Arnold Schoenberg · section 62 of 66

8. Chromaticism and Tonality

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I am writing this section after completing the book, prompted by objections and criticisms from Dr. Robert Neumann, a young philosopher whose sharp intellect makes me extremely curious about his own work. He criticized two things. First, that the principle by which dominants are erected on secondary degrees is nowhere stated, so that one might think secondary dominants were introduced only because they derive from the church modes. Second, that I have established no relationship between the key and certain minor chords, but introduce them only generally in a schematic presentation on page 434. I find the first objection partly unfair; the second gives me an idea.

On the first point:

It is not incorrect that the principles of my presentation are nowhere stated together. The question is whether this is absolutely necessary, since they are repeatedly applied at the appropriate places. Nevertheless, I shall recapitulate them here. This will show how unified my presentation is, even though it does not arrive at a system.

The following psychological assumption is primarily fundamental: the development of harmonic artistic means is explained above all by the conscious or unconscious imitation of a model, and by the possibility that every imitation thus arising can itself become a model and be imitated again.

On the basis of this assumption, the scale is explained as a horizontal imitation, and chords as vertical, more or less faithful imitations, of the natural model: the tone. The faithful but incomplete vertical reproduction, the major triad, together with the scale, generates another, more distant reproduction: the minor triad. The remaining diatonic chords are then explained as reproductions of the triad's idea, 1–3–5, regulated and restricted by the requirements of the scale. Secondary dominants transfer the basic major triad to the secondary degrees, influenced by the model of the scale, whose seventh tone, as leading tone, is the third of a major triad. This conception also follows from another principle running through the book: the observation that a bass tone strives to assert its overtones and thus needs to become the root of a major triad. It has the advantage of permitting all the functions demonstrated by the basic triad to be transferred, reproduced, on the new secondary dominants. Above all the most important function, established as every root's strongest need: the effort to resolve into a root a fifth below. This formulation is necessary because the mistaken idea can also arise that the secondary dominant exists only for this resolution, as shown by Dr. Schenker's idea of a process of tonicization. Yet such a secondary dominant can also arise purely for its own sake, without intending to move to a secondary tonic. Once the diminished seventh chord was understood as a ninth chord on V, this idea too could be transferred to secondary degrees, to secondary dominants. The same appeared when the functions and variants of II were explained: the Neapolitan sixth, augmented six-five, four-three, and second chords, and other vagrant chords were reproduced on secondary degrees. Likewise the augmented triad, adopted from minor into major.

Then came the minor-subdominant relationships. If, as I do, one regards tonality as a possibility of the root, which in its vertical dimension already offers the analyzing ear an incredible wealth of apparently foreign combinations, it becomes possible to understand everything occurring in modulation to the third and fourth circles of fifths as bound by tonality. Reproducing the events of a modulation thus permits these nondiatonic events to be introduced within the key as well. Here I might perhaps have gone one step further by also recommending the reproduction of those connections from all degrees where this relationship alone does not produce them. But this would still not yield all triads, as is easily verified. I shall show later how this nevertheless becomes possible.

The principles of my presentation cannot be discussed without recalling certain ideas gained through polemic and applied for polemical purposes. Although negative in nature and therefore not themselves foundational, they are no less fruitful than positive principles. If they do not themselves form the foundation, they have cleared a place for one. They are: 1. The demonstration that the teaching of musical composition does enough when it is purely the teaching of craft, without regard to a natural system or aesthetics. 2. The recognition that consonance and dissonance differ only in degree. 3. The demonstration that the supposed three laws of dissonance treatment—descend, ascend, or remain—have long been overtaken by the already very old reality of a fourth law: or leap away. 4. The thesis that there are no tones foreign to harmony, only tones foreign to the system of harmony.

Taken together, all this yields, though not in a closed systematic presentation, what art has already produced: the possibility of understanding more distant, many-voiced combinations as artistic resources of harmony. This is as far as I have come. I know that I cannot go further, and say so often enough in this book.

Now to the second criticism.

This is justified, for I have indeed shown no relationship for a series of minor chords. In C major these are the minor chords on D-flat, E-flat, F-sharp or G-flat, A-flat, and B. I do not believe that a direct, immediate relationship between these chords and C major can be demonstrated. But thanks to this objection, several ways of showing indirect relationships have occurred to me.

The first possibility is the one already demonstrated when introducing secondary dominants: occasionally replacing G–B–D with G–B-flat–D, a major triad with a minor triad. Since the major triads on D-flat, E-flat, and A-flat were introduced through the minor-subdominant relationship, the one on G-flat already occurred as an imitation of the Neapolitan sixth on V in major and minor, and the one on B is a secondary dominant on VII—B–D–F-sharp could incidentally also be modeled on II of A minor—this would be one way to establish the relationship. Indeed, in 290 at NB I find the sixth chord E, or rather F-flat,–A-flat–D-flat as a passing formation toward the Neapolitan sixth.

A second way would be to exploit the minor-subdominant function of IV. I have an objection to this, though not a very weighty one: it troubles me that this would be the function at the second fifth below, which is not very compelling because two fifths above it oppose it. But since these are more distant relationships, this carries little weight. This relationship would not provide everything missing, but it would supply some things: the minor chord on E-flat and the major chord on G-flat. Combined with the first method, however, it also introduces D-flat, A-flat, and G-flat as minor chords. This double relationship can only benefit these more distant relatives of the key.

A third and more significant way would be to carry out an idea already mentioned in this book: to base the discussion not on the seven tones of the major scale but on the twelve of the chromatic scale. Such a theory might begin as follows:

I. The material of all formations produced by combining tones is a series of twelve tones. The fact that twenty-one note names appear here and that they are presented from C corresponds to and arises from our imperfect notation. A more perfect notation will know only twelve note names and assign an independent sign to each.

II. From these twelve tones, various scales can be formed, in historical and pedagogical order: 1. twelve sets of seven church modes; 2. twelve major and twelve minor keys; 3. a number of exotic keys and the like unused or rarely used in European art music, among which the two whole-tone scales, potentially referable to twelve roots, are best included; 4. twelve chromatic keys; 5. one chromatic key.

III. To achieve stylistic and formal coherence, the particular qualities arising from the premises of each series of tones are clearly developed: laws of tonality.

IV. Tonality is expanded: a) through mutual imitation and reproduction, the keys become more alike; b) what is similar is regarded as related and, under certain conditions, treated as identical—for example, chords over the same root.

V. The reduction of the eighty-four church modes to twenty-four major and minor keys, and the development of the relationships among these twenty-four keys, takes place: 1. Horizontally. a) Relationship based on chords of identical or similar construction divides the church modes into major-like and minor-like modes.

b) Mutual imitation of cadences allows major to absorb everything from the major-like church modes and minor everything from the minor-like ones, and later brings major and minor so close together that they resemble one another except at the beginning and end. c) Of the seven times eighty-four, or 588, triads of the church modes—partly different, partly merely differently related—a large portion consisting of the same tones is referred to a smaller number of keys. This leaves seven times twelve, or eighty-four, chords referred in two ways, major and minor, each of which nevertheless appears in several major and minor keys. d) The chord relationships mentioned under a), and e) those based on a common root, bring closer together the keys one, three, and four steps apart around the circle of fifths. f) The smaller number of boundaries and the simplified character of the keys; the continuing ambiguity of chords and scale segments; the diminished triads and corresponding seventh chords arising from the constraint of the scale—a free reproduction of the natural triad—and their imitation on other degrees also bring the more distant keys closer together: those two, five, and six steps apart around the circle of fifths.

2. Vertically. The vertical relieves the horizontal through the use of four- and five-part sonorities. Since a seventh chord contains four tones of the scale, it contributes one-third more to tonal characterization than a triad; a ninth chord contributes two-thirds more.*

* Properly understood, chords with more voices and genuine polyphony do not serve to make an otherwise uninteresting piece modern, but to accelerate the pace of presentation. The art of language seeks to express thoughts clearly and comprehensively with the fewest words, chosen, weighed, and placed according to their weight of meaning. In addition to the weight of meaning of its smallest components—tone, succession of tones, motive, figure, phrase, and so on—music has one further means of economy at its disposal: the possibility of simultaneous sounding. Perhaps this is why it says more to everyone than the other arts do. In any case, viewed this way, the value of the achievements of our music today is unmistakable and independent of contemporary taste. The method may change; the goal remains.

VI. The transition from twelve major and twelve minor keys to twelve chromatic keys. This transition occurs in Wagner's music, whose harmonic significance has by no means yet been established theoretically.

VII. The polytonal chromatic scale.

Through point V inclusive, this presentation corresponds to the course of my book. I go no further for various reasons stated in different places. Here I should like to add another. I believe that no further development of the theory of harmony can be expected at present. Modern music, which uses chords of six or more parts, seems to be at a stage corresponding to the first epoch of polyphonic music. Accordingly, one might reach a judgment about the construction of chords through a process resembling figured-bass notation sooner than attain clarity about their function through methods of referring them to degrees. For apparently, and this will probably become increasingly clear, we are turning toward a new epoch of polyphonic style. As in earlier epochs, the combinations of tones will result from voice leading: justification through melody alone!