M4 



VIBRATION CURVE OF A MUSICAL TONE. 



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at once by their specific quality. Wherein lies the essence (" Wesen ) of tone-colour ? The 

 investigations of v. Helmholtz have proved that, amongst mechanisms which produce tones, 

 only those that produce pendulum-like vibrations, i.e., the to-and-fro vibrations of a metallic 

 rod with one end fixed, and tuning-forks, execute simple pendulum-like vibrations. This can 

 be shown bv making a tuning-fork write off its vibrations on a recording surface, when a com- 

 pletely uniform wave-line, with equal elevations and depressions is noted. The term " tone 

 is restricted to those sounds, hardly ever occurring in nature, which are due to simple pen- 

 dulum-like vibrations. . . 



Other investigations have shown that the tones of musical instruments and ot the human 

 voice, all of which have a characteristic quality of their own, are composed of many single 

 simple tones. Amongst these on* is characterised by its intensity, and at the same time it 

 determines the pitch of the whole compound musical "tone-picture." This is called the 

 fundamental tone or key-note. The other weaker tones which, as it were, spring from and 

 are mingled with this, varv in different instruments both in intensity and number. They 

 are " upper tones," and their vibrations are always some multiple 2, 3, 4, 5 .... times of 



the fundamental tone or key-note. In general, 

 we say that all those outbursts of sound which 

 embrace numerous strong upper tones, especi- 

 ally of high pitch, in addition to the funda- 

 mental tone, are characterised by a sharp, 

 piercing, and rough quality, such as emanates 

 from a trumpet or clarionet, and that conversely 

 the quality is characterised by mildness and 

 softness when the overtones are few, feeble, and 

 low, e.g., such as are produced by the flute. It 

 requires a well-trained musical ear to dis- 

 tinguish, in an instrumental burst, the over- 

 tones apart from the fundamental tone. But 

 this is very easily done with the aid of resonators 

 (fig. 600). These consist of spherical or funnel- 

 shaped hollow bodies, made of brass or some 

 other substance, which, by means of a short 

 tube, can be placed in the outer ear. If a 

 resonator be placed in the ear, we can hear the 

 feeblest overtone of the same number of vibra- 

 tions as the fundamental tone. Thus, musical 

 .rig. oy/. instruments are distinguished by the number, 



Curves of a musical tone obtained by com- intensity, and pitch of the overtones which they 

 funding the curve of a fundamental tone p ro a uce . A vibrating metallic rod and a tuning- 

 with that of its overtones. fork have no overtones ; they only give the 



fundamental tone. As already mentioned, the term simple tone is applied to sounds due to 

 simple pendulum-like vibrations, while a sound composed of a fundamental tone and overtones 

 is called a " klang " or compound musical tone. 



Vibration Curve of a Musical Tone. When we remember that a musical tone or clang con- 

 sists of a fundamental tone, and a number of overtones of a certain intensity, which determine 

 its quality, then we ought to be able to construct geometrically the vibration curve of the 

 musical tone. Let A represent the vibration curve of the fundamental tone, and B that of the 

 first moderately weak overtone (fig. 597). The combination of these two curves is obtained 

 simply by computing the height of the ordinates, whereby the ordinates of the overtone curve, 

 lying above the abscissa or horizontal line, are added to the fundamental tone curve, while those 

 of the ordinates below the line are subtracted from it. Thus we obtain the curve C, which is 

 not a simple pendulum-like curve, but one which corresponds to an unsteady movement. A new 

 curve of the second overtone may be added to C, and so on. The result of all these combina- 

 tions is that the vibration curves corresponding to the compound musical tones are unsteady 

 periodic curves. All these curves must, of course, vary with the number and pitch of the 

 compounded overtone curves. 



Displacement of the Phases. The form of the vibration of one and the same musical tone 

 may vary very greatly if, in compounding the curves A and B, the curve B is only slightly 

 displaced laterally. If B is displaced so that the hollow of the wave r falls under A, the 

 addition of both curves yields the curve r, r, r, with small elevations and broad valleys. If B 

 le displaced still further, until the elevation of the wave, h, coincides with A, we obtain still 

 another form, so that bv displacement of the phases of the wave-motions of the compounded 

 simple pendulum-like vibrations, we obtain numerous different forms of the same musical tone. 

 The displacement of the phases, however, has no effect on the ear. 



The general result of these observations, and those of Fourier, is that the quality of a musical 

 tone depends upon the characteristic form of the vibratory movement. 



Analysis of Vowels. The human voice represents a reed instrument with vibrating elastic 



