CHAPTER XVII.

HARMONY OF TONE IN THE ARTS OF SOUND.

The Effects of Rhythm and of Harmony Illustrate the Same PrincipleWhat Causes Loudness and Pitch of Tone-What Causes QualityMusical Tones Compounded of Partial Tones Caused by Vibrations Related as 1:2, 2:3, etc.-These Partial Tones are Merely Repeated in Scales And Chords-Musical Harmony Results from Putting Together Notes Having Like Partial Effects-This True of the Most Complex Arrangements-True of Poetic Harmony.

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S stated on page 334, the most important difference between the effects of rhythm and of musical harmony is found in the fact that, in the latter, the mind is not directly conscious, as it is in the former, of divisions or subdivisions in time. It is conscious merely of an agree able thrill or glow, That this thrill is experienced in the degree in which the divisions are alike, or are multiples of those that are alike, is a scientific discovery.

The chief facts with reference to the subject for which we are indebted to science are, first, that degrees of loudness are determined by the relative amplitude of vibrations. A string of a certain texture and length will produce a loud sound in the degree in which it is struck violently, and, therefore, caused to cover a greater space with its vibrations. The second fact is, that degrees of pitch are determined by the relative time of vibrations. A string shortened in length, and therefore vibrating more rapidly, will produce a higher tone. It is from this fact, that, by very simple experiments, the law

was discovered that harmonic tones are related to one another according to certain definite ratios.

After physicists had proved that degrees of loudness in sound are determined by the amplitude of vibrations, and degrees of pitch by the time of vibrations, they felt that nothing was left to determine the quality of sounds except the forms of vibrations. It was natural to suppose, too, that the waves of sound produced by strings, or by wind-instruments,-a trumpet, or a human throat, for instance, deviated as they are from a straight course by a number of curves and angles,-must necessarily be more or less compound, and, being so, must differ in form for different kinds of instruments. Considerations of this sort caused investigations to be made into the forms of vibrations; and by means of very ingenious expedients,-by magnifying, for example, the vibrations of a cord or pipe, and making them visible, through using an intense ray of light to throw an image of them upon a canvas in a darkened room,—the forms assumed by the vibrations caused by many of the ordinary musical instruments have been accurately ascertained. These forms have been resolved, according to well-known mathematical principles, into their constituent elements. For instance, if the form of vibration be as in the first of these examples, it may be resolved into the forms that are in the second.

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In short, investigations of this character have shown that musical sounds may result, and usually do- result, not from simple but from compound forms of vibrations; that is to say, in connection with the main waves there are other waves. All these are not invariably present, but when present they are related to the main wave—i. e., in tones that make music as distinguished from noiseas 2:1, 3:1, 4:1, 5:1, 6:1, 7:1, 8:1, 9:1, or even in some cases as 10:1. In other words, these smaller accompanying waves may vibrate two, three or four times, and so on up to ten times, while the main wave is vibrating once. But this is not all. The sounds of these compound waves have been analysed. By means of instruments like Helmholtz's resonators, which are small brass boxes or globes each made of such a size as to respond sympathetically to a certain pitch, it has been found that each form of wave represented in a note produces a separate pitch of its own. When, therefore, a tone is sounded on a violin, we hear in it not only this tone caused by the vibrations of the whole length of the string, but also in connection with it a number of other partial tones, as all the constituents of any one note are called, each of which tones has its own pitch, produced by vibrations of onehalf, one-third, or one-fourth, etc., of the length of the string.

The difference in the number, the combination, and the relative loudness of these partial tones in a musical sound is what determines its quality or timbre. In instruments like kettle-drums, cymbals, or bells, one side is almost invariably thicker than the other. For this reason, the main vibrations are not uniform, and, of course, the partial tones cannot be so. Such instruments, accordingly, are less musical than noisy, and are

used on only exceptional occasions. But in ordinary musical sounds the partial tones, if present at all,-they differ as produced by different instruments,—are indicated in the notation below. Notice that the prime tone is counted as the first partial tone; also that the second, fourth, and eighth partials are the same as the prime tone with the exception of being in higher

The notes that are used, odd♪♪, in the degree in which they are long, indicate tones which the reader needs most to notice; and the marks after the letters indicate the relative distance of a tone from the octave of the tone which is the standard of pitch. C', F', or G', for instance, are one octave below C, F, or G, and these are one octave below c, f, or g, and two octaves below c', f', or g'.

Glancing at the above, suppose that we were to sound the note C, and then to sound, either after or with it,for the laws of harmony have to do with the methods of using notes both consecutively and conjointly,-notes

whose partial tones connect them most closely with C, -what notes should we sound? We should sound F‚— should we not?-of which C is the third partial, and G, which itself is the third partial of C. This, inasmuch as every C, F, or G of whatever octave has virtually the same sound, would give us the following:

C F G C

But these are the very tones accredited to the "lyre of Orpheus," which represented the earliest of the Greek scales.

Let us add to these notes those whose partial tones are the next nearly connected with C, F, or G. They are D the third partial of G, E the fifth partial of C, A the fifth of F, and B the fifth of G. This gives us

C-D-E-F-G-A-B-C,

which is our own major scale, the main one that we use to-day; and is similar to one used by the Greeks after theirs had been expanded to seven notes.

Now let us examine the tones that are used conjointly in what are termed chords. As a rule, the notes of the ordinary major scale are harmonised thus:

Let us compare these notes with the scheme of the upper partial tones of C, F, and G. that C, F, and G are the three bass

We at once notice

notes used in har