General Science

by Bertha May Clark

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.

FIG. 185.—A string can vibrate in a number of different ways simultaneously, and can produce different notes simultaneously.

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.