90 



C. Barus — Combination Tones of the 



the diatonic scale along any of these diagonals are indicated by 

 dots and lettered in the usual way, and these are obviously 

 much more crowded in the lower regions (n < 696), where the 

 pitch of the siren changes with proportionate rapidity, than in 

 the upper regions (?i > 696). 



Thus, the first order of difference tones (D 1 = P—S)* is 

 shown by the diagonal descending from n — 696 and t — at 

 an angle of 45° below the horizontal to the abscissa n = in 

 the left half of the diagram, and rising from the abscissa ?i=0, 

 at an angle of 45° to the original level n — 696 in the right 

 half of the diagram as shown at D\. These are the chief dif- 

 ference tones in question. Where they were heard either 

 directly or indirectly (including beats) the line is drawn in full 

 and the notes indicated. Otherwise the line is broken. Of 

 course it is almost impossible to recognize the precise pitch at 

 which the difference tone is first heard, since the ear is obliged 

 to depend on musical intervals for orientation. With more 

 practice the limits could doubtless be extended. 



The interesting feature of this order of difference tones 

 (Z> a , D/), which are quite sweeping and easily heard, is the 

 transition (at abscissa t = 8) of the descending into the ascend- 

 ing cadence. 



The difference tone here passes beyond the limits of audition, 

 thereafter to emerge again. With his many-voiced siren 

 Helmholtz used an analogous phenomenon to test these limits. 

 In the present experiment the vanishing of the difference tone 



is approached by a marked chord of the seventh, Fo"e' f" , 



followed by the effective musical sequence in the key of i? , 

 which is nearly 



^-b 



C3>_ 



\ 



etc. 



e 



=? 



w-^j 



\ 



a 2 



finally while the treble is sharpened descending from .2^(^=43) 

 to (I think I could say in my case) A 2 , where n = 27. The last 

 sensations however are much as though the head were being 

 profoundly shaken and the pitch recognized probably imagi- 



* The frequency of V> x is obtained, in other words, by deducting the frequency 

 of the note of the siren from that of the organ pipe, all referred to the same ver- 

 tical. 



