James Dillon describes his childhood as a contradiction.

“I was a Mod teenager who was obsessed with Delta blues. I discovered the Stones when I was 12 and found this name Muddy Waters on the back of their LPs. It took me ages to figure out he was actually a person. Nobody was called Muddy Waters in Glasgow.”

Now 61 and arguably the most singular and innovative Scottish composer of his generation, Dillon is four years into a professorship at the University of Minnesota. This too is a bit of a contradiction; he is largely self-taught and by his own admission is “not made for institutions”. He started a foundation year at the Glasgow School of Art when he was 18 but dropped out before his exams. He’s no diplomat, either; he speaks his mind and seems prone to making instant enemies of bureaucrats. He has a reputation for difficulty, both musically and temperamentally. The image of him coaching college students in the heartland of “Minnesota Nic” is baffling.

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“It does make me a little schizophrenic,” he explains as he ushers me into his West London home. “When you teach, you start taking on problems that aren’t yours. I can’t seem to let go.” He’s just back from the US, on his way to Norway to oversee rehearsals for a new work to be premiered at the Huddersfield Contemporary Music Festival on Saturday.

When he arrived in Minnesota the university had no ensemble to perform student works or contemporary repertoire, so he set one up. He refuses to use the university concert hall because it’s ugly, and banned American music for the first two years. “There was a mass intake of breath around the room when I announced that one… In the third year I allowed some Morton Feldman.”

“So many professors just pick up their salary while the kids rack up enormous debts. If there’s anything I can offer, I’d like them to leave school more open-minded than if they hadn’t met me.” The alternate persona he adopts in the US seems to bemuse him. “There probably is a gregarious side to me. I probably enjoy it. I’m probably okay at it.”

More of a concern is that he can’t compose there. It’s not the time spent teaching, but the mental space it occupies. He returns to London whenever he can, to the brick terrace house by Queen’s Park where he has lived for 25 years. “The minute I walk in here I start to compose,” he says.

Dillon first came to London as a retreat. He needed to get away from a communal house in Cornwall he says was killing him. “Everyone was into psychedelia and there was a lot of acid around. My body wasn’t made to cope with that kind of abuse. I ended up with TB in hospital. Then I met a girl – I was 19 and she saved me. Together we escaped to London.”

He had moved to Cornwall to escape the vices of another scene – Glasgow’s folk clubs in the late 1960s. He’d signed up for the art school but learned how to drink instead. He bought a guitar in a junk shop on Great Western Road and started strumming along at pub sessions.

He enjoyed the authenticity of the folk music (“or at least, the authenticity of its delivery”), but felt burnt out and claustrophobic so headed south – for the second time. Aged 10 his family moved to Huddersfield – “of all places!” There he battled through high school with a funny accent and supporting the other team at football. His Scottish identity “was honed by going to school in England; I’m no nationalist, no flag-waver or kiltie, but I am Scottish.” Now his accent speaks like an audio biography: Glasgow solidly at its core, softened by Yorkshire and London and even mid-west America.

He offers various guesses at why he’s found his relationship with Scotland strained. “Maybe it’s because I’ve chosen not to live there and people resent that. Or maybe because I’m seen – simplistically – as an arch-Modernist. If Britain has struggled with so-called Modernism, Scotland really has.” As he mulls over the “idiotic” labels that have been attached to his work, it is the only point in the conversation when Dillon comes close to irritable.

His new piece for Huddersfield is the second of three triptychs, each named after its commissioning city; 2009’s Leuven Triptych is an extraordinary response to the art of Rogier van der Weydan, and next summer a New York Triptych is due for premiere at Darmstadt. The current preoccupation, though, is Oslo. “I’ve given the musicians cheap voice transformers to play with,” he says; they sound “nasty and interesting” but are temperamental. “If the performers get it wrong I look like an idiot! Which is why at the last minute I’ve decided to go over to Norway…”

Dillon’s music is notoriously challenging. That’s mostly because he’s after particular sounds, he says, which are only attainable at extreme ends of instruments. But he admits there’s an element of provocation, too. “It’s about concentration and engagement. Players are so highly trained today that they easily drift into a comfort zone.”

At the heart of his polemic is concern with performance experience. Going into a concert should be like “stepping into a magic circle,” he says, and much of his work explores ways of finding that. Nine Rivers, staged by the BBC SSO last year, tried vast proportions. The current triptychs retreat to a more pragmatic scale, but continue the search.

Cikada perform Oslo/Triptych on Saturday afternoon in St Paul’s Hall, Huddersfield.