SINCE Pythagoras, musicians and scientists have known (or thought they knew) that the lowest pitch a string stretched taut can produce — the fundamental — is the pitch it produces when vibrating freely. "Stop" the string anywhere between the end points, and the vibrating section sounds at a higher pitch. Theoretically, there is no ceiling. As with dancing, the sky's the limit, but the floor is always the floor.
For the last five centuries, give or take, the range of a violin bottomed out on the G below middle C, the pitch of the open G string. But fiddlers are not like dancers after all. For nearly two decades, the Japanese violinist Mari Kimura, 48, has been exploring unsuspected subterranean sounds as much as an octave deeper.
Complementing the familiar concept of harmonics (pitches drawn from the overtones of a given fundamental), Ms. Kimura has named her freshly discovered sonorities "subharmonics." So far she has mastered the subharmonic octave, third, second and fifth. She is now pursuing the elusive subharmonic fourth, undeterred by a suspicion that it may be an impossibility.
"I began to discover these low sounds when I was preparing 'Tzigane,' " Ms. Kimura said recently in the Upper West Side apartment she shares with her husband, Hervé Brönnimann, a French computer scientist, and their two school-age children.
Ravel's "Tzigane," a Gypsy-inspired rhapsody, opens with a moody two-minute solo on the G string. Seeking to give her tone in that introduction greater brilliance, Ms. Kimura modified exercises her first teacher — Armand Weisbord, a student of the Belgian master Eugène Ysaÿe — had taught her for achieving greater brilliance on high notes, drawing the bow very slowly and steadily, with slightly greater pressure than usual.
"I heard low notes I had never heard before and thought, 'What is that?' " she said. "I wouldn't have pursued it except that I was taking private lessons in composition with Mario Davidovsky. So I was looking for new things I could do on the violin. And I thought, 'Maybe I can use this.' I scratched and scratched and finally got to the point of making the octave."
Born to a professor of law and a professor of architecture in Tokyo, Ms. Kimura trained in Canada, Japan and the United States with Mr. Weisbord, Toshiya Eto, Roman Totenberg and Joseph Fuchs, four grand old men of violin pedagogy, mentors she continues to revere. But along the way she encountered Marvin Minsky, the guru of artificial intelligence and for a while her next-door neighbor. It was he who first suggested she compose.
"Why?" Ms. Kimura demanded at the time. "I'm a violinist." But then the idea took.
"I was like a horse with blinders on," she now says. "Marvin took my blinders off, and all of a sudden I could see the world."
Ms. Kimura's coterie of fellow trailblazers in music and science should be out in force for her next Manhattan concerts. Characteristically, these will be off-the-radar affairs: May 20, a recital at the Bohemian National Hall on the Upper East Side, under the aegis of the Vilcek Foundation, a boutique philanthropy that supports foreign-born innovators in the arts and biomedical sciences; and on June 25, a duo program with the pianist Stephen Gosling, presented by the New Spectrum Foundation at the Tenri Cultural Institute, which is dedicated to the study of the Japanese language and of international art forms.
Ms. Kimura set off on her road less traveled with a New York debut recital in 1994. Presented by the League of Composers/I.S.C.M. at Merkin Concert Hall, the program constituted an experimentalist's tapestry light-years beyond Paganini. She played pieces of her own and the American premieres of Luciano Berio's hallucinatory Sequenza No. 8 and Salvatore Sciarrino's scarcely decipherable "Six Capricci," as well as rarities by the likes of Conlon Nancarrow and John Cage.
In a glowing review, Edward Rothstein, then the chief music critic of The New York Times, dwelt on those mysterious low notes. "Ms. Kimura did not use them for novelty's sake," he wrote, "but as elements in a sweet, ghostly composition meant to expand musical territory as well." (That review, Ms. Kimura says, helped her get a green card.)
In the violin's conventional range, any competent concert artist is expected not only to sound pitches but also to control attack, dynamics and expression. Subharmonics, Ms. Kimura admits, are options she can only switch on and off. Finer shadings are not yet available. Even so, she deploys the colors of her arsenal with considerable variety. In stark contrast to Mr. Rothstein's description, a recent Times review by Zachary Woolfe ascribed to Ms. Kimura's Bach deconstructions, which also feature subharmonics, a "ferociously guttural power."
While acousticians who have studied her techniques under laboratory conditions still find them deeply perplexing, a graphic formula Ms. Kimura has come up with may capture all the lay public really needs to know. Step 1 in producing a subharmonic is "clunk," a brusque, decisive smack of the bow on the G string. Step 2 is "drag," the stroke itself, executed under unusually high pressure, at unusually slow speed and with unfailing steadiness. Step 3 is "release," effectively the clunk in reverse. (A home video on her Web site, marikimura.com, illustrates.)
But clunk-drag-release is not the be-all and end-all of Ms. Kimura's quest for the new. Her work with an electronic 3-D bowing-motion sensor has likewise caused a stir. Developed at Ircam, the musicians' think tank in Paris, it consists of a half-finger glove equipped with electrodes that monitor the angle and speed of her bowing arm, allowing her to synchronize real-time acoustic performance with recorded material. More nebulously, it affects expression in ways impossible to quantify.
Frédéric Bevilacqua, who directs Ircam's real-time musical interaction team, noted that others have used this technology, too. "What's special," he said, "is that Mari is at the same time a performer, composer, improviser, all in the same person. She achieves an extraordinary intimacy between her acoustic violin and the electronic sound. She makes everything expressively coherent."
Jean-Claude Risset, a founding father in the field of music for computers and a composer, has been fascinated by Ms. Kimura's adventures on the acoustic and the cybernetic fronts. "The sounds that Mari gets out of the violin are novel," he said recently from Marseille, "yet one senses that they are deeply anchored in the genius of the instrument."
As for pieces predicated on electronics, Mr. Risset noted that their shelf life is often brief. "Technology changes so quickly," he said. "Ligeti always refused to work on an interactive piece for fear that it would not be playable for long." All the same, in his first composition for Ms. Kimura, Mr. Risset used a technique called signal processing.
"I like to suggest going beyond limits, 'plus oultre,' " Mr. Risset said, citing the motto of Emperor Charles V in its original archaic French. "And Mari's skills and adventures certainly do exemplify 'going beyond.' "
Yet by her own account, Ms. Kimura remains a traditionalist, too, if a traditionalist with a difference.
"I studied with very old people," she said. "They were all my grandfather's age. Through them, I feel a connection to the era of the 1920s or even before, when violin playing was more creative than it is now. Today there's a division of labor between composers and interpreters. I'm trying to bring back the old way that was the norm for Vivaldi or Corelli or Tartini in the 17th and 18th centuries. They wrote for themselves and invented their own techniques. That's what made them who they are. That's how they made their mark in violin history. The tradition of the violin lies in creation. By being creative, you learn about tradition."