THE LAWS OF PHYSICS AND SOUND
If human eyesight were sharp enough to see the vibrations and alterations set up in the air through which a voice was passing, we might make some wonderful additions to our knowledge. (In ordinary conversation, the physical both precedes and arouses the psychical (emotion); spoken language, which gives us pleasure, or pain, rouses us to anger or soothes us to peace, exists for a time between us and the speaker as a purely mechanical condition.)
Noise affects us as an irregular succession of shocks. We are conscious of a jolting and jarring of the auditory nerves, whereas a musical sound flows smoothly and regularly. How is this smoothness secured? By rendering the impulses received by the tympanic membrane perfectly periodic. The motions of a common pendulum, for example, are periodic, but they are far too sluggish to excite sonorous waves. To produce a musical tone we must have a body which vibrates with the unerring regularity of the pendulum, but which can impart much sharper and quicker shocks to the air. The only condition necessary to the production of a musical sound is pulses should succeed each other in the same interval of time. If a watch, for example, could be causes to tick with sufficient rapidity, the ticks would blend to a musical tone; and if the strokes of a pigeon’s wings could be greatly accelerated, the progress of the bird through the air would be accompanied by music. The humming bird actually attains the necessary rapidity. If the puffs of a locomotive could be increased to fifty or sixty second, the approach of the engine would be heralded by an organ peal of tremendous power.
The production of a musical sound can be illustrated by causing the teeth of a rotating wheel to strike the quick succession against a card.
This gyroscope consists mainly of a heavy brass ring D, along with which rotates a small-toothed wheel W. On touching this wheel with the edge of a card C, and rotating the brass ring, a musical sound is produced. By increasing the rotary motion the tone becomes higher; by reducing the motion the tone becomes deeper. This proves the important fact that the pitch of a note depends upon the rapidity of its pulses or vibrations.
DEFINITION OF PITCH
If two notes coming from two distinct sources are of the same pitch, their rates of vibrations are the same. If the tuning fork yields the same note as an organ pipe or the tongue of a concertina, it is because the vibrations of the fork in one case are executed in precisely the same time as the vibrations of the column of air in the organ pipe, or of the tongue in the concertina. The same holds good for the human voice. If a violin string and a voice yield the same note, it is because the vocal chords of the singer vibrate in the same times as the string vibrates.
The pitch of a musical note depends solely upon the number of vibration concerned in its production. The more rapid the vibrations, the higher the pitch. To enable a musical string to vibrate, it must be stretched between two rigid points.
Figure 140 is an instrument employed to stretch strings and to render their vibrations audible.
From the pin P, to which one end of the string is firmly attached, it passes across the bridges B and B, being afterward carried over the wheel H. The string is firmly stretched by a weight of twenty-eight pounds, attached to its extremity. The bridges B and B, which constitute the rear ends of the strings, are fastened to the long wooden box MN.
The whole instrument is called a monochord or sonometer.
Plucking the stretched string at its middle, you hear a sound, but the sonorous waves which strike the ear do not proceed directly from the string. The amount of wave motion generated by so thin a body as the string is too small to be noticeable at any distance. But the string is tightly drawn over the two bridges, and when it is made to vibrate, its tremors are communicated through these bridges to the entire box. And the box, after intensifying the vibrations, transmits them to the surrounding air, thereby setting it into motion.
LAWS OF VIBRATING STRINGS
Having learned how the vibrations of strings rendered available in music, we must next investigate the laws of such vibrations. Plucking the string of FIGURE 140, the sound is heard as the lowest of fundamental note of the string, to produce which it swings as a whole, to and fro.
By placing a movable bridge under the exact middle of the string and pressing the string against the bridge, the string is divided into two equal parts. Plucking either of those two divisions, a note is obtained which is exactly an octave above the fundamental note. In all cases, and with all instruments of whatever kind, the octave of a note is produced by doubling the number of vibrations. One-half of this string vibrates with twice the rapidity of the whole string. In the same way one-third of the string vibrates with three times the rapidity, producing a note one-fifth above the octave; while one-fourth of the string vibrates with four times the rapidity, producing the double octave of the whole string. In general terms, the number of vibrations is inversely proportional to the length of the string; the smaller the divisions of the string, the higher the tone. Again, the more tightly a string is stretched, the more rapid are its vibrations. By plucking the string with one hand, while the other hand alternately lifts and presses upon the weight, the quick vibrations of the tension will produce a varying, wailing tone. An octave consists of the eight notes of the scale; thus C to C on the piano is an octave.
By applying different weights to the end of the string and determining in each note the number of vibrations executed in a second, we find the numbers thus obtained to be proportional to the square root of the tension. A string, for example, stretched by a weight of two pounds, executes a certain number of vibrations a second. If we wish to double the number of the vibrations, we must stretch the string by a weight of four pounds; if we wish to treble the vibrations we must apply the weight of sixteen pounds, and so on.
The vibrations of a string also depend upon its thickness. If, for instance, of two strings of the same material, equally long and equally stretched, one has twice the diameter of the other, the thinner string will execute double the number of vibrations of the other in the same time. If one string be three times as thick as the other, it will execute only one-third the number of vibrations, and so on.
Finally the vibrations of a string depend upon the density of the matter of which it is composed. If the density of one string be one-fourth of that of another of the same length, thickness and tension, it will execute its vibrations twice as rapidly; if the density be one-ninth that of the other, it will vibration with three times the rapidity, and so on. Therefore, the number of vibrations is inversely proportional to the square root of the density of the string.
In the violin and other stringed instruments we avail ourselves in thickness instead of length to obtain deep tones. The human voice is a mechanical instrument only in so far as the different parts constituting it must be in exact uniformity to produce equal results with mechanical instruments. Also, it is subject to the same laws in regard to velocity (number of vibrations), elasticity, density and intensity. That is, the same number of vibrations per second produce the same pitch either in a mechanical instrument or in the human voice. The elasticity of the vocal organ is another necessary adjunct, for if this organ were in a tight, stiff state, it could not vibrate freely.
In the same way there must be a certain density of vocal chords, otherwise the tone would be devoid of intensity; it would be too faint and thin to produce tones of character and substance. But the vocal instrument is in all other respects until the mechanical instrument, because the vocal instrument is subjected to our will and directed by our intelligence, enabling it to be trained to the highest perfection. For instance, many musical instruments require provision for each separate tone and the means of changing the character, intensity, tone color, etc., are small, but in the vocal organ such changes are so manifold that the same note can be produced with constant vibrations, creating ever new results. In the piano, for instance, you have a separate key for each tone, and after the key is struck you cannot change or modify the tone.
OVERTONES – TONE QUALITY
It has been shown that s stretched string can either vibrate as a whole or divided into a number of equal parts, each of which vibrates as an independent string. Now, it is not possible to vibrate one section of the string without at the same time affecting, to a greater or less extent, its subdivision; that is to say, added to the vibrations of the one section we have always, in a greater or less degree, the vibrations of its aliquote parts.
In the experiment with the monochord, when the wire was to be shortened, the movable bridge was employed, against which the wire was pressed so as to deprive the point resting on the bridge of all possibility of motion. This strong pressure, however, is not necessary. If we press the feather end of a goose quill lightly against the middle of a string, and draw a violin bow ever one of its halves, the string yields the octave above the note yielded by the whole string.
The mere damping of the string at the center by the light touch of the feather is sufficient to cause the string to be divided into two vibrating segments. Nor is it necessary to hold the feather there throughout the experiment; after having drawn the bow, the feather may be removed; the string will continue to vibrate, emitting the same note as before.
To prove that when the center is damped and the bow drawn across one of the halves of the string, the other half also vibrates, place across the middle of the untouched half a rider of paper. Damping the center and drawing the bow, the string shivers and the rider is overthrown.
When the string is damped at a point which cuts off one-third of its length, and the bow drawn across the shorter section, not only is the shorter section thereby thrown into vibration, but the longer section divides itself into two ventral segments with a node between them.
Damping the string at the end of one-fourth of its length, if the bow is drawn across the shorter section, the remaining three-fourths divide themselves into three ventral segments with two nodes between them. Damping the string at the end of one-fifth of its length, the remaining four-fifths divide into four ventral segments, with three nodes, and so on.
The higher notes produced by these subdivisions are called the harmonics of the string. And so it is with other sounding bodies. We have in all cases a coexistence of vibrations, that is, the higher tones mingle with the fundamental lower one, and it is their intermixture which determines what we term the quality of the sound. It is this union of high and low tones which enables us to distinguish one musical instrument from another.
A clarinet and violin, for example, though tuned to the same fundamental note are not confounded; the auxiliary tones of the one are different from those of the other, and these latter tones, uniting themselves to the fundamental tones of each of the two instruments, differentiate the identity of the sounds. All bodies and instruments employed for producing musical sounds emit, besides their fundamental tones, others due to higher rates of vibration. Such sounds are known under the general term of “overtones” or aliquot tones. These combinations constitute resonance.
Color depends upon rapidity of vibration, blue light bearing to red the same relation that a high tones does to a low tone. A simple tone, then, may be defined as the product of a vibration which cannot be decomposed into more simple ones. As assemblage of tones, such as we obtain when the fundamental tones and the overtones sound together, determines tone quality.
To the voice student the question of tone quality is the all-important one; upon it depends the success or failure as a singer, for no matter how much technique he may require, or however pleasing his personality may be, if his voice is deficient in quality his success will be meager. Even in a purely technical sense, he will fail to meet the demands of higher artistic interpretation because his voice will fail him at the moment of climax. He has give all he has long before the apotheosis of ecstasy in the song is reached. The spirit may be willing, but the flesh – the vocal organ – is weak, too weak for the demands made upon it.
On the other hand, if the vocal organ is fully developed, then the quality of the singer’s tone will arouse enthusiasm, even with the simplest song.