Sounding of two Notes. 519 



place the little wooden board which strikes so hard by a piece 

 of card, the rattle is hardly to be discerned at all, and the note 

 c stands out with greater clearness. If we turn the wheel 

 only once in two seconds, so that we only produce 64 strokes in 

 the second, we can still more easily observe the almost entire 

 disappearance or withdrawal of the note C from the rattle of 

 the 64 strokes. There exists consequently the most perfect 

 agreement between the ratio of primary impulses and that of 

 the beats. 



It is obvious that the simultaneous audibleness of single 

 strokes and of the notes which arise from their sequence, as also 

 the cessation of the audibleness of single strokes when these 

 surpass a certain number, are fully explained by the theory of 

 hearing put forward by Helmholtz. According to this theory, 

 as is known, there exist in the ear certain elastic bodies 

 " greatly muffled" {Tonempfindung , p. 226), which serve 

 for the perception of swiftly passing irregular shocks — and 

 also " less-muffled elastic bodies," which are much more 

 powerfully affected by a musical note of correspondingly high 

 pitch than by single beats. Each of the single beats pro- 

 duces, therefore, an impression upon a body of the former 

 sort, so long as these strokes do not succeed each other in a 

 shorter interval of time than is necessary for the muffling of 

 the concussion produced in it. • But, further, the periodical 

 movement produced by the sequence of the strokes is composed 

 of a sum of vibrations like those of the pendulum — that is to 

 say, of simple notes, which can each affect an elastic body of 

 the second nature. The more, therefore, the movement of the 

 air caused by single strokes differs from the simple pendulum 

 movement, the greater will be the perceptibility of the single 

 strokes and the weaker the intensity of the note arising from 

 their sequence ; while, on the other hand, the intensity of the 

 latter increases, and the audibleness of the single impulses 

 becomes weaker, as this periodical movement approaches 

 nearer to the simple pendulum movement; so that at last, with 

 almost entirely simple pendulum vibrations as they are pro- 

 duced by tuning-forks, at above 32 and 36 nothing more is 

 perceptible of the single impulses, and the note only is heard. 



Helmholtz has remarked further that an undulating clang 

 may be compared to a note of periodically changing in- 

 tensity, and that "undulations and intermissions resemble 

 each other, and also that at a certain number they produce 

 that kind of noise which we call a rattle " (Tonempfind. p. 266). 

 If intermissions, then, always produced only a rattle, the great 

 resemblance which they show when not too numerous to the 

 vibrations might make us suppose that these latter are only 

 capable of producing a rattle ; but intermissions, just like 



