St. Louis, unfortunately, is one of the few large cities in this country where Carter and his music are not being celebrated in a big way.

Carter periodically receives his due from Synchronia, the local ensemble that specializes in the work of living composers. This season, however, the group has opted to focus its energies on Morton Feldman and other American composers.

Once in a while - but not lately - pieces by Carter figure into the agenda of the St. Louis Symphony. They tend to appear on the chamber music events, not the orchestral concerts. The reason for that, possibly, is music director Leonard Slatkin's admitted dislike for Carter's scores; although Slatkin is one of the few conductors on the scene today who can readily meet their technical demands, he has said on several occasions that he ''just can't warm up to them.'' But who can tell what will happen? This season the St. Louis Symphony is celebrating the 10th anniversary of Slatkin's appointment a year early, so perhaps next season it will celebrate Carter's 80th birthday a year late.

It would be good if that were the case. Slatkin did conduct Carter's 1955 ''Variations for Orchestra'' in Powell Hall two years ago; whether he'd warmed up to the music or not, his interpretation seemed penetrating, and the performance was certainly enthusiastic. There's a wealth of newer Carter masterpieces waiting to be given the same kind of treatment here. The audience deserves to hear them.

The audience deserves, too, to know what to expect from the typical Carter work.

Getting back to the relationship between the composer and the St. Louis Symphony's music director, one of the more intriguing incidents in recent musical history took place in Chicago in the spring of 1984. Slatkin was conducting the Chicago Symphony in a program that included Carter's 1976 ''Symphony of Three Orchestras.'' Carter was in the audience, and he made headlines nationwide when he stormed out of the hall during a pre-performance address Slatkin was giving to the audience.

A pirate recording of Slatkin's speech soon made the rounds of music journalists. What Slatkin had to say about the score's rhythmic intricacies was accurate, and there was nothing particularly offensive about his somewhat casual manner of delivery. It was the content of the remarks in general that set Carter a-raging. As Carter later explained, Slatkin was simply off base. He focused on the wrong thing; he missed the point.

In a way, Slatkin's missing of the point is understandable.

Especially for persons who understand them, the temptation is great to discuss only the technical aspects of Carter's music. Since the 1940s, when Carter first settled into the style by which he is known today, his compositions have been filled with ''learned devices'' of the sort that whet the appetites of academically inclined commentators. But Carter's music, complex though it is, is not about complexity. Rather, it is music concerned fundamentally - and ultimately - with emotion.

Some of the impact of a Carter work derives from the solidity of its large-scale structure and from the dynamism of its small-scale fluctuations of tension and resolution. Most of it, however, results from the shape and movement of the phrases. No matter how ''intellectual'' are the combinations of notes that make up these phrases' contents, the phrases themselves are in effect gestures that seem to spring not so much from the composer's brain as from his spirit.

These musical gestures declare themselves openly and eloquently. They clash with and complement one another. They ebb and flow as forcefully as the tides of human feeling, and they lose their momentum only in dramatic pauses that in themselves are analogous to certain human feelings. The gestures are nonspecific; still, they are credible, graspable and - above all - potent.

Carter has written much about his own music and the music of his contemporaries. Interestingly, but not altogether surprisingly, most of what he has to say about his own compositions deals with tangible, more or less easily explainable technical matters. One of the few paragraphs in which he deals not with musical mechanics but with the elusive ''meaning'' of his work is found in his liner-note essay for the Nonesuch recording of his 1948 Cello Sonata. Even here, however, one is reminded that creative geniuses are typically reluctant to probe deeply into their own psyches. Carter is candid enough, but his statement less an independent declaration than a simple response to the observations of another writer.

In his 1964 book ''Music in a New Found Land,'' British critic Wilfrid Mellers prefaced his chapter on Carter with these lines from Wallace Stevens' poem ''L'Esthetique du Mal'':

Out of what one sees and hears and out
Of what one feels, who could have thought to make
So many selves, so many sensuous worlds,
As if the air, the midday air, was swarming
With the metaphysical changes that occur
Merely in living as and where we live.

Carter writes that in choosing this quotation ''Mellers draws attention to some of the main aims of my work. It is quite true that I have been concerned with contrasts of many kinds of musical characters - 'many selves'; with forming these into poetically evocative combinations - 'many sensuous worlds'; with filling musical time and space by a web on continually varying cross references - 'the air . . . swarming with . . . changes.' And to me, at least, my music grows 'Out of what one sees and hears and out/Of what one feels,' out of what occurs 'Merely . . . as and where we live.' ''

The Cello Sonata was the last work in which Carter maintained allegiance - but only in the second movement - to the traditional tonal system that had previously governed his music. It was also the first work in which he seriously explored, on his own terms, the idea of simultaneous and contrasting musical events that presumably had been in the back of his mind ever since his boyhood association with the American maverick composer Charles Ives.

Receptivity to the effect of these simultaneous and contrasting music events is crucial to appreciating Carter's music.

In his excellent and thorough 1983 book ''The Music of Elliott Carter,'' David Schiff uses kinetic words to describe certain situations in the Cello Sonata. Schiff writes that in the first movement the piano ''marches'' while the cello ''swims,'' and even when they are moving at the same speed they seem to ''collide and then bounce away from each other.'' In the finale, when ''echoes of the second and third movements'' begin to be heard, their ''backward pull'' is ''resisted,'' then yielded to until the music finally ''takes flight'' and then ''seems to sweep over a great peak.''

The language is colorful but not fanciful. Carter's music is kinetic, and therein lies its force.

It was in 1948, with the Cello Sonata, tha t Carter first realized the medium that best suited his message. Since then he has consistently held to it, even in such deliberately lyrical pieces as the 1975 ''A Mirror on Which to Dwell'' (a setting of six poems by Elizabeth Bishop), the 1978 ''Syringa'' (with text by John Ashbery) and the 1981 ''In Sleep, In Thunder'' (with text by Robert Lowell).

That the music deals with opposition of forces is obvious in the titles of many of Carter's instrumental works, in the 1961 ''Double Concerto'' for piano, harpsichord and two chamber orchestras, for example, or in the ''Symphony of Three Orchestras,'' or in the 1983 ''Triple Duo.'' But it figures just as importantly in the last three of his four string quartets - from 1959, 1971 and 1986 - and in other compositions for homogeneous ensembles.

In all of these, the building blocks are compact phrases - superimposed, juxtaposed - whose collective impact is, indeed, almost physical. When a phrase, or gesture, in a steady tempo is set against one that systematically speeds up and slows down, the listener not only hears the resistance but feels it.

The notes and rhythmic patterns that make up these compositions are, after all, just notes and rhythmic patterns; to focus one's attention exclusively on them is - as Carter so boldly demonstrated in Chicago four years ago - to miss the point.

Elliott Carter's is, to be sure, complex and rigorously intellectual. But it is also music that is profoundly, palpably expressive. It is for this latter quality that it ranks among the truly great music of the 20th century.