422 Dr. R. Konior on the Simultaneous 



o 



to be perceived, out of which, however, again at 344 v. s., a 

 clear quick roll appears, which gradually becomes slower, till 

 at 360 to 364 v. s. 12 to 10 beats become singly audible ; these 

 at 368, 372, 376, and 380 v. s. decrease to 8, 6, 4, and 2, and 

 at # = 384 v. s. (1 : 3) disappear. 



The number of the beats audible close to the octave is equal 

 to the difference of the double vibrations of the higher notes 

 and of the octave of the fundamental note ; and the number of 

 beats close to the twelfth is equal to the difference of the double 

 vibrations of the higher notes and the twelfth from the 

 fundamental note. 



The order of the intervals here observed of this second 

 period, from n : 2 n to n : 3 n, is therefore precisely the same 

 as that which we observed of the intervals of the first period 

 from n : n to n : 2 n. Each interval, n :2 n -\- m or 3 n — w! y 

 again exhibits two kinds of beats, which are equal to in and 



m f : if m is much less than -, we hear only the lower beats ; 



if m is much greater than -, only the upper beats can be dis- 



n 

 tinguished ; and if m is about the same as ^ the two kinds of 



n 

 beats exist together. In this period w=^ in the interval 



2:5 = 320 v. s.). 



The beats in the interval n : 2 n + m are therefore equal to 

 those in the interval n :n + m. 



In this period also the upper beats are weaker than the 

 lower; and both upper and lower beats are weaker than the 

 corresponding beats in the first period. 



The next higher period reaches from C : g to C : c', n : 3 n 



to n : 4 n ; and its centre, in which m = - is in the ratio of 2 : 7 



(128: 448 v. s.). 



We find in this the same order as in the two first 

 periods, only we cannot follow the two kinds of beats quite 

 so far, as they have again become weaker than in the former 

 periods. If, beginning at g (384 v. s.), we again raise the 

 second note higher and higher, the first single audible beats fall 

 into a roll at 404 v. s. (10 beats), which at 420 v. s. becomes 

 a weak confused rattle. This changes at about 456 v. s. to a 

 mere roughness, from which another clear rattle is only dis- 

 tinguished at 480 to 484 v. s. (16 to 14 beats), which becomes 

 slower till at 492 v. s. we have 10 single audible beats, gra- 

 dually diminishing in number till at c' (512 v. s.), the double 

 octave, they entirely disappear. 



