It was 40 years ago that Pierre Boulez wrote his revolutionary Livre pour quatuor, a string quartet so technically tortuous that it took nearly six years for a performance to happen, and even then only the first two movements were performed. The complete performance of the work took place no sooner than 1985, on the occasion of the composer’s 60th birthday. The quartet brought in to do it was the Arditti, quickly canonized by Boulez as “the best string quartet in the world.” The London-based Arditti, founded in 1974 by first violinist Irvine Arditti and colleagues at the Royal Academy of Music, was the first quartet formed to be exclusively devoted to new music. Unlike the more popular Kronos Quartet, which frequently commissions quartets from jazz and rock artists who often have no real knowledge of how to write for the medium, Arditti has concentrated on composers whom they feel have something unique to offer the genre. They also strive for a cutting-edge sound that, combined with their adventurous and contrasting repertoire, always makes for thrilling concerts. Arditti’s first extended residency in Chicago, at the Ravinia Festival, includes two concerts; the first is devoted to all new scores, including pieces by Gyorgy Kurtag, Elliott Carter, Bernadette Speach, David Felder, Conlon Nancarrow, and Bent Sorensen, with the second devoted to 20th-century classics such as the late Romantic Schoenberg First, the Bartok Third, and the Berg Lyric Suite. Monday and Tuesday, 8 PM, Murray Theatre, Ravinia Festival, Green Bay and Lake Cook Rds., Highland Park; 728-4642.