"Ladies and gentlemen, I'm Clint Eastwood, and I love jazz." So begins old Stoneface's brief and humble oration towards the end of the double-CD, Eastwood After Hours, a remarkable recording of a Carnegie Hall concert held in the actor and director's honour in October last year, and released on his own Malpaso label (via Warner Brothers). What makes the album so special is not the reaching out of jazz to Eastwood or vice versa, but rather the fact that the whole enterprise is so damn good.

From the theme-tune to Rawhide to the immortal "Misty", to music from The Bridges of Madison County, to Clint himself playing piano in a heavy- rolling boogie that is eventually joined by the massed horns of the Carnegie Hall Jazz Band, everything testifies to a truly joyful event full of marvellous music.

The orchestra, led by trumpeter John Faddis, produces exactly the kind of burnished-to-a-sheen big band arrangements that such a grand occasion calls for, and the list of guest stars is as, well, starry as you would expect. There's James Moody, James Carter, Joshua Redman, the wonderful singer Jimmy Scott, Kenny Barron, Slide Hampton, Jay McShann, plus Clint's bass-playing son Kyle with a quartet, and enough strings to smother an even bigger band than the one here.

The reflections of Eastwood's own career are numerous, but sentiment is not allowed to stand in the way of the music itself. The Charlie Parker references are numerous: Charles McPherson (who played many of Parker's parts in the movie Bird) solos on "Cherokee"; James Moody plays "Parker's Mood", and Parker's first employer Jay McShann plays a mean "Hootis Blues", as well as vamping away on the Tex-Mex grooves of "San Antonio Rose", celebrating Eastwood's leanings to country as well as jazz. With McShann still sounding so spry at 88, you can't help but think what the much younger Parker might have sounded were he still around. But then, of course, there probably wouldn't have been a Bird in the first place.

The centrepiece of the album is the "Eastwood After Hours Suite", arranged by Niehaus, and featuring a beautiful, heart-rending version of Eastwood's own gorgeous composition "Claudia's Theme" from The Bridges of Madison County. The suite continues with Paul Desmond's "Take Five", before an astonishingly daring bossa-nova version of "Misty" where the band vamps endlessly on a single phrase while Faddis's trumpet solo ascends to the kind of stratospheric heights that only dogs can appreciate fully. It's stunning stuff.

Eastwood's films are full of jazz. In the first film he directed, the excellent thriller Play Misty for Me, Errol Garner's "Misty" repeats throughout the film like a magical incantation. On soundtracks for cop-capers like The Gauntlet, Eastwood took the trouble to commission jazzy scores and hired players like Art Pepper and John Faddis to play them, and he executive- produced one of the truly great jazz films, Charlene Zwerin's documentary about Thelonious Monk, Straight No Chaser (whose title tune gets a run- out on the album). He also helped to secure finance for Bertrand Tavernier's wonderful Round Midnight. And though it is undervalued as a film, the soundtrack of The Bridges of Madison County featured some of the best jazz-oldies ever heard on film, introducing millions to the rich, burbling baritone of the neglected Johnny Hartman. For that act alone, Eastwood would be worth celebrating. By introducing listeners to this album (which he co-produced) to the even greater gifts of the even more neglected vocalist Jimmy Scott, he is continuing a very worthy cause.

So Clint has more than done his bit for jazz. How fitting, therefore, for the favour to be returned in such a tasteful yet undeniably full-blooded way, giving the star his due without taking anything away from the music. As a summary of the very American virtues of the most American of musics, Eastwood After Hours just about says it all. "So you must tell your friends, and you must pass this legacy on to the next generation," Clint's oration continues, "because they have to learn to appreciate this great American art-form." Far from asking someone to pass the sick-bag, you'd be more than happy to go out and buy the thing and make Clint's day. Punk.