320 Notices respecting New Books. 



power of separating and recognizing individual tones in a com- 

 posite mass of tones, in such a way that Ohm was led to enun- 

 ciate this law : — " Every motion of the air which corresponds to a 

 composite mass of musical tones is capable of being aualyzed into 

 a sum of simple pendular vibrations corresponding to a simple tone 

 sensible to the ear, and having its pitch determined by the periodic 

 time of the corresponding motion of the ear." If we direct our 

 attention closely to the tones of a piano or violin, we become 

 conscious of higher tones mingling with the fundamental tone ; and 

 the more we accustom ourselves to discriminating these, the easier 

 and fuller is our recognition of them. In Prof. Helmholtz's theory 

 their presence is considered as determining quality of tone ; and 

 they are also, in this theory, the chief cause of the difference be- 

 tween consonant and dissonant intervals. 



It is therefore an important inquiry, are there any objective 

 signs of their existence ? and if so, how can we most easily and 

 distinctly apprehend them? The phenomena of sympathetic 

 resonance are a full answer to the first question. They all depend 

 on the power of a vibrating body to set in vibration even a large 

 mass, provided that this mass have a proper period of its own the 

 same as that of the vibrating body. Thus a large bell may be set 

 ringing by a very small force, provided that the pulls are of the 

 same period as the proper swing of the bell ; and a very small 

 forward and backward motion of the hand will put into vibration 

 a ball which it holds suspended by a thread, provided only that the 

 proper period of the ball pendulum coincides with one of the 

 periods of the hand's motion when resolved into simple pen- 

 dular vibrations by Fourier's theorem. 



It is the same with the small vibrations of sound. Take for 

 example a piano-string sounding g' ; the string C being struck and 

 then damped, g 'is heard to sound. Here the vibration of the 

 sounding-board gives small impulses to the string of g' at its points 

 of attachment ; these impulses accumulate, each going to help the 

 previously acquired swing of the string, and the result is the 

 tone g . 



By means of his globe resonators, which strongly reinforce tones 

 in unison with their proper note, Prof. Helmholtz was able to 

 examine the upper partials of different notes. All these cases are 

 instances of a mechanical selection of simple pendular vibrations. 



The ear at first experiences great difficulty- in detecting upper 

 partials, because the whole training of ordinary ears is towards 

 fusing them, and discriminating the fused results from each other. 

 But we may train ourselves to detect them by such expedients as 

 first sounding the higher harmonics, and then the prime tone of the 

 harmonic, or by first detecting them with the resonator, and then 

 fixing our attention on them when the fundamental tone is sounded. 

 Having in this way trained ourselves to detect the harmonics, we 

 may then do without assistance. 



By comparing the upper partial tones of various instruments 

 with their quality of tone, these general results are obtained. 



