744 



SPECIAL SENSES. 



the same way the harmonic 5ths and 3ds overpower other overtones ; for the 

 string is subdivided again and again into overtones, which are not harmonious 

 like the notes of the common chord of the fundamental. 



The presence of overtones, resultant tones and additional tones, which 

 latter will be described hereafter, can be demonstrated, without damping the 

 strings, by resonators. It is well known that if a glass tube, closed at one 

 end, which contains a column of air of a certain length, be brought near a 

 resounding body emitting a note identical with that produced by the vibra- 

 tions of the column of air, the air in the tube will resound in consonance 

 with the note, while no other note will have this effect. The resonators of 

 Helmholtz are constructed upon this principle. A glass globe or tube (Fig. 

 267) is constructed so as to produce a certain note. This has a larger open- 

 ing (a) and a smaller opening (b), which latter is fitted in the ear by warm 

 sealing-wax, the other ear being closed. When the proper note is sounded, 

 it is re-enforced by the resonator and is greatly increased in intensity, while 

 all other notes are heard very faintly. By using resonators graduated to the 

 musical scale, it is easy to analyze a note and distinguish its overtones. The 

 resonators of Helmholtz, which are open at the larger extremity, are much 

 more delicate than those in which this is closed by a membrane. 



A very striking and instructive point in the present discussion is the fol- 

 lowing : All the overtones are produced by vibrations of divisions of the 

 string, included between the comparatively still points, called nodes ; and if 

 a string be thrown into vibration by plucking or striking it at one of these 



nodal points, the overtones 

 which vibrate from this 

 node at a fixed point are 

 abolished. It is readily 

 understood that when a 

 string is plucked at any 

 point, it will vibrate so vig- 

 orously at this point that 

 no node can be formed. 

 This fact has long been 

 recognized by practical 

 musicians, although many 

 are probably unacquainted 

 with its scientific explana- 

 tion. Performers upon 

 stringed instruments ha- 

 bitually attack the strings near their extremities. In the piano, where the 

 strings may be struck at almost any point, the hammers are placed at a dis- 

 tance of -J- to \ of the length of the strings, from their extremities ; and it has 

 been ascertained by experience that this arrangement gives the richest notes. 

 The nodes formed at these points would produce the 7ths and 9ths as over- 

 tones, which do not belong to the perfect major chord, while the nodes for 

 the harmonious overtones are undisturbed. The reason, then, why the notes. 



FIG. 267. Resonators of Helmholtz. 



