U4: 



DR. KCENIGS RESEARCHES ON 



beats will both be present. We shall have four tones altogether — two 

 primary tones and two beat tones. The forks 1 select are ute = 2048, 

 as before, and a fork which is tuned to vibrate exactly 11 times as 

 rapidly at ut^ — it is the eleventh harmonic of that note, but does not cor- 

 respond i)recisely to any note of the diatonic scale. It has 2816 vibra- 

 tions, and is related to nte as 11:8. The two remainders, will now be 

 768 and 1280, which are the respective frequencies of soU and mt's. 

 Dr. Kn'iiig will lirst sound those notes on two other forks, that you 

 may know beforeiiand what to listen for. Now, on striking the two 

 shrill forks in rapid succession, the two beat tones are heard. 



If I self^ct, instead of the eleventh harmonic, the thirteenth harmonic 

 of wfj, vibrating 3328 times in the second, to be sounded along with 

 utc, the same two beat tones will be produced as in the preceding case; 

 but wnV, = 1280 is now the inferior one, corresponding to the positive re- 

 mainder, whilst .s'0/4 = 768 is the superior tone, corresponding to the 

 negative remainder. It is certainly a striking corroboration of Dr. 

 Koenig's view that the beat tones actually heard in these last two ex- 

 periments should come out precisely alike, though on the old view, 

 that the combinational tones were simply the summational and differ- 

 ential tones, one would have been led to expect the sounds in the two 

 experiments to be quite different. 



One other example I will give you of a beat tone belonging to the 

 second period. The two jirimary notes are given by the forks tif^ = 

 1024 and vt,; =2304. The beat tone which you hear is uf-i = 256, which 

 corresponds to the positive remainder. 



It will be convenient to draw uj) in tabular form the results just 

 obtained. These maybe considered as abbreviations of the much more 

 extended tables drawn up by Dr. K<enig, which hat)g upon the walls, 

 and which are to be f\)und in his book, " QueUiues Experiences 

 d'Acoustique," 



Taui.k II. — Sounds of primary hcotrt. 



