Schoenberg's Sketches and the Teaching of Atonal Theory

October 1, 1980

It must be one of the effects of the Fall of Man that research and teaching, which ought to be helpmates and friends, so often fall out and when they meet at all, it is only to compete bitterly for our time and energy. This glum thought has occurred to me in the midst of grading dozens of counterpoint exercises which seem impossibly disconnected from my research into Schoenberg's compositional methods as they are revealed in his sketches. Those sketches are not disconnected from the teaching of twentieth-century music, however, and an invitation to present a paper at the 1979 meeting of the Music Educators National Conference encouraged me to formulate ways that a teacher can make use of compositional sketches in an undergraduate course. What follows is a revised version of that paper on "Comprehensive Musicianship and the Teaching of Atonal Theory."

The sketches discussed here have not been published and are therefore available at this time only to scholars qualified to use the archives at the Schoenberg Institute. My initial work has convinced me that Schoenberg's sketches require a substantial revision in our view of his twelve-tone method, and their importance will no doubt spur publication of editions and teaching texts containing those sketches essential for understanding his compositional methods.

Comprehensive musicianship in the words of one of its advocates is an integrated approach to harmony, counterpoint, and analysis through study of a variety of pieces representing different historical periods.1 The student is encouraged to comprehend these pieces—modal, tonal, chromatic, atonal—by developing a single set of analytical categories which will form the groundwork of later studies in music. Comprehensive musicianship is a laudable aim, but there is danger that the urge to comprehend all musical styles and methods will lead to misrepresentation of each one of them. This danger is most acute for atonal music because the single set of analytical categories aimed at can easily become too common a denominator, one that submerges the important and characteristic features of twentieth-century music. I want to suggest that comprehensive musicianship as a pedagogical method must embrace and include its opposite: an approach that distinguishes the categories appropriate for different kinds of music and insists that they are different.

An analogy with language may be useful. It is a commonplace now sadly seldom preached and less often followed that study of a foreign language sharpens one's sensitivity to the features and resources of one's native language. Study of atonal music similarly forces a student to put tonal music in perspective, as only one of many equally arbitrary systems for organizing sound into music. In either music or language that perspective, that fluency in a second system, raises fluency in the first. The question then is not whether to teach atonal music but how to teach it most effectively.

In the best of all possible academic worlds students would be bilingual and equally familiar with tonal and atonal literature. Equal familiarity would guarantee what Schoenberg called "comprehensibility," which in his view is determined by use alone.2 As dissonant harmonies become familiar they cease to sound dissonant; dissonance is no longer part of their meaning because dissonance and consonance are extrinsic to atonal harmony. They have meaning only in contrast to tonal expectations. We are far from Utopia, however. Our students speak one language and hear one kind of music. In fact many have a certain resistance to twentieth-century music. In order to teach atonal music effectively, we have to capitalize on this resistance, not capitulate to it. And here is the danger in comprehensive musicianship, for if we encourage students to understand atonal music in tonal terms, if we apply the same categories to both systems, we are yielding to our students' resistance and molding the music to the limitations of the audience.

I would like to pursue my analogy with foreign language, for it illustrates several essential points. First, tonal harmony is our native musical language. Children grow up immersed in it; perhaps I should say submerged in it, considering radio and television, popular music, and those mellow harmonies that soothe anxieties in elevators, banks and supermarkets. Children acquire fluency in tonal music as they acquire fluency in their native language but few of them are exposed to atonal music. Thus teaching atonal music resembles teaching a foreign language. If the analogy holds it follows that special methods are required, and I think that these will necessarily be more abstract or theoretical than the process by which both English and tonal harmony were acquired. Like language teachers we have to teach grammar and syntax and cannot rely on "what sounds right." An approach to atonal music then, however much listening it may undertake, must at bottom be theoretical.

Second, language teachers usually try to discourage translation, because a student is not fluent, nor likely to become fluent, if he must translate questions into English, formulate answers in English and then translate back. Similarly we ought to discourage translation of atonal music into tonal music. Students will never become fluent in atonal harmony if they are forever trying to find its tonal aspects or analogues.

Third, if poetry is what is lost in translation, as Paul Valéry said, real fluency in a language involves appreciating the poetry and understanding why it is lost in translation. In other words fluency implies more than the ability to speak and understand; it includes the knowledge that some languages can express ideas that others cannot. Fluency in atonal music is similarly characterized by knowing what makes it distinct from tonal music, what it can say that tonal music cannot conceive. For these three related reasons it is important to capitalize on students' resistance to twentieth-century music by confirming their suspicion that they are indeed hearing a strange new language, and that therefore they must learn a new vocabulary and grammar even to begin to understand it.

Let me give a few examples of ways to implement this approach. One will want to begin with attractive pieces; not pieces attractive because they sound like tonal music, but pieces attractive because they exploit the same effects as certain types of contemporary music. For example, the third of Schoenberg's Orchestral Pieces, Opus 16, entitled "Farben" or "Colors," will attract students because it uses contrasting timbres, an effect they will recognize from popular electronic music. The "Mysterioso" movement of Berg's Lyric Suite has effects similar to electronic feedback and will not, therefore, sound completely unintelligible though it will sound tonal.

If attractiveness must be the first criterion, the second ought to be simplicity. Melodic ideas ought to be simple but resolutely atonal. Compositions that emphasize whole-tone motives or harmonies meet this criterion well, the Debussy prélude Voiles, for example. Whole-tone structures are particularly useful because they exclude perfect fifths and therefore cannot be translated into tonal patterns. Schoenberg's Opus 33a meets this criterion of simplicity in another way. It emphasizes a group of rotated tetrachords and should therefore discourage the assumption that atonal harmonies, like tonal ones, must be limited to three pitches. Thus an attractive and simple piece has made clear the necessity of a new theoretical concept: the tetrachord. If students cannot fall back on tonal concepts to describe pieces that are both attractive and simple, they will recognize their need to acquire a new grammar and syntax if they wish to be fluent.

At this stage simple ear training exercises become valuable. These exercises might consist only of identifying the twelve types of trichords, but even that would give students mastery of the concept of total intervallic content. This concept then allows an appropriate comparison with tonal harmony, when students see that atonal music uses all twelve trichords, while tonal music uses only three or four. Tonal music comes into clearer perspective this way, I think, than if we take the opposite approach and try to describe atonal effects through tonal categories.

I have been describing the introductory portions of a course or unit on atonal music, but once students have learned the necessary theoretical concepts, the grammar and syntax of their new language, they are ready for literature and complex atonal works which may invite and perhaps even reward various kinds of analysis. It is important at this stage not to let complexity overwhelm the lessons of the simple introductory pieces and seem to authorize a reversion to tonal categories. Here is where I find composers' documents and sketches helpful, for they can make explicit and therefore convincing the intentions embodied in the music. (I should say that compositional sketches are in general grist for the mills of graduate students and research scholars, but there are sketches simple enough to make effective supplementary material in a beginning undergraduate course.)

Let me illustrate the use of sketches and documents to address three common problems which students have in learning to listen to atonal music. A recurring problem, which has recurred in my remarks, is the tendency to hear tonal centers in atonal music and to give special importance to the fifth. To discourage student suspicion that fifths are there for them to grasp, one might cite a short note Schoenberg wrote in 1923, when he was composing his first twelve-tone works.

In twelve-tone composition consonances (major and minor triads) and also the simpler dissonances (diminished triads and seventh chords)—in fact almost everything that used to make up the ebb and flow of harmony—are, as far as possible, avoided. . . . At the root of all this is the unconscious urge to try out the new resources independently, to wrest from them the possibilities of constructing forms, to produce with them alone all the effects of a clear style, of a compact, lucid and comprehensive presentation of the musical idea. To use here the old resources in the old sense saves trouble—the trouble of cultivating the new—but also means passing up the chance of enjoying whatever can only be attained by new resources when the old ones are excluded!3

This rejection of tonal intervals as structural entities—and there are many others—is confirmed by several compositional sketches. One appears in Example 1, a sketch for the Wind Quintet, Opus 26, and illustrates what I mean.4


Ex. 1: Schoenberg, Wind Quintet, Op. 26 (#1111)



This sketch shows Schoenberg exploring transpositions of the inverted chromatic scale which, when set against the chromatic scale itself, will yield a sequence of intervals which does not include fifths and octaves. He tries all twelve transpositions and when one produces a fifth or octave he circles the offending interval and crosses out the transposition. A sketch as unambiguous as this one, uncomplicated as well by a specific musical context, can go a long way toward convincing students that the structural intervals of tonal music may mean nothing in atonal music.

A second common problem is student reluctance to believe that atonal composers built their pieces on harmonies containing more than three or four pitches. It will be as difficult for native listeners to tonal harmony to believe that harmonies can have five, six, seven, or even eight pitches as for native speakers of English to believe that Eskimos recognize and name twenty-one different kinds of snow. Against doubts that composers can have intended such large harmonies to function structurally, one can set a sketch like that in Example 2.5


Ex. 2: Schoenberg, Suite, Op. 29 (#1181)



Here Schoenberg considers the simultaneous unfolding of three permutations of the row for his Suite, Opus 29, and he carefully circles the large vertical harmonies that intersect all three row forms: each circled harmony contains one trichord or tetrachord from each of the three row forms. Yet these intersecting harmonies are not limited to the three pitches that would be heard as literal simultaneities, but rather contain seven, eight, or nine different pitches. This sketch also demonstrates that Schoenberg is not merely interested in the correct ordering of a single twelve-tone row, but also in the harmonies that intersect and tie together row forms that unfold simultaneously.

A third common problem results from atonal composers' tendency to use forms associated with tonal music such as the sonata, variation, or various dance forms. With this kind of encouragement, students often resist trying to hear any forms not derived from tonal music. The kind of sketch reproduced in Example 3 can provide a useful counter to their resistance.


Ex. 3: Schoenberg, String Trio, Op. 45 (#1067)



In it Schoenberg is working out the form of his String Trio, Opus 45. He systematically determines the duration in beats and seconds of every phrase and arrives at a balance both within each part and among all parts of the composition. Notice how his measurement in seconds requires him to determine a metronome marking for each change in tempo and points to a kind of symmetry that would not be revealed by merely adding beats and measures. This example exposes a formal dimension easily missed, especially if one is looking for features characteristic of tonal forms.

To conclude, sketches such as these, normally the objects only of advanced study, can also be used effectively at the introductory level, where they can help to clarify and highlight the distinguishing features of twentieth-century music and impress on the student that he must cling to his new theoretical tools if he wants to understand even the simplest pieces.

My argument boils down to a plea that if we want truly comprehensive musicianship, we not jump too quickly to synthesis. A student who understands atonal music by translating its unique patterns and possibilities to tonal ones loses all the poetry. But a student whom we help to persevere in his struggle with the new and foreign gains the genuine perspective acquired only through fluency in a second language or a second system of composition.

1William Thomson, "Musical Analysis and Evaluative Competence," Monographs on Music in Higher Education: Papers and Reports from Conferences Sponsored by the Contemporary Music Project (1973), pp. 2 ff.

2Arnold Schoenberg, "Composition with Twelve Tones (1)" in Style and Idea, ed. Leonard Stein, trans. Leo Black (New York: St. Martin's Press, 1975), pp. 216-217.

3Arnold Schoenberg, "Twelve-Tone Composition (1923)" also in Style and Idea, p. 207.

4The sketches discussed in this article are hitherto unpublished sketch material in the Arnold Schoenberg Institute, University of Southern California, Los Angeles. They are included in Filmfile No. 5—Chamber Music, "Manuscripts of Arnold Schoenberg."

5Example 2 is a photocopy of one of Schoenberg's original sketches for the Suite, Opus 29 (no. 1181). I have added in parenthesis the row labels P3, I4, and I0.

4933 Last modified on October 25, 2018