There are two kinds of free jazz: one was pioneered by Ornette Coleman, Cecil Taylor, Albert Ayler, and John Coltrane and dispenses with traditional rhythmic and harmonic structures in favor of swirling, adventurous explorations of sound and spontaneity; the other is the kind that doesn't cost any money. This month there is an almost overwhelming assortment of the latter, in a variety of styles, available to jazz fans in New York. June is jazz festival month in New York with both George Wein's stately JVC (née Kool, née Newport) Festival holding forth in prestigious venues like Avery Fisher and Carnegie Halls from June 20-28, and the Knitting Factory's much more cutting edge Texaco-New York (née What is Jazz?) Festival presenting shows in a wide variety of spaces from June 16-30. While JVC favors established jazz names like Herbie Hancock, McCoy Tyner, Ray Charles, and George Benson, as well as pop stars like Aretha Franklin and Patti LaBelle, Texaco's lineup reads like a who's who of the avant-garde with artists like the Art Ensemble of Chicago, the World Saxophone Quartet, Charlie Haden's Liberation Music Orchestra, and Roscoe Mitchell, as well as the Knitting Factory's usual assortment of young trailblazers. Tickets for most of these concerts, even JVC's Carnegie Hall and Linoln Center dates, are not unreasonably priced (the cheapest seats for most shows cost as little as $15), however the sheer number of enticing bills could quickly bankrupt the serious jazz fan. Fortunately, both festivals are offering a tremendous number of free concerts featuring some of the most exciting performers in jazz. As it has for the past several years, JVC is presenting three late afternoons and evenings of free music at midtown's recently (and beautifully) renovated Bryant Park. On Wednesday, June 25, from 5-10 p.m., the James Carter Quartet heads a lineup that also includes Regina Carter and Avenue Blue. Drummers take center stage on Friday, also from 5-10 p.m., as two of the all-time greats, Elvin Jones and Roy Haynes, appear with their groups, along with downtown drummer (and Knitting Factory stalwart) Joey Baron's Baron Down and pianist James Williams' Jazz Gospel Ensemble. Saturday's eclectic bill, from 3-8 p.m., has a decidedly downtown edge to it, as Don Byron's Bug Music, Ed Palermo's Big Band Zappa, and the Thomas Chapin Trio, join the Danish Radio Big Band featuring Bob Brookmeyer and Elaine Elias. The Texaco-New York Festival features free concerts at a number of venues in lower Manhattan, as well as in the beautiful borough of Brooklyn. On Thursday, June 19, downtown saxophonist /composer / provocateur John Zorn and his group Masada bring their unique blend of screeching avant-garde jazz and klezmer to Battery Park. On Friday evening, guitarists Charlie Hunter and Gary Lucas may be seen at the South Street Seaport. The action shifts to Brooklyn on Saturday the 21st, when the wildy talented, inventive, and amusing Jazz Passengers, the Knitting Factory's unofficial house band, appear at the Prospect Park Bandshell, along with saxophonist Eric Person's sextet. Among the performers who can be seen at the World Financial Center Plaza, on the Hudson River near the World Trade Center, are two icons of Southern piano blues: New Orleans' Dr. John and his band on Monday the 23rd, and Mississippi's Mose Allison on Wednesday the 25th. Also on the 25th, in an interesting lineup, free jazz pioneer Pharoah Sanders will join rock groups Morphine and Ben Folds Five at Central Park Summerstage. Latin jazz great Eddie Palmieri brings his band to Battery Park on Thursday, June 26th. Finally, back in Prospect Park on Friday the 27th, in another very strong double bill, Kenny Barron, one of the world's truly brilliant pianists, performs in a duo with Mino Cinelu; and Dr. Art Davis, the former Coltrane bassist, teams up with veteran pianist Horace Tapscott. All in all, a great month for free jazz in New York.