AS OUR CENTURY NEARS AN end, it seems a good bet that Steve Reich will turn out to be the oldest 20th-century composer in whom 21st-century musicians will find a kindred spirit.

This proposition can now be tested conveniently with the help of Nonesuch Records, which has commemorated the composer's 60th birthday with a big box of new and reissued recordings containing just about every composition on which Mr. Reich's reputation is based (79451-2; 10 CD's).

That such an item strikes a major classical label as marketable suggests that perhaps classical music is not coming to the dead end so many have predicted but rather undergoing a systemic evolution. And it is particularly fitting to honor Mr. Reich's achievement with recordings, because recordings are what made that achievement, and that evolution, possible.

To composers imbued with a 19th-century world view, artistic traditions are transmitted ''vertically.'' Nineteenth-century music historiography is an epic narrative of texts arranged in single file. It assumes that artists are primarily concerned -- whether to emulate or to rebel -- with the texts of their immediate precursors. These assumptions have led to an obsession with lines of stylistic influence, with stylistic pedigree, ultimately (and destructively) with stylistic purity or, worse, progress. This is the altogether anachronistic view most classical composers still imbibe in college or conservatory.

Mr. Reich went to college, at Cornell, but majored in philosophy. To him the main medium of musical transmission was not texts but recordings, and his view of the music surrounding him, accordingly, was ''horizontal.'' The epiphany that made him a composer, he has said, came at the relatively advanced age of 14, when he heard in close succession recordings of Stravinsky's ''Rite of Spring,'' Bach's ''Brandenburg'' Concerto No. 5 and bebop.

Someone trained to look at music in terms of vertical traditions would not have sought a common denominator here, nor would such a person, at least in 1950, have thought jazz, a largely unwritten music, to be commensurable with the others. But the common denominator leapt from the records to Mr. Reich's happily unprejudiced ear.

Stravinsky's ''Russian'' style, Bach's style and bebop are all driven and regulated by what music theorists call a ''subtactile pulse'': a strongly articulated, rock-steady rhythmic unit that lies beneath the level of the ''felt beat,'' or tactus, the beat that conductors show or that we normally walk or waltz or exercise to. (When the drill sergeant tells the platoon to march ''double time,'' he is telling it to march at the rate of the subtactile pulse.)

Most ''Western'' music of the Germanic ''common practice'' period is strongly tactile, with at best a weakly articulated subtactile component. But much music of the rest of the world -- Asian or African music; earlier, later or more easterly European music, and of course, American popular music -- is intricately coordinated at the subtactile level, allowing overwhelming cumulative processes, or fascinating asymmetrical patterning, or viscerally compelling lurches to take place at the tactile surface. (Think of the ''Danse Sacrale'' from ''The Rite,'' or the harpsichord ''cadenza'' in ''Brandenburg'' No. 5.)

Later Mr. Reich found more musics (always, at first, through recordings) that exhibited this ''rhythmic profile,'' as he calls it: West African drumming, Indonesian gamelan, medieval organum and hocket. These provided the models for the ubiquitous chug-chug-chug without which Reich would not be Reich, against which the gradually unfolding or playfully shifting surface processes of his music are measured and become intelligible.

The best early demonstration of its magic is ''Four Organs'' (1970), the first Reich piece to win a large audience, in which the systematically expanding phrases on the surface would be as uninterestingly arcane as most contemporary classical music, instead of riveting and elating, but for the maracas that sound out the subtactile pulse.

Eventually Mr. Reich went to Ghana and to Berkeley, Calif. (where Balinese gamelans flourished), to gain hands-on experience and body involvement with the styles that now fascinated him. A few earlyish pieces sound a bit like imitations of ''oriental'' musics in the manner of Cage's prepared-piano works or Colin McPhee.

But Mr. Reich's most characteristic pieces fuse everything into a unique personal idiom that arises out of the glorious assumption of an ecumenical heritage stored electronically, in which sounding music from every time and place is instantly available as part of a notional Here and Now to which we all have equal eclectic access.

At more technical levels, too, Mr. Reich's breakthroughs would have been unthinkable without recording technology. The earliest pieces that are recognizably Reichian are his ''phase'' pieces of the mid-60's. The technique was a serendipity discovered when Mr. Reich played two copies of a single tape loop through different tape recorders into the two channels in a set of headphones. (They contained the phrase ''It's Gonna Rain,'' drawn from a gospel sermon.)