Around the middle of the last century, the musical vocabulary of western art music broadened, or loosened - some might even say decayed - to the point where the listener lost the sense of a home key (tonality), or even of a special relationship between any two chords (functional harmony). All twelve notes of the chromatic scale were given equal weight. Harmonies were extended to include notes traditionally thought of as dissonant, without necessarily bringing any resolution of the tension. Listeners were to be re-educated to stop expecting a note or chord to resolve in a certain direction, to cease being surprised when they did not, and finally to accept whatever they heard without conscious reference to a system of rules.
Musical structures were related to a twelve-tone series (tone row), ordered in a sequence of intervals whose distinctiveness allowed it to be transposed into other keys, flipped backwards and/or upside down, combined in chords, distributed across an enesemble of instruments, plugged into rhythmic patterns, etc., while retaining its identity. "Serialism" was born, and some of its disciples vied with each other to achieve a transcendant state of atonality. Such composers brainstormed ways of ordering a tone-row so that none of its permutations (inversions, retrogrades, etc.) or six-note segments (hexachords), or four-note ditto (tetrachords), could be combined in a manner that even remotely suggested tonal harmony. Their quest for atonal rigor resulted in unreadably dense music theory texts, mined with such words as semicombinatoriality.
Listening to some serialist music can require a degree of mental discipline akin to doing Zen meditation on a commuter train during rush hour. I once borrowed the complete works of Anton Webern from the library - they fit on a set of 3 CDs - and poured over the scores while listening to them on a boom-box during an evening on lobby duty when I was a dorm monitor in college. The music had a noticeable effect on traffic passing through the lobby. One student finally came forward and asked: "Why are you punishing us like this?" I couldn't wholly disagree with his opinion of Webern's music. I was trying to understand it. But it required a lot of work on my part, and it gave scant rewards in return.
Admittedly, serialist music wasn't helped by the sketchy performances captured on recording, especially in the early years of the movement. One gathers that it didn't sound the way the composers intended, at least until a new generation of musicians developed the performance techniques demanded by the music. Besides, there are many approaches to serialism. Some of them aren't as strict in their mathematical precision, erring on the side of expressiveness and textural transparency. Alban Berg, Arnold Schoenberg, and other notable serialists wrote music that was, above all, musical, music that has moved audiences emotionally and that I have personally enjoyed.
But I think their doctrinaire devotion to atonality got in their own way. I'm sure many musicians and composers felt likewise. Only thus can you explain the story one of my college profs (also a professional composer) once told me. He said he was driving along I-10 in the Los Angeles area when he heard a radio personality interviewing a disciple of Schoenberg who declared that serialism was dead. On hearing this, my prof-to-be pulled his car onto the shoulder, stepped out and gave the horizon a round of applause. For too long, serialism had been a force of musical orthodoxy, apart from which no modern composer could be taken seriously. Many composers were delighted to see it fall.
Happily, I have lived in times when tonal music is making somewhat of a comeback. I think there are good reasons to encourage the return of tonality and functional harmony to the world of fine-art music. And those reasons aren't simply a reactionary retreat to the past. Without necessarily offering an original thought, let me try to put the main reasons out there for musical laymen to consider.
First, there's the matter of how music enters the human mind, how our mental apparatus receives it and perceives it. I am with those who think that a system of twelve equal tones, without an intrinsic hierarchy, is incompatible with the human brain.
Second, with a hierarchical system of tonality comes, inevitably, a system of functional harmony. This chord leads, by a natural progression, to that chord. Depending on which direction the chord-progression moves, one can get a sense of the music either pulling uphill or relaxing downhill, turning unexpected corners, glimpsing distant vistas, or settling down at home. Unexpected notes (dissonances) and delays in resolving them generate tension. Chords whose notes could be arranged as a stack of thirds (triads, and to a lesser extent their extended forms such as seventh and ninth chords) offer the largest and most diverse range of harmonic choices of any harmonic system, a remarkable variety of possible sonorities that included twelve different major triads, twelve minor triads, twelve diminished, and (if you must know) four augmented triads, each susceptible of up to two "inversions" (i.e., you can make them sound like a different chord just by putting a different member of the triad at the bottom). Extended triads and their inversions allowed even more color and variety. The functional progressions between all these chords gave music a sense of direction that could be modulated in a huge number of ways.
Compare this system of functional triads to, say, the late-late-tonal harmony of Scriabin. Scriabin leaned heavily on certain sophisticated chords, sophisticated compared to the humble triad. But such a chord used up so many of the available notes that it was basically the same no matter how you turned it, and it could only be transposed into one or two keys before the transpositions started repeating themselves. You could fill an entire symphony with such advanced chords, and have as a result much less harmonic variety, and a much weaker sense of the physics of chords pushing and pulling this way and that. A Scriabin symphony could therefore have very sophisticated chords in it, yet be (from a harmonic standpoint) relatively static and even monotonous, compared to the way triadic harmony was used to increasingly vibrant effect between the heyday of Haydn and the time of, let's say, Brahms. I think, after that point, tonal harmony continued to be used effectively but, as its vocabulary became broader and more inclusive, the grammar of functionality broke down.
Three is a holy number, so I'll stop at three main reasons why I think tonality and functional harmony are essential to make new music as powerful as it can be. But it's a view that, I anticipate, will provoke a lot of dissent and debate. After all, even the argument that hierarchy is essential to musical perception (Reason #1) remains a hot topic for debate, and I'm sure the directionality/variety argument (#2) is a pill some will have a hard time swallowing. But this one really takes the cake. Let me know what you think about it in the Comments, but don't expect me to change my opinion. I think - here it comes - that tonal music better reflects a confession of faith in an all-creating God, who has ordered the cosmos according to a rich design; and that He has given His creation a perceptible structure in which everything has its rightful place, both obeying laws built into its design and continually revealing new facets (mysteries). And I think atonal serialism, at bottom, suggests a random universe where anything can happen, given enough time - a world in which meaning is imposed by the mind of the observer, by analogy to itself and by means of the perceptive filters that selectively interpret or ignore the sensory data that flood into it. In short, I would choose tonality, even if it went against the intellectual orthodoxy du jour, as a confession of my faith and an extension of my worldview.