The Psychology of Beauty, Ethel D. Puffer [the ebook reader .txt] 📗

body and soul, seem to be IN the rhythm. We make it, and we wait to make it. The satisfaction of our expectation is like the satisfaction of a bodily desire or need; no, not like it, it IS that. The conditions and causes of rhythm and our pleasure in it are more deeply seated than language, custom, even instinct; they are in the most fundamental functions of life. This element of music, at least, seems not to have arisen as a “natural language.” IV

The facts of the relations of tones, the elements, that is, of melody and harmony, are as follows. We cannot avoid the observation that certain tones “go together,” as the phrase is, while others do not. This peculiar impression of belonging together is known as consonance, or harmony. The intervals of the octave, the fifth, the third, for instance, that is, C-C’, C-G, C-E, in the diatonic scale, are harmonious; while the interval of the second, C-D, is said to be dissonant.

Consonance, however, is not identical with pleasingness, for different combinations are sometimes pleasing, sometimes displeasing. In the history of music we know that the octave was to the Greeks the most pleasing combination, to medieval musicians the fifth, while to us, the third, which was once a forbidden chord, is perhaps most delightful. Yet we should never doubt that the octave is the most consonant, the fifth and the third the lesser consonant of combinations. We see, thus, that consonance, whatever its nature, is independent of history; and we must seek for its explanation in the nature of the auditory process.

 

Various theories have been proposed. That of Helmholtz has held the field so long that, although weighty objections have been raised to it, it must still be treated with respect. In introducing it a short review of the familiar facts of the physics and physiology of hearing may not be out of place.

 

The vibration rates per second of the vibrating bodies, strings, steel rods, etc., which produce those musical tones which are consonant, are in definite and small mathematical ratios to each other. Thus the rates of C-C’ are as 1:2; of C-G, C-E, as 2:3, 4:5. In general, the simpler the fraction, the greater the consonance.

 

But no sonorous body vibrates in one single rate; a taut string vibrates as a whole, which gives its fundamental tone, but also in halves, in fourths, etc., each giving out a weaker partial tone, in harmony with the fundamental. And according to the different ways in which a sonorous body divides, that is, according to the different combination of partial tones peculiar to it, is its especial quality of tone, or timbre. The whole complex of fundamental and partial tones is what we popularly speak of as a tone,—more technically a clang. These physical agitations or vibrations are transmitted to the air. Omitting the account of the anatomical path by which they reach the inner ear, we find them at last setting up vibrations in a many-fibred membrane, the basilar membrane, which is in direct connection with the ends of the auditory nerve. It is supposed that to every possible rate of vibration, that is, every possible tone, or partial tone, there corresponds a fibre of the basilar membrane fitted by its length to vibrate synchronously with the original wave-elements.

The complex wave is thus analyzed into its constituents. Now when two tones, which we will for clearness suppose to be simple, unaccompanied by partial tones, sounding together, have vibration rates in simple ratios to each other, the air-waves set in motion do not interfere with each other, but combine into a complex but homogeneous wave. If they have to each other a complicated ratio, such as 500:504, the air-waves will not only not coalesce, but four times in the second the through of one wave will meet the crest of the other, thus making the algebraic sum zero, and producing the sensation of a momentary stoppage of the sound. When these stoppages, or beats, as they are called, are too numerous to be heard separately, as in the interval, say, 500:547, the effect is of a disagreeable roughness of tone, and this we call discord.

In other words, any tones which do not produce beats are harmonious, or harmony is the absence of discord. In the words of Helmholtz,<1> consonance is a continuous, dissonance an intermittent, tone-sensation.

 

<1> Lehre v.d. Tonempfindungen, p. 370, in 4th edition.

 

Aside from the fact that consonance, as a psychological fact, seems positive, while this determination is negative, two very important facts can be set up in opposition. As a result of experimental investigation, we know that the impression of consonance can accompany the intermittent or rough sound-sensations we know as beating tones; and, conversely, tones can be dissonant when the possibility of beats is removed.

Briefly, it is possible to make beats without dissonance, and dissonance without beats.

 

The other explanation makes consonance due to the identity of partial tones. When two tones have one or more partial tones in common they are said to be related; the amount of identity gives the degree of relationship. Physiologically, one or more basilar membrane fibres are excited by both, and this fact gives the positive feeling of relationship or consonance. Of course the obvious objection to this view is that the two tones should be felt as differently consonant when struck on instruments which give different partial tones, such as organ and piano, while in fact they are not so felt.

 

But it is not after all essential to the aesthetics of music that the physiological basis of harmony should be fully understood. The point is that certain tones do indeed seem to be “preordained to congruity,” preordained either in their physical constitution or their physiological relations, and not to have achieved congruity by use or custom. Consonance is an immediate and fundamental impression,—psychologically an ultimate fact. That it is ultimate is emphasized by Stumpf<1>

in his theory of Fusion. Consonance is fusion, that is, unitary impression. Fusion is not identical with inability to distinguish two tones from each other in a chord, although this may be used as a measure of fusion. Consonance is the feeling of unity, and fusion is the mutual relation of tones which gives that feeling.

 

<1> Beitrage zur Akustik u. Musikwissenschaft, Heft I, Konsonanz u. Dissonanz, 1898.

 

The striking fact of modern music is the principle of tonality.

Tonality is said to be present in a piece of music when every element in it is referred to, gets its significance from its relation to, a fundamental tone, the tonic. The tonic is the beginning and lowest note in the scale in question, and all notes and chords are understood according to their place in that scale. But the conception of the scale of course does not cover the ground, it merely furnishes the point of departure,—

the essential is in the reference of every element to the fundamental tone. The tonic is the centre of gravity of a melody.

 

The feeling of tonality grew up as follows. Every one was referred to a fundamental, whether or not it made with it an harmonious interval. The fundamental was imaged TOGETHER WITH

every other note, and when a group of such references often appeared together, the feelings bound up with the single reference (interval-feelings) fused into a single feeling,—

the tonality-feeling. When this point is once reached, it is clear that every tone is heard not as itself alone, but in its relations; it is not that we judge of tonality, it is a direct impression, based on a psychological principle that we have already touched on in the theory of rhythm. The tonality-feeling is a feeling of form, or motor image, just as the shape of objects is a motor image. We do not now need to go through all possible experiences in relation to these objects, we POSSESS their form in a system of motor images, which are themselves only motor cues for coordinated movements. So every tone is felt as something at a certain distance from, with a certain relation to, another tone which is dimly imagined. In following a melody, the notes are able to belong together for us by virtue of the background of the tone to which they are related, and in terms of which they are heard.

The tonality is indeed literally a “funded content,”—that is, a funded capital of relation.

 

These are the general facts of tonality. But what is its meaning for the nature of music? Why should all notes be referred to one? Is this, too, an ultimate psychological fact?

In answer there may be pointed out the original basic quality of certain tones, and the desire we have to return to them.

Of two successive tones, it is always the one which is, in the ratio of their vibration rates, a power of two, with which we wish to end.<1> When neither of two successive tones contains a power of two, we have no preference as to the ending. Thus denoting any tone by 1, it is always to 1 or 2, or 2n that we wish to return, from any other possible tone; while 3 and 5, 5

and 7, leave us indifferent as to their succession. In general, when two tones are related, as 2n:3, 5, 7, 9, 15—in which 2n denotes every power of two, including 2o=1, with the progression from the first to the second, there is bound up a tendency to return to the first. Thus the fundamental fact of melodic sequence may be said to be the primacy of 2 in vibration rates.

But 2n, in a scale containing 3, 5, etc., is always what we know as the tonic. The tonic, then, gives a sense of equilibrium, of rest, of finality, while to end on another tone gives a feeling of restlessness or striving.

 

Now tone-relationship alone, it is clear, would not of itself involve this immediate impulse to end a sequence of notes on one rather than on another. Nor is tonality, in the all-pervasive sense in which we understand it, a characteristic of ancient, or of mediaeval music, while the tendency to end on a certain tone, which we should to-day call the tonic, was always felt. Thus, since complete tonality was developed late in the history of music, while the closing on the tonic was certainly prior to it, the finality of the tonic would seem to be the primary fact, out of which the other has been developed.

 

We speak to-day, for instance, of dissonant chords, which call for a resolution—and are inclined to interpret them as dissonant just because they do so call. But the desire for resolution is historically much later than the distinction between consonance and dissonance…. “What we call resolution is not change from dissonant to consonant IN GENERAL, but the transition of definite tones of a dissonant interval into DEFINITE TONES of a consonant.”<1> The dissonance comes from the device of getting variety, in polyphonic music, by letting some parts lag behind, and the discords which arose while they were catching up were resolved in the final coming together; but the STEPS were all PREDETERMINED.<2> Resolution was inevitably implied by the very principle on which the device is founded. That is, the understanding of a chord as something TO BE RESOLVED, is indeed part of the feeling of tonality; but the ending on the tonic was that out of which this resolution-feeling grew.

 

<1> Stumpf, op. Cit., p. 33.

<2> Grove, Dict. Of Music and Musicians. Art. “Resolution.”

 

Must we, then, say that the finality of the tonic is a unique, inexplicable phenomenon? giving up the nature of melody as a problem if not insoluble, at least unsolved?

 

The feeling of finality in the return to 2n