Christopher Keene likes to tell the story about being in London for composer Aribert Reimann's violent operatic setting of what is itself a violent play, Shakespeare's "King Lear." An old woman, who sat next to him, got increasingly agitated throughout the performance and, as it ended, seemed to pass out.

"Are you all right, madam?" Keene asked."I'm more than all right, dear boy," the old woman told him. "I'm bloody marvelous. I especially loved the part where they tore out his eyes."

"That's opera in a nutshell," said Keene as he tore hungrily into a steak - cooked rare - at dinner. "It (opera) is all the primal emotions: money, power, sex, love, revenge, cruelty and hate."

Keene, who conducts the Baltimore Opera Company's production of Offenbach's "Tales of Hoffmann," is perhaps the second most important person in America's operatic world. Last month the 42-year-old musician succeeded Beverly Sills as general director of the New York City Opera, the country's second most important house. Only conductor James Levine - Keene's opposite number at the Metropolitan Opera - has more clout.

Keene came to his new job after 20 years of conducting at City Opera, including four of them, from 1982 to 1986, as its music director, and no one is better prepared to bring it into the 1990s.

But when his appointment was announced in September, it was greeted with a certain amount of surprise. Keene is at once one of the most familiar figures on New York area podiums and one of the most criticized. While Keene gets positive reviews outside New York, he has consistently - with the possible exception of the New York Philharmonic's music director, Zubin Mehta - been the favorite whipping boy of the music critics of The New York Times.

No one disputes the energy and enthusiasm that Keene brings to new works or to undeservedly neglected ones.

He put together a much-praised performance of Wagner's "Ring" tetralogy on a shoestring budget at Artpark, the summer festival near Buffalo, N.Y., with which he has been associated since 1974. He made a celebrated City Opera debut in 1970 with the premiere of Alberto Ginastera's challenging and complex "Don Rodrigo." He led Alban Berg's "Lulu" in collaboration with film director Roman Polanski.

He has performed Philip Glass' "Satyragaha" and "Aknahten," Reimann's "Melusine" and Hans Werner Henze's "We Come to the River." He has revived Frank Martin's "Vin Herbe" and Heitor Villa-Lobos' "Yerma." On symphonic podiums, he regularly champions such composers as Franz Shreker, Eduard Tubin, William Schuman, Henry Cowell and Roger Sessions.

As even Henahan has written, "Nobody ever accused Mr. Keene of being a young fogy."

But Keene has not apparently lost his interest in such bread-and-butter staples of the repertory as "The Tales of Hoffmann."

Keene is one of the most literate musicians around and perhaps the only conductor who can claim to have read most of the works of E.T.A. Hoffmann, the great 19th-century German fabulist upon whose bizarre and grotesque stories Offenbach and his librettists based their opera. Offenbach was the greatest composer of light music of his time, and there are listeners who look down at "Hoffmann," the composer's only attempt at a grand opera.

Keene is not among them, however. He points to the opera's cornucopia of remarkable songs and its sustained lyricism.

"The people who look down at Offenbach are probably the same ones who look down at Gershwin's `Porgy and Bess,' " the conductor says. "But if one mark of greatness is the ability to create music that remains in the mind long after we've heard it, then Offenbach and Gershwin are among our greatest composers."

Keene has always attacked administrative duties with enthusiasm, energy and skill. Next year, 10 years after he founded the Long Island Philharmonic, he will leave that institution as one of the nation's flourishing regional orchestras. In nine years (1975-1984) as music director of the Syracuse Symphony, he brought the orchestra from obscurity into prominence. And during his four-year tenure as the City Opera's music director, the level of its orchestral playing made a quantum jump.

Perhaps what Keene suffers from are the expectations raised by his early career. He is a member of a brilliant generation of American conductors - Leonard Slatkin, Michael Tilson Thomas, James Levine and the late Calvin Simmons are some of the others - of whom much was expected because so much had been given.

"We were the lucky ones," Keene admits. "We got to important American podiums without the European apprenticeships that even slightly older conductors . . . had to serve."