The Psychology of Beauty

er," 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

asing 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 fi

ighty objections have been raised to it, it must still be treated with respect. In introducing it a

al tones which are consonant, are in definite and small mathematical ratios to each other. Thus the rates of

etting 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

empfindungen, p. 3

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;

ree 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

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 i

Musikwissenschaft, Heft I, K

damental 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 scal

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

e 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, wit

h 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

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

<2> Grove, Dict. Of Music and

nique, inexplicable phenomenon? giving up the nature of

f 2n vibrations would have the character of rest and equilibrium. This explanation might hold if we were ever conscious of the two-division as such, in

to make every note more consonant with its neighbors. And naturally the tonic is the tone with which all other tones have the most unity. Now this "return" phenomenon is a simpler case of the desire for the feeling of unity. The tonic is the epitome of all the most perfect feelings of consonance or unity which are possible in any particular sequ

minor second is ugly that we dislike it, for it will be a concord some day,-he is only partly right. The minor second may be a "concord," that is, we may like it, some day; but that will be because w have extended our feeling of tonality to include the minor second. When that day comes the minor second will be so closely linked with other fully consonant combinations that we shall hear it in terms of them,

Studies in Mod