Call it the rebirth of the cool. To most people, jazz's '50s heyday seems as dead as Coltrane. But in the '90s, the music is far from past tense-the names have just changed. Here's a clip-and-save guide to the next generation of jazz's young lions, all of whom are based in New York: JOSHUA REDMAN: Age: 25 Style: The Harvard-educated tenor saxophonist and son of jazz great Dewey Redman got a perfect score on his LSATs. And on his first CD, he sounded like someone who would-soulless and a bit too clean. But lately Redman has shown a rich, velvety side to his music that makes him the young tenor to watch. Philosophy: ''I'm conscious of jazz's tradition, but I try not to be too backward-looking. I want to play music for people living today.'' Recommended Album: His third and best, MoodSwing (see review on page 60).

ROY HARGROVE: Age: 24 Style: The trumpeter, discovered at 16 by Wynton Marsalis, is equally at home spurting out furious flurries of notes with the rat-a-tat sound of a '60s Freddie Hubbard, or finessing the occasional come- hither bluesy ballad. Philosophy: ''I just try to sing through my instrument.'' Recommended Album: With the Tenors of Our Time, where Hargrove's sound is more mature, thanks to the presence of guest sax greats like Joe Henderson.

WALLACE RONEY: Age: 34 Style: Roney has been labeled a Miles Davis wannabe by jazz critics, and his long, sad, open notes do sound a lot like his mentor's did during the mid-1960s. But that glib description only sells this accomplished trumpeter short. Philosophy: ''I want to take what he (Davis) saw in me and justify that in my playing.'' Recommended Album: Misterios, on which Roney interprets ballads and Brazilian tunes to the accompaniment of strings.