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 reenforce 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