It is the most iconic composer-place partnership in British contemporary music, every bit as deep-seated and fruitful as Benjamin Britten's relationship with the Suffolk coastline.

Peter Maxwell Davies – fondly known as Max – moved to Orkney in the 1970s and has since composed and premiered a plethora of works on and about the islands. When he helped set up the St Magnus Festival in 1977 his aim was to involve local audiences in the kind of new music that's too often the preserve of a rarefied urban few. The festival is now run by composer Alasdair Nicolson and still straddles a balance of community engagement and cutting edge commissions. And as ever, Max's music is at the heart of the programme.

This year's headlining new work is an Oboe Quartet for the Hebrides Ensemble and Emanuel Abbühl, former student of Heinz Holliger and regular principal oboist of the London Symphony Orchestra. The instrumentation was Max's idea, but whether he'll be able to attend the premiere is still in doubt: in May it was announced that the 78-year-old has leukaemia and is undergoing chemotherapy in London. So while the composer was sadly unavailable to discuss the new work, cellist and Hebrides artistic director William Conway was happy to share his first impressions.

"It's rare that my breath is taken away quite so completely after just one reading of a new score," he says. "Already I've noticed a lot of the signature ingredients I'd expect from Max – ingredients I can trace right back to the Cello Concerto he wrote for me in the 1980s [one of 10 Strathclyde Concertos commissioned by the Scottish Chamber Orchestra] and the String Trio he wrote for the Hebrides in 2008. Scotch snaps, augmented fourths, straining dissonances, a sense of determined, wistful elegy... Rhythmically, asymmetrical time signatures soon come to sound like symmetry: there are a few bars in 4/4, but he's much happier in 7/16 or 9/16." If that sounds a little abstruse, there's a logic that makes the lopsidedness sound organic, even necessary. "If Max writes tricky rhythms there's always a point to it," says Conway. "The rhythms creates a tension and a discourse in which everything makes sense."

Max's writing has been challenging since the early days, as anyone who heard the Hebrides' recent performances of his ferociously radical 1960s monodrama Eight Songs for a Mad King would probably attest. Even for a musician such as Conway, the technical language remains testing. "When we first looked at the String Trio there were some fiendishly difficult passages that we had to ask him to alter. Now, though, there's a kind of clarity that meant we could read through the Oboe Quartet more-or-less in one take."

Certainly the way Conway talks suggests that Max has created something remarkable with the Oboe Quartet. He describes a moment about two-thirds through the piece, round about the golden section, when through the dense discordant textures the cello suddenly lapses into simple triads, like a clear vision out of the mist. "I've known him to write similar passages as pastiches in his music theatre works, but I've never seen it happen so nakedly in his instrumental music," says Conway. The end of the work reaches a B major/minor chord which gradually gets pushed upwards to a C, then a D, then further. Even at 78, Max and his music search restlessly on.

With such a close relationship to Orkney it's perhaps too easy to hear landscape in the music. Is it simplistic to pick out the musical onomatopoeia of crashing waves, howling winds and wide-open skies? "There's an incredible sense of timelessness to this music," says Conway. "It's often quite fierce, but there's always an answer. Max's sense of peace when he finds it is unlike that of almost any other composer I can think of working today."

Alongside its high-profile premieres, the St Magnus Festival also runs a composers' course, which this year welcomes the Hebrides as resident ensemble. Eight participants spend a week under the guidance of tutors Alasdair Nicholson and Sally Beamish plus the members of the Ensemble – "I'm looking forward to it with trepidation," says laughing. He has no idea what he'll be asked to play – it hasn't been written yet.

The third Hebrides programme at St Magnus is a tantalising line-up of music for clarinet (Yann Ghiro) and small ensemble by Penderecki, Lutoslawski and Bartok, plus the epic G-minor Piano Quartet by Brahms. The Hebrides intends to repeat its best festival programmes within its upcoming seasons. Certainly the new Oboe Quartet will enter its line-ups regularly. "With this one I can just tell," says Conway. "It's something special."

The Hebrides premiere Peter Maxwell Davies's Oboe Quartet on June 21. On June 26 they showcase work from the composer's course and perform a programme of Brahms, Bartok, Penderecki and Lutoslawski. The St Magnus Festival runs from June 20-28.