A VISITOR TO Sante Fe, N.M., was strolling through town recently, looking for a Navajo rug as a memento of this year's season of the Santa Fe Opera.

He spotted an 11-by-7, just right for the living room. Then he looked at the price tag -- in shock. This handsome little number costs $12,500.

In quick retreat, he bought a Georgia O'Keeffe poster instead.

The price is an indication of what is best -- and most intimidating -- about this city. With numerous residents and an influx of visitors from around the world who can plunk down that kind of money for a rug, Santa Fe can support what seems to be more fancy shops and commercial galleries per capita than any place this side of Florence.

And that is one reason why, for the last 23 years, the city has been able to support the country's most prestigious and ambitious summer season of opera, in an outdoor theater so visually and acoustically impressive that Wolf Trap or the Post Pavilion pale by comparison. It's also why Santa Fe, coincidentally, could have just completed the eight year of a chamber music festival of such quality that it is being transferred this weekend, lock, stock and barrel, to Lincoln Center's Alice Tully Hall.

Furthermore, audiences in Santa Fee take their culture very seriously indeed. This viewer did not see a single empty seat during six successive nights of performances. Perhaps such a turnout was not surprising for the Opera's lovely new production of Verdi's "La Traviata." But who would have expected the response would have been the same when the Opera presented three of the least-well-known vocal works by that master of the arcane, Arnold Schoenberg, whose one-act opera "Von Heute and Morgan" ("From Today Until Tomorrow") received its first American staging on the program.This is the sort of programming that no Washington impresario has dared to try.

The artistic caliber of Santa Fe, though, is not just a furtunate fluke growing out of wealth that exists in (or passes through" the area -- even if it could not have happened without it. Equally important is the sophistication of the audience. Northern New Mexico is not especially populous, but the intellectual level of those who have come there to live or to visit is astonishingly high. The audience nucleus is in Santa Fe, which has been a popular haven for writers and artists for most of the century. Taos soon followed suit gaining enormous celebrity after D. H. Lawrence moved there. And finally, there was the brain power brought in as Los Alamos grew out of the desert to develop the atomic bomb. These are not the kind of people content to sit at home with commercial television every night.

Yet another reason is the salubrious 7,000-foot-high climate, which attracts visitors for culture and sunshine in summer and for skiing in winter. Eight nights ago, during a performance of Tchaikovsky's "Eugene Onegin," the desert air dropped to a bracing 49 degrees.

So it was not exactly a pipe dream on which the 30-year-old John Crosby started an opera company there in 1957. Crosby is a New Yorker whose wealthy family regularly summered in Santa Fe, and Crosby even briefly attended (for health reasons) the once remote, log-timbered Los Alamos School, just before it was secretly converted into the headquarters of J. Robert Oppenheimer's atom bomb project.

Later, after years of doubting that a musical career was a good idea for his son, the elder Crosby was finally convinced of the feasibility of such an enterprise. With a $200,000 gift from his father, Crosby bought a ranch about seven miles north of Santa Fe, on a hillside nestled at the western edge of the 13,000 foot Sangre de Cristo range and overlooking the vast desert through which the Rio Grande flows, with the Jemez mountains far in the distance.

Crosby built the opera house on that hillside facing west, so that listeners get the full measure of the New Mexico sunset (the music doesn't begin until 9 p.m.). Then, in the dark to the right, there is Los Alamos, gleaming like diamonds 20 miles distant. The setting could hardly be more romantic, and is enough to dull the critical faculties of anyone to the music per se. Even Anna Russell might sound good there.

Crosby's conviction that the demographics were right in this state capital -- which even now has only about 50,000 persons -- was not doubt more intuitive that scientific. But today one need go no further than the lavish program booklet for proof that he was right. In pages listing thousands of contributors, there are the names of persons from every state but Vermont. There are listings from nine foreign countries, and huge numbers of donors from New Mexico, Texas, Colorado, Oklahoma, Arizona, New York and California.

Crosby, now 54, runs just about as much of a one-man show as anyone in the arts. Not only is he founder and principal benefactor, but he is also general director and principal conductor. And, quite aside from all that, he heads New York's Manhattan School of Music as well, while he presides over the Santa Fe Opera from his four-story townhouse on the Upper East Side.

Santa Fe's five productions each summer have grown into one of the most cosmopolitan repertories in the world. There have been 72 operas in 23 years, including four world premieres, 15 American premieres and three American stage premieres. Stravinsky and Hindemith both conducted their works there. At least 38 of them are works that have never reached the stage of the Met. Last summer the news was the first American performance of the completed version of Alban Berg's brilliant "Lulu," which will finally reach the Met this season. Staying ahead of the big international companies is a Santa Fe trademark.

This year's season had no "Lulu" to put it in the spotlight.

The premiere of Schoenberg's "Von Heute auf Morgen," which the father of atonalism called a "a comedy of manners" and which dates from the '30s, was a misconceived downer. Regardless of what the composer labeled it, Noel Coward -- not to say Mozart -- this is not. It is a cliched tale about marital jealousy triggered by wandering eyes during a night out to which Schoenberg utterly mismatched some of his most rigorous -- and impenetrable -- 12-tone formulas. It is as if the only "comedy" is perverse trick to confuse the audience. When it was over I commented to another critic, "I sure didn't get very much out of that on first hearing." He astutely replied, "Well, I doubt that you'll ever get another hearing." Both the production and the singing (in English) were all the composer could have asked.

Joining "Von Heute" on "A Schoenberg" were his early mono-drama "Erwartung" ("Expectation"), which was not written to be staged and does not wear particularly well for this listener, and his oratorio "Die Jakosleiter" ("Jacob's Ladder") in which he uses atonalism less strigently and with considerable eloquence. It came as balm at the end of a hard evening. Gabriel was sung majestically by William Dooley and the song of the "The Chosen One" was lovingly performed by Washington's William Parker, who won the recent Rockefeller Foundation-Kennedy Center competition.

Otherwise, only Mozart's "The Magic Flute was a dissappointment, with a production that hammed up the show-biz side of the opera excessively and a performance that cut too many corners on both the subtlety and depth of the score. Parker's Papageno was overgeneralized, and only Ellen Shade as Pamina sang with the purity of line, the vocal sheen and the rhythmic precision Mozart needs.

The new "Traviata," by playing things straight and following Verdi's directions, was a welcome corrective to the preserve Ponelle staging here last season for the Washington Opera, which one observer has labeled "La Travastia." Ashley Putnam, who was Washington's Lucia last season, shows promise of becoming a first-rate Violetta, one of the more demanding soprano challenges in Italian opera. Putnam was beautiful in the part and she acted with real authority. Her extended scene ending the first act was impeccably articulated, but it lacked sufficient variety of color and drive -- partly because Crosby's conducting was laggard. But these problems disappeared as the opera went on. Once again, Brent Ellis was a fine Germont.

But Crosby's conducting unexpectedly took fire the next night in Strauss' "Elektra," also a new production, and he carried the well-drilled orchestra along with him. Danica Mastilovic was quite professional, if sometimes a little shaky, in the grueling title role. Eszter Kovacs was spectacular in every respect as Chrysothemis, and the famed Rosalind Elias was an unlikely, and smashingly good, choice as Klytemnestra. Dooley sang a good Orest, just as he does at the Met.

Finally, the "Onegin" did not reach for Bolshoi-style brilliance, but was quite solid. John Nelson, of the Indianapolis orchestra, generated considerable fervor. The settings were lavish but not extravagant, Patricia Welles was a compelling Tatiana. David Rendall sang a lyric Lenski and Richard Stillwell seemed almost type-cast in the title role, until inexplicable vocal breaks began to plague him.

Next year: the world premiere of Henry Brant's "Everybody, Inc.," new productions of Rossini's "The Barber of Seville" and Stravinsky's "The Rake's Progress" and a revival of Puccini's "La Boheme."

Among the chamber music festival's 11 programs were an impeccable string recital of quintets by Mendelssohn and Dvorak, with recently discovered viola sonata of Paul Hindemith -- along the lines of what might be played in Washington by the Theater Chamber Players or the Chamber Music Society of Lincoln Center. In fact, the leaders were both veterans of the Lincoln Center group, violinist James Buswell and violist Walter Trampler.

Trampler played the Hindemith sonata for only the second time in the country. The work was intimate and lyric in the first two movements, followed by an athletic finale. It sounded like Brahms with less richness and starker intervals.

In the same spirit of daring that characterizes the Opera, the festival invites a resident composer to come each year, and commissions a new work. This year the guest was Ned Rorem, who presented "The Santa Fe Song," settings of 12 poems of Santa Fe poet Witter Bynner. The singer was Will Parker, who bounced back and forth from the Opera to the festival.

There is no formal tie between the two events, but the try to avoid scheduling conflicts. Usually the chamber concerts begin at 6, giving listeners time to go on to the Opera. The institutions work more in tandem than in collaboration -- as do most aspect of the exceptional Santa Fe cultural scene.