The leadership of the National Symphony Orchestra changed hands yesterday for the third time in 28 years as the orchestra's new music director, Mstislav Rostropovish, announced plans for its first season under his baton.

Rostropovich, the world-famous Russian cellist and conductor, was named a year and a half ago to succeed Antal Dorati as conductor of the National Symphony when Dorati's contract expired this year. Dorati will return next season as principal guest conductor.

In a press conference at the Kennedy Carter, Rostropovich accepted a baton given as a symbol of transition by Dorati, and revealed that:

The National Symphony will travel overseas at the end of the 1978-79 season in what will be the orchestra's first major European tour.

He feels "it is not possible to have a perfect orchestra in a city without a base, an academy," and will urge the founding of such a music conservatory in Washington as soon as possible.

His initial season will include four world premieres. Three of these, by Leonard Bernstein, will be heard on the second program of the season, Oct. 11-14. On that program Bernstein and Rostropovich will play in Three Meditations for cello and orchestra. That concert will also include the first hearing of a new Bernstein work called "An American Songfest." The fourth world premiere is a composition by Henri Dutilleux of France.

The orchestra will make its first recording under his direction with violinist Isaac Stern in the Tchaikovsky Concerto this fall and will continue to record. (The NSO made nine records on the London label under Dorati's directions.)

In his first season with the orchestra, he will have no associate or resident conductor. Rostropovich explained that there are many young American conductors, of whom several will lead the orchestra during the coming season. (Murry Sidlin, who is now the orchestra's resident conductor, is expected to announce his own plans at a later date.)

Rostropovich named Rudolf Serkin as the soloist in his opening concerts on Oct. 4, 5 and 6. Saying that it was of the greatest importance for the orchestra "to be in contact with the greatest musicians in the country," the new music director said that next year's guest conductors, in addition to Bernstein, Aaron Copland and Dorati, would include Seiji Ozawa of the Boston Symphony and Stanislaw Skrowaczewski of the Minnesota Orchestra.

Rostropovich will celebrate his 50th birthday Sunday when he conducts the National Symphony in his New York debut as a conductor. Yesterday he talked about the "very talented young musicians in the U.S. I have played with John Mauceri and with James Conlon. They will conduct the National Symphony next season."

In his first year with the orchestra, Rostropovich said: "I have no changes [WORDS ILLEGIBLE] orchestra to feel [WORDS ILLEGIBLE] we have only one [WORDS ILLEGIBLE] Sundays, we have only one [WORDS ILLEGIBLE] rehearsals. So Sundays from 3 to 6 after rehearsal, I have master classes with each member of the orchestra. We will have a piano; it will not eb 'Come in and play for the music director.' It will be a friendly atmosphere. I want the orchestra to be happy. I will dedicate all my time to make it best for each performer. I will ask, "Only try your best."

Before Rostropovich spoke, Oleg Libanov, the orchestra's new managing director presented him with a baton, a gift from Dorati, who remains music director for the remaining weeks of the current season, and who was in Philadelphia yesterday as guest conductor of the Philadelphia Orchestra.

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Dorati, who will become music director of the Detroit Symphony next year, wrote his successor here saying, "Call on me for any help. I can give from my experience. I embrace you warmly.

David Lloyd Kreegner, president of the National Symphony board of directors, said, in introducing Rostropovich, "Without the progress of the orchestra under Maestro Dorati, which has been nothing short of spectacular, it would not have been possible for us to bring Maestro Rostropovich to the National Symphony."

Rostropovich is the orchestra's fourth music director since it was founded in 1931 by Hans Kindler, whose successor, Howard Mitchell, was followed by Dorati.