Giant of modernism, towering figure of contemporary classical music, Carter was an American who embodied the European avant-garde, an intellectual who - boldly, prolifically and usually with a twinkle in his eye - wrote music that is unashamedly erudite but shimmers with wit and character.
While America was seduced by the thrumming primary colours of minimalism, Carter furrowed ahead with works of glittering intricacy. His music is like life itself, impossible to boil down into one set of chords or one homogeneous rhythm. He lived to 103 and composed profusely until just a couple of months before he died. "Writing music has just become a habit," he once said. "I can't give it up."
It's hard to know where to begin with a composer who spanned a century of cultural life. Carter was a New Yorker through and through: born in the city on December 11, 1908 (he was a day younger than Olivier Messiaen) and resident of the same apartment in Greenwich Village from 1945 until his death in 2012. As a child he was bright and inquisitive; he lapped up Joyce and Proust and he devoured new music. He was at the first performance of Rhapsody In Blue and the first American performance of The Rite Of Spring, an earnest teenager with ears buzzing in the audience.
Carter took lessons with Gustav Holst and befriended Charles Ives and Aaron Copland; the influence of all three is audible in his confident, wholesome early works. Like several generations of budding composers he headed to Paris to study with the formidable pedagogue Nadia Boulanger, who had a fairly conservative notion of aesthetics (he returned to the United States and scribed neo-classicism for a while) but who left him with a rock-solid grounding in theory and an iron grasp of counterpoint. This would prove critical, this ability to make lines twist and turn along their own path yet still somehow fit together.
In 1950, Carter spent a year in the desert near Tucson, Arizona, and it was during this period of semi-retreat that he made his major breakthrough. The First String Quartet is a big deal because it introduces "metric modulation" - essentially a way of melting different speeds and pulses together. Paradoxically, Carter's notoriously fiendish rhythms offer something that is human at heart.
"We do not measure time regularly, like clocks do," writes the pianist and musicologist Charles Rosen, "but with many differing rates of speed. In the complexity of today's experience, it often seems as if simultaneous events were unfolding with different measures. These different measures coexist and often blend but are not always rationalized in experience under one central system."
Carter's music is a kind of utopian society, in which teaming complexity stands for the riches of diversity. Rosen again: "Things happen for different instruments at different tempos -none of them dominates the other, and an idiosyncratic character is often given to the different instruments that preserves their individuality. Carter is never dogmatic, and the different measures of time may occasionally combine briefly for a moment of synthesis." Not a bad model for politics (and oh, to see our Holyrood leaders at City Halls tonight).
In the end the music seemed to flood out of Carter. He wrote reams and reams even in his last decade - more than 60 works after his 90th birthday. He just never stopped working, and his music never stopped sounding contemporary. Is it inaccessible? Carter himself would have probably shrugged. In 1978 he said: "It seems to me that if a work has something remarkable to say, then someone who wants to whistle it will find something in it to whistle."
Another thing that's striking about Carter is just how many friends he had. Today his music is often played by musicians who knew him well, and towards the end of his life he only wrote for orchestras that had previously played his music, such was the level of expertise required to pull off his tricks.
This week we are in safe hands: few orchestras are more capable of tackling a fiendish contemporary score than the BBC SSO, and they are joined by a clutch of musicians who not only knew Carter but who premiered many of his late works - percussionist Colin Currie, pianist Nicolas Hodges and conductor Ryan Wigglesworth.
"I got to know his music at university, around the same time that I got to know him," says Wigglesworth. "I spent quite a lot of time with him as a student in New York. He was in his late 90s at that point, pushing 100, and yet he remembered everything. It occurred to me that if he had been my age talking to someone his age, that person could have been Brahms or Schumann. It was a unique situation in the history of Western music, to have someone in their 90s still writing music of such force and energy, impervious to the sway of fashion. His music was modernist, yes, but it was so full of life."
Wigglesworth fondly describes visiting Carter's flat in New York: "He lived in this old-style Manhattan apartment, lots of little rooms, full of incredible things like first-edition Joyce that he had bought as a student in Paris. It wasn't that he was a collector - he just kept hold of what he had bought when he was young."
Hodges, too, remembers visiting Carter at home.
"We were very close - I always popped in to see him whenever I was in New York.
"For me he was always avuncular and supportive. And he was fun. The last photograph I took of him, he was with his six-year-old neighbour who was dressed as Dorothy from The Wizard Of Oz. He's just grinning."
No, his music isn't so difficult to play, says Hodges. "It's musically challenging but technically not too bad - which is far better than the other way around. The late works are so bubbly and light and Haydnesque.
"I once sat next to Carter through a performance of his Variations For Orchestra. He sang the melody the whole way through. He was clearly having a whale of a time."
The BBC SSO's Elliott Carter retrospective is tonight and tomorrow at City Halls, Glasgow