraphy is arranged into the shapes of animals. Beamish describes Peacock's work as "simple and unpretentious, just made for people to understand the Hafez originals", and the two have already worked together on various musical settings.
This latest version features Michael Popper, an operatic bass who both sings and dances as part of the show. He's accompanied by flute, recorder, trumpet, cello and, crucially, harp: Beamish acknowledges the influence of the setar, a lute-like Iranian instrument whose six strings are played with one incredibly fast finger, on her score.
The Intoxicating Rose Garden has been something of a family enterprise, too. Beamish's ex-husband, Robert Irvine, is Red Note's founder and cellist, and their son Laurie is creating the video animations. "This is the first time that Laurie and I have worked together," she says. "It's been great. There's a lot of mutual respect there."
In general she's a great one for collaborating, despite that solitary composing hut at the bottom of the garden. "I get a thrill from working with other creative minds," she says, "especially minds from a different background than my own."
Certainly the three new works premiered in Scotland already this year attest to that. Seavaigers was a concerto for harpist Catriona MacKay and fiddler Chris Stout. "I'm smitten by the way they work together," says Beamish, "the way they use their ears and respond to each other." Dance Variations was a percussion concerto for Colin Currie: "Colin's performances are almost like choreography, the way he moves on stage." And a saxophone sonata, Albatross, was written for the jazz musician Branford Marsalis. It's an impressively broad spectrum within the space of just a few months.
It's no wonder Beamish enjoys working with performers quite so closely: she was a violist herself for many years. She brushes away her accomplishments – "I was alright in chamber music but not much of a soloist. I used to think 'gosh, there are so many fantastic players; do I really have something special to offer?'"
More to the point, she always meant to be a composer. "I thought of the viola as something I'd do to earn a living. When I had my first baby, my husband at the time, a Scot, wanted to bring the kids up here. I was looking for a way to quit playing and become a composer for real." And then her viola was stolen. In a fairly remarkable piece of silver-lining thinking, Beamish "decided to turn the theft into a positive". She moved to Scotland and started composing full-time.
She now looks back on the move – to Scotland and to composing – as "a fantastic decision. As soon as I arrived here I was given all sorts of opportunities I wouldn't have had if I'd stayed in London. Plus there was the folk music, which took me completely by surprise." She bought a fiddle in a junk shop and joins in now and again at ceilidhs in the village hall. She still doesn't have a viola, but has started playing the piano again. "I even performed in public recently" – she premiered Albatross with Marsalis – "and it actually went alright. I'd like to do more." Funnily enough, she never performed her own music on the viola. "I couldn't get near it; I never even tried. It would have limited me. I imagined the ideal viola player playing it, not me."
When I ask what's coming up, her list of commissions is daunting. There's a piece for the Academy of St Martin in the Fields to celebrate Britten's centenary. There's a new opera called Hagar In The Wilderness – a half-hour "sort-of church parable" to pair with Britten's Curlew River at the Presteigne Festival. There's a piece for the Scottish Chamber Orchestra to commemorate the Battle of Flodden, a piece for the 600th anniversary of St Andrews University, a solo cello piece in memory of cellist Kevin McCrae, a string trio for the Britten Sinfonia-
"I do get a bit scared sometimes," she says. "I wake up in the middle of the night and think about how much I've got to write. But once I get going, I usually work pretty fast. I almost have the music in my head before I start. It's just the annoying process of working out how to write down the colours that I'm hearing that takes time. Sometimes I start to lose confidence at that stage."
Beamish doesn't deny that the kind of industry affirmation she's earned this year – she won a coveted RPS award and was BBC Radio 3's Composer of the Week – means a lot to her. "It really helps. I've always got that internal creative voice saying that I'm not the genuine article, that I'm going to get caught out somehow. That demon never goes away, but I've learned to deal with it. I simply have to keep going. Even if it feels like I'm writing rubbish, I say, 'fine, I'll just write rubbish then.'"
Joining an author's group helped solve a particularly bad composer's block a few years ago. And, typically, when she tried her hand at writing she found she was rather good at it. She published a short story, took a BBC scriptwriting course, wrote a play – and only stopped when she started missing the music.
Beamish is the kind of composer who can't not compose. I'm beginning to understand why performing other people's music wasn't quite her thing. "Not to diminish the role of performers for an instant," she stresses. "Performance is 50% of any piece. I'm always fascinated by what people do with my music. Mostly, I want my players to feel a million dollars. It's important to me, because I know how it feels to struggle."
She is a performers' composer and a magnet for inspiration. "Yes, I suppose I'm a bit of a chameleon," she agrees. "But there's something in all my pieces that is somehow me." Exactly what that "me" is she can't, or won't, say. "It's like my accent, which all my English friends tell me sounds Scottish now. I can't hear it. But I hope my music has some kind of an identity."
There's no question that it does. And part of that identity is her ability to incorporate her collaborators, and to make her players feel a million dollars.
The Intoxicating Rose Garden is performed by Red Note Ensemble at The Tolbooth, Stirling, on November 15; Woodend Barn, Banchory, on November 17; and Traverse Theatre, Edinburgh, on November 22. www.rednoteensemble.com