In a way, the impact on music of Mischa Schneider, who died in Buffalo recently at 81, can be summarized in a single sentence: He was the cellist of the Budapest String Quartet. Simple as that, so replete is that statement with musical history.

Schneider, who joined the Budapest in 1930 just before its first American trip, was a commanding figure -- some would say the commanding figure -- of an ensemble that came to dominate chamber music in a way none had done before, and, probably, none has done since.

After the tour, it took less than a decade for the Budapest to assume its unique position. By 1938, the quartet was an American institution -- emigrating from Europe. And two years later it became a Washington institution, opening its 22 years as official quartet-in-residence of the Library of Congress. The Budapest's brilliant legacy was broad.

Its presence here made this city uncontestably big-league in chamber music -- opening a path toward musical maturity that continues today. Even more important, though, the unprecedented possibilities of broadcasting and recording that accompanied the Budapest's activities created a worldwide audience for the matchless literature of the quartet. That changed the face of music, and may well be the most lasting of the Budapest's many achievements.

Schneider's personality embodied two essential qualities that made the Budapest the phenomenon that it was.

One was -- pure and simple -- excellence. As Annabel Bogdonoff, one of his many friends here and Schneider's correspondent to the very end, leafed through a pile of memorabilia the other day, she mused on "Mischa's great seriousness, his great concentration."

Schneider's younger brother, solo violinist and conductor Alexander (Sasha) Schneider, who had two tours of duty as the Budapest's second violinist, referred the other day to Mischa's "extraordinary dedication of not being a soloist. He did not give a damn. For him the thing to do was to do what he had to do."

Both Sasha Schneider and Bogdonoff mentioned another side, a presence and "wit" that endeared Mischa Schneider to audiences. In an article written in 1979, Mischa described how the addition of violist Boris Kroyt in 1936 made the quartet all-Russian in origin (Schneider was born in Vilna, Lithuania). That development gave rise to the axiomatic joke, Mischa cracked, that "One Russian is a nihilist, two Russians are a chess game, three Russians are a revolution and four Russians are the Budapest String Quartet."

Sasha Schneider says the joke originated with Jascha Heifetz.

A string quartet is a curious social unit -- too small for autocracy (as in the symphony orchestra) but too large for laissez faire'. And the greatest works for quartet -- no form has inspired a higher level of production -- are like conversation at its most elevated. The players, married as they often are for the course of their careers, must tread a narrow line between individuality and order. The solution with the Budapest was to keep their lives as separate as possible. They seldom ate together or traveled together.

Joseph Wechsberg once wrote this description of the group's "contrapuntal" entrance to a New York studio: "The four arrive at the recording studio in characteristic Budapest Quartet style -- singly. Joseph Roisman the first violinist is there half an hour before starting time, pacing about with his fiddle under his chin. Mischa Schneider arrives ten minutes later, sits down, and begins meticulously tuning up his cello. The two men don't speak. Another ten minutes passes, and Kroyt arrives; he talks to everyone, and doesn't touch his viola. Alexander Schneider comes in breathless one minute late, and immediately stirs up a violent musical argument."

Last week, when Sasha Schneider, who is 4 1/2 years his brother's junior, was reached, he had just received a letter about his brother from another cellist, Frank Miller, the famed first chair of Toscanini's NBC Symphony and Reiner's Chicago Symphony.

Miller wrote, said Sasha Schneider, " 'Nobody had such dedication. Nobody could play that way.' "