One of the fruits of the interest in ''provincialism'' is a growing recognition of Scandinavian art. Scandinavians are certain to be uncomfortable about the word ''provincial,'' with its implication that artists are ignoring, either deliberately or naively, the innovations and forces for change in the world's art centers. But this is not the kind of provincialism found in most Scandinavian art. What is gaining notice is that Scandinavian artists have had an instinctive and obstinate regard for their national ethos, while at the same time keeping an eye on the rest of the world. The latest manifestation of this recognition is an exhibition, coinciding with the just-ended Edinburgh Festival, which offers a survey of ''Two Centuries of Art and Craft in Denmark'' called ''From the Golden Age to the Present Day.'' The works span nearly two centuries, from 1809 to 1995. The exhibition continues at Edinburgh's City Art Centre through Sept. 30. Danish artists and craftspeople always seem to have been stimulated by the activities and innovations in important centers of the art world. It is almost as if, to convince themselves and their fellow artists of the validity of their art, they have had to frequently look over their shoulders (depending on the period) at Rome or Paris or New York, and sometimes, more recently, at the Far East. They may come home, to stay and work, but the need to travel is apparently an unavoidable part of being Danish. This said, what is really intriguing about such diverse painters as Anna Ancher, Vilhelm Hammershoi, or J. F. Willumsen, is not the evidence of foreign influence in their work, but the qualities that make them highly original. Anna Ancher, one of the leading painters working at Skagen (where she was born) in the northernmost tip of Denmark, was as influenced by the other incoming Danish artists as she was by her infrequent travel to other countries. When in 1888 she finally visited Paris, she studied under Puvis de Chavannes, yet her own work has something of the lightness of Impressionism (Puvis was no Impressionist), and is domestic and local in subject. It has none of Puvis's carefully arranged symbolic classicism. Hammershoi is sometimes described as a kind of Danish Whistler. He was influenced early on by Whistler. But apart from a penchant for gray tones, the tranquil order of Hammershoi's silent interiors, and his paintings of buildings that appear to be haunted by their own bleak Northern loneliness, could hardly be further from the atmosphere of Whistler's mix of Japonism, showmanship, and Parisian sophistication. From Hammershoi's scrupulous, unpretentious pictures you would not easily guess that he travelled abroad a great deal. What could be more Danish? The comparative wildness of Willumsen, his changes of style, his obvious awareness of Gauguin and Van Gogh and some of the excesses of turn-of-the-century Symbolism, and even the subject matter of some of his later landscapes of Venice mark him as cosmopolitan in outlook. Yet of the mere couple of paintings by Willumsen in this exhibition, the one called ''Sophus Claussen reading his Poem 'Imperia''' seems to be everything that an indelibly Scandinavian painting might be. It has a kind of passionate respect for intellectual and imaginative intensity, as if the very thought of the poem could be captured in paint as it passes from the reader to his listeners. The first stages of the show look at the so-called Golden Age painters and their predecessors. Christoffer Wilhelm Eckersberg in the early-19th century laid a groundwork of realistic, straightforwardly observed landscape painting - mostly of places around Rome. These are rational and well-painted topographical images. The paintings that blossomed in the ensuing first half of the 19th century are an undisturbing pleasure: ''Small, bright and harmonious pictures - dreams of Arcadia and Elysian Fields,'' as Ane Hejlskov Larsen puts it in the catalog. Painters during the Golden Age also started to really paint the landscape of Denmark itself. Danish artists were jolted out of quiescence by humiliating international criticism leveled at their work in the 1878 World Exhibition in Paris. One critic hit home cruelly by writing: ''That which particularly characterizes Danish painters is that their brush is always clean, yes, far too clean, it is sleek, and nature is never sleek.'' The Skagen painters, including such fine performers with the loaded, not-too-clean, light-sensitive brush, Peder Severin Kroyer and Carl Locher, as well as Anna's husband Michael Ancher, were a fresh flowering of strong Danish art. They brought their French-inspired brilliance to play on a specific and remote Danish locale. In the 20th century, Danish artists have variously responded to such developments as Expressionism, Abstraction, Surrealism, assemblage art, Pop Art, and the trans-avant-garde, and have been affected by such giants as Matisse, Picasso, and Pollock. Yet again there have been outstanding stars in this northern sky who have made entirely original contributions, gaining deserved international admiration. The moving force of the COBRA group in the late 1940s and early '50s, Asger Jorn, was a painter of gargantuan potency and tortured vision. But COBRA was a collaboration of individuals from three countries - Belgium and Holland as well as Denmark - and started in Paris. It was indeed a kind of crude spit-in-the-eye aimed at some of the slick, balanced, too-easy assumptions of Parisian art. Per Kirkeby emerged in the '60s and '70s as an individualist, also well aware of creative developments abroad such as Pop, ''happenings'' and minimal art. But he arrived at his own almost Romantic abstraction, which suggests, though never specifically states, innate qualities of landscape. His work is instantly recognizable and can be mistaken for nobody else's. A large section of the show is given to Danish crafts. It is a rich part of Danish culture. Included are Georg Jensen's immaculate, sensitive silverwork; Gutte Eriksen's bold, earthy pots; a cluster of fragile-looking, ceramic bowls with imaginatively various textured and speckled decorations by Jane Reumert; tall vessels by Ivan Weiss, mixing freedom and control in equal measure (are they truly, as described on the label, ''hand-thrown''? - the mind boggles given their size). The exhibition displays an array of other works, including textiles and glass. All told, the degree of assurance in this Danish work is unmistakable and tremendously enjoyable.