Concert pianist Dolores Fredrickson was desperate. Clutching the score of Prokofiev's Eighth Sonata, she raced to Chicago's O'Hare Airport to catch the next flight to New York. Arriving at La Guardia three hours later, she dashed to a phone and pleaded: "I've got to see you. Can you put me on standby?"

The crisis? Baffled by troublesome passages in Prokofiev, Fredrickson was appealing for help from her coach, the Juilliard School's celebrated Sascha Gorodnitzki. To her relief, Gorodnitzki checked his appointment book and announced, "I think I can take you the hour before dinner."

Fredrickson's pilgrimage was extravagant but not without precedent. The 74-year-old Gorodnitzki's students have been known to fly in unannounced from Texas, Montreal and even Tokyo. Though his consultation fees run to nearly $100 an hour, there are no complaints. "Do you think any of us would do this," asks Fredrickson, herself a senior faculty member at Chicago's American Conservatory, "if he weren't really worth it?"

Based on performance, the answer is obvious. In the past two years alone Gorodnitzki's students have won 40 major awards in world-class competition. Marvels Juilliard's Dean Gideon Waldrop, "It's an incredible record."

Gorodnitzki's style, like that of many successful coaches, is both supportive and intimidating. Pacing his fifth-floor studio and listening intently as Korean pianist Miryo Park prepares for a Carnegie Hall competition, he offers an uncompromising critique. "You know, it's very good, dear, but it's not wonderful," he says. "I wouldn't take money out of my pocket to hear you do it that way." Moving to the keyboard to demonstrate a passage, he urges: "You need more charm, dear: It must be a seductive phrase."

Why do pupils as accomplished as Gorodnitzki's put up with such assaults on their egos? "The difference between Sascha and other teachers," Fredrickson explains simply, "is that even more than a coach, he's an artist who can play better than any of us."

Born in the Ukraine, Gorodnitzki came to the U.S. as an infant with his parents, who founded a college of music in Brooklyn. He earned a place on the faculty by the time he reached high school, won the coveted Schubert Memorial Competition in 1930 and went on to a long and distinguished concert career. But his mastery was never as effortless as it appeared. "I would sometimes lose as much as eight pounds during a performance because I perspired so badly," he admits, "and I never wore my glasses. They would steam up so I couldn't see the keys."

At 38, Gorodnitzki was still a bachelor. ("It never occurred to me to date one of my students," he says. "I was concentrating too hard on their playing.") Then, in 1940, he met 23-year-old Virginia Henderson—a student, but not one of his. For once, Gorodnitzki's mind was not on his music. "I bought him a copy of Rachmaninoff's E-Minor Symphony," she recalls. "He gave me a perfume—Tigress." They were married two years later.

Today Gorodnitzki occasionally teaches in their seven-room apartment overlooking Central Park. An unending stream of visitors includes their photographer daughter Diane Sue, 30, devoted students and sometimes even royalty. King Gustaf of Sweden sat in on one of Sascha's classes; Princess Irene of Greece turned up at another. Gorodnitzki, however, never lets the glitter go to his—or his student's—head. When his pupil André Laplante won a silver medal at the Sixth Tchaikovsky International Piano Competition in Moscow last June, the maestro fired off a typical cable of congratulations. "Thrilled. Proud," the telegram read. "But still room for improvement."