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Udo Kasemets doesn't look like an anarchist. With silver hair swept back from a smooth brow and clear blue eyes, their colour echoed in neat denims, he appears the quintessential civilized man -- gentle, erudite, charming. Yet anarchist he is.

Any confusion, the 80-year-old composer might say, comes from the corruption of the word "anarchy" by its association with political violence. But look closely at the etymology of anarchy, which derives from the Greek an, without; and archos, ruler. Anarchy describes a state without a ruler, not a state without rules. Even chaos, as recent fractal research has shown, is ordered. And for Kasemets, that order -- and its paradoxical co-existence with freedom -- is as applicable to music as to anything else.

"Anarchy," says Kasemets, "is creativity. Anarchy means taking responsibility for one's own actions, and collaborating with others voluntarily in a benign way." And if that sounds as much like a life philosophy as a way of writing music, that is what Kasemets is all about.

Born in Estonia, Kasemets emigrated to Canada in 1951. He taught theory and piano at several institutions, conducted, wrote a gently subversive piano method for children that is still in print, even worked, from 1959 to 1963, as a music critic for the Toronto Star. He was fired, he recalls, for positive reviews of Stockhausen and Bartok.

Always fascinated by mathematics, numbers are for Kasemets much more than abstractions. "Math is a misunderstood phenomenon," he says. "It's really -- like music -- a way of notating and trying to explain how nature works." Indeed, the congruence between natural laws and various mathematical and even mystical systems -- from quantum mechanics to the I Ching -- has inspired most of Kasemets's music in recent years.

A quartet of Sunflower compositions, based on the connection between phyllotaxis (the principles governing leaf arrangement on plants) and the Fibonacci number series (each successive number is equal to the sum of the two preceding numbers), is one example. Another is his epic Time Trip to Big Bang and Back -- which explores structural parallels between the genetic code, the binary numerical system and the 64 I Ching hexagrams, makes an acoustic atlas of star magnitudes and planetary orbits, and uses an 18th-century catalogue of star clusters as the basis for an extended improvisation on percussion instruments made from glass. Kasemets has used the map of the Zodiac and the circular Mayan calendar as scores; he has spun long essays out of the harmonic series; and he has converted the mathematical data of the fractal known as the Devil's Staircase into precisely notated pitches and timings.

But he wasn't always of such a visionary frame of mind. He got there by what he describes as a series of "Ah's!", musical epiphanies that carried him from early work that was relatively traditional to the graphic scores and experiments in sound, indeterminacy and structure from the sixties on. The first "Ah!" came in response to the mysteries of (strictly two-dimensional) order in the music of Palestrina; the second came with his discovery that extramusical orders -- like the 12-tone system of Schoenberg, and the related serialist experiments that followed -- could be applied to music. The third and most revelatory "Ah!" was Kasemets's encounter with John Cage's book Silence in the early sixties.

"With Cage I was born again," says Kasemets, and he still speaks of Cage with an acolyte's humility and passion. "Cage was the person who showed that music is not a fixed discipline," he explains, "but one that relates to life in many ways, as one system related to all systems. It was Cage who showed that music belongs in the universe at large."

Kasemets never looked back. He introduced the gospel of Cage to Canada in self-produced concerts, in the articles he wrote for various journals and in his classes at the Ontario College of Art where, from 1970 to 1987, he presented the ideas of Marcel Duchamp, Buckminster Fuller and Marshall McLuhan alongside those of Cage. His own music changed, too, leading him to disown most of what he had composed B.C. -- before Cage. Thenceforward his music dealt with many of the issues and ideas Cage championed -- the concept that time, not pitch, is the first principle of music; that the spaces between pitches -- and noise itself -- is material for composition; that chance can (and sometimes should) override choice; and that unorthodox structural models are fair game.

Even so, Kasemets, who has been called "the best-kept secret in the country," is not a Cage clone, as even his approach to the I Ching -- crucial to both -- indicates. "Cage used it to make practical decisions," notes Kasemets. "I used it in structural ways."

Nor has he marked time, as Stephen Clarke, a Toronto pianist who recently recorded a CD of Kasemets's solo piano music for the experimental Swiss label hat(now)ART, observes: "The one thing about Udo is his incredible openness," says Clarke. "He never becomes set -- he'll explore one thing, then go on to explore something else. And over the last 10 years, especially since Cage's death, his music has become more concrete in its notation, clearer and more refined."

What his music is not, however, is easy listening. That's not to say it isn't sometimes beautiful, or powerful. But one of Kasemets's preoccupations is with the act of listening itself, which, he feels, must never be passive. There's a challenge implicit in Kasemets's music. Length, repetition, the lack of traditional musical signposts, even, sometimes, the deliberate avoidance of "prettiness" are calls for a more concentrated listening. Kasemets's intricate methodologies often work in a spirit of "what if?" and the listener must be willing to share in the composer's curiosity. And as Linda Catlin Smith, a Toronto composer and spiritual ally of Kasemets once put it, "Sometimes you just really need to have your ears cleaned by hearing something that was made without the intention of expressing anything specific."

I like to think, as well, of the way certain mathematicians are said to be able to see complex calculations in three dimensions, and how they use the word "beautiful" to describe them. That's not something most of us can ever expect to see, but it is something that Kasemets's music almost allows us to hear.

The challenge is not just issued to the listener. These are conservative times, when many music students leave school with little sense of what new music is all about, and with even less interest. Taking to heart John Cage's statement that the avant garde is about "doing what has to be done," Kasemets forces performers to reassess their relationship with musicmaking. It's necessary work, if new music is to thrive: One merely regrets that the intimate scale of Kasemets's activities often leaves him preaching to the converted.

AnarchArtQuantuMandala, which was featured in a concert on Sunday of music by Cage and Kasemets at the Music Gallery in Toronto, is classic Kasemets. The score requires the performers to refer, independently, to digital stopwatches for information about where to start, how many measures to play at a time, and how loud to play them. But underlying these "instructions" is something more profound: Whatever you play, it must be musical.

"You find whatever music you can find in this piece," says Kasemets. "Once you've gotten acquainted with what's there and with the instructions, you simply ask yourself: What music can I make with these four bars here? As a composer, I can't be disappointed in the performance. I can only be disappointed in the performer's attitude."

Clarke, who played AQM with violinist Marc Sabat, remembers it well: "It was lots of fun preparing! But however much preparation you do, it still comes down to the moment. I remember in that performance, a third of the way in, there was a violin melody almost like a folk tune that suddenly showed up. The music was in the score. Marc just found it."

Anarchy, attitude, change, process and the serendipitous discovery: All recur in Kasemets's music. But there's another thing -- a little more elusive, perhaps -- and that's Kasemets's humanity. One senses that for Kasemets, the people who take part in his projects, and those who sit in the audience, matter as much as what the music sounds like. If music is a way of understanding the world, it's also a way of being in the world, or so he seems to say. And it has lessons to teach us all.

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