Music Theory: Case for the Prosecution

July 4, 2006

By Kyle Gann

As happens, I may have inadvertently answered the question of my previous post (oh hell, I'm not going to be cute and link to it, just scroll down) by the question I threw in at the last minute: "Is there something about musical pedagogy inherently more deadening than its visual analogue?" I think a large majority of musicians would surmise that there is. Let's think about it.

My own adolescent experiences as a budding painter gave no more pleasure to anyone than did the semester I spent playing the cello, but I learned a little bit of how the game goes, and I've read some things since then. Where better to let one's little knowledge be a dangerous thing than in a blog? Correct me if I'm wrong, but beginning exercises in drawing - dividing images with grids, camera oscura, and so on - seem designed to short-circuit one's left-brain cognitive grasp of physical objects, and focus the eye on exact contours. The exercises seem stiff and arbitrary at first, but you start to see differently, and, lo and behold, at some point you glance down at your paper, and the image you've just artificially drawn looks remarkably like the bell pepper you've been staring at, trying mightily to block out your preconceptions of bell peppers. You have become a smooth conduit for that image, and your fragile personality has stepped out of the way. It's a heady feeling, and there's something eternal about it - a sense that it must have been the same thrill for Rembrandt that it is for you. Relatively speaking, the payoff doesn't take long to arrive, and afterward, as you walk along, the shapes of trees and park benches begin to translate into surprising and exact two-dimensional forms. Get excited enough by this transformation, and you buy a barn in Saugerties and become an artist.

I don't know anything about color theory or the rest of that stuff - an art historian friend once told me that a red speck thrown in somewhere will focus a painting - and I'd love for someone trained as an artist to weigh in with details. But for contrast, let's look at four types of music theory pedagogy and their effects, three of them common in all music schools and a fourth that few of us get to practice:

1. Harmony

The teaching of traditional harmony, in my experience, is the aspect of music theory that raises the most adolescent hackles. From the professor's point of view, you are grouping pitches into the basic words and sentences of a well-known vernacular, familiar from church hymns, Broadway tunes, commercial jingles, and folk songs as well as classical masterpieces. From the student's point of view, you are not building up but cutting down, limiting her to only a tiny fraction of the myriad combinations available. She's coming to college having written a soulful song about how you shouldn't hurt the one who loves you just because you see someone else in a pink sweater over a deeply-felt alternation of C-minor and A-flat-major chords, and then I come along, great, lumbering, bespectacled ass that I am, and tell her that that's not one of the chord progressions that sounds good. Well, whatever sounds good to her sounds good to her by definition; it simply doesn't fit the classical paradigm that, for reasons obscure even to myself, I'm trying to impose on her.

What is the payoff here, and when does it come? It's that you learn to mimic the effects of music ubiquitous in the ether around you. You thus become equipped with a certain practicality for pedestrian musical functions. Learn a circle-of-fifth progression with a few secondary dominants, and you could, if the opportunity arose, write a song for your friends' musical that, who knows?, could become a hit. You can, if necessary, write out a harmony for "I've Been Working on the Railroad" and "Take Me Out to the Ballgame."

For the student, this is not stellar inducement. "Take Me Out to the Ballgame" has already been harmonized. You could look it up. It's been a few decades since pop songs were particularly indebted to the circle of fifths. This is not the same thrill that it was for Bach: every piece of music Bach ever heard used this circle-of-fifth musical language, and by learning it he gained entreƩ to a world of musicians from which he would have been otherwise excluded. For the girl with the alternating triads, resolving V/vi to vi is an invitation to re-enter the Stone Age of torch songs. I feel as though I'm empowering her by teaching her how to recreate the more complex effects from music she hears; she feels that I'm crushing her spirit by forcing her to imitate music she's not interested in. And, though this couldn't be further from my intention, she will inevitably gather that I'm pressing this music on her as superior to the music she's attracted to. I realize how far my pedagogic aims have miscarried when, as occasionally happens, a student comes up and proudly shows me that they used a conventional chord progression in an original composition, as though they think this is the only kind of music I approve of.

Say instead, though, that the student is a classical cellist? Well, the incentives are even more intangible. He can read the notes in a Bach gigue just fine without knowing which are the non-chord tones. For the average classical musician theory is an idle curiosity, like knowing why the pistons fire in the car he's driving.

For the student truly destined for Broadway or Hollywood, the practical payoffs of tonal harmony - if he has not already stumbled across them by ear - may come quickly, but for everyone else they are gradual and, I suspect, exorbitantly delayed. Ten years down the road the cellist, assuming he goes professional, may be glad to understand the internal logic of the Beethoven sonata he's playing. The singer may someday find herself in a school choir job and need to write an SATB arrangement of, god forbid, "Take Me Out to the Ballgame." The would-have-been concert pianist with carpal tunnel may find herself teaching theory. I suspect that few young musicians picture themselves someday trapped in the desolate careers for which a thorough grasp of classical harmony would be helpful....

Except for composers, for whom we promise a somewhat more metaphysical set of benefits. The composer will learn what's already been done in the language of music so that he will not waste time reinventing the wheel; he will internalize a model for a complex musical language from which he can extrapolate to a new musical language of his own. Philosophically compelling as this rationale may be, it is still difficult to command a student's full attention by teaching him in great detail a musical language that we are assuring him he will never have to use - indeed, that many composition professors will tell him he's not allowed to use.

For a million reasons - including the fact that I employ historical references and underlying conventional harmonic progressions in my own music - a knowledge of theory has done me tremendous good. I doubt that many of my composer friends, drawing harmonics from digital circuitry and improvising on saxophone mouthpieces, would say the same. Occasionally I see a student's eyes light up when he raises the third in a secondary dominant and a phrase he's written comes to life, but the experience is depressingly rare. No one is more reluctant than I am to send musicians forth into the world not knowing how the language of Mozart and Brahms works, but there are times when I've wanted to withhold the study of advanced harmony, saving it only for seniors who've developed a true curiosity about it. For most musicians, it seems less an inspiration than a hazing: if you can survive the chapter on augmented sixth chords, you've proved you want to be a musician badly enough.

2. Counterpoint

For hundreds of years, until the early 19th century, the study of music theory was the study of counterpoint. (I teach only the 16th-century variety, because few of our students build up the harmonic chops to do the Baroque version, and, frankly, I'm a lot better at Renaissance. I rely on the principles of Palestrina counterpoint every time I sit down to compose, while Bach counterpoint presumes a harmonic framework foreign to my music.) Compared to the premises of harmony, those of counterpoint seem at first even more arbitrary, but there is a fun kind of reductionism to them. Students enter into them as a playful challenge, like a crossword puzzle, or Chinese checkers. As they humorously start berating themselves for falling into parallel fifths, something similar happens as with the grid in the drawing class: all their habitual musical instincts get clicked off, and they start to focus on every interval. Every detail in the music starts to mean something.

Also as in drawing, the payoff of counterpoint comes as a surprise. Given enough time and energy, at some point the student writes a 20-measure exercise, a little three-voice motet; it gets sung in class, and with a shock she recognizes that it is... perfect. No expert could prove that it was not written by Nicholas Gombert or Adrian Willaert. If she's followed the rules religiously, she can produce something that transcends her own personality, that is demonstrably correct and solid and lovely, like an elegant mathematical equasion. Unlike harmony, which always maintains a connection to subjectivity and personal feelings, counterpoint may teach her how powerful it feels to be a mere vessel. She may learn what T.S. Eliot means when he says, "Poetry is not a turning loose of emotion, but an escape from emotion; it is not the expression of personality, but an escape from personality. But of course, only those who have personality and emotions know what it means to want to escape from these things."

This payoff may feel somewhat the same way it did for Josquin. For him, though, it meant the fulfillment of his creativity and the creation of a socially useful product, whereas for the student, it remains an enticing model, but a mere exercise - a mental state to be recaptured in other, more relevant media. Counterpoint may be a dead-end thrill, with little direct application to a world in which art and self-expression have merged, but the 16th-century counterpoint class I took (from Gregory Proctor, the year I attended the University of Texas) was a turning point of my life, and I do find that students who study counterpoint before harmony enter into the latter with more understanding and less resistance.

3. Analysis of Modernist Music

Here's a heady thrill, and a quick payoff. The young musician comes to college with romantic ideas that great music is ever the result of spontaneous inspiration. But what's this? That crazy-wild passage in The Rite of Spring - it all results from only four seventh chords, all linked by the octotonic scale. That broodingly meandering fugue at the beginning of Music for Strings, Percussion, and Celesta - it actually fills out a symmetrical precompositional plan of ascending and descending fifths. That desolate atomism of minor ninths in Webern's Symphony - simply a canon of 12-tone rows. Things are not what they seem. Modernist music appears a chaos of improvisation, but beneath the surface it is more structured than ever. The young composer senses a tempting opportunity. No more waiting for inspiration to strike; one can concoct a rationally conceived, rigorous plan, realize it, and get credit for a surface bristling with apparent spontaneity.

By now, we all know what the pitfalls of this kind of thinking are, which reached a peak in the 1970s and '80s - it is easy to be so seduced into complicated underpinnings that the listener is rather malevolently left mystified. My students tend to balk at following the primrose path as far as Post-Partitions and Gruppen, and they ever surprise me by saving their greatest admiration for pieces that truly resist analysis, like Varese and the Concord Sonata. From only a handful of schools do we still need fear excesses in this direction, but now and forevermore each new generation will be required to plumb the limits for themselves. This new knowledge so flatters the composer's sense of respectable professionalism that it is likely to remain academically paradigmatic for the next century or two at least - thus all the continuing sentimentality about Ligeti, Carter, Boulez, et al as the Last Great Men.

The same analytical insights can ensue from analysis of 18th- and 19th-century music, but, for my students at least, they are less seductive. The young quite rightly plunge into music theory not for its own sake but for what they can steal for their own purposes, and the one hulking iron piece of demode bric-a-brac that never makes it off the auction-room floor is sonata form. The urgency of bringing one's themes back in the tonic key is not a motivation to stir the blood, and thus they tend to miss the subtle feats of tonal logic they could glean from Brahms and Bruckner until they return to them later in life. The premodern pieces that can excite them, in my experience, are those pervaded and rendered cohesive by motivic saturation, like the late Beethoven sonatas, the Tristan Prelude, and certain movements of Mahler. Analysis of individual works remains an encounter with subjectivity, but unlike the teaching of harmony, it never requires the professor to dissemble or hedge. The text on the page is what it is.

4. Acoustics

Underlying the patchwork discipline of harmony is a set of immutable physical facts. Multiples of a given frequency by 1, 2, 3, 4, 5, 6, 7, and so on make up the harmonic series, which one can demonstrate (not with godlike exactitude, but close enough) by running your finger up and down a piano string while striking it. In this Gibraltar of facts the student finds a comfortingly eternal solidity. The frequency ratio 3:2, a perfect fifth, yielded an intelligible consonance in Pythagoras's day 4000 years ago, and will continue to do so after the human race has perished. For many, the payoff of this mathematically inviolable knowledge is fairly immediate. Point out that 4/3 x 4/3 x 4/3 x 5/4 x 4/3 (four perfect fourths and a major third) does not quite equal 4/1 (two octaves), and every guitarist in class suddenly realizes why he can't get his ax in tune. Listen to meantone, and the prohibition against omitting the thirds of triads makes perfect sense. Teaching the acoustics of pitch, one can throw away the litany of mumbled excuses about German and Italian musicians that run through conventional theory classes. No longer is something "true" just because a human being once did it and it caught on. Numbers, for a musician, are nature.

Of course, the obvious downside (beyond the fear of arithmetic that makes this subject off-limits for some musicians) is that the teaching of just intonation finds so little cultural resonance. Its terms and definitions are not widely used, its practice is still in the experimental stage. The student who gets all wrapped up in pure tunings will grasp the vast truth underlying the disorderly history of harmony, and gain the background wisdom his contemporaries have missed - and will graduate to find that there are only 400 people in the country he can converse with, 200 of whom are weirdos.

* * * * * * * * * * * *

Then there's also Schenkerian Theory, which, since it is faith-based rather than evidence-based, I urge relegating to the religion department.

The upshot is, I think, that in studying art you've always got a home base to return to, while in studying music you're at the mercy of whatever reference point the professor has chosen. Musicians have nature in the number series, but we don't use it; we rely instead on a changing series of approximations for it and references to it arrived at by generations of poor working schlubs in response to social conditions we can no longer imagine. Those of us who have gone through the experience and survived and relatively prospered know that neither the starting point nor the road chosen really matters, you'll get to the same place anyway. The student starting out doesn't have that confidence. I'm sure there are art professors with strange theories and weird pedagogies who manage to murk up the path, but it strikes me that the young artist, starting out, gets a pretty clear view of the road ahead, and knows more or less why he is led into each new step. I don't think this is true for the music student, who sees instead a winding, circuitous route, with arbitrary conventions standing as prerequisites for things that would make more sense. The art student can be given the answer, "Because that's how the brain processes visual reality." The music student has to settle for "Because that's the way Bach or Schenker or Schoenberg or Duke Ellington or Bob Dylan did it."

Perhaps it ultimately doesn't matter. Certainly many musicians see such training as a filtering process, winnowing out the weak and uncommitted. But it does strike me that the problem is not so much in the nature of the medium as in the slow accretion of contradictory historical practices that we get stuck with through habit and inertia. Creative music, considered as a current cultural whole, and brilliant counterexamples notwithstanding, is not in a terribly impressive state. Perhaps the general level would be higher if the possibility of being pedagogically misled were not so ubiquitous; perhaps not. All I can say for sure is that, when teaching the theory curriculum in the accustomed progression, I spend an awful lot of time apologizing and making short-cuts and detours to ameliorate its deficiencies and absurdities, and I wish I didn't have to do that.

Copyright 2011 by Kyle Gann

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