The sunlit sea that has been made to appear night after night on the stage of the Royal Theater here is in sharp contrast to the perpetually gloomy skies outside. But the weather has not deterred tourists from around the world who came to Denmark last week to enjoy the genial ballets of August Bournonville (1805-1879).

Almost all his remembered works are bing performed by the brightest young dancers and the grandest old mimes the Royal Danish Ballet can muster, in a week-long festival that celebrates the centennial of his death on Nov. 30. The past week has revealed the lasting influence Bournonville had on Danish style in all the arts (for he was a painter and poet as well as ballet master) and his choreography's vitality and his techniques' utility to audiences and dancers abroad.

Tickets to festival performances, at a $10 top, were a bargain. But the Royal Theater is small by opera-house standards and the foreign advance sales were big, so many Danes have been unable to obtain seats. While they grumbled at first, their curiosity, pride and superb manners soon combined to made strangers feel welcome. And after all, this year the Bournonville repertoire will be scattered throughout the Royal Danish Ballet's regular season.

Attending a regular Bournonville performance on Nov. 23, the night before the festival opened, was like being invited into a Danish home. Queen Margarete II and her children were in the royal box, and the audience behaved as if among good friends. The dancing was relaxed, virtuosity was casually displayed, and the applause was like the warm handshake.

On festival nights, the atmosphere was charged. The dancing became more pungent than mellow, waves of synchronous clapping filled the theater after the final curtain, and throughout one was aware of stars on both sides of the footlights. Yvette Chauvire entering the foyer in furs and jewels was a fabulous apparition.

An American man commented, "She must be famous." His lady replied, "She must be French." Nicknamed "la Chauvire Nationale," she was indeed the greatest of Parisian ballerinas during the de Gaulle years.

Galina Ulanova, Russia's prime ballerine of the Stalin era, was quietly dressed but seems to be wearing the empty space that forms around her in the crowd. Britain's octogenarian Marie Rambert, America's Robert Joffrey, Austria's Gerhard Brunner and such Ballets Russes emeriti as Serge Lifar and Marcel Luipart are here among the official or self-appointed dance representatives and diplomats from over 20 nations.

In such an assemblage, international politics and Terpsichore occasionally intrude on conversation, but the 10th muse, Gossip, really rules. Was Ulanova amused or not by Warhol's Mao portrait when she toured the museum? Is the New York City Ballet being cool to Baryhsnikov's request to rejoin the company in spring because the management has higher hopes for its latest Danish acquisition, young Ib Andersen of the brilliant footwork and bold line? Will Andersen's chief rival here, the velvety Arne Villumsen, also leave, for foreign plaudits? Will the Joffrey Ballet replace the locked-out American Ballet Theatre dancers at Kennedy Center in spring? (Robert Joffrey says no.)

The effect of seeing Bournonville's ballets on their home ground, night after night, is cumulative -- a comfortable exhilaration that grows and grows.

Most visitors here knew already that the Bournonville shown abroad consists of dance plums plucked from his pantomimic puddings.It is good to report that the dancing doesn't suffer on being excerpted, and that the mime could almost hold an audience on its own. The small size and horseshoe shape of the Royal Theater helped: No seat is really far away.

Undoubtedly, the limits imposed on choreography by this fairly narrow stage led Bournonville to avoid long lines of performers that sail forth so impressively in Russian ballets. Instead, he developed step variety, ingenious linkages, weather-vane changes of direction and bounce.

Such dancing, of course, is predominantly sunny; and together with the picturesque locale and bandstand music it serves as a tonic against Denmark's long dark winters. Shadows do fall across the story lines of Bournonville's domestic, folktale and political ballet. Sex, race and power pose problems for the characters. In the typically "Danish" pieces, however, the moral resolutions -- like hand clasps -- are astonishingly final and matter of fact.

To the words "not for pleasure alone" written above the Royal Theater proscenium, Bournonville's addendum might read, "Also for practicality."