THE QUINTESSENTIAL jazz story of New York is that so many musicians use T it as home base. So clubowners never know who is going to walk through the door and simply sit in with the booked group.

"Headliners just walk in and play," says Mel Litoff, a co-owner of Sweet Basil, which opened in Greenwich Village in the 1970s and by the '80s became one of the world's top jazz clubs.

Cab Calloway, still in robust voice, sat in one night to sing "Minnie the Moocher." Jo Jones, once a legendary Count Basie drummer, sat in with Louis Bellson's group. George Coleman and other horn players sit in regularly at Bradley's in the Village. Even a drummer, Frank Gant, made a surprise appearance there, despite zoning laws against drums in this small, musicians' handout. He played only with brushes on a makeshift drum--actually a Rand McNally Atlas. And a score of jazz musicians, including pianist Kenny Barron, who was booked at Bradley's, and the customers cheered for Gant.

He's one of the hundreds of jazz musicians, for whom all roads lead to Sweet Basil, Fat Tuesday's, the Blue Note, Lush Life, the Village Vanguard, the Village Gate, the Village West, Seventh Avenue South, Sounds of Brazil (Called SOB), Marty's, the Cookery and assorted piano-and-bass rooms, most of them new, all over Manhattan. Other, smaller clubs have opened in the boroughs and suburbs in the past few years, in what is the closest thing to a renaissance of jazz in the United States since King Rock eclipsed all other music in the '60s and '70s.

By 1982, New York City had enough major clubs to organize a festival. Thirteen out of about two dozen Village clubs participated as festival sponsors, selling tickets at a discount and also $100 gold passes. They allowed a buyer to visit every event in the festival free of all other charges. Money from the 17 gold passes sold, plus a percentage of discount tickets, brought in about $5,000 to the festival sponsors.

They plan to start a Greenwich Village Jazz foundation to grant scholarships, commission new works, and subsidize workshops. Drummer Max Roach has agreed to be chairman of the fledgling foundation committee.

For jazz fans the festival showcased a variety of jazz from the swing of the 1920s and '30s to the avant-garde of the '80s. And the clubs regularly show off all the steps of progress in the increasingly sophisticated art. During the festival and as regular fare, Sweet Basil schedules old-timer Doc Cheatham, early bebopper Eddie Chamblee, many later musicians, from Ahmad Jamal to Hannibal Peterson, and a new Brazilian group.

"Not since the 1940s have so many jazz clubs been thriving in New York City," said Sandy Borcom. She manages Lush Life, a bilevel, intimate Village club that opened last year with all the requisite candles and spotlights. From the start, Lush Life scheduled all the eras of jazz, from avant-garde saxophonist Chico Freeman to Jon Hendricks and Company, a direct descendant of a premier bebop singing group.

Most big cities have at least one jazz club that survived the rock blitz. And little clubs are opening now, too. Singer Jo Stafford noted that her daughter, a singer, was beginning to work in small clubs around Los Angeles. And jazz stars are busy making the rounds of the well-known clubs: Blues Alley in Washington, Stephen's in Chapel Hill, N.C., Rick's Cafe in Chicago, the Keystone Korner in San Francisco--and about 20 more that musicians name quickly as good places to work outside New York.

But last year, New York City had more jazz clubs per square inch and hip musician than any other place. Musician Barry Harris opened a new club at 368 Eighth Ave., and a rock club, Gildersleeves, on the Bowery reinstituted jazz last fall. Paris, which became home to scores of great musicians in the '50s, has only two major clubs left. So the expatriates are coming home. Drummer Arthur Taylor, who lived in Paris and Belgium in the '60s and '70s, came back to New York a couple of years ago to play with Slide Hampton and others.

Nobody knows exactly why New York has so much jazz lately. In the 1970s, the Village Vanguard featured other kinds of music to keep going. Last year, bebop pianist Mal Waldron came home from Munich, saying he was homesick, and played intense sets at the Vanguard for the lines of fans formed outside. Free jazz saxophonist Arthur Blythe, who can wail like a banshee in the night, took his odd sound into the Vanguard for a few weeks before Waldron appeared. Blythe is finding fans who avoided his kind of music like the plague 10 years ago and more. It became clear by 1982 that jazz was having a heyday. And the avant-garde and contemporary musicians were working their way into the mainstream.

Maybe it's because jazz historically becomes popular when the economy turns sour. People like to cheer themselves up with jazz. Maybe it's because rock is selling fewer records and filling fewer concert seats as well. One news story said young people are spending money on video games. And people with a yearning for sophisticated, popular music started going to jazz clubs.

Furthermore, jazz has become establishment without losing its excitement. Since the Equal Opportunity Act in 1968, schools have instituted jazz programs. The National Endowment of the Arts gives grants for composition and performance to jazz musicians.

And jazz has a quixotic way of establishing itself in one city for a decade, then moving on, usually because the economic fertility of a town has dried up. In the 1920s, stride pianists made Harlem jump. The Cotton Club opened. Ethel Waters settled in town, along with Calloway, Louis Armstrong and hundreds of others. By the '30s, the corrupt political machine in Kansas City spawned scores of clubs, which started such stars as Charlie Parker and Count Basie on routes to international fame. Then New York's hotels needed resident big bands for people who wanted to dance. And West 52nd Street, now called Swing Street in honor of its history, came alive with dozens of clubs in the '40s and '50s, with Birdland as the crowning glory.

In post-war Europe, Europeans loved jazz as a more spontaneous and exotic art than they had ever created for themselves. Now European musicians have learned from expatriate Americans and taken the available jobs. Americans still headline at major festivals. But the majority of American musicians have a good, economic reason to go home.

All these factors have contributed to the expanded scene in New York.

"There's a lot of new energy, a lot of new names on the lists," says tenor saxophonist Ricky Ford, 28, who graduated from Boston's New England Conservatory of Music, won two NEA grants and plays often in the clubs. Leaving Boston to tour with Charles Mingus and Mercer Ellington in the '70s, Ford finally settled in New York City, deciding it was the most vital place to establish himself as an enterprising freelancer.

A lot of the action takes place in clubs featuring piano-bass duos. "We used to be the only game in town," says Bradley's waitress, Judy Mortlock. "About nine years ago, we started featuring jazz every night. At first it was slow. Now it's a goldmine. The volume of business has grown, especially in the past three years." The crowd at Bradley's has changed from neighborhood regulars and writers to music students and jazz fans.

And so the best jazz pianists in the world are on display in New York City. Many are so busy working in town they've curtailed touring, no longer living the typical gypsy life of jazz musicians. They can play at Bradley's, Knickerbocker, Star and Garter, Zinno's, the Cookery, the Jazz Forum, Griff's Plaza Cafe, Mortimer's, Gregory's, and others. Even an elegant Italian restaurant, La Camellia, on the Upper East Side, hired Hal Schaefer to play its huge, white piano with a built-in bar this fall. The man who booked Schaefer and others to follow used to promote Nat King Cole's records during the last jazz heyday in the '50s.

When Birdland closed in the 1960s, jazz seemed to fold up its wings, too, for about 15 years. "It seemed like that was the key to the whole scene," says Frank Gant, who spent 12 years touring as Ahmad Jamal's drummer. Even though Gant notices that many New York clubs aren't zoned for drummers, who disturb apartment dwellers above clubs, he still counts more full-scale jazz clubs in New York than in any other city. He finds work with the musicians who come to New York to play for a while, such as Phineas Newborn, or others who have settled in, as Gant has, after years on the road.

As a sign of the times that New York is headquarters, a 21-year-old drummer named Marvin Smith from Waukegan, Ill., who went to school at Berklee School of Music in Boston, met Jon Hendricks in Vermont, toured with Hendricks' bebop singing group, then decided to go free-lance in New York.

"This is the place where the most musical events happen," says Smith. "The West Coast has the most recording. But if you hang around Greenwich Village, there are 20 places you can go to hear live jazz music every night. For live jazz, New York's the place."

The major NYC clubs include:

Bradley's, University Place at East 10th Street.

Blue Note, West Third Street at Sixth Avenue.

Cookery, West Eighth Street at University Place.

Eddie Condon's. West 54th Street between Sixth and Seventh avenues.

Fat Tuesday, Third Avenue at East 17th Street.

Griffy's Plaza Cafe, Third Avenue at East 37th Street.

Lush Life, Thompson Street at Bleecker Street.

Marty's, 1265 Third Ave. at East 73rd Street.

Michael's Pub, 211 E. 55th St.

Seventh Ave. South, 21 Seventh Ave. S.

Sounds of Brazil, 200 Varick St. (lower Seventh Avenue South)

Village Gate, Bleecker Street between Thompson and LaGuardia Place.

Village Vanguard, Seventh Avenue at Greenwich Avenue.

Village West, 577 Hudson St.

West End, Broadway at 113th Street.