WHAT A PITY, the traveler thinks, to go to Europe and perhaps miss the chance to attend performances by some of the great music, dance and theater companies on their home stages. Would it be wise, or for that matter possible, to reserve seats before crossing the Atlantic?

Unfortunately, that is no easy task, particularly for the cultural buff who is on a tight budget. Even in the age of Ticketron and computerized airline reservations, Europe's box offices are only minimally linked with the American ticket buyer.

Nevertheless, without reservations the theatergoer courts disappointment, travel agents warn. On star-filled nights, the famed concert and opera halls of Europe sell out just as rapidly as they do at home.

As the fall and winter season gets under way, how can an American tourist boost the likelihood of a glittering night at the Vienna State Opera, the Berlin Philharmonic, Amsterdam's Concertgebouw Orchestra, the Royal Danish Ballet or a hit show on London's West End?

Of them all, getting a ticket in advance to a London theater is probably the easiest, though it will cost more than showing up at the box office in person and hoping the "sold out" sign hasn't gone up.

Edwards & Edwards, a London-based ticket agency recommended by the British Tourist Authority, operates a New York office that books seats at most of London's 45 theaters as well as many other performing attractions in the city and elsewhere in Britain, including Royal Shakespeare Theatre productions at Stratford-Upon-Avon. The agency goes after the seats in the higher price range, so don't expect a top-balcony bargain.

Depending on what's being presented, the charge is between $5 and $9 more than a theatergoer would pay at the box office, or about $20 to $30 total per seat. The tickets can be charged to American Express cards or paid for by check. If there is time, they will be mailed out, or they can be picked up at the London box office. In most cases, the reservation can be confirmed immediately.

(For more information, write Edwards & Edwards, 226 W. 47th St., New York, N.Y. 10036, or call 800-223-6108. Ask for an entertainment guide for upcoming shows.)

A music fan headed for the Netherlands might consider buying a $5 "Holland Culture Card" from the Netherlands National Tourist Office. With the card in hand, the traveler has first call on tickets set aside for card holders at two booking agencies, A.U.B. and VVV. Present the card at least 24 hours prior to curtain time in the city you are visiting. The card also provides free entrance to national museums and a 50-percent discount on first-class daytime train fares within the Netherlands.

(To obtain a card, send a $5 check to Netherlands National Tourist Office, 576 Fifth Ave., New York, N.Y. 10030.)

On the rest of the Continent, things get a little stickier.

Generally, travelers will have to make their own reservations by writing well in advance to the theater they wish to attend. A good first step is to phone or write the country's U.S. tourist office for theater addresses and, if possible, a schedule of performances. A number of tourist offices have detailed information on how to send for tickets. (A travel agent should be able to give you the tourist office number and address. Most have a New York branch.)

The foreign box office may require that the tickets be paid for in advance in that nation's currency. This can be done by sending a foreign bank draft, obtainable from most banks, but it could cost up to $10 or more for each ticket order.

The Vienna State Opera (and other Vienna stages) has an excellent reputation for handling mail inquiries efficiently and satisfactorily (and with no pre-payment required). One Washington couple, to their delight, obtained second-row-center orchestra seats for "The Magic Flute" in a sold-out house. But the same isn't true for Milan's La Scala, where the box office -- coping with frequent last-minute schedule changes -- may never answer your letter.

Two potential complications in writing abroad: The response, if one does come, may not be in English. (The same Washington couple had to borrow an Italian-English dictionary to find out if they had reservations at the Teatro dell'Opera in Rome. They did.) And, if the trip must be cancelled, there may not be time enough to get a refund.

As an alternative to doing-it-yourself, some travel agents, for a service fee, can be helpful in obtaining tickets. Large firms such as Thomas Cook and American Express with offices in many European cities will wire their branches to obtain tickets for customers who have booked their trip through the agency. Extra costs include approximately $12 per ticket order for the wired request and response, plus any charge for sending a messenger in person to the box office.

If music, and especially opera, is a must on a European trip, then the tourist might consider one of the tours offered by Dailey-Thorp Travel, Inc., of New York, which specializes in music-minded itineraries in Europe and the United States.

Upcoming in December is a seven-day extravaganza that begins with performances in Paris of "The Merry Widow" (Theatre Musical de Paris), "Tales of Hoffmann" (Opera Comique) and "Falstaff" (Paris Opera, Seiji Ozawa conducting), followed by an overnight trip on the refurbished Orient Express to Milan and climaxed by opening night seats at La Scala on Dec. 7 (a new production of Verdi's "Ernani," starring Placido Domingo and Renato Bruson, with Riccardo Muti conducting).

The price: A hefty $2,297 per person, plus $729 roundtrip airfare from New York. (La Scala's opening night orchestra seats and the gala dinner afterwards at Biffi Scala, at approximately $300 per person -- black-tie recommended -- make up part of that tour price. Also included is the $390 cost of a first-class berth on the Orient Express.)

(For information: write Dailey-Thorp Travel, Inc., 654 Madison Ave., New York, N.Y. 10021, or call 212-486-9555).

Several airlines flying to London regularly offer tour packages that include several nights of theater.

Beyond this, travel agents suggest checking with the hotel concierge on arrival (or even writing ahead) for tickets, though that may double the box-office price. Some European cities, such as Vienna, have booking agencies that, once you are abroad, can help in obtaining seats in that city or at other stops on an itinerary. The fee can be 20 percent or more. If a friend or business associate lives in the destination city, ask for a favor.

In the last resort, the traveler can gamble on a ticket by showing up personally at the box office, as many do successfully. That probably is the best way of obtaining lower-priced seats. A few of the great halls of Europe reserve a certain number of tickets to be sold only on the day of performance, and many provide for inexpensive standing room a few hours before curtain time.

The best bet, in this case, is to make the box office a first stop (after checking into the hotel) to find out if any seats are available during your stay. The rest of the visit can be fitted around a gala night at the theater