The Tchaikovsky music competition opened here today, drawing more than 400 of the world's most promising young classical pianists, violinists, cellists and singers -- including 102 Americans -- for three weeks of recitals that will launch a talented few to international fame.

This evening's opening ceremony, highlighted by recitals by the U.S.S.R.'s talented teen-age starlets and a flowery statement from Soviet leader Mikhail Gorbachev, climaxed a day of sightseeing, wreath-laying and jitters for the contestants, who represent 46 countries.

"Let the expression 'When the muses speak, the guns fall silent' sound today as a call for efforts to save our planet from a holocaust," Gorbachev said in a statement read at ceremonies in the grand hall of the Moscow Conservatory by Pyotr Demichev, Soviet minister of culture.

A huge banner portrait of Tchaikovsky, the 19th-century Russian composer whom the competition honors, draped the wall behind Demichev as he spoke from a stage crowded with dozens of the competition judges. For this, the eighth in the competition series held every four years, the United States sent by far the biggest group of entrants. As Daniel Pollock, the California pianist, teacher and only American on the international jury for pianists, noted today, for budding young musicians from the United States, placing in the Tchaikovsky contest has become a ticket to contracts and fame.

Since the competition began in 1958 with U.S. pianist Van Cliburn grabbing a gold medal and Pollock a bronze, its prestige has burgeoned, and the number of international entrants with it. Since 128 participants entered in 1978, the tally has tripled.

Moscow will give out more than 40,000 rubles ($52,000) in prize money to winners, including 2,500 rubles ($3,250) each to gold medalists. The majority of judges in each of the four areas of competition come from the U.S.S.R. and other Socialist countries.

Starry-eyed American hopefuls flew to the Soviet capital with their parents and dreams from all over the United States: cellists from Texas and San Francisco, violinists from Louisiana and New York, and pianists from Alabama and Kentucky. Most paid their own way, but Leslie Spotz, a 29-year-old pianist from Bethesda, said, "My friends, relatives and supporters all chipped in so I could come."

After brief speeches by Demichev, Pollack and various other judges, tomorrow's first round of recitals was prefaced with strong performances by three of the Soviet Union's musical prote'ge's, including 14-year-old Evgeniy Kisin.

Kisin, a colorful, temperamental pianist, played pieces by Rachmaninoff, Prokofiev, Scriabin and Chopin with a strength and maturity far beyond his age and boyish appearance.

Vadim Repin, a young, up-and-coming violinist, also drew loud applause from the audience. The competitors will play a mixture of works by various foreign and Russian composers, including Tchaikovsky.