“AND SO sometimes,” says John Tilbury, rounding off another fine anecdote, “sometimes I feel there is too much general respect for me just because I’m old. A legend and what have you.”

"Legend-and-what-have-you" is about right: the 80-year-old pianist is a formidable interpreter of contemporary music, champion of the ultra long-form works of Morton Feldman, author of the definitive biography of Cornelius Cardew and a member since 1979 of the British improvising group AMM alongside Keith Rowe and Eddie Prevost. At this year’s Tectonics — Glasgow’s pioneering orchestral experimental music festival hosted by Ilan Volkov and the BBC Scottish Symphony Orchestra at City Halls over the next two days — Tilbury performs works by Annea Lockwood and Michael Pisaro, a new piano concerto written especially for him by Howard Skempton, and an improvised duo with his own former student Sebastian Lexer.

Too much respect, then? “Yeah,” he chuckles down the phone from his home in Deal on the coast of Kent. “I remember Cornelius Cardew once saying how much he admired a lack of politeness in an audience. How he thought music should always make waves in the environment, and that a passionate reaction should include rudeness. I would agree with that, but nobody ever heckles me these days.” Tectonics audience: take note.

As an improviser, Tilbury is acutely aware of how his environment interacts with the music he makes, and of how modern life seems prone to cluttering up that creative process.

“Now we’re expected to do it all,” he points out. “We’re expected to be our own bankers, our own travel agents, to diagnose our own illnesses on NHS websites. It clogs up the brain.” Life has no breathing space, he says. “It’s overly congested, which means that something with real space in it, like the music of Morton Feldman [an American composer known for overwhelmingly quiet, placid pieces that last for hours] becomes a question of need. We need the breathing space. A few hours without images or sound-bites.”

It’s not about switching off the brain, more about switching on. Tilbury describes improvising as “satisfying an impulse to be in touch with immediate reality. It’s about being in a state of heightened consciousness.” He draws a comparison with the current trend in "mindfulness". “It teaches you to be alert to everything that happens around you. Well, that’s improv.”

He tells me a story about a saxophonist friend who went to a student’s house to teach a lesson. On the way through the front door, the saxophonist encountered his student’s sister, who offered him a strawberry. “So he puts down his instrument case, takes the strawberry, examines it, tastes it, considers the taste, talks with the girl for a few minutes and only then goes inside to teach the lesson. Nowadays most people would grab the fruit and walk straight on by. Or only stop long enough to live-Tweet the experience.”

Tilbury talks of Cornelius Cardew as the most innately aware person he ever met. “Having a coffee with him was a masterclass in awareness. He would comment on the shadow on the coffee cup, on the smell and dimensions and acoustics of a room. Not in any pretentious way; he was just alive to absolutely everything.”

And that dictum of aliveness doesn’t refer only to the performers, by the way: the onus is on us listeners, too. Tilbury refers to “creative listening” as an “under-appreciated and under-investigated” part of the creative process.

“Listeners are absolutely part of any performance, especially in improvised music. The audience isn’t passive. They are moving toward the music and making sense of it and becoming part of the fragility and vulnerability, part of the sense that any moment can be destroyed in a flash. Plenty of moments are destroyed, but that risk is what makes live music feel alive.”

Tilbury’s conversation is hugely enjoyable: unhurried and courteous and inquisitive, full of side stories and reminiscence. For some time we discuss the issue of mindfulness and politics in improvised music (do you have to be a socialist to be a good improviser? "Sure, probably") and the quiet beauty of the new Skempton concerto he’ll premiere tomorrow night at Tectonics (he calls it “charming and civilised music; people will like it but they might not know quite why”).

Only at the end of the interview does he sheepishly admit that he’s had the television on the whole time, watching snooker out of the corner of one eye. “So much for mindfulness!” he laughs. “Then again, snooker players are ultimate masters. No one knows better about being aware of the fragility and vulnerability of a moment.” He pauses. “I am forgiven?”

John Tilbury performs at Tectonics Glasgow, which takes place at City Halls and the Old Fruitmarket this Saturday and Sunday