SIR RUDOLF BING retired from the post of general manager of the Metropolitan Opera in 1972. In his memoirs, published that year, he wrote: "I leave a time bomb I am greatful did not go off in my time, which is the question of the relations between European artists and the American Internal Revenue Service."

Last December Egon Seefehlner, general manager of the Vienna State Opera, was discussing that company's forthcoming visit to the Kennedy Center. "I would like to bring our production of 'Tristan und Isolde,' to Washington," he told a reporter. "It is our best Wagner production. But I cannot because we have no Isolde. Birgit Nilsson will not return to the United States, and we do not have another Isolde of sufficient quality."

Why won't Birgit Nilsson, long the world's favorite Isolde, Brunnhilde, and Turandot, come back to sing in this country? Because the Internal Revenue Service says she owes the United States a cool $500,000 in back taxes and penalties. And Nilsson chooses not to pay.

"How does one of the world's busiest, and highest-paid, singers run up a tax bill that size?" I recently asked Schuyler Chapin who was, for three years, Bing's successor at the Met.

"That's easy," he said. "If no tax is paid for a while, and then penalties are added at the rate of 25 percent, it doesn't take long."

An official of the Collection Division of the Internal Revenue Service confirmed last week that tax liens had been filed against Nilsson.

Henry Lauterstein of the Metropolitan Opera's law firm of Lauterstein and Lauterstein said recently, "in discussions with the IRS, I pointed out that Nilsson could still concertize here, appear in opera and continue a busy career. I asked if something could be worked out to help wipe the slate clean. The man with whom I was speaking told me, 'I'm going to have to do something - I can't tell you, but I must do what I must do.'

"It turned out," Lauterstein added, "that at that point Nilsson defaulted, and a judgment for $500,000 was entered against her.Since then she has not returned to sing in the United States." Nilsson's last appearance at the Metropolitan was as Sieglinde in "Die Walkuere" on April 2, 1975.

What is the tax situation in this country about which foreign artists and their American managements complain, and even to the length of not paying?

At present, with some exceptions, the law requires that the Metropolitan Opera for example, or the U.S. agent, take 30 percent of the artist's fee and send it to the Internal Revenue.

But the impact depends on several factors, among them:

What country the artist comes from, and what tax treaty the United States has with that country.

How long the artist will be performing in this country within the taxable year.

Lauterstein explained: "A number of artists in Europe are contracted by a corporation, say the United Kingdom X Corp. might have Mirella Freni (the popular Italian soprano). They have her worldwide.

"These big earners may have Swiss residences, or some other place that is not so difficult. But for a Freni we pay 30 percent to United Kingdom X," he went on. "There are other treaties. We have one with Germany under which taxes paid here are credited against an artist there. The best treaty I ever heard of was the one Nixon negotiated with the Soviet Union.

"The Soviet artists pay no tax here. But God help them when they go back!" His comment is of particular pertinence at this moment because the Metropolitan has just announced the unprecedented fact that five stars of the Bolshoi Opera in Moscow will be at the Met next fall.

Generally, payments for Soviet artists, all of whom receive annual salaries from their government, are made directly to GOSCONCERT, the official artist agency for the Soviet Union.

Patrick Hayes, managing director of the Washington Performing Arts Society, recalls, however, that at one period, checks for Russian artists who appeared on his concerts were made out to the ambassador of the Soviet Union.

Hayes explained how a local manager today handles tax payments for foreign artists. "If a New York agent is involved," he said, "we send the entire fee to them and they handle the tax. However, if we are dealing directly with an artist, then we fill out the proper forms and send them, with a check, to the Internal Revenue Service."

When you add other factors to what a singer may regard as an unfair tax situation, the result can be the unavailability of a desirable artist.

Freni, Teresa Berganza, Montserrat Caballe and others have often been reported unwilling to sing in the United States as much as their admirers would like because of U.S. tax problems.

Freni, for example, withdrew from her Met contract this year, with some suggestion that she was ill, though subsequently she sang regularly at La Scala.

But Lauterstein believes there might be reasons other than taxes for Freni's not coming to the Met. And Freni herself told me a year ago in September, when she was singing here with both La Scala and the Paris Opera, that the Met had offered her "only" 10 or 12 Mimis in "La Boheme." She would have preferred to sing a number of other roles she has recently added to her repertoire.

The Metropolitan is making an effort to help its artists manage their financial affairs. "Lots of artists here are getting good advice," Lauterstein said, "and some of them are very wealthy. If they would all hire reputable tax people, it would help. The tax rate is not after all so bad - I think it is around 15 or 16 percent." He paused. "But sometimes there is very little one can do for them."

The word "reputable" brought up one of the most unsavory incidents mentioned in Bing's Memoirs. "Nearly all the Europeans at the house had their tax returns prepared for years by an accountant who is now in prison for violating tax laws," he wrote. "Truly remarkable deductions were taken . . . wives became managers, poodles became secretaries. Artists would come to the Metropolitan for 10 weeks, make $100,000 and show a loss on their tax returns."

In June 1970, the tax accountasnt was convicted in federal court in New York of having made false statements in the tax forms of a number of Metropolitan Opera artists, and of having given bribes to IRS employes. He was found guilty on 25 counts of an 88-count indictment.

Among his falsifications were such items as a $4,600 payment for a claque (members of an audience paid to applaud) for soprano Renata Tebaldi, who swore in court that she had never paid a cent for a claque; $125 for a claque for prompter Antonio Petronio, who pointed out that as a prompter he had never in his life appeared in front of a curtain, and various deductions for tenors Jon Vickers, Sandor Konya, and Franco Corelli; soprano Montserrat Caballe, mezzo Christa Ludwig, and conductor Sixten Erhling. The total of false claims charged against ther accountant was over $300,000.

In July 1970, he was sentenced to five years in jail and fined $16,200. None of the artists was ever accused of any wrongdoing.

Bing pointed out last week that "a singer's professional life is a short one, whereas a lawyer at 80 can still make a very good income and many do." He argues for a change in our tax laws, pointing out that opera singers get special tax advantages "everywhere else in the world . . ."

The country's concert managements are as concerned over the problems raised by the tax situation as are the opera companies. Ann Colbert, the head of one of the most conscientious and successful agencies in New York, says "It's a dreadful situation.They take 30 percent off the top, then there is our commission and there may be city or state taxes. And the terrible part of it is that the artists have to wait 18 months for any refund. We cannot take care of it when the artist leaves the country the way we used to."

She explained: "The artist may make some money in January '78, but we cannot file until the end of the year. The IRS attitude is that you cannot tell in January how long the artist will be in the country.Of course we do know. It is shocking," she declared. "A few years ago the rules for visas were changed. They demand now to know, when we apply for a visa, how many engagements there will be. And they send a copy of that information to the IRS.

"We have to watch that an artist does not stay more than 183 days - that's six months. Because if they stay more than six months, then they must file on the same basis as an American citizen.

"It makes it very difficult," Colbert continued, "for, say, either a young chamber ensemble, or even an established one, like the Quartetto Italiano. We tell them that the public wants to hear them, as they very much do. But the Quartetto (which is one of the world's finest string quartets) doesn't want to come over because they go home with practically nothing.

"Often that 30 percent is the difference between making a little bit and ending up with a loss. And European fees are now going up too." For many years fees in this country were much higher than in Europe and artists wanted to come here for the money. Now that that picture is altering, the tax bite becomes even more burdensome.

"A while ago I was ready to close, to go out of business over this whole business," she said. "You want to bring over a young artist whom you know is right on the verge of a career. But with the bad situation with the dollar and the tax problem, how can you do it?"

Harold Shaw, head of Shaw Concerts, is one of the managers who played a major role in working for changes in the tax law. "It helped mightily," he says, "about two years ago to have the law changed from 30 percent of the gross to 30 percent of the net . One trouble with the whole thing," he said, "is that our laws were written for major corporations, not for individual cases. They need changing from that standpoint.

"Then there are such differences in the treaties with different countries. Someone from France can come in, work 180 days and pay no tax at all. From Japan they can take off the first $3,000, but then they have to pay for the very same period."

Shaw does think some helpful changes are coming in the new tax law now before Congress. Like the Met's lawyer, he spoke of tax-sheltered places: the Channel Islands and Lichtenstein for two.

"If an artist management operates out of one of those," he said, "it can help the artist. But from our standpoint, the most helpful thing was when two or three IRS agents were assigned to New York specifically to work in our field.They know the provisions of the code and they also know the specific problems."

Problems? Lauterstein, speaking of the high incomes of the big-name singers, offered some perspective: "You and I should be in such a position!" Nevertheless there are problems. Bing says flatly, "If the government insists that (foreign) opera singers must pay in full in America, the Metropolitan will be unable to engage the singers and conductors its public expects and deserves. The house will suffer enough in the next few years from the impact of currency devaluation without imposing the trauma of real taxation."

But is the Met "unable to engage the singers and conductors its public expects?"

Not from the looks of next season's roster, which is the strongest list of singers the Met has put out in some years. The fact that there will not be more of the world's great conductors has less to do with taxes than with the problems of scheduling opera rehearsals and performances over a 30-week period in such a way that the top conductors can or will become involved.