Mr. Babbitt, who was trained in mathematics as well as in music, was the prime architect of Serialism, an extension of the 12-tone system that predetermined not only pitch but also rhythm, duration and other elements of composition. Strict application of the technique would sever all audible links with the past. As a result, Serial music -- shorn of familiar elements like tonal center, melodic profile and rhythmic pulse -- was profoundly disorienting to the average listener.

Proponents of Serialism argued that its multiple layers of systematization were no more constraining than the conventions imposed by the tonal system. No one made more strident claims on its behalf than the French composer Pierre Boulez, for whom it had all the force of a historical imperative. ''Every musician who has not felt -- we do not say understood, but indeed felt -- the necessity of the Serial language is USELESS,'' he wrote in 1952.

The Two Histories Of 'One True Faith'

Although Mr. Babbitt and his disciples were far less dogmatic, the underlying message was clear: if you wished to be taken seriously as a composer, you had better employ Serial technique. And it is here that the parallel histories of American music arise. Tonal composers recall an era of Serial control during which they were ridiculed and their music scorned. Serial composers recall a time in which they struggled for recognition and support, and could find it only in the university.

''Serialism's most publicly aggressive proponents, early and late, presented and still present it as the only true faith,'' said George Rochberg, who was entranced by Serialism in the 1950's but re-embraced tonality in the 60's. ''As such, they have proclaimed an orthodox cultural church, with its hierarchy, gospels, beliefs and anathemas. After the end of World War II it very quickly captured and dominated American academic circles, which it monstrously and bluntly politicized.''

''Dominated'' is the key word. Many now maintain that the Serialists took over academia, insuring that their quasi-scientific method, which was ideal for the university, was the only one encouraged. As they gained prestige, the argument continues, they took control of grant-giving bodies, new-music ensembles and competitions. Everyone else was shut out, especially those reactionary tonal composers.

''There's this notion that we somehow dominated the prestigious Ivy League schools,'' Mr. Babbitt said, ''but we never dominated anything. This is propaganda. It was simply not the case. I was here at Princeton with Roger Sessions. Was there anybody then at Columbia or Yale or Harvard? The attitude was very anti-Serial. And consider how long it took most of us to get a Guggenheim, if ever, or any other award.''