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. [Illustration: 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 reenforce and enrich the fundamental tone.