Eliane Radigue - composer, performer, pioneer of electronic music, maverick of longform minimalism - opens a bottle of champagne at the end our interview.

She goes into the kitchen to fetch the crystal glasses and the snacks herself, though at 83 doesn't feel quite strong enough to shimmy out the cork with her own hands. "Who knows where it would go!", she giggles, and passes over the bottle.

We're in the composer's apartment in the 14th arrondissement of Paris, here to talk about two concerts featuring her music at the BBC Scottish Symphony Orchestra's Tectonics festival next month. Radigue has lived in this apartment block since the 1970s and the place is packed with striking artworks, many of them made by her ex-husband, the sculptor Arman. There are bronzes and resin wall pieces, as well as shelves of family photographs (Radigue is a great-grandmother several times over).

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What there isn't much trace of is the ARP 2500: that's to say, the particular model of analogue modular synthesiser that for 30-odd years was Radigue's mouthpiece to the world. It used to take up about a quarter of the living room, she tells me, indicating a large chunk of wall opposite the main door. Recently she asked an architect friend to dismantle it and store it in his basement: nowadays, for the first time in her six-decade career, she writes only for acoustic instruments.

Radigue was born in Paris in 1932. She sang in choirs and played piano and harp as a girl, then had a creative epiphany when she discovered the musique concrète of Pierre Schaeffer in the 1950s. "One morning I heard it on the radio and I said to myself, 'well, that's it!'" she recalls. "It was the realism of the sounds, you know? That you could take any ordinary object and find music in it, and leave aside what you didn't want."

She got in touch with Schaeffer and began working in his Studio d'Essai, immersing herself in the new realms of sound art and electronic music being discovered there. I ask what it was like to be a woman operating in the predominantly male environment of 1950s French experimental music. "Oh yes," she replies, "these men were all very macho. I remember one of the technicians saying, 'it's nice to have Eliane in the studio because she makes the place smell good'."

Radigue was an extraordinary beauty, a very natural beauty, although she says that she never realised it. "I was always simply 'Arman's wife' rather than Eliane Radigue, composer'," she says. "I would only get my hair done when I had to go to his gallery openings." Today she is casually elegant, with chic cropped hair and a silk scarf slung around her shoulders in that way only the French can pull off. She gestures irritatedly at a zimmer frame pushed into the corner of the room. "It's so ugly! Don't you think it makes me look old?" She might be too frail to travel, more-or-less housebound by a bad back, but no, she doesn't seem in the least bit old. I've rarely met such a vibrant mind.

Radigue's work as an assistant to Schaeffer, and later to the composer Pierre Henry, largely consisted of recording sounds and splicing together reel upon reel of magnetic tape. Gradually she started pursuing her own musical vision, which went deeper, slower and longer than the pieces Schaeffer and Henry were producing. Often she honed in exclusively on the ephemeral sounds generated by electronic feedback.

It was painstaking work but thrilling for those who had the patience - and if there is one thing Radigue has in abundance, it is patience. A committed Buddhist since the 1970s, her unhurried art is steeped with the meditation she practises daily. She describes herself as 'totally slow': "In classical music I have always been more interested in slow movements than fast ones. I take my time in every part of life. I do one thing at a time. Don't expect to push me because I will just say no!"

In the early 1970s, she travelled to New York and found there a community of kindred artistic spirits. "I discovered that another kind of relationship with men was possible when I went to the United States," she says. "My music had real recognition from other musicians there: James Tenney, Philip Glass, Steve Reich, David Behrman, Bob Ashley... All my musical family was in the States, and mainly on the West Coast."

It was through a residency at New York University that she met her first ARP synthesiser, an encounter that launched decades of inspiration. She took the innards of the instrument back to Paris and threw herself into extracting the most exquisite sounds it could muster. At first she felt almost shy of this temperamental beast and addressed it as 'Monsignor', an archaic term once reserved for only the highest clergy of the Catholic church. Later, as she and the instrument became more friendly, she fell into the habit of calling it plain 'Jules'.

Her work with Jules was meticulous, and always slow. "The first thing I did with it was to put aside all the strong effects, which were not my cup of tea. I looked for the smallest range of sounds, tried to catch the subtlety within the sounds." Sometimes she spent two or three years crafting a single piece.

Then something shifted at the beginning of the 21st century and Radigue began writing for acoustic instruments. Her face lights up at the mention of the word 'collaboration'; the process of constructing music with other people - instrumentalists who come to her apartment to work on new scores - seems to have filled her with a bright, girlish kind of energy that has produced a flood of new works over the last decade.

Tectonics will feature cellist Charles Curtis, harpist Rhodri Davies, tuba player Robin Hayward and bassoonist Dafne Vicente-Sandoval playing works from the ongoing OCCAM OCEAN. Radigue laughingly calls the series her "future unachieved pieces" because of the endless possible permutations of its instrumental combinations (currently the number of soloists stands at 22). Each work is an in-depth exploration of the fundamentals, harmonics and partials that its instruments can produce. "The music requires huge virtuosity from the players," Radigue says. "I don't mean fast virtuosity, of course. I mean the control they need over their instruments." From the audience, too, she demands a kind of slow virtuosity of listening. Sinking into Radigue's music requires the same acute attentiveness and longform patience with which it is made.

Eliane Radigue's music features at Tectonics, May 1-3 at City Halls, Glasgow