Arnold Schoenberg · section 5 of 30

Consonance and Dissonance

At its lowest level, art is simple imitation of nature. But it soon becomes imitation of nature in the broader sense of the term: imitation not only of outer nature, but also of inner nature. In other words, it then represents not merely the objects or occasions that make an impression, but above all these impressions themselves, possibly without regard to their what, when, and how. Inference back to the external object that caused them may now be only of subordinate importance, because it is so indirect. At its highest level, art concerns itself exclusively with reproducing inner nature. Its sole purpose is to imitate impressions that have now, through association with one another and with other sensory impressions, entered into combinations forming new complexes, new movements. At these levels, inference back to the external occasion is almost unquestionably inadequate. At every level, imitation of the model, the impression, or the complexes of impressions is only relatively accurate: on the one hand because our faculties are limited, and on the other, consciously or unconsciously, because its medium of reproduction differs from the material or materials of the occasion, so that visual or tactile sensations, for example, may be reproduced in the medium of auditory sensations.

If even the simplest imitation of nature may rest on a complex made up of many parts, and if answering the question of the external objects after which it is modeled presents understandable difficulty, then analysis encounters insuperable difficulties when the impression upon the observing subject is taken as the starting point of investigation. Yet a true theory, as Schopenhauer shows in his theory of colors, would presumably always have to proceed from the subject alone. And just as he regards colors as physiological phenomena, “as states, modifications of the eye,” so one would have to return to the subject, to the sense of hearing, if one wished to establish a true theory of tones. Now it is neither my intention to offer such a theory, or indeed a theory of harmonies, nor do I possess the ability and knowledge to do so. I seek only to give an account of harmonies as an artistic means in music that allows direct practical application. It might, of course, happen that I achieve more along this path than I intend, since my sole aim is clarity and richness of connections in the presentation. But however little reason I would have to resent that, it is still not my purpose. And so, when I theorize, what matters is less whether these theories are correct than whether, as comparisons, they are suited to making the subject clear and giving our consideration of it perspective.

Thus I may dispense with taking the subject as the basis of my discussion for two reasons. First, because I wish to give not a theory of tones or harmonies, but only an account of certain artistic means; second, because this account makes no claim to be taken for a theory. I may therefore bring the object, the material of music, into the discussion if I succeed in reconciling what I wish to show with what is known or conjectured about it.

The material of music is the tone; what it acts upon in the first instance is the ear. Sensory perception sets off associations and connects tone, ear, and the world of feeling. Everything perceived as art in music depends on the interaction of these three factors. Even if the artistic impression has properties other than those that could be derived from each of its individual components, just as a chemical compound has different properties from the elements composing it, one is nevertheless entitled, in analyzing the phenomenon as a whole, to consider certain properties of its basic constituents for certain purposes. After all, the atomic weights and valences of the constituents also permit inferences about the molecular weight and valence of the compound. It may be untenable to try to derive everything that constitutes the physics of harmony from one of the components, say from the tone alone. Yet certain distinctive features can be deduced from it, if only because the ear, as the organ destined to receive tone, certainly has a constitution related to that of the tone somewhat as concave and convex parts that fit together well are related. But one of the three factors, the world of our feelings, eludes closer examination to such an extent that it would surely be rash to rely on the few conjectures for which observation leaves room with the same assurance as on the conjectures otherwise called science. In this sense, it matters very little whether one proceeds from a correct or an incorrect hypothesis. Both the one and the other will surely be refuted someday. All that can matter is to take as our basis conjectures that, without claiming to be laws of nature, satisfy our formal need for meaning and coherence. If it were possible to derive and interpret the phenomena, explain and solve the problems, from the physics of tone alone, it would matter little whether our physical understanding of the nature of tone is correct. It is quite possible, despite an incorrect observation taken as a basis, to arrive at correct results by inference or intuition; whereas it is by no means established that more correct or better observation must necessarily yield more correct or better conclusions. Thus the alchemists, despite their inferior instruments, recognized the possibility of transforming the elements into one another, while the far better equipped chemists of the nineteenth century upheld the now-disposed-of view that the elements could not be decomposed or changed. If this view has now been overcome, we owe this neither to better observations, better understanding, nor better inferences, but to an accidental discovery. The advance, then, was not one that occurred of necessity, not one whose arrival could be predicted on the basis of a certain amount of work accomplished, but one that occurred despite every effort: unexpected, unearned, and perhaps even unwelcome. Although correct interpretation must be the aim of all research, even though its result is almost always incorrect interpretation, this need not spoil one's pleasure in striving to interpret. On the contrary, one should be content with that pleasure as perhaps the only positive thing all the effort yields.

In this respect, then, it matters little for the interpretation of harmonic problems whether science has already refuted the function of overtones or has only begun to question it. If, as I have said, it were possible to interpret the problems meaningfully and present them clearly, even though overtone theory were false, the purpose could nevertheless be achieved, even if it emerged after some time—as need not necessarily happen—that both the overtone theory and the interpretation were false. I may attempt this with all the less anxiety because, to my knowledge, no indisputable refutation has yet been made; and since no one can examine everything for himself, I too am obliged to make do with the knowledge available for as long as I may and can believe in it. Thus in my considerations I shall proceed from the possibly uncertain overtone theory, because what I can derive from it seems to coincide with the development of harmonic means.

Once again: the tone is the material of music. It must therefore be regarded as capable of artistic use in all its properties and effects. All the sensations it arouses—these are, after all, the effects that disclose its properties—influence in some sense the form of which it is a constituent, the piece of music. In the overtone series*), which is one of its most remarkable properties, a number of more weakly sounding overtones appear after a few that sound more strongly. Undoubtedly the former are more familiar to the ear, while the latter, scarcely perceptible to it, are less familiar. In other words, the nearer overtones seem to contribute more, or something more perceptible, to the total phenomenon of tone recognized as a pleasing sound capable of artistic use; the more distant contribute less, or something less perceptible. But it is surely certain that they all contribute, more or less, and that nothing of the tone's acoustic emanations is lost. And it is equally certain that the world of feeling somehow engages with the whole complex, and thus with these too. Even if the distant overtones do not enter the awareness of the analyzing ear, they are nevertheless perceived as tone color. This means that the musical ear, though it abandons the attempt at precise analysis here, does take note of the impression. They are received by the subconscious; and when they rise into consciousness, they are analyzed and their relationship to the total sound is established. That relationship, to repeat, is this: the nearer contribute more, the more distant less. The difference between them is therefore merely one of degree, not of kind. As their frequencies also express, they are no more opposites than two and ten are opposites; and the terms consonance and dissonance, which designate an opposition, are false. It depends only on the growing capacity of the analyzing ear to familiarize itself with the distant overtones too, and thereby to broaden the concept of pleasing sound capable of artistic use until the entire phenomenon given by nature finds a place within it.

*) The pupil can demonstrate part of the overtone phenomenon by silently depressing the keys c′, e′, g′ and then striking C, and possibly the octave below it, contra-C, once, briefly and forcefully (without pedal). The tones c′, e′, g′, the overtones, will then be heard with a sound like harmonics.

What is distant today may be near tomorrow; all that matters is being able to approach it. And music has developed along a path that has brought more and more of the possibilities for simultaneous sounds contained in the tone into the realm of artistic means.

If I nevertheless continue using the terms consonance and dissonance, although they are unjustified, it is because there are signs that the development of harmony will demonstrate the inadequacy of this classification within a short time. Introducing another terminology at this stage would serve no purpose and could hardly succeed satisfactorily. Since, however, I must work with these concepts, I define consonances as the nearer, simpler relationships to the fundamental, and dissonances as the more distant, more complicated ones. Consonances arise as the first overtones and are the more perfect the nearer they lie to the fundamental. That is, the nearer they lie to the fundamental, the easier it is to grasp their similarity to it; the easier it is for the ear to fit them into the total sound, to assimilate them; and the easier it is to identify their sounding together with the fundamental as a pleasing sound “at rest,” requiring no resolution. The same should also hold for dissonances. If it does not, if the capacity of customary dissonances to be assimilated cannot be judged by the same method, if distance from the fundamental is no measure of the degree of dissonance, this is no evidence against the view advanced here. For it is more difficult to weigh these differences precisely against one another, since they are relatively small. They are expressed by fractions with large denominators; and just as reflection is needed to say whether 8/234 is greater or smaller than 23/680, while mere estimation can mislead, so estimation by the ear is equally unreliable. The endeavor to use the more distant consonances—those called dissonances today—as artistic means must therefore necessarily have led to many an error, many a detour. The course of history, as it reveals itself in what is customary about the customary dissonances, hardly leads here to a correct judgment of the actual relationships. This is demonstrated by the incomplete or peculiar scales of certain peoples, who surely may also appeal to nature. Their tones may even often be more natural—that is, more exact, more correct, better—than ours; for the tempered system, which is only an expedient for overcoming difficulties of the material, resembles nature in very few respects. This may be an advantage, but scarcely a merit.

The most perfect consonance, after the unison, is the tone that occurs earliest in the overtone series, hence most frequently, and consequently sounds most strongly: the octave. The next most perfect is the fifth, then the major third. The minor third and the major and minor sixth are in part not relationships to the fundamental, in part not in an ascending direction. This explains why the question of whether they are consonances at all could formerly remain open. By contrast, the fourth, designated an imperfect consonance, is a relationship to the fundamental, but in the opposite direction; it could therefore, like the minor third and the major and minor sixth, be counted among the perfect consonances, or simply among the consonances, as indeed sometimes happens. But here the development of music has taken a different course and given the fourth a special position. Only the following are designated dissonances: the major and minor second, the major and minor seventh, the ninth, and so forth; also all diminished and augmented intervals, thus the diminished and augmented octave, fourth, fifth, and so forth.