In his new plaid knickers, red buckle shoes, and white socks rolled down around the ankles, six-year-old Brinel strutted past his classmates like a peacock in full plume.

Time was drawing near and he smiled obediently, exposing a missing front tooth to the bright lights of the French television crew. This little fellow was about to show, with the clumsy stroke of a pen, that Goethe may have been onto something when he called architecture ''frozen music.''

Brinel sidled up to a large drafting table and grasped the fat pen with the long gray cord growing out of its eraser end. With it he scrawled a suitably awkward squiggle on the graph paper. Then, he waited. The audience in the red velvet seats held its collective breath.

Furiously a teletype chattered, followed by the soft whir of a computer disc. Next, from the loud speakers on stage, erupted something resembling a xylophone played under 10 feet of tapioca. The assembled press corps applauded tenatively, and young Brinel offered comments into the television camera. ''Bizarre! Tres bizarre!'' he shyly blurted out about the sounds he had just drawn.

The sounds he had just drawn? Tres bizarre is right.

Six-year-olds from L'Ecole Maternelle Gambetta were actually drawing music. Among this bunch were no closet Mahlers; in most cases their scribbling was more intriguing than the corresponding noises. Nevertheless the machine's inventor, Greek composer-architect Iannis Xenakis, had made his point: You don't have to be Beethoven to compose music. On this nifty little composing machine, a doodle will do just fine.

Perhaps more importantly, Xenakis was drawing attention to a new kind of computer music notation which, he believes, will revolutionize the composition of 20th-century music. Critics of Xenakis's composing machine yawn: ''It's just another musical gadget'' and perhaps they are right. But Xenakis, an iconoclast in the Paris music world who has been the talk of this town off and on since the 1950s, has parachuted back into the news with his latest contraption.

In the basement of Forum des Halles, where Xenakis staged his demonstration, the walls were papered with the composer's own scores. They looked like woodcuts and etchings of trees and shrubs, unsettling to anyone used to sheet music with bass clefs and quarter notes. One of Xenakis's scores resembled the root system of an oak tree; another looked like a topographical map of an eroding mesa; a third like the satellite weather report on the 6 o'clock news. Nothing as graphically elegant as one would expect from the master of this new-fangled machine.

Xenakis set us straight: ''Don't be trapped by pretty designs. They sound the worst,'' he said. ''This machine can design any sound we like. The red you see here,'' he says, peering through half-glasses at the drafting table, ''that controls the timbre, which makes the difference between two instruments. Blue is the intensity, which we can move from pianissimo to fortissimo. Green is the pitch or notes. And remember, every single point on a drawn line is interpreted by the machine as a note. We aren't restricted to single lines. You can have a complex of lines, like bushes, which, of course, will produce higher order forms.''

Xenakis is a composer of eclectic talents. Inventor of new forms of music and architecture, he spent most of the 1950s collaborating in Paris with the world-famous architect Le Corbusier. Xenakis is a combination of engineer, mathematician, physicist, archaeologist, philosopher, and astronomer. With the hyperbole expected of a publisher, Indiana University Press goes so far as to claim on the jacket of his book ''Formalized Music: Thought and Mathematics in Composition'' that Xenakis is ''without question the most important living theorist of music compositon. . . .''

Xenakis lives and works in Pigalle, a north Paris neighborhood known for its artists, jazz clubs, and ribald entertainment.

Xenakis's studio is a four-minute walk from the Pigalle Metro stop, just past a peeling pink stucco dance hall and a row of shops with electric guitars in the windows. The studio is on the top floor and through the high windows on the north wall comes the lilting saxophone solo of a would-be Charlie Parker who lives in a flat across the street.

The creative chaos of Xenakis's workshop is untainted by tidiness. An impromptu workbench, resting on wooden sawhorses, is strewn with Kodachrome slides of his designs. At one end is poised a vase of two dozen wilting pink roses. Chalk hieroglyphics cover the blackboard. Near the drafting table, where he composes standing up, the wall is plastered with photographs of Jupiter torn from a magazine. In the center of the room is his only island of comfort, two overstuffed easy chairs covered in corduroy. There, he keeps a few astronomy books, one on Aztec art, another on Buckminster Fuller, an Agatha Christie thriller, and three briefcases - two brown, one black.

Xenakis is an athletic, handsome man with salt-and-pepper hair and an aquiline nose. Good-humored and quiet to the point of shyness, he is hardly the egomaniac his critics make him out to be. To be sure, he is confident and quite comfortable with himself. His clothes show no pretense: a blue plaid cotton shirt, olive corduroy trousers, black deck shoes, and green argyles.

Leaning forward in one of the armchairs, Xenakis offers a color slide of the summer house he designed for a French composer on the tiny Greek island of Amorgos. ''My kayak is waiting there right now,'' he says with a gleam of anticipation. For several weeks every summer (''I wish it were several months,'' he laments) he and his wife, Francoise, a French novelist and literary editor for the newspaper Le Matin, paddle a two-person kayak between the Greek islands. ''When we see one with goats on it we know we've found fresh water.'' He adds: ''My wife comes from the interior where there are only lakes, so she was frightened at first of traveling in the open sea. Sometimes it is frightening but that is exactly why I like it. In the English language the sea is 'it.' In French and Greek the sea is feminine. That says a lot to me.''

Xenakis grew up by the sea. He was born in 1922 into a wealthy Greek family in Braila, a Romanian port town on the Danube, where his father, Clearchos, worked as a shipping agent for a British import-export business. The eldest of three sons, Iannis was raised by a governess after his mother died. When he was 10 his father sent him to an elite Greek boarding school on the island of Spetsai, in the archipelago near Hydra. ''I was miserable there,'' said Xenakis, recalling how his Constantinople accent and rural naivete instantly cast him as the new class pariah. Vicious taunting from the other grade schoolers forced his quiet retreat to the school library, where he found refuge and literary companionship in the works of Plato, Sappho, and Victor Hugo. ''I was an outsider,'' he said, ''and my only escape was to study. I read most of the books in the library.''

When Xenakis was 13, a new British headmaster arrived at his school with a gramophone and classical record collection. It was Iannis's first taste of Beethoven and the great European composers. He was soon taking piano lessons and singing Italian Renaissance music in the school choir. In 1938, the year Hitler invaded Austria, Xenakis left Spetsai for Athens to continue his studies in physics, math, classical literature, and music.

While he was completing his exams at the Polytechnic in Athens, Mussolini's troops marched into Greece. The Italians converted the college into a prisoner-of-war garrison - and Xenakis, like many of his patriotic classmates, joined the Greek resistance. It was a time in Greece when strikes were rampant and shortages a daily occurence. Food was scarce and the winters devastating. ''The winters of '4l and '42 were terrible,'' Xenakis recalled. ''People died from hunger and cold. . . . There was no coal or wood, nothing to make a fire. My blankets were thin, like paper. Instead of having the weight of warmth, I used to pile furniture on my bed. I used chairs and tables to give the feeling of warmth. We were desperate.''

Following a brief, disillusioning stint with the right wing of the resistance movement, he joined the Communist Party. ''The Communists were fighting in a much more efficient way and their new ideas about society, changes, and socialism were closer to the things I was reading as a patriot.'' He became a regular in the front-line street demonstrations and was in and out of prison. When the British finally liberated Greece, they sided with the Greek military regime, declared martial law in Athens, and outlawed the Communist Party.

Feeling betrayed by the British, the Greek resistance refused to surrender its weapons. Barricades were erected around the city and street fighting broke out again. ''It was a pity the British aligned themselves with the right wing,'' Xenakis said. ''It was a political mistake that turned the people against them. Oddly enough, the same sort of thing happened to the French and Americans in Vietnam.'' In 1944 Xenakis was appointed political leader of the Lord Byron, a Greek student battalion that won a reputation for overcoming its inexperience with heroism. ''We were not trained and had only guns to fight against the British and their Sherman tanks,'' says Xenakis, who still has deep facial scars caused when he was struck by shrapnel from a British tank shell during the final days of the street fighting.

After three months in a hospital, Xenakis was back on the streets. But he soon went into hiding. Months later, with a cardboard suitcase and passport forged by a friend of his father, Xenakis stowed away on a cargo ship out of Piraeus, escaped to Italy, and was eventually smuggled into France by the Communist Party. In his absence a Greek military tribunal in Athens sentenced him to death.

He arrived in Paris on Armistice Day, Nov. 11, 1947, with dreams of eventually visiting his uncle in America where he would study archaeology and astrophysics. In the meantime he needed to pay the rent and used his engineering degree from the Polytechnic to land a job with one of Europe's finest architects , Le Corbusier. The designer was assembling a group of 40 young engineers and architects for work on L'Unite d'Habitation de Marseille, a large apartment complex. Xenakis was hired as part of the new batch.

Simultaneously, Xenakis began studying musical composition under Darius Milhaud, Hermann Scherchen, and Olivier Messiaen. ''I worked very hard,'' he says of his moonlighting. ''I was doing architecture during the day and my nights and weekends were for music. During the 12 to 2 lunch break I would write my music while the others went to eat.'' He still refuses lunch.

Xenakis was no lover of modern architecture but continued his apprenticeship with Le Corbusier for other reasons: ''I felt architecture had gone downhill since classical times, but I was attracted by the problems that Corbusier was dealing with, issues of technique and structures. I had the same problems in music. I asked Corbusier one day if I could do a project with him. He agreed and we did Le Couvent de la Tourette.'' Le Corbusier worked closely with his young assistant who, as principal architect, produced some 200 plans for the monastery.

While Xenakis was making his architectural debut he was also writing ''Metastasis,'' his first important musical composition. Cross-fertilization between the two projects was evident. ''As I was working on the monastery's facade,'' he remembers, ''I saw it had a certain rhythm with the changes in density. It was a kind of rhythm of space, the same kind as in music. The relationship of lines on the facade had actual rhythm so I measured off relative distances of the facade on recording tape and actually transposed the architectural -design into music.'' By examining his new design. Xenakis could actually ''listen'' to the monastery's facade the way he might ''hear'' the score of music he was reading.

Not suprisingly critics said his ''Metastasis'' reverberated with architectural structure. Using probability calculus and set theory along with mathematically abstracting social and natural occurrences (such as swarming bees and chanting crowds), Xenakis was penetrating the surface of music into deeper substructures. ''I introduced the concept of clouds of sounds,'' he said. ''You can have 100 musicians, each playing four or five sounds per second. That's 400 sounds per second which is a dense cloud of events for our poor ears. Those sounds are like what I heard when I was camping in my youth, the wind in the trees and rain on the tent. And the sounds I remembered from the resistance days , the huge demonstrations and shouted slogans, the clash in the streets with the Germans, the sound of the tanks and machine-gun bullets in the night.''

Twisting surfaces the way he twisted sounds, Xenakis collaborated with Le Corbusier on a number of major designs, including the Philips Pavilion for the Brussels World's Fair in 1956 and later the Maison de la Culture in Firminy, the Stadium of Baghdad, and the Concours d'Urbanisme in Berlin. Growing differences between these two strong-headed men led, however, to heated arguments and finally in 1959 Xenakis left Le Corbusier. ''I was involved in all his designs for eight years beginning in l952,'' said Xenakis. ''In his relations with me he appreciated my work but also feared it. In the beginning he gave me great freedom and showed me off to his clients, but in the end he thought I was gaining too much importance. Finally we came to a clash.

''His architecture taught me an important lesson, however, for my music. In classical music today you generally start with a theme, a melodic passage, then you have rules how to make the whole composition. So you go from the detail to the macro form. Most of the time in architecture it is the inverse. When somebody asks you to design something he gives you the size of the surface you have to occupy, the cost, the type of materials, and any other problems of the space. So you have 50 percent of the shape formed from the beginning. Then you go to the details. Corbusier could deal with both ends, the macroscopic and the microscopic, at the same time. He was very proud of that. He would tell us 'I did the whole shape of that house starting from the shape of the gutter.' That was a good lesson for me.''

After leaving Le Corbusier, Xenakis did a smattering of free-lance design but primarily devoted himself to music. He was breaking new ground, examining the interplay of science and music, experimenting with sonic sculpture, three-dimensional sound and light concerts. In the early 1960s he began using an IBM computer in his compositions. In the mid-1960s he founded Centre d'Etudes de Mathematiques et Automatique Musicales, with the hope of beginning a research institute for computer music. He traveled and lectured widely in Europe, South America, Japan, and the United States. From 1967-1972 he served as associate professor of music at Indiana University in Bloomington where he founded the Center of Mathematical and Automated Music.

''Many people object to computer music because they say it is too mechanical, '' Xenakis says. ''Musicians have always used mathematics, sometimes without knowing it. Bach made beautiful melodic patterns with a technique that was highly mathematical.''

Criticism of his new composing machine often results from a similar misunderstanding: ''If you draw a picture of a house or dog (on the composing machine), it doesn't mean the corresponding sounds will be interesting,'' he says. ''Just because you use computers it doesn't guarantee your music will be good. On the contrary. To use a machine in music is like an architect using a ruler or sliderule. If he is gifted he can produce something interesting.''

During one of his trips to Japan, Xenankis visited the Imperial Palace and saw a performance of traditional Kabuki, Gigaku, and No theater. It reinforced his interest in ancient music forms as well as in what he called ''total theater ,'' the intertwining of instruments, songs, chants, drama, and spoken dialogue.

Meanwhile, his reputation as an ''environmental artist'' continued to grow. In 1967 Xenakis was invited by the French government to design a sound and light show for its exhibition at the Montreal Expo. He followed that in 197l with similiar spectacles on the ruins and mountain at Persepolis in Iran and a year later at the Roman Baths of Cluny. After the fall of the Greek junta, Xenakis, who had been in exile since World War II, was invited back to his homeland. The former resistance fighter, who had long since bowed out of left-wing politcal causes, presented his music at a 1978 festival held in the Peloponnesus at Mycenae, the ancient ruined city and, according to tradition, the residence of King Agamemnon.Xenakis, maestro of the spectacle, pulled out all the stops. He offered a 21/2-hour feast of movement, light, and music including several pieces written on the new composing machine. At dusk he boldly illuminated the Mycenae hillside with antiaircraft light projectors, accompanied by flickering flashlights carried by some 300 children and 500 goats.

Many consider Xenakis' piece de resistance to be ''Diatope'' which he erected that same year in front of the Centre Pompidou. The structure was a swirl of soft red textile with laser beams beneath and on top of the glass floor. It included a total of 1,680 lights and his original music scores. ''In a cinema you have light reflected on a surface, but in the Diatope,'' said Xenakis pointing to a wire mesh model on the shelf, ''you can actually play with laser light, light material itself.''

After several hours, our morning interview in his Pigalle studio had grown into an afternoon chat. Xenakis announced he had business to tend to and invited me to tag along.

First were the phone messages. One came from the head of interior design for the Paris Metro, who wanted to exhibit blow-ups of Xenakis' computer scores in one of the downtown train stations. Next was a call regarding the post Xenakis has just been given as president of an organization to promote jazz in Paris. (''I accepted because I know nothing about jazz and thought it was about time to learn,'' he said.)

Putting down the phone, Xenakis checked his watch. He was running late for an appointment at the television station for the premiere of a one-hour documentary on his life and music. He quickly stuffed a handful of papers in one of his briefcases and bounded down the wooden stairs three at a time. On the ground floor, he loped into the street, flailing his arms at a taxicab in the next block. Within minutes he was instructing the driver on a favorite shortcut through the back alleys of Montparnasse. Xenakis has that admirable knack for rushing without losing control. He is well-known throughout the city but when it comes down to getting a taxi, restaurant table, or office appointment, he tends not to throw his weight around. He exercises patience instead of privilege.

With a minute to spare, Xenakis kept his 2 p.m. appointment in TV 3's third-floor screening room. At the end of the showing he gently scolded a paunchy producer for the selection of music, and by 3:05 Xenakis was on his feet again, scurrying into the Montparnasse Metro station, and headed for Forum des Halles. There, he began ironing out the last wrinkles in the composing machine which was scheduled for a demonstration with blind students the next morning. At 4:50 he slipped out a rear basement door with his American assistant, a high-strung computer whiz in red sunglasses, trailing at his heels. Trying to keep up with his long strides, she scampered beside him up three flights of stairs and through the cobblestone streets leading to the Centre Pompidou.

The 5 p.m. rehearsal of one Xenakis's piece by the Ensemble InterContemporain was about to begin. In the Grande Salle a cello and two French horns were tuning up. A soprano, with dark Mediterranean eyes and an American accent, shouted to Xenakis ''Bongiorno'' and planted a kiss on his cheek.

The composer had not eaten all day and looked fatigued as he took a seat in the back of the concert hall to test the acoustics. The tone of one of the French horns was slightly off. Xenakis ran down the aisle to help adjust the microphones and the positioning of the grand piano. Moments later he was clowning with one of the sopranos over her muffing three quarter notes. Xenakis listened quietly through the rest of the rehearsal, then, following a brief word with the conductor, grabbed his briefcase and caught the subway back home to dinner in Pigalle.

After a day of trailing the composer through Paris, I wondered breathlessly what makes Xenakis run?

''Maybe it's because I'm unhappy by constitution,'' Xenakis confessed. ''You know, I once thought about doing astrophysics or mathematics and I suppose I only decided to do music because I was so miserable doing anything else. Music was my only escape. There seem to be deep common links between astronomy, philosophy, and mathematics. For me, music is that crossroads.''

And what sort of ambidexterity does it take to direct traffic at that crazy crossroads?

''Xenakis has been compared to the artist-philosophers of ancient Greece, to the scholar-painters of the Renaissance, to the Encyclopedists and the great discoverers of the Enlightenment,'' writes his biographer Nouritza Matossian, in her book ''Iannis Xenakis'' (just published in Paris in the Fayard/Sacem series ''Musiciens d'aujourd'hui.'') Her conclusion: ''Xenakis has never stopped being a Resistance fighter. He simply moved his field of battle into music, he transformed physical and political combat into the struggle of ideas and sounds and therein forged his own aesthetic with a lyric passion of which he never stopped to give account. The gesture of his music is the dynamic of his life. Iannis Xenakis is the last heroic composer.''

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