“Smoke” — the Upper West Side place on Broadway at 106th — is surely the most genuine, congenial and best-run jazz club in the city. It’s an intimate jazz/supper club that seats about fifty people for dinner at tight tables with another eight or 10 seats at the bar. Everything is a little cramped but in the right way. Waitresses snake merrily through the crowd; the Manhattan-size bathroom lies behind a closet door tucked between the bandstand and another door that opens onto a precipitous staircase down to the basement kitchen, up which come food porters miraculously balancing several plates. The décor is elegant, not fancy. Low light, dark wood and — for Christmas — a huge, gorgeous three-layer wreath atop the bar. Dinner at Smoke is cuisine, first-class, not just food. Executive Chef Patricia Williams produces a one-star Michelin-quality menu. While you’re happy to eat a fine meal, everyone is there for the music and behave so even if a few guidebook-driven tourists show up from time to time.

Last evening’s attraction — the Erik Alexander/Harold Mabern Quartet, featuring drummer Jimmy Cobb and bassist Doug Weiss — proved that modern jazz can still be urgent, exciting, joyous, committed, life-affirming. Eric Alexander is one of the major, most-satisfying mainstream tenor saxophonists of the era. Harold Mabern, born in Memphis, Tennessee in 1936 (yes, 79 years old) is one of the hardest-charging pianists you might have heard over the past sixty years, and a raconteur sine qua non. The taciturn, vigorous drummer is Jimmy Cobb, born in 1929 (yes, 86 years old). Cobb was almost present at the birth of bebop during the last few years of WWII, just as Louis Armstrong, born in 1901 in New Orleans, was one of the inventers of jazz (then, Dixieland) just after WWI, still playing at his death in 1971 and still doing star-turns on the Ed Sullivan Show. Doug Weiss, the remarkable bassist (raised in Chicago, fifty years old — Eric Alexander is 47), seems unremarkable until you realize how strong and inventive is his playing.

Tuesday evenings are usually given over to Mike LeDonne’s Hammond B3 organ group (a special treat for those who don’t know the organ as a jazz instrument, as a basis of soul/gospel jazz). Most evenings the music is fine but make a special trip when the Eric Alexander/Harold Mabern Quartet is the bill.