General Science by Bertha May Clark (free novels TXT) 📖
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FIG. 184.—When a string vibrates as a whole, it gives out the fundamental note.
When a string is plucked in the middle without being held, it vibrates simply as a whole (Fig. 184), and gives forth but one note; this is called the fundamental. If the string is made to vibrate in two parts, it gives forth two notes, the fundamental, and a note one octave higher than the fundamental; this is called the first overtone. When the string is made to move as in Figure 183, three distinct motions are called forth, the motion of the entire string, the motion of the portion plucked, and the motion of the remaining unplucked portion of the string. Here, naturally, different tones arise, corresponding to the different modes of vibration. The note produced by the vibration of one third of the original string is called the second overtone.
The above experiments show that a string is able to vibrate in a number of different ways at the same time, and to emit simultaneously a number of different tones; also that the resulting complex sound consists of the fundamental and one or more overtones, and that the number of overtones present depends upon how and where the string is plucked.
269. The Value of Overtones. The presence of overtones determines the quality of the sound produced. If the string vibrates as a whole merely, the tone given out is simple, and seems dull and characterless. If, on the other hand, it vibrates in such a way that overtones are present, the tone given forth is full and rich and the sensation is pleasing. A tuning fork cannot vibrate in more than one way, and hence has no overtones, and its tone, while clear and sweet, is far less pleasing than the same note produced by a violin or piano. The untrained ear is not conscious of overtones and recognizes only the strong dominant fundamental. The overtones blend in with the fundamental and are so inconspicuously present that we do not realize their existence; it is only when they are absent that we become aware of the beauty which they add to the music. A song played on tuning forks instead of on strings would be lifeless and unsatisfying because of the absence of overtones.
It is not necessary to hold finger or pencil at the points 1:3, 1:4, etc., in order to cause the string to vibrate in various ways; if a string is merely plucked or bowed at those places, the result will be the same. It is important to remember that no matter where a string of definite length is bowed, the note most distinctly heard will be the fundamental; but the quality of the emitted tone will vary with the bowing. For example, if a string is bowed in the middle, the effect will be far less pleasing than though it were bowed near the end. In the piano, the hammers are arranged so as to strike near one end of the string, at a distance of about 1:7 to 1:9; and hence a large number of overtones combine to reënforce and enrich the fundamental tone.
270. The Individuality of Instruments. It has been shown that a piano string when struck by a hammer, or a violin string when bowed, or a mandolin string when plucked, vibrates not only as a whole, but also in segments, and as a result gives forth not a simple tone, as we are accustomed to think, but a very complex tone consisting of the fundamental and one or more overtones. If the string whose fundamental note is lower C (128 vibrations per second) is thrown into vibration, the tone produced may contain, in addition to the prominent fundamental, any one or more of the following overtones: C', G'', C'', E'', C''', etc.
The number of overtones actually present depends upon a variety of circumstances: in the piano, it depends largely upon the location of the hammer; in the violin, upon the place and manner of bowing. Mechanical differences in construction account for prominent and numerous overtones in some instruments and for feeble and few overtones in others. The oboe, for example, is so constructed that only the high overtones are present, and hence the sound gives a "pungent" effect; the clarinet is so constructed that the even-numbered overtones are killed, and the presence of only odd-numbered overtones gives individuality to the instrument. In these two instruments we have vibrating air columns instead of vibrating strings, but the laws which govern vibrating strings are applicable to vibrating columns of air, as we shall see later. It is really the presence or absence of overtones which enables us to distinguish the note of the piano from that of the violin, flute, or clarinet. If overtones could be eliminated, then middle C, or any other note on the piano, would be indistinguishable from that same note sounded on any other instrument. The fundamental note in every instrument is the same, but the overtones vary with the instrument and lend individuality to each. The presence of high overtones in the oboe and the presence of odd-numbered overtones in the clarinet enable us to distinguish without fail the sounds given out by these instruments.
The richness and individuality of an instrument are due, not only to the overtones which accompany the fundamental, but also to the "forced" vibrations of the inclosing case, or of the sounding board. If a vibrating tuning fork is held in the hand, the sound will be inaudible except to those quite near; if, however, the base of the fork is held against the table, the sound is greatly intensified and becomes plainly audible throughout the room.
The vibrations of the fork are transmitted to the table top and throw it into vibrations similar to its own, and these additional vibrations intensify the original sound. Any fork, no matter what its frequency, can force the surface of the table into vibration, and hence the sound of any fork will be intensified by contact with a table or box.
This is equally true of strings; if stretched between two posts and bowed, the sound given out by a string is feeble, but if stretched over a sounding board, as in the piano, or over a wooden shell, as in the violin, the sound is intensified. Any note of the instrument will force the sounding body to vibrate, thus reënforcing the volume of sound, but some tones, or modes of vibration, do this more easily than others, and while the sounding board or shell always responds, it responds in varying degree. Here again we have not only enrichment of sound but also individuality of instruments.
271. The Kinds of Stringed Instruments. Stringed instruments may be grouped in the following three classes:—
a. Instruments in which the strings are set into motion by hammers—piano.
b. Instruments in which the strings are set into motion by bowing—violin, viola, violoncello, double bass.
c. Instruments in which the strings are set into motion by plucking—harp, guitar, mandolin.
FIG. 186.—1, violin; 2, viola; 3, violoncello; 4, double bass.
a. The piano is too well known to need comment. In passing, it may be mentioned that in the construction of the modern concert piano approximately 40,000 separate pieces of material are used. The large number of pieces is due, partly, to the fact that the single string corresponding to any one key is usually replaced by no less than three or four similar strings in order that greater volume of sound may be obtained. The hammer connected to a key strikes four or more strings instead of one, and hence produces a greater volume of tone.
b. The viola is larger than the violin, has heavier and thicker strings, and is pitched to a lower key; in all other respects the two are similar. The violoncello, because of the length and thickness of its strings, is pitched a whole octave lower than the violin; otherwise it is similar. The unusual length and thickness of the strings of the double bass make it produce very low notes, so that it is ordinarily looked upon as the "bass voice" of the orchestra.
c. The harp has always been considered one of the most pleasing and perfect of musical instruments. Here the skilled performer has absolutely free scope for his genius, because his fingers can pluck the strings at will and hence regulate the overtones, and his feet can regulate at will the tension, and hence the pitch of the strings.
Guitar and mandolin are agreeable instruments for amateurs, but are never used in orchestral music.
272. Wind Instruments. In the so-called wind instruments, sound is produced by vibrating columns of air inclosed in tubes or pipes of different lengths. The air column is thrown into vibration either directly, by blowing across a narrow opening at one end of a pipe as in the case of the whistle, or indirectly, by exciting vibrations in a thin strip of wood or metal, called a reed, which in turn communicates its vibrations to the air column within.
The shorter the air column, the higher the pitch. This agrees with the law of vibrating strings which gives high pitches for short lengths.
The pitch of the sound emitted by a column of air vibrating within a pipe varies according to the following laws:
1. The shorter the pipe, the higher the pitch.
2. The pitch of a note emitted by an open pipe is one octave higher than that of a closed pipe of equal length.
3. Air columns vibrate in segments just as do strings, and the tone emitted by a pipe of given length is complex, consisting of the fundamental and one or more overtones. The greater the number of overtones present, the richer the tone produced.
273. How the Various Pitches are Produced. With a pipe of fixed length, for example, the clarinet (Fig. 189, 1), different pitches are obtained by pressing keys which open holes in the tube and thus shorten or lengthen the vibrating air column and produce a rise or fall in pitch. Changes in pitch are also produced by variation in the player's breathing. By blowing hard or gently, the number of vibrations of the reed is increased or decreased and hence the pitch is altered.
In the oboe (Fig. 189, 2) the vibrating air column is set into motion by means of two thin pieces of wood or metal placed in the mouthpiece of the tube. Variations in pitch are produced as in the clarinet by means of stops and varied breathing. In the flute, the air is set into motion by direct blowing from the mouth, as is done, for instance, when we blow into a bottle or key.
The sound given out by organ pipes is due to air blown across a sharp edge at the opening of a narrow tube. The air forced across the sharp edge is thrown into vibration and communicates its vibration to the air within the organ pipe. For different
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