342 DR. koenig's researches on 



slightly, and then bow it, at once you hear beats. It was in studying 

 the beats of these higher periods that Dr. Koenig made the observation 

 that, whereas the beats of an imperfect unison are heard as alternate 

 silences and sounds, the beats of the (imperfect) higher periods — twelfth 

 tone, double octave, etc. — consist mainly in variations in the loudness 

 of the lower of the two primary tones, an observation which was inde- 

 pendently made by Mr. Bosanquet, of Oxford. 



Passing from the beats themselves, I approach the question, What 

 becomes of the beats when they occur too rapidly to produce on the 

 ear a discontinuous sensation ? On this matter there have been several 

 conflicting opinions, some holding, with Lagrange and Young, that 

 they blend into a separate tone ; others, with von Helmholtz, main- 

 taining that the combinational tones can not be so explained and arise 

 from a different cause. Let it be observed that, even if beat-tones exist, 

 it is quite possible for beats and beat-tones to be simultaneously heard. 

 A similar coexistence of a continuous and a discontinuous sensation 

 is afforded by the familiar experiment of producing a tone by pressing 

 a card against the periphery of a rapidly rotating toothed wheel. There 

 is a certain speed at which the individual impulses begin to blend into 

 a continuous low tone, while yet there are distinguishable the discon- 

 tinuous impulses, the degree of distinctness of the two co existing 

 sounds being dependent on the manner in which the card is pressed 

 against the wheel, that is to say, on the nature of the individual im- 

 pulses themselves. The opponents of the view that beats blend into a 

 tone state plainly enough that, in their opinion, a mere succession ot 

 alternate sounds and silences cannot blend into a tone different from 

 that of the beating tone. Having said that the beats can not blend, 

 they then add that they do not blend j for, say they, the combinational 

 tones are a i^urely subjective phenomenon. Lastl.y, they say that even 

 if the beats blend they will not so explain the existence of combinational 

 tones, because the combinational tones have frequencies which do not 

 correspond to the luimber of the beats. 



In the teeth of all these views and opinions. Dr. Kcenig — without 

 dogmatizing as to how or why it is — emphatically affirms that beats do 

 produce 6ea< tones; and he has pursued the matter down to a point that 

 leaves no room for doubting the general truth of the fact. The alleged 

 discrepancy between the frequency of the observed combinational tones 

 and that of the beats disappears when closely scrutinized. Those who 

 count the beats by merely taking the difference between the frequen- 

 cies of the two prinuuy tones, instead of calculating the two remain- 

 ders, will assuredly find that their numbers do not agree in pitch with 

 the actual sounds heard. But that is the fault of their miscalculation. 

 Those who use harmonium reeds or polyphonic sirens instead of tuning 

 forks to ])roduce their primary tones must not expect from such impure 

 sources to reproduce the effects to be obtained from pure tones. And 

 those who say that the beats calculated truly from the two remainders 



