Including the late-night sessions in various glitzy Art Deco clubs on the south end of Miami Beach, more than 50 concerts took place between held Dec. 2 and 4. Beyond that, the local National Public Radio station offered special programming, a series of 13 commissioned works aired daily between 2 and 3 p.m. and between 11 p.m. and midnight. Site-specific sound installations were placed in the sculpture court of Miami's Center for the Fine Arts, at the Miami Space Transit Planetarium and at most of the stations of the downtown monorail system Miamians call the People Mover. An on-going exhibit of new music videos was screened at the Miami Public Library. On the fourth-floor terrace of Miami-Dade Community College, panel discussions dealt with such thorny issues as post-modernism in music, opera in the late 20th century and technology in the musical vernacular.

The Miami version of New Music America left much to be desired in matters of punctuality, documentation and amenities of some of the venues. But it easily met two of the criteria by which any festival should be measured. The schedule was full enough to leave even the hardiest of listeners feeling exhausted; it also left them feeling more than a little frustrated, because to take it all in was logistically impossible.

Worn out yet unsated as I headed for home after a five-day indulgence, I pondered the diversity of the works I'd heard. It seemed not nearly so overwhelming as when - nine years ago, in New York - I soaked up the offerings of the first of these annual showcases of new and experimental music.

The question-and-answer session of the Dec. 7 panel titled ''Post-Modernism/Post-Minimalism'' came to mind as I settled comfortably into the hum of the airplane engines.

''But why do we need to put labels on things?'' asked an audience member who was probably a composer of maverick persuasion.

''We need labels so we can talk about things,'' replied panelist Sally Banes, a dance historian and author of ''Terpsichore in Sneakers,'' the most authoritative book to date on the post-modern movement in choreography. ''Labeling is what critics do,'' she said. ''We look at what's out there. We sort it and categorize it. It's like going into the wilderness and drawing a map; if we do it right, it helps other people find their way.''

What has changed, I concluded, is not so much the musical avant garde as my approach to it. With experience has come a greater facility in sorting things out, in labeling, in drawing the maps. To identify what it is that makes a certain composition a success, of course, remains as difficult as it ever was. But it seems easier now to pinpoint the common denominators, to hear the threads of style and aesthetic that link one piece with another.

With that in mind, it struck me that there are four trends manifest in the 60 or so works I heard in Miami. And these four trends - apparent not just in the New Music America fare but in new music wherever it's found - can be split into two primary currents, each of them a kind of bi-polar thing made up of tendencies whose means are similar but whose ends are quite opposite.

One is a continuation of the current - the mainstream, really - that has flowed through Western music since the Middle Ages.

Simply stated, its premise is that a work of music is something in which almost all of the elements are specified by the composer. Improvisation, if it enters into this music at all, is controlled and limited. To perform the work means to follow the instructions contained in the written score; according to some aestheticians, if the instructions are not precisely followed, then the piece has not in fact been performed.

The other primary current - the mainstream in most non-Western cultures and introduced to the West by way of jazz and blues - involves music that is for the most part not notated.

That division - into music that is notated and music that is not notated - is simple, and at first glance it seems the differences are slight. But it gets complicated when you start thinking about what might be the essences of these two kinds of music.

Here's a theory to try on for size, just for fun:

A composition that holds to the traditions of Western music is not so much a sonic as a quasi-literary ''object.'' The performance is a mere realization of an artistic concept that exists, in its purist form, on paper. There is but a single, immutable ''object'' we can call, for example, Beethoven's Ninth Symphony, and all the performances of it are just so many attempts to translate its true material - its ideas - into audible sound.

Non-notated music, on the other hand, exists not as an ''object'' but as an activity. Since the composition is to an extent spontaneous, the performance is the piece; if it were recorded and later written down in note-for-note detail, the resulting document would be a mere transcription of ideas that existed in their purist forms only at the moment of their creation.

Now, for even more fun, here's another theory:

Some music makes sense. In other words, it's designed so that its events unfold in what might be perceived as logical order. There's a cause-and-effect relationship between the music's various components. The listener, presumably, can understand this relationship at least somewhat; he has a grasp of the music's language, so to speak, and thus he can follow its argument.

But some music doesn't make sense, at least not in the usual way. Instead of presenting an argument to the listener, it presents only a sonic phenomenon. Instead of getting out of this music something of what the composer has put into it, the listener gets only what he's able to extract from it on his own; what matters is not the music per se as the listener's personal involvement with that music.

In Miami, then, there was notated music that developed along traditional lines as well as notated music that had the effect of floating in timeless space. And there were goal-oriented improvisations as well as Dadaistic improvisations whose entire reason for being, it seemed, was to make noise.

Naturally, failures outnumbered successes in all four categories. Still, for better or for worse, just hearing all this stuff amounted to a good experience. After all, what better way is there to keep tabs on what's happening around the country, or to get a taste - as the Miami festival unprecedentedly allowed one to do - of new music activity in Latin America?

The collective experience was a good one, but the real pay-off of this late autumn trek to sunny Miami came with some of the pieces that - whether notated or not - put the burden of responsibility on the listener.

Along with the homage to Latin America, one of the festival's themes was the work of the late Morton Feldman, and surely the festival's high point was the Dec. 5 performance by the Kronos Quartet of Feldman's 1983 String Quartet No. 2.

If taken at the prescribed tempo, the piece would last more than six hours; the Kronos group played it in a mere four hours and seven minutes, but that was long enough to make the event seem more like an exercise in meditation than a concert. Like the other Feldman works on the festival agenda (the 1983 ''Crippled Symmetry,'' the 1978 ''Why Patterns,'' the 1984 ''For Philip Guston''), the Quartet No. 2 is an example of music in which every detail, every nuance, is precisely spelled out in the score. Yet it is music totally devoid of rhetoric, music whose delicate and beautiful combinations of pitches exist not to make a point but only to exist.

To be bored by Feldman's music is to miss the point entirely, and likewise with Yasunao Tone's multi-media ''Molecular Music,'' Alvin Lucier's ''Silver Streetcar for the Orchestra'' and John Cage's ''Five Stone Solo.''

Tone's piece is a blend of film and electronic music triggered by the light of the movie projector dancing over photo-electric cells. The film is perhaps over-loaded with visual imagery, but the music - although loud and scratchy - is so consistent in texture that eventually it functions like a balm for sore ears.

Lucier's oddly titled ''Streetcar'' consists of little more than 20 or so minutes of incessant banging on a triangle. But what a fascinatingly complex sound comes from this simple instrument, especially when the player's free hand hovers closely around its vibrating legs. Percussionist Brian Johnson looked as though he were ''mesmerizing'' the triangle, and in the process he cast a potent spell over most of his audience.

Even more sublime was the ''Five Stone Solo,'' authored by Cage even though its actual content is doubtless attributable less to Cage than to Michael Pugliese, the percussionist who premiered it. Pugliese's and Cage's medium was a set of five double-mouthed earthenware jugs that emitted, when gently tapped and caressed, surprisingly liquid tones, and their format was an overlay of quiet improvisations both live and pre-recorded. It lasted 45 minutes, and its lengthy silences seemed as precious as its occasional moments of sound.

Cage is the iconoclast American composer who long ago said that anything could be music, as long as you listened to it attentively.

Feldman, although he had been closely associated with Cage since the 1950s, never went along with that idea. For Feldman, music was not something you found but something you created, and he preferred to be always in control of what his audience heard. The more I encounter Cage's music in performances at which the composer is present, the more I'm convinced that Cage - his statements about the virtues of happenstance to the contrary - likewise exerts an extraordinary amount of control over every detail of music that bears his name.

I thought about all this, and about the fun-and-games theories presented above, as I was flying back to St. Louis.