Few cities conjure up so magical a vision in the mind's eye as Salzburg, birthplace of Mozart - for centuries the "German Rome." Then how exhilarating it is, upon arrival, to find that your imagination could never do this city justice.

The name (Salt town or stronghold) comes from the lowly table condiment that has been mined nearby for centuries. But mystics of the late Middle Ages invented a more glorified concept.The ibex and lion - respectively the heraldic beasts of the locally prominent Hohenems family and the archbishopric that so long resided in Salzburg - are intertwined in a Salzburg seal; a paradox, since in the Zodiac these two signs, Capricorn (water) and Leo (fire) are diametrically opposite, so can never meet. But the Christian alchemist's mysticism brought them together.

"Two elements which fan the flames of an inexorable enmity between them come together in a marvelous compound, salt. For salt is all fire and all water," said historian Filippo Picinello.

Salt was also considered to be "lapis," the philosopher's stone, which was the alchemistic parallel for Christ. And despite the modern growth surrounding it, the Old Town still works a powerful alchemy on the visitor; for here, there seems to be no dross, only precious gold and silver.

Originally a Roman trading town, Salzburg became a bishopric in 798, and was not made an Austrian duchy for more than a thousand years. As an important seat of the Catholic religion, early Salzburg was dominated by powerful archbishops, many of them also princes of great wealth, who lavished their means on building great religious edifices, and making themselves as comfortable as possible in a country which many of them found depressing at best and barbaric at worst.

Most influential of these was Wolf Dietrich von Raitenau (bishop 1587-1612). A Medici by blood, his impress is still on the city, which was laid out according to his architects' plans.

Wolf Dietrich and the wealthy bishops who followed him brought the high baroque to its fullest, most ornate flowering in Salzburg, and so it has remained for centuries. Fortunately World War II destruction was not excessive; what was damaged has been repaired, and the city glows again.

Actually, one need expect little sunshine in Salzburg, where clouds and rain are more the rule than the exception. Even in August, one feels as if in a northern clime, where the dim sunlight seems to filter in obliquely.

But there is incandescence inside the many glorious churches, replete with glistening statuary, marble floors and columns, towering organs, saints in niches, ornate high altars, and angels in flight or born aloft on banks of clouds. The city's domes and towers, its natural-looking gardens, its innumerable courtyards with fountains, its classic squares, even its solemn little burying grounds wear a luminous aura.

Whatever you do see, you are going to miss a lot, since almost everything in town is worth exploring. Salzburg facades promise much, and when you step inside, their promise is fulfilled and running over. It is impossible to "do" the city in a couple of days. To savor the experience, plan at least four or five days, possibly a week, so you can stroll at a leisurely pace, finding the little hidden nooks that await your personal discovery.

The streets are filled with people riding in fiacres, or open carriages. For Salzburg has long been a horse-conscious society, as many statues of horses attest; not businesslike equestrian statues with soldier-riders, but noble Grecian celebrations of sleek equine lines. Indeed, central to the town is the old horse pond, surrounded by stone horses in spirited stances, designed by Raphael Donner. The centuries-old court stables nearby were converted into the Festspielhaus of the Salzburg Festival.

If you climb the Moenchberg to the old Hohensalzburg Fortress, you will look out over an idyllic panorama of Bavarian-style countryside - gently rolling vistas, green as Ireland, dotted with fine buildings and homes.

But attention quickly focuses to the north, where the famous bend in the Salzach River cradles the Old Town's inviting prospect of spires and stately buildings.

Salzburg's high season is of course during its world-famous music festival, which keys its programming around the works of favorite son Wolfgang Amadeus Mozart. Hence musical guests crowd the town during July and August, but many prefer Salzburg at other times of the year. (I went during the festival, but intend to return some other time to commune privately with Mozart. Old, proud money appears to dominate the festival's paying events.)

The fashionable Getreidegasse with its many shops invites strolling, but you'd best buy your souvenirs elsewhere; the place is pricey, and quality not always good. Nonetheless the street contains a treasure for every music lover: the birthplace of Mozart, and his home for the first 17 years of his life.

The shrine is on the third floor of a yellow row-type house, where the family appears to have lived in a fair degree of comfort. Especially affecting is the birthroom, where his grand piano stands. No "hands off" here during festival; a hostess is nearby to explain about the instrument and play for guests.

Also displayed are his clavichord, his child violin, and a collection of family paintings, notably an unfinished painting by Joseph Lange (1789), which his contemporaries felt was the best likeness of the mature Mozart. A few personal possessions, autographed scores and dioramas of his operas complete the exhibit.

Places of pilgrimage for Mozart devotees are numerous. Try the Mozarteum, with its music academy, two concert halls and archives. In the garden stands the "Magic Flute" summerhouse, relocated from Vienna, wherein Mozart wrote his last opera. The Mozarteum was built near the old "dancing master's house" with its more commodious quarters for the family Mozart after they moved from Getreidegasse, but the house was destroyed. A booklet available at the birth house will guide you to many other little shrines about the city.

The famed Salzburg Marionettes, created by the Aicher family, delight audiences around the world. But you'll find them at home to the young in heart in their own Salzburg theater, where they present folk tales and sometimes Mozart operas.

The Cathedral, Wolf Dietrich's masterpiece (though completed by his successor, Marcus Sitticus) is built along lines very similar to St. Peter's in Rome, and is hailed as the finest Italianate edifice in Austria. Covering 40,500 square feet, it can accommodate 10,000 people with ease. Here are heard many of the festival concerts. Resplendent special music may be heard during the Easter season as well, and regular Sunday music is among Europe's finest.

In the Domplatz outside the Cathedral, the morality play "Everyman" is performed on Sunday evenings during the festival. (Though we did not see "Everyman," nature treated us to an awesome natural display - a violent thunder squall in the Residenzplatz that sent crowds scurrying for cover as bolts of lightning struck nearby.) Here also are almost nightly concerts that those without prior reservations may hope to attend.

Among Salzburg's other treasures is the Collegiate Church, a prime example of baroque at its best, and favorite of many visitors. The old St. Peter's Abbey with its several chapels, and the Nonnberg Convent, both sheltered under the Moenschberg, offer insights into the ecclesiastical history of Salzburg.

The central Mirabell Gardens, leading to the Mirabell Palace, exemplify formal beauty with clipped hedges, statuary, fountains, colorful flower beds and birdsongs. The palace, built by Wolf Dietrich for his mistress, Salome Alt, is crowned by a magnificent stairway with cupids by Donner.

It is beautifully maintained, as is the Residenz, a prime example of Italian Renaissance architecture, which was the in-town home of Salzburg archbishops for centuries. Now an ornate museum, the Residenz is also the scene of serenade concerts during the festival, to which standing room is sold.

The pleasure dome of Marcus Sitticus at Hellbrun is worth a little detour to the suburbs, easily reached by bus. Suffering from melancholy in the northern clime much of the time, the bishops hit upon a cure that has lately been scientifically credited - large doses of light. In his gardens, good for strolling, Marcus incorporated many water tricks and fountains, and the palace itself is light and airy, with peaceful views.

How about lodgings in Salzburg? That depends upon your preference and your resources. If you must stay at such fine hostelries as the Goldener Hinde or the Oesterreichischer Hof, you will pay dearly and have difficulty getting in.

On the other hand, you may write to the Salzburg Tourist Office, Auerspergstrasse 7, A-5024 Salzburg, Austria, which seems to have a large supply of housing outside the Old Town lined up for reservation. I had little difficulty securing a comfortable room with eiderdown coverlet, shared bath and an excellent breakfast, within 15 minutes' bus ride of the Old Town, for about $20 a night.

Several first-rate restaurants may be found in the Old Town, most of which are high priced. But there are many European versions of the fast food industry, and carts serve good wurst sandwiches, drinks and pastries in the squares. Weather permitting, you will surely want to relax over a snack at an open-air cafe in an ambient square.

And above a choice location in Getreidegasse, the Lion of Salzburg holds an authentic-looking guild sign; amid greenery and scrollwork, voila - the golden arches of McDonald's! So whether your tastes (and means) are patrician or plebian, you will not go hungry in Salzburg's streets.

* Dorothy Stowe vacationed in Salzburg last summer.