SALLY Beamish had never written a piano concerto in her life until she wrote three within a year. Things had not been planned that way: orchestral commissions tend to come with long and fickle gestation periods, so she was as alarmed as anyone to find the pieces suddenly queued up in rapid-fire succession.

“Actually, the daft challenge forced me to be extra inventive,” she tells me ahead of the European premiere of the third concerto by the Royal Scottish National Orchestra this week and the first radio broadcast of the second by the BBC Scottish Symphony Orchestra a fortnight ago. We’re in London, where she has been presenting a radio programme for International Women’s Day. She describes her mood as “great! relieved!” – relieved at how well the radio show went, but mainly to be out the other side of her accidental concerto triple immersion.

“I had to really push myself to draw new sounds and expressions out of the piano,” she admits. “I couldn’t rely on defaults or fall back on instinct or repeat the same tricks I’d already used up the previous week…” So how did she summon three such different responses? It helped that she wrote each concerto for a specific soloist, and that she really shaped each score around their personalities: the bright clarity of Ronald Brautigam in the first; the robust, no-fuss intellect of Martin Roscoe in the second; the finesse and poetic intrigue of Jonathan Biss in the third. It helped, too, that the forces differ, with the piano joined by only strings in the first, a full symphony orchestra in the second and a mid-sized Beethoven band with added jazz drum kit in the third.

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But for all their variety, the concertos are a trilogy of sorts, together exploring the land, sea and cities of Scotland. The first is called Hill Stanzas (Beamish returns often to the notion of stanzas, with its interlinking episodes inspired by descriptive writing). The music is rich with references to Nan Shepherd’s book The Living Mountain. Movements are headed by words like glaumerie – Scots for witchcraft or the supernatural. There are snippets of James Scott Skinner tunes, and a piece Beamish wrote in memory of the cellist Kevin Macrae based on the legend of the De'il Amang The Tailors, in which three tailors took on the challenge of dancing through the night in the Cairngorms and died of exposure.

Many composers would buckle under Beamish’s workload, but she writes swiftly. The first concerto was sketched out in Glen Shee: four days, four movements, and the music is lithe, sinewy, springy like heather. She was staying in a cottage with her daughter and the harpist Catriona McKay – “they played tunes all day while I wrote the piece,” Beamish remembers with a smile. “The sound of the harps is everywhere through the piece.” She took recordings of streams and the noises birds make when they’re not singing. Wings beating, grouse rising from the hillside. These she translated into delicate, vivid string textures.

Here’s hoping for a performance of Hill Stanzas in Scotland before long. It premiered in Amsterdam then travelled to Sweden, France and Italy; it will go to Switzerland this summer, where Beamish plays in the ensemble with pianist Alasdair Beatson as soloist. Viola was her first profession, and she says the fact she has started playing again makes a big difference to the way she’s writing. “Especially when I’m writing the viola parts. I think, ‘I’d better be careful here. I’m going to end up playing this!’ All three concertos have viola solos in them. I think that is my voice.”

The second concerto is called Cauldron of the Speckled Seas, and Beamish describes it as one of her most personal works. The official inspiration was the Corryvreckan – that great raging whirlpool off the north tip of Jura caused by rock pinnacles under the surface of the sea. She took a boat trip to see the phenomenon with Martin Roscoe and her three children, but says that the timing wasn’t right. “My mother had just died. I was feeling emotional. I thought, right, I have to be inspired by this whirlpool, but I really struggled. When I got home, my partner, Peter, said, ‘this piece is not about the whirlpool, it’s about your mum.’ And he was right.”

To set the piece in motion, Beamish sat at the piano while Peter narrated her own life story. “Basically I sat and improvised for half an hour and he recorded it all into his phone. That got me through.” The score opens with a violin solo representing Beamish’s mother, and the same theme is played at the end, but this time offstage. “It was about letting her go. This piece was really important for me. Actually, I think it’s one of the best things I’ve done.”

The third concerto, City Stanzas, is charged with a different kind of hurt. It was written for Jonathan Biss, an American pianist who lives in New York. Beamish met him last November and remembers him being “so distressed about the political situation at home that after the presidential election I didn’t hear from him for ages. He went completely off the radar. Cities are about what humans do to the landscape. This is our mark. And after that election I started thinking about the planet, and how we take care of it, and whether or not that is going to happen, and whether there might be people now in charge who really don’t care about it at all.”

The last movement parodies the Rondo of Beethoven’s First Piano Concerto. “The music is grotesque and ugly,” says Beamish. “The pianist is a voice crying in the wilderness. An outpouring of desperation. The orchestra keeps cutting across him all the time.” There are other voices in the mix: Scottish rock bands, traces of Iggy Pop with violins over top “doing sounds like poison gas”. The slow movement is a lament “about the loneliness of being in a city. How you can be surrounded by all these people and yet be totally lonely.”

The premiere took place on a Friday morning in Saint Paul, Minnesota. It happened to be the same day – indeed the exact same hour – as Donald Trump’s inauguration. Beamish was invited to talk about the piece from stage. “I was nervous to say much,” she recalls. “I mean, here’s this British person criticising decisions made in their country, but I went up there and I talked about our responsibility in curating the planet. About cities being the mark we make.” After the performance, as the orchestra was walking off stage, one of the musicians turned to her and said, “well, the Titanic went down, but the band kept on playing.”

Jonathan Biss and the RSNO perform Sally Beamish’s Third Piano Concerto, City Stanzas, at Caird Hall, Dundee, tomorrow; Usher Hall, Edinburgh, on Friday; and Glasgow Royal Concert Hall on Saturday. The BBC Scottish Symphony Orchestra premiere of her Second Piano Concerto, Cauldron of the Speckled Seas, was broadcast on BBC Radio 3 on March 18 and is available online.