Vienna begins each New Year with a festive but curiously unsentimental look at itself. Every New Year's Eve, as dependable a part of the celebration as champagne, chocolate and whipped cream, there is a gala performance of "Die Fledermaus" at the Staatsoper, which is possibly the finest opera house in the world. This double-edged operetta, with a strong element of social satire underlying its jolly surface, launches a year of brilliant performances in what is unquestionably the most musical of cities.

The real subject of "Die Fledermaus" (under a thin overlay of marital infidelity, bourgeois social pretensions, practical jokes and comic revenge) is the way New Year's Eve is, or should be, celebrated in Vienna. The central action is a masked ball in the palace of a decadent prince with a Slavic name. This prince, Orlofsky, has a contralto voice and a habitual attitude of total ennui. In his palace, dancers from the local ballet company rub elbows at the roulette table with the warden of the town jail and people who may be (but probably are not) a French marquis and a Hungarian countess. It is a party where international celebrities drop in and the world's greatest entertainers stop by casually to sing, dance or tell jokes.

But above all, it is a party where music is treated as one of the most important things in life. The entire guest list becomes a chorus, again and again, to sing thepraises of brotherhood and champagne, the other two most important things in life. The guest claiming to be the Hungarian countess does not show a passport to establish her credentials; she sings a czardas. A chambermaid, trying to pass as a member of the corps de ballet, asserts her qualification not by dancing but by singing.

We, the audience, are not expected to believe that Vienna is actually populated by singing chambermaids any more than New York is populated (a la "Guys and Dolls") with singing and dancing crap-shooters. But there is a truth in the spirit of the operetta that says something very important about Vienna and about the Hapsburg family that made Austria a massive empire. This was an imperial family that extended its empire more through artfully calculated marriages than through the force of arms -- though Vienna was where Turkish invaders were turned back in 1683.

Love of music seems to have been as hereditary in the Hapsburg family as a prominent chin. Several of the emperors were composers -- notably Ferdinand III, Leopold I and Joseph I, who reigned consecutively from 1637 through 1711. Charles VI, who reigned after Joseph I to 1740, was not a composer but a good violinist and conductor. Following such a tradition, the emperors in the 18th and 19th centuries took pride in maintaining outstanding musical establishments at their courts and employing the world's finest composers and performers.

Members of the lesser nobility and even some diplomats living in Vienna followed suit, according to their means. For centuries, Vienna was the home of men with at least a passing resemblance to Orlofsky -- men of great wealth, bearing titles of nobility and often non-Germanic names, because Vienna was the capital of an empire that included substantial parts of Italy and most of central Europe. Look through a list of those to whom Beethoven dedicated his compositions and you find not only the solidly Germanic Waldstein but also Razumovsky, Kinsky, Lobkowitz -- men who made the cultivation of good music a matter of personal and dynastic pride. These aristocrats made Vienna, for nearly three past centuries and perhaps the indefinite future, the world's center for classical music.

Many well-known composers were born in Vienna, from Franz Schubert to Arnold Schoenberg and with two generations of people named Strauss in between. But native talent could hardly begin to satisfy this city's musical demands, and Vienna became a magnet for the world's leading musicians -- such men as Gluck, Haydn, Mozart, Beethoven, Brahms, Bruckner and Mahler. The artistic immigrants even included another Strauss: Richard, who was born in Munich and learned to play with the modern symphony orchestra as brilliantly as Paganini played with his violin.

Vienna still sets the standard for performance of the central repertoire in classical music, most of which was composed within its limits. It may not be the center for composition of classical music today, as it was in the days when Haydn, Mozart and Beethoven (or, in a later generation, Brahms, Mahler, Bruckner and Richard Strauss) all lived there. But it remains the city where the tradition symbolized by those names is most carefully cherished and preserved.

Now as in Mozart's time, Vienna's musical center of gravity is the opera, where the pit orchestra is the Vienna Philharmonic, in many ways the world's greatest symphony orchestra. But there is a wealth of other activities throughout the year to attract music lovers and make them reluctant ever to depart. No matter when you choose to visit, there will be few evenings when you cannot attend an outstanding performance of your favorite music, whether waltzes, Lieder, opera or atonal string quartets.

When you are not listening to music, you can visit the house where Schubert was born, any of the dozens of places where Beethoven lived and composed, numerous libraries and museums dedicated to music, the theater where "The Magic Flute" first saw the light of day and the graves of musicians including Beethoven and Johann Strauss Jr. -- though not Mozart, who was buried in an unmarked pauper's grave. Those willing to go a bit outside the city can find even more landmarks within an hour's drive -- Esterhaza Palace, for example, where Haydn used to work. Or his birthplace, a thatch-roofed farmhouse in the village of Rohrau, in a region where storks still build their nests atop people's chimneys.

And when sightseeing leaves you footsore, there is still the whole galaxy of pastry, or the universe of gourmet dining. That is matter for another article, or a book, but we may digress for a moment to point out a few key words that should get you most of what you need.

Sekt is champagne, though any waiter worth his Trinkgeld (tip) will recognize the French term. Schlag or Schlagobers is whipped cream; it is served abundantly without asking in most desserts, particularly with Torte, which are pastries. But you can also order a separate portion with Kaffee (coffee) or chocolate. The word for that ubiquitous substance is Schokolade. You can get it by simply pronouncing the English word as though you had consumed too much Sekt -- as you well may have. Schlag goes well with most Viennese food, though it should be used sparingly on dishes involving Knoblauch (garlic) and Kalbfleisch (veal), two ingredients that Viennese chefs blend as artfully as their musicians blend voices and instruments.

Actually, there are four major New Year's performances of "Die Fledermaus" in Vienna. Besides the Staatsoper, "Fledermaus" is a specialty of the Volksoper, the less glitzy but enormously popular theater that is the natural habitat not only of Johann Strauss but also of Franz Lehar, Emmerich Kalman and others (such as Ziehrer, Millo cker, Zeller and Suppe') who have made the operetta, along with the waltz, a distinctly Viennese musical form. The Staatsoper and the Volksoper each perform "Fledermaus" on New Year's Eve and again on New Year's Day, and if they did a dozen performances on those days, they would probably sell all the tickets with no trouble.

Those who can't get tickets to a "Fledermaus" can console themselves with no fewer than six New Year's orchestral concerts, with the Vienna Philharmonic, the Vienna Symphony and the Vienna Hofburg orchestras each playing on New Year's Eve and again on New Year's Day. The New Year's Day concert of the Vienna Philharmonic is always sold out and usually broadcast internationally, so wherever in the world you may be you can revel in the musical Tortes and Schlag of the Strauss family and clap along with the Viennese when the "Radetzky March" comes on (as it inevitably does) as an encore. Claudio Abbado will conduct the Philharmonic's New Year's concerts this season, a position that the Viennese rank only slightly below that of God.

Where do you go for music in Vienna? There are dozens of places; here are the best known.

Staatsoper The Staatsoper opened as the Imperial and Royal Court Opera in May 1869 with Mozart's "Don Giovanni." It became the State Opera after Austria became a republic. Seriously damaged by bombing in World War II, it was rebuilt to duplicate the original building as closely as possible and was reopened in 1955 with Beethoven's "Fidelio."

The Vienna Staatsoper is one of the most lavishly subsidized and artistically demanding performing arts institutions in the world. The management likes to see its patrons in formal evening wear, but will allow dark business attire except on special occasions. Ticket prices range from a few dollars for standing room to a bit more than $100 for the best seats, and to slightly less than $150 for the best seats on special occasions. Medium price for a good seat is about $65. Standing room is abundant (567 places, along with 1,642 seats) and there is a fair chance of getting a place on an ordinary evening. The season runs virtually every evening (not on Good Friday, for example) from Jan. 1 through June 30, reopening Sept. 1.

The Staatsoper's 1988 season will include a half-dozen major premieres of opera and ballet productions, besides regular performances of productions in its active repertoire. Nearly all the operas familiar to music lovers are regularly available. The first three months of 1988 will offer the following titles, usually in several performances: "Die Walku re," "La Bohe`me," "Die Fledermaus," "Il trovatore," "Tannhau ser," "Tosca," "Salome," "Der Rosenkavalier," "Maria Stuarda," "The Barber of Seville," "The Flying Dutchman," "Lucia di Lammermoor," "Idomeneo," "Werther," "Ariadne auf Naxos," "Carmen" and "Parsifal." On occasional nonoperatic evenings, such ballets as "The Three-Cornered Hat," "Liebeslieder Waltzes" and "Swan Lake" will be presented.

There also will be premieres of Rossini's "Il Viaggio a Reims," Jan. 20, with Abbado conducting and Montserrat Caballe' in the cast; Tchaikovsky's "Eugene Onegin," Feb. 7, with Seiji Ozawa conducting and two alternate star casts: Lucia Popp, Bernd Weikl, Neil Shicoff and Matti Salminen in February and Mirella Freni, Wolfgang Brendel, Peter Dvorsky and Nicolai Ghiaurov in May; "The Magic Flute," March 19, with Nikolaus Harnoncoourt conducting and Matti Salminen, Hermann Prey, Heinz Zednik, Jerry Hadley and Patricia Schuman in the cast; Puccini's "La Fanciulla del West," April 12, with Leonard Slatkin conducting and Mara Zampieri and Placido Domingo in the cast; Debussy's "Pelle'as et Me'lisande, June 21, with Abbado conducting and Ghiaurov, Christa Ludwig, Francois Le Roux and Frederica von Stade in the cast.

Ballet productions include premieres of two works with choreography by Jiri Kylian -- "Dream Dances" (music by Berio) and "Verkla rte Nacht" (music by Schoenberg) -- as well as Stravinsky's "Les Noces" in the choreography of Bronislava Nijinska. No date has been set for another premiere, "The Idiot," with music by Hans Werner Henze and choreography by Bernd R. Bienert, scheduled for the end of February.

The address is: Vienna State Opera, Opernring 2, A-1010 Wien, Austria; phone (222) 52 76 36.

Volksoper The Volksoper is not as old and prestigious as the Staatsoper, dating only from 1898 -- yesterday in Vienna. But it is dearly loved by the Viennese, and it embodies some aspects of the Viennese spirit more thoroughly than the more pretentious Staatsoper. Its prices are considerably lower, from a few dollars for standing room to a top of just under $40 on special occasions. Medium-price tickets range from about $25 to just over $30. Its specialty is Viennese operetta, which it turns out in productions that are often quite striking, but it has a repertoire that ranges from "My Fair Lady" to Mozart ("The Magic Flute," "The Abduction From the Seraglio" and "Cosi fan tutte") and Puccini ("La Bohe`me" and a double feature of "Gianni Schicchi" and "Il tabarro" -- or, as they sing in German, "Der Mantel.")

New productions of "Fledermaus," "Cosi fan tutte" and "The Merry Widow" have already been given this season; others coming up include Kalman's "Die Zirkusprinzessin" ("The Circus Princess") in February and Weber's "Der Freischu tz" ("The Sharpshooter") in May. Also in the repertoire this winter and spring are "Daughter of the Regiment," "Hansel and Gretel," "Tiefland," "The Barber of Seville," "Fra Diavolo," "The Bartered Bride," "The Gypsy Baron," "Tales of Hoffmann," "Martha" and "Madame Pompadour."

The Volksoper's address is Wa hringer Strasse 78, A-1090 Wien, Austria; phone (222) 34 36 27.

Theater an der Wien While the Staatsoper was being rebuilt after World War II, the company moved briefly into the Volksoper, but then it settled down for a long stay in the Theater an der Wien, a venerable institution (dating back to 1801) that was the scene of the premieres of Beethoven's "Fidelio," "The Merry Widow" and "Die Fledermaus," not to mention his Fifth and Sixth symphonies. The building declined after the Staatsoper moved back into its own home, but it was renovated in the 1960s and is now used mostly for Broadway-style musicals -- "Cats" has been playing there for years.

On May 8, however, during the Vienna Festival (Wiener Festwochen), "Cats" will be replaced by a new project that some music lovers eagerly anticipate: a production of Schubert's opera "Fierrabras" sponsored by the Staatsoper with Abbado conducting. Schubert's operas are among the last great unexplored territories in classical music. Only snippets of them (mostly overtures) are at all familiar to nonspecialists; according to available information, the music is fine (being by Schubert, how could it be anything else?) but the librettos are full of problems. This new production (which will go to Brussels in 1989 and play at the Staatsoper in 1990) may be a sign of a new interest in Schubert's operas, which should increase steadily between now and the bicenntenial of his birth in 1997.

For further information or reservations, write to Theater an der Wien, Linke Wienzeile 6, A-1060 Wien, Austria; or phone (222) 57 96 32.

Other places for music in Vienna:

The Musikverein (Bo sendorferstrasse 12, A-1010 Wien, phone (222) 65 86 81) has two halls: the large and acoustically magnificent Grosser Saal, used for the Vienna Philharmonic and other orchestral concerts, and the smaller Brahms Saal, used for chamber music. Its major attractions this winter and spring will include concerts by the Vienna Symphony scattered through the season and visits by the RIAS Orchestra of Berlin Feb. 27 and 28, the Dresden State Orchestra April 9 and 10, and the Buffalo Orchestra April 28 and 29.

The Konzerthaus (Lothringerstrasse 20, A-1030 Wien, phone (222) 72 46 86) has a large Grosser Saal, a medium-size Mozart Saal and a small Schubert Saal. It departs somewhat from the traditional programming common in Vienna and is the city's prime venue for 20th-century music. Its programs this winter and spring will include performances by the Vienna Symphony Orchestra, the ORF Symphony Orchestra Jan. 12, Feb. 11 and June 10; the Academy of Ancient Music, Jan. 27; Bach's "St. John Passion," Feb. 12 and 13; and the Chamber Orchestra of Europe, April 6 and 7.

The Burgkapelle (formerly the Imperial Chapel) is the natural environment for the Vienna Choir Boys and the masses of Beethoven, Mozart, Haydn, Schubert and Bruckner. A sung mass by one of the great Viennese composers is presented each Sunday and Catholic holy day from September through June, with adult chorus members and instrumentalists from the Staatsoper joining the choir boys. Tickets for the 600 seats (ranging in price from $3.85 to about $10) are hard to get during tourist season but more easily available from November through April. The chapel can be reached through the Swiss Courtyard of the Imperial Palace.

Travelers with a special interest in the music of Haydn might want to time their visit to coincide with Haydn Days, March 10-20. Other festivals are the Viennale at the end of March, the Vienna Festival from May 15 to June 19 and the Vienna Music Summer from June 28 through Sept. 10.

Tickets for the Staatsoper and Volksoper (but not for the New Year's Eve performances and not for other theaters or concert halls) may be reserved at the Bundestheaterverband, Goethegasse 1, A-1010 Wien, Austria. No payment should be enclosed; tickets are payable when you pick them up in Vienna.

Additional information is available from the Austrian National Tourist Office, 500 Fifth Ave., New York, N.Y. 10110; 1-212-944-6880.