TRAVELING WITH the National Symphony on its recent whirlwind tour of Argentina, Uruguay and Brazil was an astonishing sensation, very much like having the uncles, aunts and cousins you have known all your life suddenly turning into a cluster of superstars.

Once outside the three-mile limit, this family one has come to take for granted assumes an utterly different profile as it becomes the focal point for crowds of roaring, demonstrating, wildly enthusiastic music lovers.

The biggest family star, music director Mstislav Rostropovich, was at the core of the frenzied admiration during the eight-day tour. Airport press conferences centered around him almost as soon as the plane carrying the misicians touched down. On hand there was always a translator -- Russian to Spanish, or Russian to Portuguese -- as Rostropovich fielded questions on every conceivable, and sometimes inconceivable, subject with a skill that presidents sometimes vainly seek in secretaries of state.

At one he was asked some personal details about Solzhenitsyn. He replied, "You would have to ask him that question. I am his friend but not his secretary." When someone wanted his view on the U.S. boycott of the Moscow Olympics, he answered with Solomonic flair, "I would not wish to discuss that matter. But I would like to shake the hand of every person who did not go!"

People were amazed at his apparently indefatigability. The tour physician was asked if he knew the conductor's ability to keep going. "I'm not sure just what it is," he replied, "but he certainly seems to have endless sources of energy".

When Rostropovich came onstage at the beginning of the orchestra's first concert in the historic Teatro Colon in Buenos Aires, several things happened simultaneously: The orchestra, which still felt some legitimate fatigue from travel (having arrived 12 hours behind schedule because of an unforgivable airline foul-up) became fired up under his magnetic, driving energy and proceeded to play its collective head off. And at the same time the audience roared a greeting for Rostropovich, who continued to be lionized as long as he could sign one more autograph.

At the end of the big concert -- Berlioz' "Roman Carnival Overture," Barber's First Symphony and Tchaikovsky's Fifth Symphony -- shouts thundered through this great house. With its 70-year-old tradition of affording visual splendor and acoustical perfection, the Colon is the opera theatre of which the incomparable Rosa Raisa spoke years ago when she said, "You think I sing loud in Chicago? You should hear me in Buenos Aires!"

The citizens of Buenos Aires, who are justly proud of their musical history, went all out for the National Symphony and Rostropovich. General director of the Colon, Guillermo Gallacher, said, "I have never seen so many people in the standing room. There are 2,800 seats in the house and there are 3,300 people here tonight!"

They stood in every available space behind the rows of seats that rise in six tiers to the very top of the theatre, and spilled out into the aisles on the main floor. Those in the top tiers were under 25. They were there with tickets for which they had paid no more than the price of a movie admission, thanks to the work of the Mozarteum Argentino, the organization that sponsored the NSO's South American tour.

Antonio Pini, artistic director of the Mozarteum, said that the prolonged demonstration after the orchestra's two Colon concerts were far beyond any ordinary display. At last, after the applause had lasted nearly 10 minutes, Rostropovich came out again and gave the orchestra the signal for an encore.

Usually during the tour the first encore was the Rachmaninov "Vocalise," which under Rostropovich's hands becomes ravishing poetry. It also rouses crowds to even greater heights of thrilled, and thrilling applause. Suddenly, as if on cue, the applause switches to a rhythmical clapping that sweeps the house, with stamping feet joining in perfect unison. Back again and again the smiling conductor comes, and at last there is another encore. Sometimes it is Andreas Makris' arrangement of the Paganini "Moto Perpetuo," with all the violins standing up for the flashing solo passages. Taken at a furious clip, it is a dazzler that only whets the audiences's lust for more.

But Rostropovich does not hand out encores lightly. He returns for more bows, brings the musicians to their feet time after time, before coming back for a final thriller, which he always announces in his own Spanish or Portuguese, a touch that further delights his listeners: "The death of Tybalt from the ballet 'Romeo and Juliet' by Prokofiev." This is a swirling miniature tone poem of immense dramatic impact that makes a stupendous ending for the concert.

It must be noted that a part of the orchestra's huge success in the Colon was due to the glorious acoustics of the hall, which also intensified the sound of the audience's enthusiastic approval. The orchestra may never have sounded better, nor been heard to better advantage, than in that theatre. The enthusiasm was not confined to the general public. A commentator on a national radio broadcast remarked, "There is a tradition in the United States of referring to the 'five great orchestras.' We cannot subscribe to that tradition any longer. The National Symphony Orchestra of Washington is one of the great orchestras."

Always after the concerts there followed official receptions and parties given either by the embassies or consulates or by the sponsoring Mozarteum. After the orchestra played in the Teatro Solis in Montevideo, where eight of the musicians had played in 1959 when the National Symphony first visited South America, the change d'affaires, representing the U.S. ambassador, who is in the process of being moved from Uruguay to Paraguay, described the impact of the NSO's visit: "This is the best way to bring a knowledge of our artistic life to the rest of the world."

The orchestra moved fast, spending less than one full day in Montevideo and the same brief time in Sao Paolo. But it was acting as a musical ambassador everywhere it went and brevity of time did not affect the quality of its playing. In Sao Paolo, it played in another acoustically excellent hall, the Teatro Municipal -- which is the only facility for operas and concerts in the central area of the city. The orchestra was performing in the largest city in Brazil, an immense metropolis bigger than New York City, that in 20 years is expected to become the second largest city in the world, exceeded only by Mexico City. The consul general in that city. Terrell E. Arnold, commented after the concert that "This is the ideal kind of exchange between our countries and there should be far more of it."

And again the post-concert rituals continued: Hundreds of people waited for Rostropovoch at the stage door of the theater, pressing on him his recordings or the evening's programs for his autograph, which he signed for 20 or 30 minutes. Still later, when he finally arrived back at his hotel, there were always people there hoping to catch a glimpse of the musician and man they idolize.

In their free time -- and even playing five concerts in five days, there were hours in each day when they were free -- the musicians were tourists just like any others, interested in seeing as much as possible, testing restaurants, indulging in shopping sprees, buying things for which the countries are famous: in Buenos Aires leather, furs and semi-precious stones; and in Sao Paolo, again the jewelry, and coffee.

The returning plane trip was sheer fun. The work was over and the musicians were glowing in the memories of those wildly applauding audiences who could not get enough of their music-making. And Rostropovich was in his most affectionate, expansive mood. Accessible to every musician in the orchestra who might want to talk to him, Rostropovich at just the right moment took the plane's microphone in hand for one of his characteristic speeches.

"My beloved colleagues, my dear brothers, my dear sisters," he began and you could feel the intimacy of the friendship between the conductor and his players. And with good reason. At every single concert, during the applause, he had moved through the orchestra to bring Edwin Thayer to the podium to acknowledge the audience's appreciation of the hushed beauty with which he played one of the world's most popular French horn solos from the slow movement of the Tchaikovsky Fifth.

The very same appreciative honor was shown to Carol Stephenson's exquisite phrasing in the radiant oboe solo in the slow movement of the Barber Symphony. Rostropovich had asked each individual section of the orchestra to stand during the prolonged applause so that the entire audience could adequately thank the musicians. There are not many conductors who so generously acknowledge the musicians who so handsomely carry out their wishes.

"My beloved colleagues" is one of Rostropovich's favorite greetings to his friends in the National Symphony and they know his real meaning. He told them that two of the players were having birthdays during the tour. For Joel King, the stage manager, Rostropovich had bought an amber turtle which King said would be Number 104 in his collection. While the whole orchestra sang "Happy Birthday" under the direction of one of the world's foremost musicians, there appeared a glorious Brazillian chocolate cake, with "Happy Birthday" written on it and holding a single candle.

And for George Marsh, a violinist whom Rostropovich said he thought was the youngest member of the orchestra, there was "Money -- a young man always needs money." Rostropovich gave Marsh a hand-tooled leather wallet, "for luck. And so he has money, one dollar." And a second chorus of "Happy Birthday" and a second chocolate cake properly inscribed.

For the long hours in flight, there were players happily wandering up and down the aisles, taking pictures, playing unending bridge and poker, drinking wine and stronger spirits, or sleeping the first of several sleeps that would be needed before the fatique of the tour was past. But what a way to tire oneself out: Making such music with Rostropovich before thousands of fans who, though they might not speak your language, understand your music. It is a great way to take this country's artistic achievements to other countries.