A few weeks ago, in these very pages, the Sunday Times classical-music critic Paul Driver wrote: “It worries me that John Cage’s music is not being quickly forgotten.” Bad news, Paul. Not only is Cage’s music not being forgotten, its influence is clearly spreading — at least it must be, if we accept the thinking behind the upcoming Ether festival at the Festival Hall (March 6-18). For the second year running, Ether will include an evening where the works of Cage (and other 20th-century classical composers, including Steve Reich and Edgard Varèse) will be performed by the London Sinfonietta alongside pieces by pioneers of electronica such as Squarepusher and Aphex Twin.

The man making these connections is Glenn Max, contemporary culture producer at the South Bank. “The original idea came from understanding that there was a passionate audience out there that was focused on DJ culture and had no relationship with the concert-hall-going experience,” says Max. “My view was that if there were people who were passionate about music and they weren’t showing up here, then that was wrong. Ether is designed to address this.” When Max says that the line-up “reads like a Hall of Fame of pioneers of electronic music”, he’s not far wrong. Tangerine Dream, Plaid, Luke Vibert and Kraftwerk are all performing. Max can’t hide his delight at securing the reclusive Kraftwerk. “That’s something I’ve been pursuing for a long time,” he says. “I feel blessed.”

But it’s the evening when the London Sinfonietta and Squarepusher get up on stage together (March 12) that carries the most musical significance. Does Squarepusher’s relentless pursuit of almost-but-not-quite-unlistenable music make him the 21st-century heir to the work of the classical avant-garde? “I hear those connections,” says Max. “Ligeti and Cage, Squarepusher and Aphex Twin — I don’t think it’s too much of a stretch to say that here are ideas being explored across centuries. But it’s a connection we’d best leave to the composers and arrangers to work out.”

At least one of the composers isn’t so sure about the connection. “I personally do not see myself alongside those people,” says Squarepusher, aka Tom Jenkinson. “I am utterly grateful that chance has never taken me near an academy of music. If I had attended one, it would have killed my interest in music. You either end up a carbon copy of your tutors or some sort of embittered reaction against them. I am glad my work is tainted with none of that rubbish.”

Jenkinson will concede that, though he may never have studied the 20th-century greats, “my work may well have been influenced by these people ... but it is as influenced by acid house or the sounds of various forms of traffic going past my window”.

Aha! Traffic as music! How John Cage is that? Jenkinson is clearly au fait with Cage’s ideas and shares some of them. “What Cage sensed was that in the process of composition, you are not present. Ideas and intentions give way to a tide of unconscious activity. Thus, when the work is completed, it barely feels related to you,” he says. “I hold that this is the only way to work.”

The most obvious connection the leaders of the 20th-century classical avant-garde have with those currently at the leading edge of electronica is that their music depends on the arrival of new technologies that allow sounds to be created in new ways or — more importantly — new sounds to be created. Perhaps this is true of all musical development, but Cage and Aphex Twin take this further, adapting existing technologies in an attempt to make the hardware keep up with their ideas.

Cage’s prepared pianos have an echo in the Twin’s self-modified synths.

This determination to find sounds in a piece of technology that its inventors didn’t know were in there is a theme that runs from Cage, through Stockhausen’s Morse-code signals and Kraftwerk’s synthesized “drums”, into Squarepusher’s envelope-pushing programming.

Another connection is that the contemporary recording studio, based in computer software, makes applying Cage’s ideas concerning composing through “chance operations” all too easy. One keyboard click can transform a piece of music into something completely different. Many sounds in modern music are derived from the none-too-musical process of simply clicking away until something listenable emerges.

Cage saw this as one way of lessening the importance of the composer behind the work — a mission that has not, as Jenkinson points out, been very successful. “Try as he might, Cage could never have surmounted the enthusiasm for putting artists on pedestals. He is clearly on a pedestal now,” says Jenkinson, a man whose oeuvre has seen him placed on a pedestal of his own.

On Squarepusher’s latest album, Ultravisitor (out on March 8), Jenkinson continues to explore what happens when you try to resolve two extremes: usually frenetic and inspired electronic programming on the one hand, and the organic sounds of his bass-playing on the other. As ever, this resolution is not comfortable, but it is fascinating.

“Modern music is a kind of cultural deodorant,” says Jenkinson. “Our attempts to perfume our world also bury the human heritage of extremes. My music is uncomfortable if you want music to act as a distraction. If it has any value, it might be to remind you of the visceral life we left behind in the name of modernity. I’m the first to admit that my work is quite often ridiculous. But human beings are ridiculous things.”

Last year, Squarepusher’s work was performed by the Sinfonietta, but this year Jenkinson will be joining them on stage to perform a track from Ultravisitor. He has also written a piece specifically for them. His greater involvement is a measure of the success of last year’s Ether. When he first heard about the idea, Jenkinson was wary. “It smacked of old people trying to be cool,” he says. But he considered the performance “an interesting experiment. What mattered was that a new door had been opened”.

When this year’s Ether is done, the man behind it has other doors he wants to open. “I’m thinking of doing an acoustic Ether,” says Max. “Electronica Unplugged!”