94 



PERCEPTION OF TIMBRE. ANALYSIS OF VOWELS. 



If, for example, the first resonator has B as its fundamental tone (which is easily 

 heard by blowing upon it) , then the tone of the second resonator is b (of the fol- 

 lowing octave), that of the third is f 1 (three times the rate), that of the fourth 

 b 1 (the second higher octave), that of the fifth d 11 (five times the rate). Then 

 come f n , as 11 , b 11 , etc. 



If such a resonator be applied to the ear, it is easy to distinguish the weakest 

 overtone of the same rate of vibration in the sound of a musical instrument 

 and v Helmholtz found that each instrument possesses a definite number of 

 overtones, differing in pitch and intensity. The tuning-fork, and the simple 

 swinging metal bar, however, have no overtones, but yield only the single funda- 

 mental tone. Following v. Helmholtz, only the simple oscillatory sound-vibra- 

 tions are designated simple tones, while sound-vibrations consisting of funda- 

 mental tone and overtones are designated musical tones (Klange) . 



If it be borne in mind that each musical tone possesses a fundamental tone, 

 and a number of overtones of definite intensity, which* determine its quality, 

 it becomes possible to construct geometrically the vibration-curve of the tone by 

 a combination of the vibrations of the fundamental tone and those of the overtones. 

 In Fig. 327 the continuous curved line A represents the vibration-curve of 

 the keynote, and B that of the first, moderately weak overtone. The combination 

 of these two curves is made by putting together the heights of the ordinates, 



whereby the ordinates lying above the 

 horizontal are added to those of the 

 keynote, and those below the hori- 

 zontal are subtracted. In this way 

 the curve C is obtained, which does not 

 correspond to a simple oscillation, but 

 to an unsteady movement. To the 

 curve C a new curve of the second 

 overtone, with three times the rate of 

 vibration, can be added, etc. The final 

 result of all such combinations is that 

 the vibration-curves corresponding to 

 compound musical tones are irregular, 

 periodic curves. All of these curves 

 must, naturally, differ according to the 

 number and the height of the combined 

 overtone-curves. Hence, if the number 

 and the intensity of the overtones in 

 the sound of an instrument have been 

 analyzed by the resonators, the geomet- 

 rical vibration-curve of the sound can be 

 constructed therefrom. 



The form of vibration of the same 

 tone may vary considerably, if in com- 

 bining the curves A and B the curve B is displaced laterally. If B is displaced to such 

 an extent that the depression r falls under A, the addition of the two curves 

 yields the curve r r r with narrow summits and broad valleys. If B is displaced 

 still further, until the summit h coincides with A, still another form is produced. 

 Hence, by displacing the phases of the wave-movements of the simple oscillatory 

 vibrations that are to be combined, there arise numerous different forms of 

 the same musical tone, but this displacement of the phases has no influence what- 

 ever upon the ear. 



The simple tones, produced by simple oscillations, have a uniform increase 

 and decrease in the oscillations, while the musical tones, according to the number 

 and the strength of their overtones, have a characteristic form of elevation and 

 depression of the vibration-curve. 



Just as the irregular curve of vibration of a musical tone may be constructed 

 from several simple oscillating tones, so every such curve may be analyzed. In 

 fact, Fourier has shown that each complicated, irregular curve of vibration may 

 be resolved into a sum of simple oscillatory vibrations, whose number has a ratio of 

 1:2:3:4 . . .. . There can be only one set of simple tones in such an analysis. 

 On the other hand, every complicated irregular movement may be resolved in 

 many ways into movements that are likewise irregular. The result of this deduc- 

 tion is that the quality of a musical tone depends upon the characteristic form of 

 the vibratory movement. 



FIG. 327. 



