With a performance of Strauss' "Salome," the three-week visit of the Vienna State Opera -- and of the Vienna Philharmonic -- draws to a close tonight at 8:45. The Viennese post the closing time as well as the starting time: They have learned to be punctilious.

It is the opera's first trip to the United States. But the Philharmonic has been here before. And on previous tours -- mostly one-night stands -- the split-second timing has been essential.

One player recalls their most recent visit to New York: "We were rushed in and rushed out, with no way to get to know the city. There was noise outside all night. And we hesitated to go out because it was a bad neighborhood."

But in Washington -- where the orchestra stayed at the Capital Hilton, traveling to and from the Kennedy Center in yellow school buses -- players have had the leisure to learn about the city and its citizens. The three weeks were filled with general good will and occasional bad tempers, with triumphs and gaffes, with culture shock and culture sharing, with giant egos and small kindnesses.

"We expected Washington to be so much more a hectic city," said Philharmonic vice president and violist Kurt Anders, "but instead it is more relaxed than Vienna, even though it is larger. There everything is rush, rush, rush."

This attitude seemed unaffected by the orchestra's rigorous workload -- 17 straight days of performing, and even more numerous rehearsals. But, one player said, "Remember that we play in the opera 300 days a year, though with careful scheduling we rotate those days. In fact we play better here because we are staying with the same three conductors for the visit. All orchestras play better when there's not a new man on the podium every night."

Most of the Viennese speak splendid English, and the cultural exchange began during the first week in rehearsals. Principal cellist Franz Bartolomey said that during a break, "a man came down and asked some of us if we would like to drive out into the country. So we got together and went to see the mountains around Frederick.And then we came back by way of Rockwall -- or, how do you say it, Rockville?"

And Washington responded in other ways, including the culinary extravaganza in the dining rooms of the Watergate Hotel, where conductors, singers, administrators and most of the visiting members of the Music Critics Association were staying.

Replacing the standard semi-Continental fare that has kept the cavernous Watergate Terrace going for the past decade was a lengthy menu headed "Oesterreichische Spezialitaten." For about a month, diners have feasted on things like Spinatpalats-chinken mit Krautermayonnaise (spinach pancakes with herb mayonnaise) as well as venison, boiled beef and schnitzels, followed by seven different forms of Viennese coffee.

When visiting in America, though, Viennese tastes go local. Several Viennese symphony members invited to a lunch insisted that they wanted only "American beef." When German beers were offered, the Viennese preferred Heineken's. The only complaint was over American coffee, which they mention with discreet incredulity. "Isn't it true that all your coffee is that powder mixed with hot water?" inquired second violinist Ernest Bartolomey, who didn't realize that Americans use coffee beans.

Many musicians were struck by the proliferation of museums in this city. "If most of them are gifts of the American rich, then your country is very fortunate," observed Anders. It is noted that Washington has nothing quite on the scale of Vienna's Kunsthistoriches Museum. Ernest Bortolomey nodded but said, "Your National Gallery is really not so different, especially with the new East Building. It is much more than either my feet or my eyes can take in one day."

The Viennese overwhelmingly have one preference in common: the Air and Space Museum. Anders said, "There cannot be anything else like it in the world." Harnony and Discord

The members of the Philharmonic and the National Symphony got together as often as they could. Early in the stay two trombone players from the Philharmonic joined two NSO members at home for an evening of trombone quartets. And last Tuesday night, the NSO gave a quiet reception for the Viennese in the Concert Hall musicians' lounge. But NSO bass violinist BillVaughn said the scheduling had made getting together difficult during the first two weeks: When one group wasn't using the Concert Hall for rehearsal, the other was. Likewise, conflicting schedules had made attending Vienna concerts difficult for the Washington players.

The contrast of Vienna and America was less clear-cut among the conductors and soloists. Most of them were not Austrian, and most were familiar to Washington.The most conspicuous -- Leonard Bernstein -- was, of course the most familiar. Not only did he conduct the largest number of performances, but when he was not directing, he seemed to be all over town. One night he was at a Joan Baez fund-raiser for Southeast Asian refugees. A day or two before he was greeting President Carter after Zublin Mehta's performance of "Salome." One Saturday he led a small group to Boehm's "The Marriage of Figaro"; last Thursday he attended the White House dinner for Irish Prime Minister Jack Lynch; and one afternoon he spent a few minutes in the Watergate lobby playing around with what appeared to be his 10-gallon hat.

Less was heard from the aged Boehm. But when asked if the conductor's health was strained by his Washington schedule, several expressed astonishment. "For heaven's sake, he's up at 6 every morning, just like in Vienna," explained one musician. "Did you know that we gave him a exercise rug two years ago? He brings it along on tours, and does his exercises on it the first thing every morning."

The least was heard from Mehta, who spent most of the period with his New York Philharmonic and was said tok be peeved that he got no more rehearsal time for his three performances. Sharps and Flats

Musical directors of any nationality are not known for their retiring natures. And Egon Seefehlner, who with his current $40 million budget runs by far the busiest and most expensive opera company in the world, seems to think that the most efficient way to manage such an institution is to forget biting his tongue and say what he thinks. At a luncheon several days before the opening concert, he dropped these observations:

Of conductor Karl Boehm, who was twice before director of the opera and under whom Seefelhner once worked before getting the job himself; "He has recently written his autobiography, and the title can be roughly translated as "I Remember . . .Precisely." After reading it I think that my book, if I should ever write it, should then be titled "I Remember . . .Better."

Of administrating opera companies: "I have always been a black sheep with finance people. In Berlin every year they told me that I cannot spend more than the budjet, and every year I did. And every year they said, "This is the last time." And finally I told them, 'Look, when I started this budget was 10 million marks and now it is 25 million. And do you think it would have gotten here if I had done as you said? We would still be back at 10 million and you would not be getting this king of opera'."

A week later, though, during a seminar in the Center's Terrace Theater, Seefelhner had to take a bit of what he had been dishing out when he designated successor, American conductor Lorin Maazel, brashly laid out his ideas of leading the company onward and upward. The seminar chairman, critic Patrick J. Smith, later described the statement as Maazel's "vision of the Grail."

Maazel outlined the century's history of opera in three parts. First, there was the period in which "divas and divos who did not serve dramatic interests" dominated. Next, there was the age of "the reformer conductor, in which stage direction consisted of Arturo Toscanini looking up from his desk and shoting 'Sing louder!' or ordering poor singers back into the shadows because of the bad acoustics there." And in the third stage, in the post-war era, came the fancy stage director "who will pace up and down for $1000 an hour explaining that he is waiting for an inspiration."

Now, declared the less than humble Maazel, at the Vienna Opera it will be his job "to try to bring all this together."

And at one point, Maazel made a crack about directors being so indifferent to details that they "made their grand plans while standing before an orchestra conducting the Beethoven Ninth." Then he stopped for a second. Persons in the audience began to giggle, and he blurted, "Well, I guess I was going to make one faux pas anyway."

Berstein was conducting the Beethoven Ninth with the Vienna Philharmonic that night in the Concert Hall.

Sittin at the table with to Maazel, Seefehlner looked generally dyspeptic and uttered not a syllable. Venerable Traditions

It was not surprise, of course, how deeply the 137-year old Philharmonic is steeped in Viennese musical tradition; in this respect it eclipses all rivals. But many Americans were surprised by some of those customs.

In these days of equal employment opportunities and multinational institutions, Vienna must be the only major orchestra that can get away with denying membership to all but Austrian citizens and admitting only one woman -- Anna Lelkes, who plays second harp.

Asked why, vice president Anders replies, "It's more a tradition."

There are others: Most players perform on instruments that have belonged to the orchestra for "three or four generations," says Anders -- that is, since the days before Mahler. No other orchestra owns more than few of its instruments.

Yet the average age is surprisingly young. Since violinist Bartolomey, who is 34, joined the orchestra in 1963, he has seen a 70 percent turnover in the cellos and a 40 percent change in the violins.The sound has remained largely the same, however, because these men were taught in the Vienna academies by their predecessors and play the same instruments.

Tomorrow, the Viennese go on to New York. After Thursday's concert at Carnegie Hall, they will return to Vienna. They will have Saturday evening free. Then it's back to work.