AND THAT YOUNG woman next to you, is she a musician, too?" we asked a woman from Colorado who sat in front of us at a recent piano recital in Vienna.

"Musician? Oh, no. She's a dietitian. She was brought over from California to help Austrian cooks learn how to prepare less-fattening foods. The government is concerned about the big intake of sweets and fats."

This incident is among the evidence that things are changing in Austria's aristocratic capital. For years it has been filled with people filled in turn with schlagober, Sachertorte, cheese and other hardly thinning foods, but this summer the scene was somewhat different.

On previous visits to Austria our pastry and ice cream desserts always have included whipped cream - great mounds of it. But today waiters and waitresses ask if it is wanted rather than assume that it is. A look around in Demel's, Lehmann's, Gerstner's, Heiner's, and other popular Viennese konditorei, and in the dining rooms of the Hotels Sacher, Bristol, Astoria, and Europa showed surprising numbers of schlag avoiders. Not that the Viennese are becoming Twiggys, but there are signs of restraint.

The enthusiastic dietician, however, did not have the weather with her. The city, known for its hot summers, was in the 80s and 90s on many days during our visit. The climate drives the citizens into the many restaurants, some of which are "air condition," as the window signs read. Visitors and locals alike are tempted to sample the arrays of slices, eclairs, tortes, and various novel baked products that make customers drool. But counteracting that is the high price of all such goodies: afternoon tea (two pots of it, lemon juice, sugar, cream, hot water, a cream slice and an ice) costs $5 or 80 shillings, for example.

Tea is not the only costly meal. We found Vienna's reputation for expensiveness deserved. First-class hotels charge $50 to $75 a day for a double room, which includes a 15 per cent service charge.In comparable restaurants moderate lunches run from $7 to $12 a person: dinners go at least one third higher. The Europe-on-$10-a-Day set is hardest hit, and complains about its 60 shillings all going for lodging. Sachertorte is $2 a slice, but backpackers do not budget for such goodies, anyway.

Also in the Henderizing campaigners' favors is the fact that the Viennese in the inner city - the area downtown within the incomplete circle of streets called the Ring - are getting more exercise. One reason is the work on new office buildings or remodeled ones and the subway construction going on; the other is the recently opened shopping mall and promenade created from the honorable old street, the Karntnerstrasse. That thoroughfare, at least the portion running from the Opera House to St. Stephen's Cathedral, and the Graben, a shorter street of exclusive shops ands restaurants, are open only to pedestrians.

Not only is the Opera area upset by the work on the new Karlsplatz station, but so are the Karlsplatz itself and many streets between it and The Ring. At the foot of St. Stephens are semipermanent construction workers' buildings, enormous cranes, and the usual road and sidewalk encumbrances of a budding subway system. It will replace the ancient one. There, and elsewhere in the city, reconstruction of many buildings continues, and the public must dodge scaffolding and materials, thus getting exercise.

All this digging and dumping has not affected Vienna's principal architectural sights. The massive Hofburg, the city within a city, for instance, still is a tourist mecca, as is the Schonbrunn palace and park.

That is one contradiction of the present Vienna: It retains its dozens of palaces, huge government buildings, museums, and other evidence of its age and one-time imperial dominance. But mixed in with these massive structures are shiny new office buildings and enormous apartment complexes. To its credit, the changing Wien has not punctured its landscape with high-rise buildings. The baroque, still reigns, and has not lost in all the newness, despite the impatience of those who prefer the simplicity of the streamlined newer buildings.

Vienna's work force also is changing. Once a restive, even revolutionary body, labor today in Vienna - as in all Austria - is in a moderate mood. The city is free of business-labor-government conflicts so common in some of the country's neighbors, particularly Italy. And Vienna is the center of this industrial peace. Here the extra-legal Parity Commission on Wages and Prices meets regularly to deal with issues. Its values, evidently also those of the relatively relaxed every day Austrian worker, are such that wages, overtime and bonuses are less important than proper living standards and job security.

The gradual closing of the streets running into the Karntnerstrasse is being accepted by taxi drivers, office workers who drive to their buildings in their small cars, and others who must find the restrictions on parking especially irksome in winter.

Not that the Viennese now are subdued. Laughter and singing are heard into the night, as has been going on for many years. Some of this joviality has been introduced by workers from other countries, who increasingly are handling manual jobs. But the Viennese themselves retain their good nature despite the physical changes.

Some older residents think temperaments have changed. One businessman said this summer that the World War II years made the Viennese less relaxed and happy-go-lucky, and even less kindly.

He is right. The loss of the famous gemutlichkeit is clear in the daily dealings. The graciousness long associated with Vienna, a natural courtesy that used to startle Americans and others unaccustomed to it, is less common. When you entered a restaurant or tea room in bygone years it was common to be greeted with "Grus Gott" or "Gnadiche frau." Today you are more likely to wander in silence to an empty table and after awhile someone may ask what you want and neglect to hand you a menu.

But it still is true that you have to ask for your bill, except in the few quick-lunch spots, and customers still may sit in a restaurant for an hour reading the day's papers or scanning the magazines, even though other diners glare at the leisurely diner who may have ordered only coffee or pastry. Such impatient people are visitors from other countries that do not have the tradition of reading in pub, bar, or dining room.

Such diners are likely to be more frequent, since Vienna is more than ever an international city. In summer, when the grand opera and major symphony orchestras are silent, few foreign visitors are likely to be serious music lovers compared with those who come in winter. In that season there are so many that tickets for opera and symphony performances must be requested from abroad one to two years ahead.

Entertainers from around the world appear on Vienna's stages in summer and fall. This summer pop combos came from Germany, Britain, the U.S., Sweden, and Denmark; now and then Bing Crosby, Jerry Lewis, or some other big name appears for a single show.

But Johann Strauss still is waltz king and Franz Lehar's "The Merry Widow" remains among the most popular operettas. But like the man or woman on the street in most countries, the Viennese appear to have little ken of the classical composers about whom the cultural organizations make so much in the city. Numerous denkmals or memorials have been erected over the years to Beethoven (who moved from one house to another 79 times during his years in Wien), Mozart, Brahms, Schumann, Haydn, and other composers who had connections with the city. Even the commercialization of Strauss and Mozart seems not to have broadened tourist or local appreciation of them. Candies and ice creams are named for them. A special tour bus visits the houses where they lived and worked (as did Schubert and others). But it is one of the least popular trips; on our day only six persons went, all Americans.

Most dramatic is the story of the neglected Brahms sculpture. He was closely connected with Vienna: the Prater, the city's "Coney Island," was one of his favorite spots to visit with his students. Two tour-bus companies knew nothing of a monument to him; neither did various music stores, the city information office, and persons in the Stadt Park, which has numerous figures of other noted composers.

Finally one map showed where it is: downtown near the city museum and the Karlsplatz. So early one morning - the best time to avoid the roar of the rushing traffic - we went searching, camera in hand. In some bushes near where the subway is being built, poor old Johannes Brahms' figure was found, the various parts of the monument numered but spread helter-skelter over the ground. The composer, in a seated, sad pose to begin with, looked even sadder in the debris around him. A brown streak from his left eye made the scene still more poignant. Art teachers at the university, we learned, are distressed at the mistreatment of the great German musician but can do nothing about it. In the new Vienna the subway comes ahead of a classical music giant, especially if he was German rather than Austrian.

Vienna shows signs of unrest among its working women. But the spirit of dissent does not compare at all to the U.S. feminist movement. Like the women of other Germanic nations, those of Austria have behind them centuries of subservience to men. But now they have heard of the National Organization for Women and other American groups, and some of them read the writings of such feminists as Gloria Steinem, Kate Millett and Germaine Greer.

Businesswomen report that thanks to general social legislation they are being paid equally with men for the same work done, but that few women rise in the ranks and that they therefore cannot count on life-long careers. A striking proof of their search for independence is the way Viennese women dress, especially the younger ones in business. They wear what they please to the office or store. That does not mean jeans or shorts, but rather blouses, low-cut tight shirts, and obvious bralessness and see-through tops. Skirts are fashionably long but deeply split; hair is short or curled tightly; jewelry and cosmetics generous but not tastelessly applied.

Vienna's men, on the other hand, have not changed with the times. Few bearded faces are seen in streets, shops, and offices. Moustaches are a little more common, but the Civil War type, popular as it was in the Germanic countries a century or more ago, is rare. Although there are few Eric von Stroheim haircuts, there are even fewer long-haired men. The males have clung to business suits, ties and sometimes even hats.

The new Vienna would hardly be considered new if it were quiet and unpolluted. Unfortunately it has neither virtue. Viennese motorists, who possibly have visited Paris or Amsterdam, driver their small cars like the lunatics behind the wheels in the Place de la Concorde. The pollution from industry and street traffic hangs over the city constantly. The Danube River, which is so far away that it does not deserve the association it has had with the city for years (nor is it any longer blue), cannot be seen most days even from such high points as the world's biggest ferris wheel at the Prater, due to the haze.

Thus the new Vienna has caught some of the characteristics of other old cities that are modernizing. Whether we like these changes or not - less schlag, more noise, greater pollution, accelerated pace, modest but modern architecture and a timid feminist movement, among others - Vienna still is eminently worth visiting.