A WEEK OF CONTEMPORARY MUSIC starts today at Tanglewood Music Center, the Boston Symphony's summer academy for advanced training in music in Lenox, Mass. The festival will feature 20th-century masterpieces, as well as recent works by George Perle, this year's composer-in-residence. LENINGRAD'S TANEYEV STRING QUARTET makes its US debut tomorrow evening in a free concert at the Cathedral of St. John the Divine in New York City. The quartet is resident at the Rimsky-Korsakov Conservatory in Leningrad. Other concerts are scheduled at the Music Mountain Festival in Falls Village, Conn. (Saturday) and the United Nations headquarters in New York (invitation only, Aug. 4). SOVIET BOLSHOI BALLERINA MAYA PLISETSKAYA is to become artistic director of Spain's national ballet, the Ministry of Culture said. Plisetskaya, regarded as one of the world's top ballerinas, has a two-year contract starting in December. Under the contract agreed between the Spanish and Soviet authorities, the dancer will spend six months a year in Spain and six months in her native country.