John Cage preferred the term "experimental" to "avant-garde"; the latter he found too aggressive, too militaristic.

The composer could be a fiercely dogmatic personality – he was notoriously put-out if he thought a performer wasn't taking his music seriously – but in practise he was a pragmatist: an artist of singular vision who knew what he wanted and knew how best to get it.

Take his approach to chance procedure. That is, to the element of indeterminacy that he increasingly integrated (with upmost precision) into his decreasingly conventional scores. "Any attempt to exclude the irrational is irrational," he declared in 1949, referring to the strict serialist mantra of Pierre Boulez and his Parisian disciples. "Any composing strategy which is wholly rational is irrational in the extreme." So he turned to irrationalism, embracing the inevitability of chance in live performance. It was basically a pragmatic move.

Or there's the story of how Cage invented the prepared piano. Besides silence, which he coined with the famous 4'33 in 1952, Cage's most iconic sound is that of a piano whose strings have been mucked about with bits of wood, plastic, rubber and metal. The so-called prepared piano came about in 1940 when Cage, then in his late 20s and known primarily as a composer for percussion, was asked to write music for a ballet by Syvilla Fort. The choreography had an African theme, and Cage imagined an accompaniment of exotic-sounding percussion instruments. But when he got to the theatre he found a tiny performance space, room only for a piano. Not willing to change conceptual tack, he found a way to have his percussion orchestra: by inserting various junk in between the strings. Purists accused him of violating the instrument, of brutalising the beauty of natural sound and dehumanising the player. Cage shot back with vehemence. "Composing for the prepared piano is not a criticism of the instrument," he said. "I'm only being practical."

Cage would have turned 100 this year, and the BBC Scottish Symphony Orchestra is celebrating. They present two all-Cage programmes – first in Glasgow, as part of the Merchant City Festival, then at the BBC Proms in London. Ilan Volkov is billed as conductor and cactus – and, yes, he will be playing an amplified cactus. In Glasgow that's for Child of Tree, a piece Cage wrote after watching a dancer pluck spines out of a dried cactus in Arizona. The score is a set of instructions on how to select the instruments (they should be made of plant materials; one should be a pod from a Mexican poinciana tree).

It's an extraordinary programme for a mainstream orchestra to tackle, even an orchestra as expert in contemporary music as the BBC SSO. Moreover, it's an extraordinary programme to broadcast on the radio. The programme deploys musicians among the audience and puts silence and weird noises at the heart of the music. It should be thrilling to experience live – but how will it work on air?

The man behind the scenes is Andrew Trinock, the orchestra's soft-spoken producer and instigator of many of its boundary-pushing programmes. "It's a significant concert," he says, simply. "And it should be an interesting radio listen, because so much of the music is spatial."

About how to record those spatial elements, Trinock said his job will require a hefty dose of experimentation. "Fundamentally it's about getting the microphones in as close as possible," he explains. "We often think of avant-garde music as loud and abrasive, but a piece like 'But what about the noise-' is just the sound of rustling bits of paper."

Centrepiece of the programme is Cage's Concerto for Prepared Piano, played by one of the greatest exponents of the instrument, John Tilbury. There's probably no pianist alive today better qualified to perform this music. Tilbury was a great friend of Morton Feldman and has long been a leading champion of the British free improvisation movement, but even he finds Cage's concerto a challenge. "For a pianist it's something of a difficult proposition," he says. "The touch one normally uses is subverted because of the preparation – you might give a real whack to a key and only a very quiet sound comes out. You have to get used to playing a whole new instrument.

"And the audience gets a shock. They see a piano but hear a combination of exotic percussion instruments, like a gamelan. The couple of notes that aren't prepared end up standing out as if they're wrong."

Tilbury last performed the concerto at Volkov's Tectoniks festival in Reykjavik, where it took him five hours to prepare the piano. "Setting up the instrument is a long process," he laughs, "but at least it's more or less the same each time. Cage specifies where to insert the objects – 4.5 inches from the damper, say – but there are adjustments I can make according to taste. I can unscrew the bolt from a screw to make it more buzzy, that kind of thing."

Tilbury describes the pieces as "melodic, certainly, with a microtonal kind of melody. I play long passages alone, and I give these the time they need". Stretches of silence start to make their way into the third movement, a reminder that this concerto was written just two years before the landmark 4'33. How does Tilbury handle these silences? "A real Cagean listener will listen to everything," he says. "They'll pick up on what is happening in the venue, and know that there are other noises going on. Really these silences are stretches of ambient noise."

Tilbury credits Cage for the open-minded listening he finds at his concerts. "People know about 4'33. The fame of that piece means they know about silence, or rather a lack of silence. That's the legacy Cage left us: a way of listening. And he taught us improvising musicians that accidental ambient sounds can be contextualised and made into music. It's ironic, because he himself rather disapproved of improvising. He was against self-expression because he thought it relied on learned habits rather than true chance."

Cage was always serious about his music: "Something of a contradiction about him," according to Tilbury. "Unlike Cornelius Cardew, who really wanted students and amateurs having a go, Cage wanted only the best performances. He wanted to have his cake and eat it too. He talked about freedom, but it was always freedom with conditions. Funny man."

John Tilbury, Ilan Volkov and the BBC SSO celebrate John Cage's centenary at City Halls, Glasgow, on July 28 and at the Proms (broadcast live on BBC Radio 3) on August 17.