Schoenberg's Harmonielehre

it is entirely possible that in spite of an observation falsely construed as fundamental we may, by inference or through intuition, arrive at correct results; whereas it is not at all a proved fact that more correct or better observation would necessarily yield more correct or better conclusions.

Thus, the alchemists, in spite of their rather poor instruments, recognized the possibility of transmuting the elements, whereas the much better equipped chemists of the 1800s considered the elements irreducible and unalterable, an opinion that has since [Carter, p 20] been disproved.

If this view has now been superseded, we owe this fact, not to better observations, nor to better perception, nor to better conclusions, but to an accidental discovery.

The advance, therefore, did not come as a necessary consequence of anything; it could not have been predicted on the basis of any particular accomplishment; it appeared rather in spite of all efforts, unexpected, undeserved, and perhaps even undesired.

Now if the correct explanation must be the goal of all inquiry, even though the explanation does almost always turn out to be wrong, we still do not have to allow our pleasure in searching for explanation to be spoiled.

On the contrary, we should be satisfied with this pleasure as perhaps the only positive result of all our trouble.

From this point of view it is thus of little importance for the explanation of harmonic problems, whether science has already refuted the function of overtones or only raised some doubts.

Should one succeed, as said, in defining the problems sensibly and presenting them intelligibly, even though the overtone theory be false, then the goal could still be reached - even if it turned out after some time that both, overtone theory and explanation, were false (but this outcome is by no means inevitable).

I can make the attempt with so much the more confidence since, as far as I know, no one has yet refuted the theory beyond all doubt; and since no man is able to examine and prove everything himself, I, too, have to get along with the existing knowledge as long as I may and can believe in it.

Therefore, I will proceed in my study from the possibly uncertain overtone theory because what I can deduce from it seems to agree with the evolution of the harmonic means.

Once again: the tone is the material of music.

It must therefore be regarded, with all its properties and effedts, as suitable for art.

All sensations that it releases - indeed, these are the effedts that make known its properties - bring their influence to bear in some sense on the form of which the tone is a component, that is, on the piece of music.

In the overtone series, which is one of the most remarkable properties of the tone, there appear after some stronger-sounding overtones a number of weaker-sounding ones.

Without a doubt the former are more familiar to the ear, while the latter, hardly perceptible, are rather strange.

In other words: the overtones closer to the fundamental seem to contribute more or more perceptibly to the total phenomenon of the tone - tone accepted as euphonious, suitable for art - while the more distant seem to contribute less or less perceptibly.

But it is quite certain that they all do contribute more or less, that of the acoustical emanations of the tone nothing is lost.

And it is just as certain that the world of feeling somehow takes into account the entire complex, hence the more distant overtones as well.

Even if the analyzing ear does not become conscious of them, they are still heard as tone color.

That is to say, here the musical ear does indeed abandon the attempt at exact analysis, but it still takes note of the impression.

The more remote overtones [Carter, p 21:] are recorded by the subconscious, and when they ascend into the conscious they are analyzed and their relation to the toatl sound is determined.

But this relation is, to repeat, as follows: the more immediate overtones contribute more, the more remote contribute less.

Hence, the distinction between them is only a matter of degree, not of kind.

They are no more opposites than 2 and 10 are opposites, as the frequency numbers indeed show; and the expressions "consonance" and "dissonance", which signify an antithesis, are false.

It all simply depends on the growing ability of the analyzing ear to familiarize itself with the remote overtones, htereby expanding the conception of what is euphonious, suitable for art, so that it embraces the whole natural phenomenon.

What tody is remote can tomorrow be clsoe at hand; it is all a matter of whether one can get closer.

And the evolution of music has followed this course: it has drawn into the stock of artistic resources more and more of the harmonic possibilities inherent in the tone.

Now if I continue to use the expressions "consonance" and "dissonance", even though they are unwarranted, I do so because there are signs that the evolution of harmony will, in a short time, prove the inadequacy of this classification.

The introduction of another terminology at this stage would have no purpose and could hope for little success.

Since I still have to operate with these notions, I will define consonances as the closer, simpler relations to the fundamental tone, dissonances as those that are more remote, more complicated.

The consonances are accordingly the first overtones, and they are the more nearly perfect the closer they are to the fundamental.

That means, the closer they lie to the fundamental, the more easily we can grasp their similarity to it, the more easily the ear can fit them into the total sound and assimilate them, and the more easily we can determine that the sound of these overtones together with the fundamental is "restful" and euphonious, needing no resolution.

The same should hold for the dissonances as well.

If it does not, if the ability to assimilate the dissonances in use cannot be judged by the same method, if the distance from the fundamental is no measure of the degree of dissonance, this is even so no evidence against the view presented here.

For it is harder to gauge these differences precisely, since they are relatively small.

They are expressed by fractions with large denominators; and as it requires some thought to say whether 8/234 is larger or smaller than 23/680, because a mere estimate can lead one astray, the mere estimate made by the ear is just as undependable.

Efforts to make use of the more remote consonances (today called "dissonances") as artistic means thus led necessarily to many an error, to many a detour.

The way of history, as we can see it in that which has actually been selected by practice from the practicable dissonances, hardly leads here to a correct judgment of the real relations.

That assertion is proved by the incomplete or unusual scales of many other peoples, who have, nevertheless, as much right as we to explain them by appeal to nature.

Perhaps their tones are often even more natural than ours (that is, more exact, more correct, better); for the tempered system, which is only an expedient for overcoming the difficulties of the material, has indeed only a limited similarity to nature.

that is perhaps an advantage, but hardly a mark of superiority.

[Carter, p 22:]

The most nearly perfect consonance (after the unison) is the first tone of the overtone series, thus the one that occurs most frequently, consequently the strongest: the octave.

The next most nearly perfect are the 5th and the Major 3rd.

The Minor 3rd and the Major and Minor 6ths are, in part, not relations of the fundamental, in part, not relations in the ascending direction.

That explains why it used to be questioned whether they are consonances at all.

On the other hand, the 4th, known as an imperfect consonance, is a relation of the fundamental, but in the opposite direction; it could, therefore, be counted with the perfect consonances, in the same sense as the Minor 3rd and the Major and Minor 6ths, or simply with the consonances, as indeed often happens.

but the evolution of music has gone a different way here and has given the 4th a peculiar position.

Only the following are designated as dissonances:

• the Major and Minor 2nds,
• the Major and Minor 7ths,
• the 9ths, etc.;
• in addition, all diminished and augmented intervals,