Sounding of two Notes. 423 



The beats of an interval w:3« + m or 4 n— mf are again 

 equal to m and mf. 



In the period of C : c? to C : ef , of n : 4 w to n :5 n, the 

 beats can be followed to only a less distance. The lower 

 beats at the number of 8 to 10 change into a roll ; but this at 

 552 v. s. (20 beats) is already so weak that it is hardly more 

 than a mere roughness. At 560 (24 beats) even this is no 

 longer distinguishable; and the two notes from this point form 

 a pure clang. Only at 616 v. s. does the roll of 12 beats 

 again appear from the pure clang, which then passes into the 

 single audible beats, which disappear at 1 : 5 (128 : 640 v. s.). 



In the period C : e' to C : g / , n : 5 n to n : 6 n, the lower 

 beats are only clear to about 10, and disappear at 664 v. s. 

 (12 beats). The upper beats are feebly audible at 748 v. s., 

 and only at 752 v. s. (8 beats) become singly quite clear. 



In the period C : g' to C : 896 v. s., of n : 6 n to n : 7 n, the 

 lower beats are only quite distinct up to 780 v. s. (6 beats), 

 and disappear at 784 v. s. The upper beats are feebly audible 

 to the number of 6 at 884 v. s., and only become quite distinct 

 at 888 v. s. to the number of 4. 



In the period of C : 896 v. s. to C : c", n : 7 n to n : 8 n, the 

 lower beats can be heard clearly to the number of 4 at 904 v. s. 

 They disappear at 908 v. s., 6 in number. Four upper beats 

 are perceptible at 1004 v. s. The two beats at 1008 v. s. are 

 quite distinct. 



I succeeded occasionally in perceiving a few beats in the 

 ratio of C : d" and even of C : e" (1 : 9 and 1 : 10); but these 

 were very weak, and could not have been perceived at all by 

 any ordinarily correct ear not specially trained for the pur- 

 pose, as all those above described can be. 



It has always hitherto been assumed that beats can only be 

 oirectly produced from two notes which are close to the 

 unison, and that the beats of all wider intervals must be pro- 

 duced with the aid of resultant notes. According to this, in 

 the interval C \d f — 2 v. d., which as we have seen allows two 

 beats to be distinctly heard, these beats must have been pro- 

 duced in the following manner : — 



c" — 2 v.d. with C (8 n — 2 with n) must have produced 892 v. s.(7n- 2) 



g / -2Y.d.(6n-2) 

 e / -2v.d.(5n-2) 

 c'-2v.d.(4n-2) 

 #-2v.d.(3™-2) 

 c -2v.d.(2n-2) 

 C-2v.d. (n-2) 

 two beats 



892 v. s. 



n 



0(7 n-2 



i) 



?l) 



V 



#'-2 v.d. 



n 



C(6n-2 



j) 



n) 



?) 



/-2v.d. 



n 



C(5n-2 



5J 



n) 



•)•) 



^-2 v.d. 



11 



C(4n-2 



?? 



n) 



?? 



#-2 v.d. 



11 



C(3n-2 



V 



n) 



11 



c -2 v.d. 



11 



C(2n-2 



?? 



n) 



11 



C-2v.d. 



11 



G (n-2 



?) 



n) 



11 



