Quality or Timbre of a Tone.

345

audibility are not exceeded when 38,000 vibrations are reached. The musical sequence of notes can, however, be fairly discerned only between the limits of 40 to 4000 vibrations per second, just as to the eye, the relative parts of a landscape escape observation beyond a limited distance.

520. Length of Musical Waves.-All musical sounds travel through the air at almost the same velocity, namely, 1120 feet per second; and as the time occupied by a wave to advance through its own length is the same as the time of a single vibration of the sounding body (Art. 475), it follows that the length of the aërial waves diminishes as the height of the note increases. For shrill notes they are short and rapid, and for low notes they are long and slow. When the middle C of the piano is struck, it vibrates. about 264 times in a second, and hence sets up air-pulses of 1120 feet divided by 264 or 4 feet in length. The first A of the bass (in a seven-octave piano) produces air-waves about 41 feet in length, while the last A of the treble sends on pulses not quite 4 inches long (Art. 519). The latter pulses are 128 times more rapid than the former, which are correspondingly longer. If the sensibility of the ear-nerves is to be judged by the range of audibility of musical tones, it far surpasses that of the optic nerves. The former ranges over eleven octaves, while that of the latter barely exceeds a single octave.

521. (iii) The third kind of difference among musical tones is that known as quality, colour, character, or timbre.

Loudness, as we have seen, depends on the extent of the airvibrations, and intensity on their rapidity. But every one knows that sounds of the same degree of loudness and of pitch may be sounded on a pianoforte, a violin, a trumpet, a harmonium, a clarionet, or with the voice, and yet that there is a something which distinguishes the tone in each case, and which enables us to say by which of the instruments it was produced. It is this peculiarity or quality of tone which enables us to distinguish the voices of different singers; and even in human speech, qualitative varieties of tone are employed in the formation of the different vowel sounds, which bear to consonants the relation of musical tones to noises.

522. We will now consider to what physical cause, this third peculiarity of tones can be traced. All musical sounds are due to vibratory or periodical motions of the sounding body and the air or conveying medium. Now a vibratory motion may vary (1) in

346

Explanation of Timbre.

extent or amplitude, (2) in rapidity, or (3) in mode or form. The two former correspond, as we have explained, to loudness and pitch of tone; the latter corresponds to quality.

The adjoining figure (fig. 146) may help the mind to conceive how this may be. A, B, and C are three waves having the same

B

Fig. 146

height or amplitude of motion and the same wave-length, and therefore rate of vibration; but obviously the modes of vibration are very different. In A it is smooth and even in its rise and fall, in B it is associated with secondary motions, and in C the motion is slow in its rise and abrupt in its fall. There is little difficulty in conceiving, then, how the number of such variations is almost unlimited; and there is no doubt that to analogous variations in sonorous pulsations the difference of quality or timbre in musical sounds has to be ascribed.

523. The existence of such varieties of wave-shape or pulse-form does not rest on mere theory, but can be actually exhibited to the eye, and even recorded on paper, by various mechanical arrangements. Perhaps the simplest means of doing this is with the tuning-fork.

For this purpose we fix a small steel or brass tracer to one of the prongs of a tuning-fork by means of a little wax. On striking the fork, or exciting it with a violin-bow, the motion of the tracer will be quite visible, and it may be permanently recorded and its regular

B

Fig. 147.

A

or pendulum-like nature shown, either by drawing underneath it a strip of smoked glass or cardboard, as represented in A (fig.147), or by holding it so that its tracer just grazes a similarly blackened cylinder or glass bottle, B, mounted so that it can be turned regularly. A sheet of paper may be

wrapped tightly round the cylinder, and removed with the wavy

The Phonautograph.

347

trace. In this way a beautiful wavy line of the form of a (fig. 147), is obtained, each wave corresponding to a vibration of the legs of the fork; and if the cylinder be turning at the rate of once a second, the number of waves that can be counted round it, will correspond to the vibration-number of the note. This is easily proved by making the syren coincide in pitch with the tuning-fork, and then noting the pulse-number indicated by its counter.

As the intensity of the sound falls, the extent of the vibrations diminishes, but the number traced per second remains the same. 524. The Phonautograph of M. Leon-Scott is a more elaborate and expensive means of tracing mechanically the sonorous vibrations of any note or sound, or mixture of notes. It is a sort of big artificial ear which reveals these vibrations to the eye. In shape it is like a drum, with a narrow and a wide end, and open at the wide end. Over the narrow end is stretched tightly a delicate membrane, and a tracer of hog's bristle is fixed on this with some sealing wax. Any note played into the open mouth of this instrument causes tremblings of the style or bristle; which, recorded on a rotating cylinder, reveal the nature of the sound.

Fig. 148.

The adjoining cuts represent tracings obtained with the phonautograph of sounds whose pitch and intensity are determined by the larger and more prominent waves; but their timbre or quality will be very different from that of other notes whose representative wave-surface is free from the minute serrations visible here.

Harmonics.

525. On attentively examining the sounds corresponding to such complex figures, a moderately delicate ear will detect not one musical tone alone, but a whole series of accompanying higher tones, rising in pitch according to definite laws, but growing gradually fainter as they rise.

To these the name of harmonics or overtones is applied, the lower tone being the fundamental, prime, or governing tone, which regulates the pitch of the whole compound musical tone. The laws

348

The Harmonics attendant upon a Tone.

according to which these harmonics arise are exceedingly simple, and are as follows:

First. The ear detects the octave of the fundamental tone; that

is, a tone with double the number of vibrations which the prime has.

Second. The fifth to this latter octave is also heard; that is, a tone making of its vibrations per second, or three times the number of vibrations of the prime tone.

Third. The second higher octave to the prime is heard; that is, a tone with four times the number of its vibrations.

Fourth. The major third to the last, that is, a tone making of its number of vibrations, or five times the number of vibrations of the prime.

And so on to tones, growing continually fainter, of 7, 8, 9, &c., times as many vibrations as the fundamental tone.

The series of harmonics arising from any fundamental tone, C, is, in musical language, as follows:

This gives the musical notation for the seven upper harmonics to the fundamental tone, c, with their vibrational relations to that tone.

526. It is a most remarkable fact, established by the researches of Prof. Helmholtz, that to the variations in loudness and pitch of these upper harmonic tones, the quality of a musical note is to be attributed. One musical tone differs from another just as one musical chord differs from another: and the analysis by the ear of such composite tones, is a most wonderful feat, when we consider that the ear is not, like the eye, capable of any comprehensive sweep. It cannot directly reveal the wave-nature of sound, much less discriminate subordinate modifications of the aërial wave-form.

Still the ear can do much more than the eye can do in decomposing compound wave-forms. Any number and variety of sounds may be conveyed at the same instant by the same body of air without destroying their individual effect. Thus, for instance, all the voices of a choir are transported through the same aërial mass,

and the ear can single out any one voice, or even analyze the chorus into its constituent voices; in other words, the ear can resolve the complex resultant aërial vibration into its individual components. Similarly, any number of liquid waves may be simultaneously passing over the surface of a lake or of the sea, and the result

A

Fig. 150.

ing disturbance is a compound of the individual effects. For example, two waves of the form of A and B (fig. 150) would combine into the form C; but the eye on seeing the latter form would be totally unable to analyze it into its two constituent waves, A and B. This, however, which to the eye is nearly an impossibility, is to the ear quite an easy matter.

Method of observing the harmonics of any tone.

527. The ear, even though unpractised in musical discriminations, may readily observe these overtones by a simple contrivance of Prof. Helmholtz, which is an application of the property of

Resonance.

Resonance may be described as a sympathetic vibration, arising from the cumulation of small periodic impulses, imparted by an oscillating body, to another whose period of vibration is synchronous with the first. Thus, the string of a piano, if its damper be gently raised by touching, not striking, its key, will be heard to vibrate in response to the same note forcibly sung or played near it. The sounding-board, taking up the vibrations of the air, communicates